MIND AS A LAYERED NETWORK OF COMPUTATIONAL PROCESSES ALL THE WAY DOWN TO QUANTUM

Abstract. Talking about models of cognition, the very mention of “computationalism” often incites reactions against Turing machine model of the brain and perceived determinism of computational models of mind. Neither of those two objections affects models based on natural computation or computing nature where model of computation is broader than deterministic symbol manipulation of conventional models of computation. Computing nature consists of physical structures that form levels of organization, on which computation processes differ, from quantum up to macroscopic levels. It has been argued by (Ehresmann, 2012) and (Ghosh et al., 2014) that on the lower levels of information processing in the brain finite automata or Turing machines might be adequate models, while on the level of the whole-brain information processing computational models beyond-Turing computation is necessary. Such a layered computational architecture based on intrinsic computing of physical systems avoids objections against early versions of computationalism such as triviality, lack of clarity and lack of naturalistic foundations.

Critique of Classical Computationalism and New Understanding of Computation

Historically, computationalism has been accused of many sins (Miłkowski, 2013) (Scheutz, 2002). In what follows I would like to answer Mark Sprevak’s three concerns about computationalism, (Sprevak, 2012) p. 108:

(R1) Lack of Clarity: “Ultimately, the foundations of our sciences should be clear.” Computationalism is suspected to lack clarity.

(R2) Triviality: “(O)ur conventional understanding of the notion of computational implementation is threatened by triviality arguments.” Computationalism is accused of triviality.

(R3) Lack of naturalistic foundations: “The ultimate aim of cognitive science is to offer, not just any explanation of mental phenomena, but a naturalistic explanation of the mind.” Computationalism is questioned for being formal and unnatural.

Sprevak concludes that meeting all three above expectations of computational implementation is hard. As an illustration of the problems with computationalist approaches to mind, he presents David Chalmers computational formalism of combinatorial state automata and concludes that “Chalmers’ account provides the best attempt to do so, but even his proposal falls short.” In order to be fully understood, Chalmers account, I will argue, should be seen from the perspective of intrinsic, natural computation instead of a conventional designed computer. Chalmers argues:

“Computational descriptions of physical systems need not be vacuous. We have seen that there is a well-motivated formalism, that of combinatorial state automata, and an associated account of implementation, such that the automata in question are implemented approximately when we would expect them to be: when the causal organization of a physical system mirrors the formal organization of an automaton. In this way, we establish a bridge between the formal automata of computation theory and the physical systems of everyday life. We also open the way to a computational foundation for the theory of mind.” (Chalmers, 1996)

In the above it is important to highlight the distinction between intrinsic /natural/ spontaneous computation that describes natural processes at different levels of organization and is always present in physical system and designed/conventional computation which is used in our technological devices and which uses intrinsic computation as its basis. Intrinsic computation appears naturally on different levels from processes on quantum level to molecular/chemical computation, computation (information processing) in neural networks, social computing etc.

Already in 2002 Matthias Scheutz (Scheutz, 2002) proposed new computationalism capable of accounting for embodiment and embeddedness of mind. In this article we will present the recent developments that show how this new computationalism looks like at present and in what directions it is developing.

In the Epilogue of the (Scheutz, 2002), Scheutz makes the following apt diagnosis:

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“Today it seems clear, for example, that classical notions of computation alone cannot serve as foundations for a viable theory of the mind, especially in light of the real-world, real-time, embedded, embodied, situated, and interactive nature of minds, although they may well be adequate for a limited subset of mental processes (e.g., processes that participate in solving mathematical problems). Reservations about the classical conception of computation, however, do not automatically transfer and apply to real-world computing systems. This fact is often ignored by opponents of computationalism, who construe the underlying notion of computation as that of Turing-machine computation.” (Scheutz, 2002) p. 176, emphasis added

Natural/Intrinsic Computation and Physical Implementation of Computational System

The way to avoid the criticisms against computational models of mind is to naturalize computation.

The idea of computing nature (Dodig-Crnkovic & Giovagnoli, 2013) (Zenil, 2012) builds on the notion that the universe as a whole can be seen as a computational system which computes its own next state. This approach is called pancomputationalism or natural computationalism and dates back to Konrad Zuse with his Calculating Space - Rechnender Raum (Zuse, 1969, 1970), with many prominent representatives such as Edward Fredkin (Fredkin, 1992), Stephen Wolfram (Wolfram, 2002) and Greg Chaitin (Chaitin, 2007) among others, see (Dodig-Crnkovic, 2011). Computation as found in nature is physical computation, described in (Piccinini, 2012) and also termed “computation in materio” by Stepney (Stepney, 2008, 2012) as well as Fresco in (Fresco, 2014). [Here introduce info-computationalism Floridi Burgin Marcin]

In his Open Problems in the Philosophy of Information (Floridi, 2004)(Floridi, 2004) lists the five most interesting areas of research for the nascent field of Philosophy of Information (and Computation), with eighteen fundamental questions that contain the following:

17. The “It from Bit” hypothesis: Is the universe essentially made of informational stuff, with natural processes, including causation, as special cases of information dynamics?

In his own work Floridi as well as Sayre argue for the informational universe (Floridi, 2003)(Sayre, 1976) claiming that the fabric of the universe is information. I would add that informational fabric of the universe is always relative to an agent, as information is relational. Thus “the universe” for a spider is vastly different from “the universe” for a human or for some artifactual cognitive system. That is constructivist view of knowledge where the process of knowledge generation in a cognizing agent starts with the interactions with the environment as potential information that actualizes and proceeds embodied and embedded in the agent’s Umwelt (Kull, 2010), that is the universe accessible via interactions from the given agent’s cognitive/computational architecture. Physicists as well contribute to understanding of physical foundations of nature in terms of (quantum) information, among them Lloyd, Vedral, Chiribella, Goyal (Lloyd, 2006) (Vedral, 2010) (Chiribella, D’Ariano, & Perinotti, 2012) (Goyal, 2012).

The synthesis of informational structural realism with natural computationalism results in the framework of info-computationalism (Dodig-Crnkovic & Müller, 2011) (Dodig-Crnkovic, 2008), which is a variety of natural computationalism, where information presents the fabric of the universe while its dynamics is computation. Physical nature thus spontaneously performs different kinds of computations that present information processing at different levels of organization (Dodig-Crnkovic, 2012). This intrinsic computation of a physical system can be used for designed computation, which would not appear spontaneously in nature, but with constant energy supply and designed architecture performs computations such as found in conventional designed computational machinery.

It should be noted that varieties of natural computationalism/ pancomputationalism differ among themselves: some of them would insist on discreteness of computation, and the idea that on the deepest levels of description, nature should be seen as discrete. Others find the origin of the continuous/discrete distinction in the human cognitive apparatus that relies on both continuous and discrete information processing (computation), thus arguing that both discrete and continuous models are necessary (Dodig-Crnkovic & Mueller, 2009) So Lloyd argues that the dual nature of quantum mechanical objects as wave/particles implies necessity of both kinds of models (Lloyd, 2006).

If now somebody writes a tricky language that goes beyond the capabilities of LISP and changes its own interpreter as well, and then perhaps it changes the operating system, and so on, finally we find ourselves at the

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level of the processor chip of the computer that carries out the machine code instructions. Now, unlike the earlier levels, this level belongs to a piece of physical hardware, where things will be done the way the machine was once built, and this can no more be a matter of negotiations. Ultimately, this is what serves as that Archimedean starting point (similar to the initial translation that opens up self-reference) that defines a constant framework for

the programs. The importance of this is that we understand: self-modification, and self-reference, are not really just issues of programming (that is, of using the right software), but of designing a whole machine in some sense. Therefore, the impossibility of achieving complete self-modification depends, ultimately, on the separability of machine from program (and the way around): the separability of software from hardware. (Kampis, 1995)

In the light of the above, we can answer the question why is natural computationalism not trivial/vacuous in spite of the underlying assumption that the whole of the universe is computational? The hierarchy of levels of computation is grounded in physical/intrinsic/natural computation. This construction is not vacuous for the same reason for which physics is not vacuous even though it makes the claim that the entire physical universe consists of matter-energy and builds on the same elementary building blocks – elementary particles. *(Here we will not enter the discussion of ordinary matter-energy vs. dark matter-energy. Those are all considered to be the same kind of phenomena – natural phenomena that are assumed to be universal in nature.) The principle of universal validity of physical laws does not make them vacuous. Thinking of computation as implementation of physical laws on the fundamental level makes it more obvious that computation can be seen as the basis of all dynamics in nature.

Chapter 4 in Fresco (Fresco, 2014), ‘The Triviality “Account” Examined’, discusses arguments against computationalism by John Searle and Hilary Putnam which criticize the computational view of cognition claiming that in effect that every physical object implements any program thus “trivializing” the notion of computation.

For any sufficiently complex physical object O (i.e., an object with a sufficiently large number of distinguishable parts) and for any arbitrary program P , there exists an isomorphic mapping M from some subset S of the physical states of O to the formal structure of P (Searle, 1990, pp. 27–28).Searle, J.R.: Is the brain a digital computer? Proceedings and Addresses of the AmericanPhilosophical Association 64, 21–37 (1990) (Searle, 1990)

In a similar vein, Putnam argues that every ordinary open system simultaneouslyrealises every abstract inputless FSA (1988, p. 121). (Putnam, 1988)Putnam, H.: Representation and reality. The MIT Press, Cambridge (1988)

Chrisley, R.L.: Why everything doesn’t realize every computation. Minds and Machines 4(4), 403–420 (1994) (Chrisley, 1994)

Thinking of intrinsic computation on the most fundamental level of natural process “in materio” (Stepney, 2008). The field of intrinsic natural computation is presented in depth in the (Rozenberg, Bäck, & Kok, 2012). For a specific study of intrinsic computation performed by neurons in the brain, see (Crutchfield, Ditto, & Sinha, 2010; Crutchfield & Wiesner, 2008). The info-computational framework for naturalizing epistemology can be found in (Dodig-Crnkovic, 2007).

Levels of Organization and Agent-based Model of Computation

FROM MY PT-AI ARTICLE Self-organization and autopoiesis is effectively described by agent-based models, such as actor model of computation (Hewitt, 2012) that we adopt. Given that processes in the cell run in parallel, the current models of parallel computation (including Boolean networks, Petri nets, Interacting state machines, Process calculi etc.) need to adjust to modelling of biological systems (Fisher & Henzinger, 2007).

Deacon (2011) proposed a framework for information processing in living systems and distinguishes between the following three levels of natural information (for an agent):

Information 1 (Shannon, syntactic information) which describes data, patterns, signals and is used in data communication

Information 2 (Shannon + Boltzmann, semantic information) which describes intentionality, aboutness, reference, representation, relation to object or referent

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Information 3 ((Shannon + Boltzmann) + Darwin), pragmatic information that describes function, interpretation, use, pragmatic consequence

Deacon’s three levels of information organization parallel his three formative mechanisms:

[Mass-energetic [Self-organization [Self-preservation (autopoetic, semiotic)]]]

with corresponding levels of emergent dynamics:

[Thermo- [Morpho- [Teleo-dynamics]]]

and matching Aristotle’s causes:

[Efficient cause [Formal cause [Final cause]]].

“Because there are no material entities that are not also processes, and because processes are defined by their organization, we must acknowledge the possibility that organization itself is a fundamental determinant of physical causality. At different levels of scale and compositionality, different organizational possibilities exist. And although there are material properties that are directly inherited from lower-order component properties, it is clear that the production of some forms of process organization is only expressed by dynamical regularities at that level. So the emergence of such level-specific forms of dynamical regularity creates the foundation for level-specific forms of physical influence.” (Deacon, 2011) p. 177.

Hierarchy of levels of emergent dynamics constitutes dynamical depth of a system:

What we term dynamical depth then, is this hierarchic complexity and irreducibility of constraint-generating dynamics, such as distinguishes teleodynamics from morphodynamics and morphodynamics from homeodynamics. Each of these transitions is characterized by the generation of intrinsic constraints on the relationships between processes at lower levels and as a result with increasing autonomy from extrinsically imposed constraints. Since constraints are a prerequisite for producing physical work, the increasing autonomy of constraint generation with dynamical depth also corresponds to an increasing diversity of the capacity to do work. Thus the flexibility with which a dynamical system can interact with its environment also increases with dynamical depth. (Deacon & Koutroufinis, 2014) 418

“A system with greater dynamical depth than another consists of a greater number of such nested dynamical levels. Thus, a mechanical or linear thermodynamic system has less dynamical depth than an inorganic self-organized system, which has less dynamical depth than a living system. Including an assessment of dynamical depth can provide a more precise and systematic account of the fundamental difference between inorganic systems (low dynamical depth) and living systems (high dynamical depth), irrespective of the number of their parts and the causal relations between them.” (Deacon & Koutroufinis, 2014)

homeodynamic (h), morphodynamic (m), and teleodynamic (t) patterns of organization, and the double subscripts indicate higher order (recursive) dynamical depth in which teleodynamic unit systems (e.g., organisms) are themselves involved in homeodynamic (ht), morphodynamic (mt), or teleodynamic (tt) patterns of interaction.

Interestingly enough, there is a parallel to Aristotle’s three kinds of soul in his hylomorphic (matter-form based) view of life :

Aristotle applies his theory of hylomorphism to living things. He defines a soul as that which makes a living thing alive.[16] Life is a property of living things, just as knowledge and health are. [17] Therefore, a soul is a form—that is, a property or set of properties—belonging to a living thing. [18] Furthermore, Aristotle says that a soul is related to its body as form to matter.[19]

Hence, Aristotle argues, there is no problem in explaining the unity of body and soul, just as there is no problem in explaining the unity of wax and its shape.[20] Just as a wax object consists of wax with a certain shape, so a living organism consists of a body with the property of life, which is its soul.

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It is important to understand that Aristotle does not consider soul as something additional to material body, but as an aspect of it. Thus for a body to be alive, it will possess certain structures. There is no dead body that would have exactly the same material structure as the living body. It will have some differences such as ruptures, chemical changes or similar. Body can be alive only in certain material forms and its soul (that is the quality of being alive is a necessary consequence of its material structure on all different levels of organization.

Computation on Submolecular Levels

In Hewitt’s model of computation, Actors are the universal primitives of concurrent distributed digital computation. In response to a message that it receives, an Actor can make local <decisions>, create more Actors, send more messages, and choose how to respond to the next message received.

“In the Actor Model (Hewitt, Bishop, & Steiger, 1973) (Hewitt, 2010), computation is conceived as distributed in space, where computational devices communicate asynchronously and the entire computation is not in any well-defined state. (An Actor can have information about other Actors that it has received in a message about what it was like when the message was sent.) Turing's Model is a special case of the Actor Model.” (Hewitt, 2012)

The above Hewitt’s “computational devices” are conceived as computational agents – informational structures capable of acting on their own behalf.

For Hewitt, Actors become Agents only when they are able to process expressions for commitments including Contracts, Announcements, Beliefs, Goals, Intentions, Plans, Policies, Procedures, Requests and Queries. In other words, Hewitt’s Agents are human-like or if we broadly interpret the above capacities, life-like Actors. However, we take all Hewitt’s Actors to be <agents> with different competences as we are interested in a common framework encompassing all living and artifactual agents.

The advantage of Hewitt’s model is that unlike other models of computation that are based on mathematical logic, set theory, algebra, etc. the Actor model is based on physics, especially quantum physics and relativistic physics. (Hewitt, 2012) Its relational nature makes it especially suitable for modeling informational structures and their dynamics.

Quantum-physical objects such as elementary particles of Standard Model, interacting through gauge bosons as force carriers (mediating the strong, weak, and electromagnetic interactions) can be modeled as actors exchanging messages. The <agency> in simplest physical systems such as elementary particles is exactly their physical capacity to act, to interact and to undergo changes.

Within the framework of info-computationalism, nature is informational structure – a succession of levels of organization of information for an agent. Of course, this reality is different for different agents. Physical reality, das Ding an sich exists as potential information that actualizes for an agent through interactions. This leads to understanding proposed by Von Baeyer in his book Information: The New Language of Science argues that (Baeyer von, 2004) who states that “information is going to replace matter as the primary stuff of the universe, providing a new basic framework for describing and predicting reality”.

Info-computational approach is supported by the current work in physicists on reformulating physics in terms of information, such as proposed by (Goyal, 2012) in “Information Physics—Towards a New Conception of Physical Reality” and (Chiribella et al., 2012) in “Quantum Theory, Namely the Pure and Reversible Theory of Information”. For the case of Statistical Thermodynamics based on information (or rather lack of information) instead of entropy, see (Ben-Naim, 2008).

Very simple systems can act as <observers> as described in (Matsuno & Salthe, 2011) who present possible approach to naturalizing contextual meaning in the case of chemical affinity as material agency.

However, if we want tools to manipulate physical systems, such as molecules in the case of studies of origins of life, our tools must be more than theoretical models – they will be computations “in materio” as Stepny (Stepney, 2008) called them, arguing aptly: “We are still learning how to use all those tools, both mathematical models of dynamical systems and executable computational models and currently developing 'computation in materio'.“ That is the reason why physical/natural computing is so important.

Molecular Computation, Self-Organization and Morphogenesis

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Both intrinsic or natural morphogenesis and designed/synthetic/artificial morphogenesis are instructive in the study of evolution and development as computational processes. At present, according to MacLennan “One of the biggest issues that embodied computation faces is the lack of a commonly accepted model of computation.” (MacLennan, 2010) As morphogenesis seems to have “the characteristics of a coordinated algorithm” it is of special interest to understand communication patterns of actors in a network that represents system with morphogenetic dynamics.

”By investigating embryological morphogenesis – a supremely successful example of what we want to accomplish – we can learn many lessons about how communication, control, and computation can be done well at very small scales.” (MacLennan, 2010)

In the development of an organism, based on the DNA code together with epigenetic control mechanisms, body of a living being is created through morphogenesis governing a short time scale formation of life. On a long-time scale, morphological computing governs evolution of species. The environment provides a physical source of biological body of an organism, as a source of energy and matter for its metabolism as well as information, which governs its behavior. Nervous system and the brain of an organism have evolved gradually through interactions (computational processes) of simpler living agents with the environment. This process is a result of information self-structuring (Dodig-Crnkovic 2008).

The environment provides an agent with a variety of inputs in the form of information and matter-energy, where the difference between information and matter-energy is not in kind, but in type of use that organism makes of it . As there is no information without representation, (Landauer, 1991) (Allo, 2008) all information is carried by some physical carrier (light, sound, chemical molecules, etc.). The same object can be used by an organism as a source of information and a source of nourishment/matter/energy. Some organisms use light signals just as information necessary for orientation in the environment, while other organisms use it for photosynthetic processes in their metabolism. Thus the question what will be used “only” as information and what as food/ energy source depends on the type of organism/agent. In general, the simpler the organism, the simpler the information structures of its body, the simpler information carriers it relies on, and simpler interactions with the environment. In that sense

“(B)iotic information is nothing more than the constraints that allows a living organism to harness energy from its environment to propagate its organization.” (Kauffman et al., 2008)

According to (Maturana & Varela, 1980) p. 78, an autopoetic “machine” is organized as a network of processes of production, transformation and destruction of components, which through mutual interactions continuously regenerate the network that produced them. Structural coupling with the environment for autopoetic systems is described as continuous dynamical process and considered as an elementary form of cognition possessed by all life forms.

We describe cognition as information processing in living organisms, from cellular to organismic level and up to a social cognition. In this framework information is a substance, computation is a process and we argue for inseparability of structure/substance and its dynamics/process. If we search for the source of the energy necessary to build the constraints and turn environmental energy into the work needed by organisms to run their metabolism, Ulanowicz’s process ecology model offers an explanation: “Basically the answer is simply that an aleatoric1 event took place in which a constraint emerged that allowed a collection of organic molecules to do the work necessary to propagate their organization.” (Ulanowicz, 2009)

(Bonsignorio, 2013) studies evolutionary self-structuring of embodied cognitive networks and proposes a framework for the modeling of networks of self-organizing, embodied cognitive agents that can be used for the design of artificial and ’reverse engineering’ of natural networks, based on the maximization of mutual information.

Biological systems are networks of interacting parts exchanging information. They are shaped by physical constraints, which also present information for a system, as argued in (Kauffman et al., 2008). A living agent is a special kind of <computational> actor that can reproduce and that is capable of undergoing at least one thermodynamic work cycle. (Kauffman, 2000)

1 Characterized by chance or indeterminate elements, Merriam-Webster online dictionary

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Kauffman’s definition (that we adopt) differs from the common belief that (living) agency requires beliefs and desires, unless we ascribe some primitive form of <belief> and <desire> even to a very simple living agents such as bacteria. The fact is that they act on some kind of <memory> and <anticipation> and according to some <preferences> that might be automatic in a sense that they directly derive from the organisms’ morphology. (Ben-Jacob, Shapira, & Tauber, 2011; Ben-Jacob, 2008, 2009) Nevertheless bacteria show clear preferences for behaviors that increase organism’s survival.

Although the agents capacity to perform work cycles and so persist in the world is central and presents the material basis of life, as (Kauffman, 2000) and (Deacon, 2007) have argued, a detailed physical account of it remains to be worked out, especially relevant is the abiogenesis. Present article is primarily focused on the info-computational aspects of life as cognitive process with its basic elements information and computation on different levels of organization of living systems.

Intrinsic Computation and Causation

Causation is transfer of information (Collier, 1999) and computation, as information processing, is causation at work, as argued in (Dodig-Crnkovic, …). What are the implications of this view for computing nature in general and computational models of mind in particular?

Collier studies the relationship between information, computation and causation in (Collier, 2011)

Craver and Bechtel present top-down causation without top-down causes (Craver & Bechtel, 2007).

Walker Sara Imari’s article on Top-Down Causation presents the Rise of Information in the Emergence of Life (Walker, 2014)

CARL F. CRAVER, and WILLIAM BECHTEL, Top-down causation without top-down causes, Biology and Philosophy (2006) (Craver & Bechtel, 2007)

KAMPIS: CAUSAL DEPTHNetwork of causal connectedness

Andre Ehresmann talks about synonymity

Memory Evolutive Systems (Ehresmann, 2012)(Ehresmann, 2014)

However, Marcin Miłkowski suggests “the physical implementation of a computational system – and its interaction with the environment – lies outside the scope of computational explanation”.

”For a pancomputationalist, this means that there must be a distinction between lower-level, or basic, computations and the higher level ones. Should pancomputationalism be unable to mark this distinction, it will be explanatorily vacuous.” (Miłkowski, 2007)

From the above I infer that the model of computation, which Miłkowski assumes is a top-down, designed computation. Even though he rightly argues that neural networks and even dynamical systems can be understood as computational, Miłkowski does not think of intrinsic computation as grounded in physical process driven by causal mechanism, characteristics of computing nature.

The problem of physical computation is related to the problem of grounding of the concept of computation. Where the following question comes from?

If we would apply the above logic, we would demand from physicists to explain where matter comes from. Where do the elementary particles come from? They are simply empirical facts for which we have enough evidence. We might not know all of their properties and relationships, we might not know all of them, but we can

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be sure at least that they exist. The bottom layer for the computational universe is the bottom layer of its material substrate, which with constant progress of physics is becoming more and more fine-grained.

Mind as a Process and Computational Models of Mind

Of all computational approaches, the most controversial are the computational models of mind. There exists historically a huge variety of models, some of them taking mind to be a kind of immaterial substance opposed to material body, the most famous being Platonic and Cartesian dualist models. Through hylomorphism, in contrast to reductive materialism, which identifies body and mind, and Platonic dualism, which takes body and mind to be separate substances, Aristotle proposes a unifying approach where mind represents the form of a material body.

It is more natural for computational approaches to consider mind as a process of changing form, a complex process of computation on many different levels of organization of matter.

“To sum up: mind is a set of processes distinguished from others through their control by an immanent end. (…) At one extreme it dwindles into mere life, which is incipient mind. At the other extreme it vanishes in the clouds; it does not yet appear what we shall be. Mind as it exists in ourselves is on an intermediate level.” (Blanshard, 1941)

Within info-computational framework, cognition is understood as synonymous with process of life, a view that even Brand Blanshard adopted. Following Maturana and Varela’s argument from 1980 (Maturana & Varela, 1980), we can understand the entire living word as possessing cognition of various degrees of complexity. In that sense bacteria possess rudimentary cognition expressed in quorum sensing and other collective phenomena based on information communication and information processing. Brain of a complex organism consists of neurons that are networked communication computational units. Signalling and information processing modes of a brain are much more complex and consist of more computational layers than bacterial colony. Even though Maturana and Varela did not think of cognition as computation, the broader view of computation as found in info-computationalism is capable of representing processes of life as studied in bioinformatics and biocomputation.

Relation between mind and cognition [Marcin’s book]

cog·ni·tion The mental process of knowing, including aspects such as awareness, perception, reasoning, and judgment.

http://www.scholarpedia.org/article/Mind-body_problem:_New_approaches

Starting with mind as life itself, a single cell, and studying increasingly more complex organisms such as rotifers (which have around a thousand cells, of which a quarter constitute their nervous system with brain) or the tiny Megaphragma mymaripenne wasps (that are smaller than a single-celled amoebas and yet have nervous system and brains) – with more and more layers of cognitive information-processing architectures we can follow the evolution of mind as a capacity of a living organism to act on their own behalf:

“(W)herever mind is present, there the pursuit of ends is present”. (…) ” Mental activity is the sort of activity everywhere whose reach exceeds its grasp.” (…) “Now mind, at all of its levels and in all of its manifestations, is a process of this kind” [i.e. a drive toward a special end]. (Blanshard, 1941)

And the process powering this goal-directed behavior on a variety of levels of organization in living organisms is information self-organization. Andre Ehresmann (Ehresmann, 2012) proposes the model of brain where lower levels are made of Turing machines while the higher levels of cognitive activity are non-Turing, based on the fact that the same symbol has several possible interpretations. In contrast, Subrata Ghosh et al. (Ghosh et al., 2014) remarkable brain model demonstrates how mind can be modelled from the level of quantum field theory up to the macroscopic whole-brain, in twelve levels of computational architecture, based on computing beyond Turing model.

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Conclusions

This article meets Mark Sprevak’s three concerns about computationalism, (Sprevak, 2012) p. 108:

(R1) Lack of Clarity: “Ultimately, the foundations of our sciences should be clear.” Computationalism is suspected to lack clarity.

(R2) Triviality: “(O)ur conventional understanding of the notion of computational implementation is threatened by triviality arguments.” Computationalism is accused of triviality.

(R3) Lack of naturalistic foundations: “The ultimate aim of cognitive science is to offer, not just any explanation of mental phenomena, but a naturalistic explanation of the mind.” Computationalism is questioned for being formal and unnatural.

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Dodig-Crnkovic, G. (2007). Epistemology Naturalized: The Info-Computationalist Approach. APA Newsletter on Philosophy and Computers, 06(2), 9–13.

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Dodig-Crnkovic, G. (2011). Significance of Models of Computation from Turing Model to Natural Computation. Minds and Machines,, 21(2), 301–322.

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Dodig-Crnkovic, G., & Mueller, V. (2009). A Dialogue Concerning Two World Systems: Info-Computational vs. Mechanistic. (G. Dodig Crnkovic & M. Burgin, Eds.)Information and Computation (pp. 149–84). Singapore: World Scientific Pub Co Inc.

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From the mail to Terry Deacon

The central claim that I wish to reflect upon is how a system "registers"* information (and a connected question why it "registers" some information and not the other). From Deacon’s text (private communication):

"The far-from-equilibrium case is of major importance also because it provides the foundation for an analysis of the nature of an interpretive process (see next section).A simple exemplar of a far-from-equilibrium information medium is a metal detector."

There is for example connection to:

Kaneko, K. and Tsuda, I. "Complex systems: chaos and beyond. A constructive approach with applications in life sciences", Springer, Berlin/Heidelberg, 2001.

http://books.google.se/books?id=7lcINfgupggC&pg=PA265&dq=Complex+Systems:+Chaos+and+Beyond+by+K.+Kaneko;+I.+Tsuda&hl=en&sa=X&ei=5RVHU8f-E6SbygGmuYGwCA&ved=0CC0Q6AEwAA#v=onepage&q=Complex%20Systems%3A%20Chaos%20and%20Beyond%20by%20K.%20Kaneko%3B%20I.%20Tsuda&f=false

They discuss different topics, but this seems to me be of interest in connection to Deacon’s paper:

Dynamics of living organism creates a sensitive state that reacts on the changes in the environment.

“Those data are in accordance with the dynamic viewpoint of the brain as proposed by Tsuda, which can be summarized as follows: a neuron and a neuron assembly are not structured to reveal a single function, but structured such that they can implement multiple functions according to the internal states of the brain and the external environment.Furthermore, these activities should reveal temporally complex behavior, which perhaps is related to the chaotic itinerancy. Thus the study of the relational dynamics among the elements involved in the information processing of the brain will be an important issue.” P.18

This in turn may be expressed in terms of von Foersters notions of eigenvalues (stable structures) and eigenbehaviors (stable behaviors established in the interaction with the environment):

“ Any system, cognitive or biological, which is able to relate internally, self-organized, stable structures (eigenvalues) to constant aspects of its own interaction with an environment can be said to observe eigenbehavior. Such systems are defined as organizationally closed because their stable internal states can only be defined in terms of the overall dynamic structure that supports them.” (Rocha 1998: 342)

Rocha L. M. (1998) Selected self-organization and the semiotics of evolutionary systems. In: Salthe S., Van de Vijver G. & Delpos M. (eds.) Evolutionary systems: Biological and epistemological perspectives on selection and self-organization. Kluwer, Dordrecht: p. 342

Similarly, the following thought may be found in Gilbert Simondon's discussion of form-information relationship:

"The notion of form must be replaced by that of information, which implies the existence of a system in metastable equilibrium that can individuate; information, the difference in shape, is never a single term, but the meaning that arises from a disparation (disappearance)."

Simondon, Gilbert (2007) L'individuation psychique et collective. Paris: Editions Aubier (p. 28, translation by Andrew Iliadis)

In the above picture of a metastable state capable of reacting to the relevant changes in the environment, two things are particularly interesting (apart from the meta-stability itself): time-dependence (dynamics) and fractality.

Both are addressed in a radically new approach to the modeling of a whole brain in the following article by (Ghosh et al., 2014):

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Ghosh, Subrata; Aswani, Krishna; Singh, Surabhi; Sahu, Satyajit; Fujita, Daisuke; Bandyopadhyay, Anirban. 2014. "Design and Construction of a Brain-Like Computer: A New Class of Frequency-Fractal Computing Using Wireless Communication in a Supramolecular Organic, Inorganic System." Information 5, no. 1: 28-100.http://www.mdpi.com/2078-2489/5/1/28

What seems interesting in this context is that the central point in the above model is the collective time behavior and (fractal) frequencies at number of different levels of organization. (Ghosh et al., 2014) suggest a possibility of connection between levels from QFT (Quantum Field Theory) up to macroscopic levels based on time dependence of physical oscillators involved. It might not be an adequate model of a brain, but as Bohr model of atom it can contain some interesting insights. (refer to Basti here)

“Here, we introduce a new class of computer which does not use any circuit or logic gate. In fact, no program needs to be written: it learns by itself and writes its own program to solve a problem. Gödel's incompleteness argument is explored here to devise an engine where an astronomically...

Abstract: Here, we introduce a new class of computer which does not use any circuit or logic gate. In fact, no program needs to be written: it learns by itself and writes its own program to solve a problem. Gödel’s incompleteness argument is explored here to devise an engine where an astronomically large number of “if-then” arguments are allowed to grow by self-assembly, based on the basic set of arguments written in the system, thus, we explore the beyond Turing path of computing but following a fundamentally different route adopted in the last half-a-century old non-Turing adventures. Our hardware is a multilayered seed structure. If we open the largest seed, which is the final hardware, we find several computing seed structures inside, if we take any of them and open, there are several computing seeds inside. We design and synthesize the smallest seed, the entire multilayered architecture grows by itself. The electromagnetic resonance band of each seed looks similar, but the seeds of any layer shares a common region in its resonance band with inner and upper layer, hence a chain of resonance bands is formed (frequency fractal) connecting the smallest to the largest seed (hence the name invincible rhythm or Ajeya Chhandam in Sanskrit). The computer solves intractable pattern search (Clique) problem without searching, since the right pattern written in it spontaneously replies back to the questioner. To learn, the hardware filters any kind of sensory input image into several layers of images, each containing basic geometric polygons (fractal decomposition), and builds a network among all layers, multi-sensory images are connected in all possible ways to generate “if” and “then” argument. Several such arguments and decisions (phase transition from “if” to “then”) self-assemble and form the two giant columns of arguments and rules of phase transition. Any input question is converted into a pattern as noted above, and these two astronomically large columns project a solution. The driving principle of computing is synchronization and de-synchronization of network paths, the system drives towards highest density of coupled arguments for maximum matching. Memory is located at all layers of the hardware. Learning, computing occurs everywhere simultaneously. Since resonance chain connects all computing seeds, wireless processing is feasible without a screening effect. The computing power is increased by maximizing the density of resonance states and bandwidth of the resonance chain together. We discovered this remarkable computing while studying the human brain, so we present a new model of the human brain in terms of an experimentally determined resonance chain with bandwidth 10−15 Hz (complete brain with all sensors) to 10+15 Hz (DNA) along with its implementation using a pure organic synthesis of entire computer (brain jelly) in our lab, software prototype as proof of concept and finally a new fourth circuit element (Hinductor) based beyond Complementary metal-oxide semiconductor (CMOS) hardware is also presented.Keywords: Turing machine; Gödel’s incompleteness theorem; non-algorithmic computing; self-assembly; wireless communication; antenna; receiver; electromagnetic resonance; synchronization; brain-like computer; creative machine; intelligent machine; conscious machine

*This expression I borrow from Brian Cantwell Smith's "On the Origin ofObjects"

Top-down causation without top-down causesCarl F. Craver & William BechtelBiology and Philosophy 22 (4):547-563 (2007)AbstractWe argue that intelligible appeals to interlevel causes (top-down and bottom-up) can be understood, without remainder, as appeals to mechanistically mediated effects. Mechanistically mediated effects are hybrids of causal

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and constitutive relations, where the causal relations are exclusively intralevel. The idea of causation would have to stretch to the breaking point to accommodate interlevel causes. The notion of a mechanistically mediated effect is preferable because it can do all of the required work without appealing to mysterious interlevel causes. When interlevel causes can be translated into mechanistically mediated effects, the posited relationship is intelligible and should raise no special philosophical objections. When they cannot, they are suspect.

The software/wetware distinction Comment on “Toward a computational framework for cognitive biology: Unifying approaches from cognitive neuroscience and comparative cognition” by W. Tecumseh FitchDaniel Dennett, Phys Life Rev 2014.

Fitch WT. Toward a computational framework for cognitive biology: unifying approaches from cognitive neuroscience and comparative cognition. Phys Life Rev 2014.

« 3 » An MES gives a constructive model for a self-organized multi-scale cognitive system that is able to interact with its environment through information processing, such as a living organism or an artificial cognitive system. Its dynamics is modulated by the interactions of a network of specialized internal agents called co-regulators (CRs). Each CR operates at its own rhythm to collect and process external and/or internal information related to its function, and possibly to select appropriate procedures. The co-regulators operate with the help of a central, flexible memory containing the knowledge of the system, which they contribute to develop and adapt to a changing environment.

« 4 » In an MES, a central role is played by the following properties of information processing in living systems: (i) The system not only processes isolated information items, but also takes their interactions into account by processing information patterns, that is patterns of interconnected information items. (ii) The MES satisfies a multiplicity principle (MP), asserting that several such information patterns may play the same functional role once actualized, with the possibility of a switch between them during processing operations. This principle formalizes the degeneracy property that is ubiquitous in biological systems, as emphasized by Edelman (1989; Edelman & Gally 2001). It permits Gregory Bateson’s sentence (§21) to be completed into “a difference that makes a difference, but also may not make a difference.” The MP is at the root of the flexibility and adaptability of an MES; it will also be responsible for the non-computability of its global dynamics.

« 5 » Once actualized in the MES, an information pattern P will take its own identity as a new component cP of a higher complexity order, which “binds” the pattern, for instance as a record of P in the memory. The binding process is modeled by the categorical colimit operation (Kan 1958): cP becomes the colimit of P and also of each of the other functionally-equivalent information patterns; thus it acts as a multi-facetted component. Such multi-facetted components are constructed through successive complexification processes (Ehresmann & Vanbremeersch 2007). The complexification also constructs the links interconnecting two multi-facetted components cP and cQ. There are simple links, which bind together a cluster of links between the

Hylomorphism http://en.wikipedia.org/wiki/Hylomorphism

From Wikipedia, the free encyclopediaThis article is about the concept of hylomorphism in Aristotelian philosophy. For the concept in computer science, see Hylomorphism (computer science).

Hylomorphism is a philosophical theory developed by Aristotle, which conceives being (ousia) as a compound of matter and form

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Matter and form

Aristotle defines X's matter as "that out of which" X is made.[1] For example, letters are the matter of syllables.[2] Thus, "matter" is a relative term:[3] an object counts as matter relative to something else. For example, clay is matter relative to a brick because a brick is made of clay, whereas bricks are matter relative to a brick house.

Change is analyzed as a material transformation: matter is what undergoes a change of form. [4] For example, consider a lump of bronze that's shaped into a statue. Bronze is the matter, and this matter loses one form (that of a lump) and gains a new form (that of a statue).[5][6]

According to Aristotle's theory of perception, we perceive an object by receiving its form with our sense organs.[7] Thus, forms include complex qualia such as colors, textures, and flavors, not just shapes.[8]

Substantial form, accidental form, and prime matterSee also: Substantial form

Medieval philosophers who used Aristotelian concepts frequently distinguished between substantial forms and accidental forms. A substance necessarily possesses at least one substantial form. It may also possess a variety of accidental forms. For Aristotle, a "substance" (ousia) is an individual thing—for example, an individual man or an individual horse.[9] The substantial form of substance S consists of S's essential properties,[10] the properties that S's matter needs in order to be the kind of substance that S is.[11] In contrast, S's accidental forms are S's non-essential properties,[12] properties that S can lose or gain without changing into a different kind of substance.[13]

In some cases, a substance's matter will itself be a substance. If substance A is made out of substance B, then substance B is the matter of substance A. However, what is the matter of a substance that is not made out of any other substance? According to Aristotelians, such a substance has only "prime matter" as its matter. Prime matter is matter with no substantial form of its own.[14] Thus, it can change into various kinds of substances without remaining any kind of substance all the time.[15]

Body–soul hylomorphism

Basic theorySee also: On the Soul

Aristotle applies his theory of hylomorphism to living things. He defines a soul as that which makes a living thing alive.[16] Life is a property of living things, just as knowledge and health are.[17] Therefore, a soul is a form—that is, a property or set of properties—belonging to a living thing.[18] Furthermore, Aristotle says that a soul is related to its body as form to matter.[19]

Hence, Aristotle argues, there is no problem in explaining the unity of body and soul, just as there is no problem in explaining the unity of wax and its shape.[20] Just as a wax object consists of wax with a certain shape, so a living organism consists of a body with the property of life, which is its soul. On the basis of his hylomorphic theory, Aristotle rejects the Pythagorean doctrine of reincarnation, ridiculing the notion that just any soul could inhabit just any body.[21]

According to Timothy Robinson, it is unclear whether Aristotle identifies the soul with the body's structure. [22] According to one interpretation of Aristotle, a properly organized body is already alive simply by virtue of its structure.[23] However, according to another interpretation, the property of life—that is, the soul—is something in addition to the body's structure. Robinson uses the analogy of a car to explain this second interpretation. A running car is running not only because of its structure but also because of the activity in its engine.[24] Likewise, according to this second interpretation, a living body is alive not only because of its structure but also because of an additional property: the soul is this additional property, which a properly organized body needs in order to be alive.[25] John Vella uses Frankenstein's monster to illustrate the second interpretation:[26] the corpse lying on Frankenstein's table is already a fully organized human body, but it is not yet alive; when Frankenstein activates his machine, the corpse gains a new property, the property of life, which Aristotle would call the soul.

Living bodies

Some scholars have pointed out a problem facing Aristotle's theory of soul-body hylomorphism.[27] According to Aristotle, a living thing's matter is its body, which needs a soul in order to be alive. Similarly, a bronze sphere's

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matter is bronze, which needs roundness in order to be a sphere. Now, bronze remains the same bronze after ceasing to be a sphere. Therefore, it seems that a body should remain the same body after death. [28] However, Aristotle implies that a body is no longer the same body after death.[29] Moreover, Aristotle says that a body that has lost its soul is no longer potentially alive.[30] But if a living thing's matter is its body, then that body should be potentially alive by definition.

One approach to resolving this problem[31] relies on the fact that a living body is constantly losing old matter and gaining new matter. Your five-year-old body consists of different matter than does your seventy-year-old body. If your five-year-old body and your seventy-year-old body consist of different matter, then what makes them the same body? The answer is presumably your soul. Because your five-year-old body and your seventy-year-old body share your soul—that is, your life—we can identify them both as your body. Apart from your soul, we cannot identify what collection of matter is your body. MEMORY! Therefore, your body is no longer your body after it dies. [NO. ARISTOTLE SAYS YOUR BODY WITHOUT SOUL IS NOT ALIVE. BY DEFINITION. BECAUSE SOUL MEANS LIFE.]

Another approach to resolving the problem[32] relies on a distinction between "proximate" and "non-proximate" matter. When Aristotle says that the body is matter for a living thing, he may be using the word "body" to refer to the matter that makes up the fully organized body, rather than the fully organized body itself. Unlike the fully organized body, this "body" remains the same thing even after death. In contrast, when he says that the body is no longer the same body after its death, he is using the word "body" to refer to the fully organized body, which (according to this interpretation) does not remain the same thing after death.

IntellectSee also: Nous, Active intellect and Passive intellect

Aristotle says that the intellect (nous), the ability to think, has no bodily organ (in contrast with other psychological abilities, such as sense-perception and imagination).[33] In fact, he says that it is not mixed with the body[34] and suggests that it can exist apart from the body.[35] This seems to contradict Aristotle's claim that the soul is a form or property of the body. To complicate matters further, Aristotle distinguishes between two kinds of intellect or two parts of the intellect.[36] These two intellectual powers are traditionally called the "passive intellect" and the "active intellect" or "agent intellect".[37] Thus, interpreters of Aristotle have faced the problem of explaining how the intellect fits into Aristotle's hylomorphic theory of the soul.

According to one interpretation, a person's ability to think (unlike his other psychological abilities) belongs to some incorporeal organ distinct from his body.[38] This would amount to a form of dualism.[39] However, according to some scholars, it would not be a full-fledged Cartesian dualism.[40] This interpretation creates what Robert Pasnau has called the "mind-soul problem": if the intellect belongs to an entity distinct from the body, and the soul is the form of the body, then how is the intellect part of the soul?[41]

Another interpretation rests on the distinction between the passive intellect and the agent intellect. According to this interpretation, the passive intellect is a property of the body, while the agent intellect is a substance distinct from the body.[42][43] Some proponents of this interpretation think that each person has his own agent intellect, which presumably separates from the body at death.[44][45] Others interpret the agent intellect as a single divine being, perhaps the Unmoved Mover, Aristotle's God.[46][47]

A third interpretation[48] relies on the theory that an individual form is capable of having properties of its own.[49] According to this interpretation, the soul is a property of the body, but the ability to think is a property of the soul itself, not of the body. If that is the case, then the soul is the body's form and yet thinking need not involve any bodily organ.[50]

……

Modern physics

The idea of hylomorphism can be said to have been reintroduced to the world when Werner Heisenberg invented his duplex world of quantum mechanics.[69]

"In the experiments about atomic events we have to do with things and facts, with phenomena that are just as real as any phenomena in daily life. But atoms and the elementary particles themselves are not as real; they form a world of potentialities or possibilities rather than one of things or facts ... The probability wave ... mean[s] tendency for something. It's a quantitative version of the old concept of potentia from Aristotle's philosophy. It

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introduces something standing in the middle between the idea of an event and the actual event, a strange kind of physical reality just in the middle between possibility and reality."

See also

Endurantism Hyle Hylozoism Identity and change Inherence Materialism Substance theory

Notes

1. Physics 194b23-242. Physics 195a163. Physics 194b94. Robinson 18-195. Physics 195a6-86. Metaphysics 1045a26-297. On the Soul 424a198. On the Soul 418a11–129. Categories 2a12-1410. Cross 3411. Kenny 2412. Cross 9413. Kenny 2414. Leftow 136-3715. Kenny 2516. On the Soul 413a20-2117. On the Soul 414a3-918. On the Soul 412a20, 414a15-1819. On the Soul 412b5-7, 413a1-3, 414a15-1820. 412b5-621. On the Soul 407b20-24, 414a22-2422. Robinson 45-4723. Robinson 4624. Robinson 4625. Robinson 4726. Vella 9227. Shields, Aristotle 290-9328. Shields, Aristotle 29129. On the Soul 412b19-2430. 412b1531. Shields, Aristotle 29332. Shields, "A Fundamental Problem"33. On the Soul 429a26-2734. On the Soul 429a24-2535. On the Soul 413b24-26, 429b636. On the Soul 15-2537. Robinson 5038. Caston, "Aristotle's Psychology" 33739. Caston, "Aristotle's Psychology" 33740. Shields, "Some Recent Approaches" 16541. Pasnau 16042. McEvilley 53443. Vella 11044. Caston, "Aristotle's Two Intellects" 20745. Vella 11046. Caston, "Aristotle's Psychology" 339

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47. Caston, "Aristotle's Two Intellects" 19948. Shields, "Soul as Subject"49. Shields, "Soul as Subject" 14250. Shields, "Soul as Subject" 14551. Kenny 2652. Cross 7053. Stump, "Resurrection, Reassembly, and Reconstitution: Aquinas on the Soul" 16154. Leftow, "Soul, Mind, and Brain" 39755. Stump, "Resurrection, Reassembly, and Reconstitution: Aquinas on the Soul" 16556. Eberl 34057. Eberl 34158. Stump, "Resurrection, Reassembly, and Reconstitution: Aquinas on the Soul" 16159. Stump, "Non-Cartesian Substance Dualism and Materialism without Reductionism" 51460. Stump,"Non-Cartesian Substance Dualism and Materialism without Reductionism" 51261. Stump, "Non-Cartesian Substance Dualism and Materialism without Reductionism" 51262. Stump, "Non-Cartesian Substance Dualism and Materialism without Reductionism" 51963. Irwin 23764. Metaphysics 1050a1565. Irwin 23766. Nichomachean Ethics 1098a16-1867. Nichomachean Ethics 1098a1-568. Nichomachean Ethics 1098a7-869. Herbert, Nick (1985). Quantum Reality: Beyond the New Physics. New York: Anchor Books. pp. 26–27.

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o "Resurrection, Reassembly, and Reconstitution: Aquinas on the Soul." Die Menschliche Seele: Brauchen Wir Den Dualismus. Ed. B. Niederbacher and E. Runggaldier. Frankfurt, 2006. 151-72.

Vella, John. Aristotle: A Guide for the Perplexed. NY: Continuum, 2008.

http://plato.stanford.edu/entries/aristotle-psychology/suppl1.html

Shields, Christopher, "Aristotle's Psychology", The Stanford Encyclopedia of Philosophy (Spring 2011 Edition), Edward N. Zalta (ed.), URL = <http://plato.stanford.edu/archives/spr2011/entries/aristotle-psychology/>.

Causal Processes

First published Sun Dec 8, 1996; substantive revision Mon Sep 10, 2007

Taking their point of departure from what science tells us about the world rather than from our everyday concept of a ‘process’, philosophers interested in analysing causal processes have tended to see the chief task to be to distinguish causal processes such as atoms decaying and billiard balls moving across the table from pseudo processes such as moving shadows and spots of light. These philosophers claim to have found, in the notion of a causal process, a key to understanding causation in general.

1. Russell's Theory of Causal Lines 2. Objections to Russell's Theory 3. Salmon's Mark Transmission Theory 4. Objections to Salmon's Mark Transmission Theory 5. The Conserved Quantity Theory 6. Objections to the Conserved Quantity Theory

o 6.1 Objection 1: Worries about Omissions and Preventions. o 6.2 Objection 2: Worries about Conserved Quantities o 6.3 Objection 3: Worries about Pseudo Processes. o 6.4 Objection 4: Worries about Causal Relevance. o 6.5 Objection 5: Worries about ‘Empirical Analysis’ o 6.6 Objection 6: Worries about Reduction.

7. Related theories of causation o 7.1. Aronson's transference theory o 7.2. Fair's transference theory o 7.3. Ehring's trope persistence theory o 7.4. Other theories

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1. Russell's Theory of Causal Lines

An important forerunner of contemporary notions of causal processes is Bertrand Russell's account of causal lines. This may be surprising to those who are more accustomed to associate the name ‘Bertrand Russell’ with scepticism about causation. Russell's 1912/13 paper, ‘On the Notion of Cause’, is famous for the quote,

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The law of causality, I believe, like much that passes muster among philosophers, is a relic of a bygone age, surviving, like the monarchy, only because it is erroneously supposed to do no harm. (Russell, 1913, p. 1).

In that paper Russell argued that the philosopher's concept of causation involving, as it does, the law of universal determinism that every event has a cause and the associated concept of causation as a relation between events, is “otiose” and in modern science is replaced by the concept of causal laws understood in terms of functional relations, where these causal laws are not necessarily deterministic.

However, in a later book written in 1948, entitled Human Knowledge Bertrand Russell outlines a similar view but does so in language which is much more flattering to causation. He still holds that the philosophical idea of causation should be seen as a primitive version of the scientific idea of causal laws. Nevertheless, his emphasis now is on certain postulates of causation which he takes to be fundamental to scientific (inductive) inference, and Russell's aim is to show how scientific inference is possible.

The problem with thinking about causal laws as the underpinning of scientific inference is that the world is a complex place, and while causal laws might hold true, they often do not obtain because of preventing circumstances, and it is impractical to bring in innumerable ‘unless’ clauses. But, even though there is infinite complexity in the world, there are also causal lines of quasi-permanence, and these warrant our inferences.

Russell elaborates these ideas into five postulates which he says are necessary “to validate scientific method” (1948, p. 487). The first is ‘The Postulate of Quasi-permanence’ which states that there is a certain kind of persistence in the world, for generally things do not change discontinuously. The second postulate, ‘Of Separable Causal Lines’, allows that there is often long term persistence in things and processes. The third postulate, ‘Of Spatio-temporal Continuity’ denies action at a distance. Russell claims “when there is a causal connection between two events that are not contiguous, there must be intermediate links in the causal chain such that each is contiguous to the next, or (alternatively) such that there is a process which is continuous.” (1948, p. 487). ‘The Structural Postulate’, the fourth, allows us to infer from structurally similar complex events ranged about a centre to an event of similar structure linked by causal lines to each event. The fifth postulate, ‘Of Analogy’ allows us to infer the existence of a causal effect when it is unobservable.

The key postulate concerns the idea of causal lines or, in our terminology, causal processes. Russell's 1948 view is that causal lines replace the primitive notion of causation in the scientific view of the world, and not only replace but also explain the extent to which the primitive notion, causation, is correct. He writes,

The concept “cause”, as it occurs in the works of most philosophers, is one which is apparently not used in any advanced science. But the concepts that are used have been developed from the primitive concept (which is that prevalent among philosophers), and the primitive concept, as I shall try to show, still has importance as the source of approximate generalisations and pre-scientific inductions, and as a concept which is valid when suitably limited. (1948, p. 471).

Russell also says, “When two events belong to one causal line the earlier may be said to ‘cause’ the later. In this way laws of the form ‘A causes B’ may preserve a certain validity.” (1948, p. 334). So Russell can be seen, in his 1948 book, as proposing the view that within limits causal lines, or causal processes, may be taken to analyse causation. So what is a causal line? Russell writes,

I call a series of events a “causal line” if, given some of them, we can infer something about the others without having to know anything about the environment. (1948, p. 333).

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A causal line may always be regarded as a persistence of something, a person, a table, a photon, or what not. Throughout a given causal line, there may be constancy of quality, constancy of structure, or gradual changes in either, but not sudden change of any considerable magnitude. (1948, pp. 475-7).

So the trajectory through time of something is a causal line if it doesn't change too much, and if it persists in isolation from other things. A series of events which display this kind of similarity display what Russell calls ‘quasi-permanence’.

The concept of more or less permanent physical object in its common-sense form involves “substance”, and when “substance” is rejected we have to find some other way of defining the identity of a physical object at different times. I think this must be done by means of the concept “causal line”. (1948, p. 333).

Elsewhere Russell writes,

The law of quasi-permanence as I intend it … is designed to explain the success of the common-sense notion of “things” and the physical notion of “matter” (in classical physics). … a “thing” or a piece of matter is not to be regarded as a single persistent substantial entity, but as a string of events having a certain kind of causal connection with each other. This kind is what I call “quasi-permanence”. The causal law that I suggest may be enunciated as follows: “Given an event at a certain time, then at any slightly earlier or slightly later time there is, at some neighbouring place, a closely similar event”. I do not assert that this happens always, but only that it happens very often- sufficiently often to give a high probability to an induction confirming it in a particular case. When “substance” is abandoned, the identity, for commonsense, of a thing or a person at different times must be explained as consisting in what may be called a “causal line”. (1948, pp. 475-7).

This has relevance for the question of identity through time, and in Human Knowledge we find that Bertrand Russell sees that there is an important connection between causal process and identity, namely, that the concept of a causal line can be used to explain the identity through time of an object or a person.

So what we may call Russell's causal theory of identity (Dowe, 1999) asserts that the identity over time of an object or a person consists in the different temporal parts of that person being all part of the one causal line. This is the causal theory of identity (Armstrong, 1980) couched in terms of causal processes or lines. A causal line in turn is understood by way of an inference which is licensed by the law of quasi permanence.

2. Objections to Russell's Theory

Wesley Salmon has urged a number of objections against Russell's theory of causal lines. (1984, p. 140-5). The first objection is that Russell's theory is couched in epistemic terms rather than ontological terms, yet causation is itself an ontic matter not an epistemic matter. Russell's account is formulated in terms of how we make inferences. For example, Russell says

A “causal line,” as I wish to define the term, is a temporal series of events so related that, given some of them, something can be inferred about the others whatever may be happening elsewhere. (1948, p. 459).

Salmon's criticism of this is precisely that it is formulated in epistemic terms, “for the existence of the vast majority of causal processes in the history of the universe is quite independent of human knowers.” (1984, p. 145). Salmon, as we shall see in the next section, develops his account of causal processes as an explicitly ‘ontic’, as opposed to an ‘epistemic’ account. (1984, ch. 1).

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There is a further reason why Russell's epistemic approach is unacceptable. While it is true that causal processes do warrant inferences of the sort Russell has in mind, it is not the case that all rational inferences are warranted by the existence (‘postulation’, in Russell's thinking) of causal lines. There are other types of causal structures besides a causal line. Russell himself gives an example: two clouds of incandescent gas of a given element both emit the same spectral lines, but are not causally connected. (1948, p. 455). Yet we may rightly make inferences from one to the other. A pervasive type of case is where two events are not directly causally connected but have a common cause.

The second objection is that Russell's theory of a causal line does not enable the distinction between pseudo and causal processes to be made, yet to delineate causal from pseudo processes is a key issue which needs to be addressed by any theory of causal processes. As Reichenbach argued (1958, pp. 147-9), as he reflected on the implications of Einstein's special theory of relativity, science requires that we distinguish between causal and pseudo processes. Reichenbach noticed that the central principle that nothing travels faster than the speed of light is ‘violated’ by certain processes. For example, a spot of light moving along a wall is capable of moving faster than the speed of light. (One needs just a powerful enough light and a wall sufficiently large and sufficiently distant.) Other examples include shadows, and the point of intersection of two rulers (see Salmon's clear exposition in his 1984, pp. 141-4). Such pseudo processes, as we shall call them (Reichenbach called them “unreal sequences”; 1958, pp. 147-9), do not violate special relativity, Reichenbach argued, simply because they are not causal processes, and the principle that nothing travels faster than the speed of light applies only to causal processes. Thus special relativity demands a distinction between causal and pseudo processes. But Russell's theory doesn't explain this distinction, because both causal processes and pseudo processes display constancy of structure and quality; and both licence inferences of the sort Russell has in mind. For example, the phase velocity of a wave packet is a pseudo process but the group velocity is a causal process; yet both licence reliable predictions.

3. Salmon's Mark Transmission Theory

In this section we consider Wesley Salmon's theory of causality as presented in his book Scientific Explanation and the Causal Structure of the World (1984). Although it draws on the work of Reichenbach and Russell, Salmon's theory is highly original and contains many innovative contributions. Salmon's broad objective is to offer a theory which is consistent with the following assumptions: (a) causality is an objective feature of the world; (b) causality is a contingent feature of the world; (c) a theory of causality must be consistent with the possibility of indeterminism; (d) the theory should be (in principle) time-independent so that it is consistent with a causal theory of time; (e) the theory should not violate Hume's strictures concerning ‘hidden powers’.

Salmon treats causality as primarily a characteristic of continuous processes rather than as a relation between events. His theory involves two elements, the production and the propagation of causal influence. (See, for example, 1984, p. 139.) The latter is achieved by causal processes. Salmon defines a process as anything that displays consistency of structure over time. (1984, p.144). To distinguish between causal and pseudo processes (which Reichenbach called “unreal sequences”; 1958, pp. 147-9). Salmon makes use of Reichenbach's ‘mark criterion’: a process is causal if it is capable of transmitting a local modification in structure (a ‘mark’) (1984, p. 147). Drawing on the work of Bertrand Russell, Salmon seeks to explicate the notion of ‘transmission’ by the ‘at-at theory’ of mark transmission. The principle of mark transmission (MT) states:

MT: Let P be a process that, in the absence of interactions with other processes would remain uniform with respect to a characteristic Q, which it would manifest consistently over an interval that includes both of the space-time points A and B (A − B). Then, a mark (consisting of a modification of Q into Q*), which has been introduced into process P by means of a single local interaction at a point A, is transmitted to point B if [and only if] P manifests the modification Q*

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at B and at all stages of the process between A and B without additional interactions. (1984, p. 148).

Salmon himself omits the ‘only if’ condition. However, as suggested by Sober (1987, p. 253), this condition is essential because the principle is to be used to identify pseudo processes on the grounds that they do not transmit a mark (Dowe, 1992b, p. 198). Thus for Salmon a causal process is one which can transmit a mark, and it is these spatiotemporally continuous processes that propagate causal influence.

To accompany this theory of the propagation of causal influence, Salmon also analyses the production of causal processes. According to Salmon, causal production can be explained in terms of causal forks, whose main role is the part they play in the production of order and structure of causal processes. The causal forks are characterised by statistical forks; to Reichenbach's ‘conjunctive fork’ Salmon has added the ‘interactive’ and ‘perfect’ forks, each corresponding to a different type of common-cause.

Firstly there is the ‘conjunctive fork’, where two processes arise from a special set of background conditions often in a non-lawful fashion. (Salmon, 1984, p. 179). In such a case we get a statistical correlation between the two processes which can be explained by appealing to the common cause, which ‘screens off’ the statistical connection. This is the principle of the common cause (due originally to Reichenbach (1956)) which, stated formally, is that if, for two events A and B,

(1) P(A.B) > P(A).P(B)

holds, then look for an event C such that

(2) P(A.B|C) = P(A|C).P(B|C)

The events A, B, and C form a conjunctive fork (For the full account see Salmon, 1984, ch. 6). In Salmon's theory of causality, conjunctive forks produce structure and order from ‘de-facto’ background conditions.(1984, p. 179).

Secondly, there is the ‘interactive fork’, where an intersection between two processes produces a modification in both (1984, p. 170) and an ensuing correlation between the two processes cannot be screened off by the common cause. Instead, the interaction is governed by conservation laws. For example, consider a pool table where the cue ball is placed in such a position relative to the eight ball that, if the eight ball is sunk in one pocket A , the cue ball will almost certainly drop into the other pocket B. There is a correlation between A and B such that equation (1) holds. But the common cause C, the striking of the cue ball, does not screen off this correlation. Salmon has suggested that the interactive fork can be characterised by the relation

(3) P(A.B|C) > P(A|C).P(B|C)

together with (1). (1978, p. 704, n. 31). Interactive forks are involved in the production of modifications in order and structure of causal processes. (1982, p. 265; 1984, p. 179). In this paper ‘interactive fork’ is used to mean precisely ‘a set of three events related according to equations (1) and (3)’.

The idea of a causal interaction is further analysed by Salmon in terms of the notion of mutual modification. The principle of causal interaction (CI) states:

CI: Let P1 and P2 be two processes that intersect with one another at the space-time S, which belongs to the histories of both. Let Q be a characteristic of that process P1 would exhibit throughout an interval (which includes subintervals on both sides of S in the history of P1) if the intersection

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with P2 did not occur; let R be a characteristic that process P2 would exhibit throughout an interval (which includes subintervals on both sides of S in the history of P2) if the intersection with P1 did not occur. Then, the intersection of P1 and P2 at S constitutes a causal interaction if (1) P1 exhibits the characteristic Q before S, but it exhibits a modified characteristic Q* throughout an interval immediately following S; and (2) P2 exhibits R before S but it exhibits a modified characteristic R throughout an interval immediately following ′ S. (1984, p. 171).

Thirdly, there is the perfect fork, which is the deterministic limit of both the conjunctive and interactive fork. It is included as a special case because in the deterministic limit the interactive fork is indistinguishable from the conjunctive fork. (1984, pp. 177-8). Thus, a perfect fork could be involved in either the production of order and structure, or the production of changes in order and structure of causal processes.

4. Objections to Salmon's Mark Transmission Theory

The major objection against Samon's account of causal processes concerns the adequacy of the mark theory (Dowe, 1992a; 1992b; Kitcher, 1989). The mark transmission (MT) principle carries a considerable burden in Salmon's account, for it provides the criterion for distinguishing causal from pseudo processes. However, it has serious shortcomings in doing this. In fact, it fails on two counts: it excludes many causal processes; and it fails to exclude many pseudo processes. We shall consider each of these problems in turn.

1. MT excludes causal processes. Firstly, the principle requires that processes display a degree of uniformity over a time period. This distinguishes processes (causal and pseudo) from ‘spatiotemporal junk’, to use Kitcher's term. One problem with this is that it seems to exclude many causal effects which are short lived. For example, short lived subatomic particles play important causal roles, but they don't seem to qualify as causal processes. On any criterion there are causal processes which are ‘relatively short lived’. Also, the question concerning how long a regularity must persist raises philosophical difficulties about degrees which need answering before we have an adequate distinction between processes and spatiotemporal junk. However, if these were the only difficulties I think that the theory could be saved. Unfortunately, they are not.

More seriously, the MT principle requires that causal processes would remain uniform in the absence of interactions and that marks can be transmitted in the absence of additional interventions. However, in real situations processes are continuously involved in interactions of one sort or another.(Kitcher, 1989, p. 464). Even in the most idealised of situations interactions of sorts occur. For example, consider a universe that contains only one single moving particle. Not even this process moves in the absence of interactions, for the particle is forever intersecting with spatial regions. If we required that the interactions be causal (at the risk of circularity), then it is still true that in real cases there are many causal interactions continuously affecting processes. Even in carefully controlled scientific experiments there are many (admittedly irrelevant) causal interactions going on. Further, Salmon's central insight that causal processes are self propagating is not entirely well founded. For while some causal processes (light radiation, inertial motion) are self propagating, others are not. Falling bodies and electric currents are moved by their respective fields. (In particular there is no electric counterpart to inertia.) Sound waves are propagated within a medium, and simply do not exist ‘in the absence of interactions’. Such processes require a ‘causal background’, some can even be described as being a series of causal interactions. These causal processes cannot move in the absence of interactions. Thus there are a whole range of causal processes which are excluded by the requirement that they would remain uniform in the absence of any interactions.

It seems desirable, therefore, to abandon the requirement that a causal process is one that is capable of transmitting a mark in the absence of further interactions. However, the requirement is there for a reason, and that is that without it the theory is open to the objection that certain pseudo processes will count as being capable of transmitting marks. Salmon considers a case where a

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moving spot is marked by a red filter held up close to the wall. If someone ran alongside the wall holding up the filter, then it seems that the modification to the process is transmitted beyond the space-time locality of the original marking interaction. Thus there are problems if the requirement is kept, and there are problems if it is omitted. So it is not clear how the theory can be saved from the problem that some causal processes can not move in the absence of further interactions.

2. MT fails to exclude pseudo processes. Salmon's explicit intention in employing the MT principle is to show how pseudo processes are different from causal processes. If MT fails here then it fails its major test. However, a strong case can be made for saying that it does indeed fail this test.

Firstly, there are cases where pseudo processes qualify as being capable of transmitting a mark, because of the vagueness of the notion of a characteristic. We have seen that Salmon's approach to causality is to give an informal characterisation of the concepts of ‘production’ and ‘propagation’. In these characterisations, the primitive notions include ‘characteristic’, but nothing precise is said about this notion. While Salmon is entitled to take this informal approach, in this case more needs to be said about a primitive notion such as ‘characteristic’, at least indicating the range of its application, because the vagueness renders the account open to counter-examples.

For example, in the early morning the top (leading) edge of the shadow of the Sydney Opera House has the characteristic of being closer to the Harbour Bridge than to the Opera House. But later in the day (at time t say), this characteristic changes. This characteristic qualifies as a mark by IV, since it is a change in a characteristic introduced by the local intersection of two processes, namely, the movement of the shadow across the ground, and the (stationary) patch of ground which represents the midpoint between the Opera House and the Harbour Bridge. By III this mark which the shadow displays continuously after time t, is transmitted by the process. Thus, by II, the shadow is a causal process. This is similar to Sober's counter-example of where a light spot ‘transmits’ the characteristic of occurring after a glass filter is bolted in place. (1987, p. 254).

So there are some restrictions that need to be placed on the type of property allowed as a characteristic. Having the property of “occurring after a certain time” (Sober, 1987, p. 254),or the property of “being the shadow of a scratched car” (Kitcher, 1989, p. 638) or the property of “being closer to the Harbour Bridge than to the Opera House” (Dowe, 1992b, sec. 2.2) can qualify a shadow to be a causal process. There is a need to specify what kinds of properties can count as the appropriate characteristics for marking. It is not sufficient to say that the mark has to be introduced by a single local interaction, for as the above discussion suggests it is always possible to identify a single local interaction.

The difficulty lies in the type of characteristic allowed. A less informal approach to the subject might link ‘characteristic’ to ‘property’ of which there are precise philosophical accounts available. (For example, (Armstrong, 1978) ). Rogers takes this approach, defining the state of a process as the set of properties of the process at a given time. (Rogers, 1981, p. 203). A ‘law of non-interactive evolution’ gives the probability of the possible states at a later time, conditional on the actual state.

However, even if that approach were successful, there are difficulties of a different kind. There are cases of “derivative marks” (Kitcher, 1989, p. 463) where a pseudo process displays a modification in a characteristic on account of a change in the causal processes on which it depends. This change could either be in the source, or in the causal background. A change at the source would include cases where the spotlight spot is ‘marked’ by a coloured filter at the source (Salmon, 1984, p. 142) or a car's shadow is marked when a passenger's arm holds up a flag. (Kitcher, 1989, p. 463).

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The clause ‘by means of a single local interaction’ is intended to exclude this type of example: but it is not clear that this works, for does not the shadow intersect with the modified sunlight pattern locally? It is true that the ‘modified sunlight pattern’ originated, or was caused by, the passenger raising his arm with the flag, but the fact that the marking interaction is the result of a chain of causes cannot be held to exclude those interactions, for genuine marking interactions are always the result of a chain of causal processes and interactions. (Kitcher, 1989, p. 464) Similarly, there is a local spacetime intersection of the spotlight spot and the red beam.

5. The Conserved Quantity Theory

The idea of appealing to conserved quantities has its forerunners in Aronson's and Fair's appeal to energy and momentum. (Aronson, 1971; Fair, 1979) But the first explicit formulation was given in a brief suggestion made by Skyrms in 1980, in his book Causal Necessity (1980, p. 111) and the first detailed conserved quantity theory by Dowe (1992). See also Salmon, 1994, 1998 and Dowe, 1995, 2000. As the versions of Salmon and Dowe vary it's worth giving both versions:

Dowe's version (1995, p. 323):

CQ1. A causal interaction is an intersection of world lines which involves exchange of a conserved quantity.

CQ2. A causal process is a world line of an object which possesses a conserved quantity.

Salmon's version (1997, pp. 462, 468):

Definition 1. A causal interaction is an intersection of world-lines that involves exchange of a conserved quantity.

Definition 2. A causal process is a world-line of an object that transmits a nonzero amount of a conserved quantity at each moment of its history (each spacetime point of its trajectory).

Definition 3. A process transmits a conserved quantity between A and B (A ? B) if it possesses [a fixed amount of] this quantity at A and at B and at every stage of the process between A and B without any interactions in the open interval (A, B) that involve an exchange of that particular conserved quantity.

A process is the world line of an object, regardless of whether or not it possesses any conserved quantities. A process can be either causal or non-causal (pseudo). A world line is the collection of points on a space-time (Minkowski) diagram which represents the history of an object. This means that processes are determinate regions, or ‘worms’, in space time. Such processes, or worms in space time, will normally be time-like; that is, every point on its world line lies in the future lightcone of the process' starting point.

An object is anything found in the ontology of science (such as particles, waves or fields), or common sense (such as chairs, buildings, or people). This will include non-causal objects such as spots and shadows. It is important to appreciate the difference between an object and a process. Loosely speaking, a process is the development over time of an object. Processes are usually extended in time.

Worms in space time which are not processes Kitcher calls ‘spatiotemporal junk’ (1989). Thus a representation on a space time diagram represents either a process or a piece of spatiotemporal junk, and a process is either a causal or a pseudo process. In a sense what counts as an object is unimportant; any old gerrymandered thing qualifies (except time-wise gerrymanders) (Dowe, 1995). In the case of a causal process what matters is whether the object possesses the right type of quantity. A shadow is an object but it does not possess the right type

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of conserved quantities; for example, a shadow cannot possess energy or momentum. It has other properties, such as shape, velocity, and position but possesses no conserved quantities. (The theory could be formulated in terms of objects: there are causal objects and pseudo objects. Causal objects are those which possess conserved quantities, pseudo objects are those which do not. Then a causal process is the world line of a causal object.)

A conserved quantity is any quantity which is universally conserved, and current scientific theory is our best guide as to what these are. For example, we have good reason to believe that mass-energy, linear momentum, and charge are conserved quantities.

An intersection is simply the overlapping in space time of two or more processes. The intersection occurs at the location consisting of all the space time points which are common to both (or all) processes. An exchange occurs when at least one incoming, and at least one outgoing process undergoes a change in the value of the conserved quantity, where ‘outgoing’ and ‘incoming’ are delineated on the space-time diagram by the forward and backward light cones, but are essentially interchangeable. The exchange is governed by the conservation law, which guarantees that it is a genuine causal interaction. It follows that an interaction can be of the form X, Y, λ, or of a more complicated form.

‘Possesses’ for Dowe is to be understood in the sense of ‘instantiates’. We suppose an object possesses energy if science attributes that quantity to that body. It does not matter whether that process transmits the quantity or not, nor whether the object keeps a constant amount of the quantity. It must simply be that the quantity may be truly predicated of the object.

6. Objections to the Conserved Quantity Theory

6.1 Objection 1: Worries about Omissions and Preventions.

If causation must involve a physical connection between a cause and its effect, than many everyday causal claims will not count as causation. ‘I killed the plant by not watering it’ (Beebee 2004). If this is a case of causation then process theories are in trouble, because neither my not watering nor whatever I did instead are connected by a physical process to the plant's dying. The same is true for ‘my failure to check the oil caused my engine to seize’. Cases of causation by omission, absence, preventing (ie causing to not happen) and double prevention (e.g., I prevent someone preventing an accident, Hall 2004) all raise the same difficulty. If these are cases of causation then the process theory cannot be right (Hausman 1998, pp. 15-16, Schaffer 2000, 2004).

There is a long tradition that asserts that such are indeed cases of causation. Lewis is adamant (1986, pp 198-93, 2004) and Schaffer presents a detailed case (2000, 2004). Others have denied these are indeed cases of causation (Aronson 1971, Dowe 1999, 2000, 2001, 2004, Armstrong 2004, Beebee 2004). Some extend their account of causation, in ways that depart from their respective central theses, to include such cases (Fair 1979, pp 246-7; Ehring1997, pp 125, 139; Lewis 2004). According to Hall (2004) and Persson (2002) these cases show that there are two concepts of causation. According to Reiber (2002, pp 63-4) the account of causation in terms of the transfer of properties can handle these cases by translating negatives into the actual positives that obtain.

Dowe and Armstrong hold that while such cases are not genuine causation, they count as a close relative, which Dowe variously calls causation* (1999, 2000) or ‘quasi causation’ (2001, compare Ehring 1997, pp 150-1). Persson (2002) coins the term ‘fake causation’. This relation is essentially a counterfactual about causation (see also Fair 1979, pp 246-7). While admitting Schaffer's (2000) point that there are cases of quasi-causation which by intuition clearly count as causation, Dowe asserts that there is also an intuition of difference- other cases of quasi-causation which intuitively are not causation (2001, see also Reiber 2002). For a detailed rebuttal of the intuition of difference see Schaffer (2004, pp. 209-11) and, from a Davidsonian perspective, Hunt (2005). Further, Dowe attempts to explain why we might confuse causation

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with quasi-causation by appealing to the similar roles they play in explanation, decision-making and inference, and justifies this similarity on the grounds of the relation between causation and quasi-causation (again, quasi-causation is essentially possible causation). Armstrong points out that another reason we might confuse the two concepts is that in practice it is often difficult to distinguish the two (2004).

Dowe offers the following account of quasi-causation:

Prevention: A prevented B if A occurred and B did not, and there occurred an x such that

(P1) there is a causal interaction between A and the process due to x, and

(P2) if A had not occurred, x would have caused B.

where A and B name positive events or facts, and x is a variable ranging over events and/or facts. (Dowe 2001, p. 221, see also 2000, ch 6.4)

For example, bumping the table (A) prevented the ball going into the pocket (B) because there is an interaction between bumping the table and the trajectory of the ball (x), a causal interaction, and the true counterfactual ‘without A, x would have caused B’.

One reason that the above is stated only as a sufficient condition is that there is a need to account for alternative preventers, of which there are two types, preemptive prevention (cf. preemption) and overprevention (cf. overdetermination), since in both cases (P3) fails. To deal with the latter, Dowe disjoins (P2) with

(P2 ) there exists a ′ C such that had neither A nor C occurred, x would have caused B or …(adapted from Dowe 2000, sec 6.4)

Suppose as well as bumping the table I also subsequently knocked the moving ball with my elbow (C), again, preventing it from sinking (overprevention). (P2) is false, but by (P2 ) A counts as a quasi-′cause of B. So too does C, since substituted for A, it satisfies P(1). Suppose on the other hand C is some completely irrelevant event, and (P1-2) hold for A and B. Then although (P2 ) holds for ′this A-C pair C will not count as a preventer of B because it does not satisfy (P1). (For a contrary view see Koons 2003, pp. 246)

Although the account in Dowe (2000) is unclear on this point, (P2 ) will not handle preemptive ′prevention. Suppose I bumped the table, but didn't hit the ball with my elbow, although I would have had I not bumped the table. We need to add the further alternative:

(P2″) had A not occurred, C would have occurred and would have prevented B.

The possible prevention here is then analysed by (P1-2) from the perspective of that possible world.

Quasi-causation by omissions or absences are analysed as follows:

Omission: not-A quasi-caused B if B occurred and A did not, and there occurred an x such that

(O1) x caused B, and

(O2) if A had occurred then A would have prevented B by interacting with x

where A and B name positive events/facts and x is a variable ranging over facts or events, and where prevention is analysed as above. (Dowe 2001, p 222, see also Dowe 2000, sec 6.5)

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For example, being careful not to bump the table (not-A) quasi-caused the ball to sink (B) because the trajectory of the ball (x) causes B and had the table been bumped that would have prevented B. Further cases can be added: prevention by omission, and prevention of prevention, prevention of prevention of prevention, etc (see Dowe 2000, sec 6.6). There is indeed a great deal of quasi-causation around, as Beebee has argued (2004).

Schaffer offers two criticisms of the counterfactual theory of quasi-causation. First, he argues, Salmon's and Dowe's process theory of causation is, ironically, ill-equipped to tell us what genuine causation is in these possible worlds (i.e. the worlds one might take to be the truthmakers of the counterfactuals in P2 and O2) since theirs is only an account of causation in the actual world, and worse, if one follows the semantics of Lewis to deal with the counterfactuals, it will probably turn out that our conservation laws don't hold in those possible worlds (2001, p. 811). At the very least, Dowe's stated view that ‘it's BYO semantics of counterfactuals’ (2001, p. 221) is not satisfactory. (For further discussion of this problem see Persson 2002, pp. 139-140.) And second, the account is semantically unstable, since as Dowe asserts quasi-causation plays the same role as causation for explanation, decision theory and inference, that relation is a better deserver of the role of best fitting causation's connotations than Salmon-Dowe's ‘genuine causation’ (Dowe 2000, p. 296, n. 13; 2001, pp. 811-2).

6.2 Objection 2: Worries about Conserved Quantities

Conservation can be defined in terms of constancy within a closed system. As Hitchcock points out (1995, pp. 315-6) it would be circular to define a ‘closed system’ as one that is not involved in causal interactions with anything external. Dowe suggests ‘we need to explicate the notion of a closed system in terms only of the quantities concerned. For example, energy is conserved in chemical reactions, on the assumption that there is no net flow of energy into or out of the system.’ (2000, pp. 95) Schaffer comments that this ‘looks to invoke the very notion of “flow” that the process account is supposed to analyze’ (2001, pp. 810). McDaniel suggests two possible responses to this. First, the theory could simply list the quantities held to be relevant to causation, Second, the theory could appeal directly to universally conserved quantities, in other words, doing away with appeal to any closed system besides the universe itself (McDaniel 2002, pp. 261).

Sungho Choi (2003) has provided a thorough examination of possible definitions of a closed system, and proposes the following:

DC: A system is closed with respect to a physical quantity Q at a time t iff

a. dQin/dt = dQout/dt = 0 at t or,b. dQin/dt ≠ - dQout/dt = 0 at t

where Qin is the amount of Q inside the system and is Qout the amount of Q outside the system. (2003, pp. 519). For vector quantities the definition must apply to all components of the vector. This, Choi argues, does not involve any circular appeal to causation.

Alexander Rueger (1998) has argued that since in some general relativistic spacetimes, global conservation laws can not be formulated it would seem to follow that in such a spacetime there would not be causal processes at all. Dowe's response is that our world is not such a spacetime (2000, pp. 97-8). (Ad hominem, this may be a particular problem for Dowe who argues elsewhere that time travel and hence causation is possible in such spacetimes. See Schaffer 2001, pp. 811)

John Norton (2007) while endorsing the Salmon–Dowe tack of not tying the theory to any particular conserved quantity since that leaves the theory hostage to scientific developments, nevertheless warns that “if we are permissive in selection of the conserved quantity, we risk

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trivialization by the construction of artificial conserved quantities specially tailored to make any chosen process come out as causal.” (2007, draft: p. 4).

6.3 Objection 3: Worries about Pseudo Processes.

The differences between Salmon and Dowe indicated above focus attention on the distinction between pseudo and causal processes. For Salmon it is important that the conserved quantity is transmitted, and indeed that a fixed quantity is transmitted in the absence of interactions, in order to rule out cases ‘accidental’ process-like energy appearances. Dowe has concerns about the directionality built into ‘transmission’, and instead attempts to rule out accidental processes via the identity through time of the object in question. So, for Salmon the spotlight spot does not transmit energy in the absence of interactions, but involves a continual string of interactions. For Dowe it is not the spot that possesses energy, but rather the various distinct patches of wall illuminated.

Hitchcock (1995) produces the following counterexample: consider an object casting a shadow on the surface of a charged plate. At each point of its trajectory the shadow ‘possesses’ a fixed charge. But shadows are the archetypical pseudo process. Dowe (2000, pp. 98-9) and Salmon (1997, p. 472) claim that it is the plate that possesses the charge, and the shadow that moves. Salmon however suggests that the more problematic ‘object’ is the series of plate segments currently in shadow (ibid), in Dowe's terminology a ‘time-wise gerrymander’. Salmon's answer to this it that this object does not transmit charge or else charge in a region would augment when the shadow passes over it, and he proposes to add the corollary to explicitly apply the conservation law to this kind of case (critiqued in detail by Choi 2002, pp. 110-14):

When two or more processes possessing a given conserved quantity intersect (whether they interact or not), the amount of that quantity in the region of intersection must equal the sum of the separate quantities possessed by the processes thus intersecting (Salmon 1997, p. 473).

On the other hand, Dowe's answer is that the worldline of the moving shadow is the worldline of an object that does not possess charge, while the ‘worldline’ of the segments of shadowed plate segments is not the worldline of an object. (But see McDaniel 2002, p. 260 and Garcia-Encinas 2004).

Sungho Choi (2002, pp. 114-5) offers a further counterexample to Salmon's version. Suppose the plate contains a boundary such that there is twice as much charge density on one side compared to the other. Suppose the shadow crosses from the lower density to the higher density. Consider the worldlines of (i) the gerrymandered object which is the segments of plate when crossed by the shadow and (ii) the segment of plate just before the boundary. Their intersection will count as a causal interaction on Salmon's account since the worldline in (i) exhibits a change in the conserved quantity.

6.4 Objection 4: Worries about Causal Relevance.

This is a generalisation of the concern in Objection 3. Salmon and Dowe claim that they are offering a theory of causation, yet each acknowledge one way or another that the definitions above at best give just a necessary condition for two events to be related as cause and effect. As Woodward notes ‘we still face the problem that the feature that makes a process causal (transmission of some conserved quantity or other) tells us nothing about which features of the process are causally or explanatorily relevant to the outcome we want to explain.’ (2003, p. 357.) For example, putting a chalk mark on the white ball is a causal interaction linked by causal processes and interactions to the black ball's sinking (after the white ball strikes the black ball), yet it doesn't cause the black ball's sinking (Woodward 2003, p. 351).

Dowe offers the following account (restricting the causal relata to facts for simplicity):

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Causal Connection: There is a causal connection (or thread) between a fact q(a) and a fact q (′ b) if and only if there is a set of causal processes and interactions between q(a) and q (′ b) such that:

1. any change of object from a to b and any change of conserved quantity from q to q occur at ′a causal interaction involving the following changes: Dq(a), Dq(b), Dq (′ a), and Dq (′ a); and

2. for any exchange in (1) involving more than one conserved quantity, the changes in quantities are governed by a single law of nature.

…where a and b are objects and q and q are conserved quantities possessed by those objects ′respectively. (Dowe 2000, sec 7.4; See Hausman (2002, pp. 720-21) for discussion).

The analysis would need to be expressed in a more general form for cases where there are more than two objects involved along the nexus of causal processes and interactions.

Condition (2) in the definition of causal connection states ‘for any exchange in (1) involving more than one conserved quantity, the changes in quantities are governed by a single law of nature’. This is an attempt to rule out accidentally coincident causal interactions of the sort identified by Miguel and Paruelo (2002). In one of their examples two billiard balls collide, and at the same instant, one of them emits an alpha particle. Condition (2) would not work for the case also mentioned by Miguel and Paruelo where the same quantity is exchanged in both interactions.

The account if successful tells us when two events are related causally, either as cause and effect or vice versa, or as common effects or causes of some event. It will not tell us which of these is the case (Hausman 2002, p. 719, Ehring 2003, pp. 531-32). To do that, both Salmon and Dowe appeal to a Reichenbachian fork asymmetry theory (Dowe 2000, ch 8). (Dowe's particular version of the latter has been subject to serious critique by Hausman (2002, pp. 722-3), which includes the point that his account of priority has nothing to do with the conserved quantity theory.)

Suppose a rolling steel ball is charged at a certain point along its trajectory. Suppose its trajectory is unaffected, and the ball subsequently hits another ball. The account should tell us that the fact that the ball gets charged not causally relevant to the fact that it hits the second ball. It does, since although on the Salmon-Dowe theory the ball's rolling is a causal process and the charging and the collision are causal interactions, and further, a change in ball's charge and the change in the ball's momentum are both the kinds of changes envisaged in (1), nevertheless there is no causal interaction linking the ball's having charge to the ball's having momentum as required in (1). Hence there is no causal thread as defined in (1) linking the two facts.

The account should also tell us that the tennis ball's heading towards the wall is not the cause of the wall's being stationary after the ball bounces off. It does, because although there is a set of casual processes and interactions linking these two events, there is a change of object along the ‘thread’—ball to wall—yet the wall undergoes no change in momentum, which it needs for the set of causal processes and interactions to count as a causal connection on this definition. (But compare Hausman 2002, p. 721, Twardy 2001, p. 268)

One might hope that the theory also tells us that the fact that a chalk mark is put on the white ball is not causally relevant to the fact that the black ball sinks since there is no causal thread as defined in (1) linking those two facts. However, such a results awaits a translation of ‘chalking a ball’ to a state involving a conserved quantity. (See the following section for a discussion of this issue.)

To this account Dowe adds the restriction that the facts that enter into causation should not be disjunctive. This is meant to deal with the following type of example. Suppose ‘… in a cold place, the heater is turned on for an hour, bringing the room to a bearable temperature. But an hour later the temperature is unbearable again, say 2°C. Then … the fact that the heater was turned

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on is the cause of the fact that the temperature is unbearable at the later time.’ (Dowe 2000, sec 7.4). According to Dowe ‘the temperature is unbearable’ is a disjunctive fact, meaning ‘the temperature is less than x’ for a certain x, which in turn means ‘the temperature is y or z or …’. The effect is simply that the room is 2°C. According to Ehring this result remains counterintuitive (2003, p. 532). (See also Lewis' discussion of fragility, Lewis 1986, ch 21, Appendix E.)

6.5 Objection 5: Worries about ‘Empirical Analysis’

The Conserved Quantity theory is claimed by both Salmon and Dowe to be an empirical analysis, by which they mean that it concerns an objective feature of the actual world, and that it draws its primary justification from our best scientific theories. ‘Empirical analysis’ is to be contrasted with conceptual analysis, the approach that says in offering a theory of causation we seek to give an account of the concept as revealed in the way we (i.e. folk) think and speak. Conceptual analysis respects as primary data intuitions about causation; empirical analysis has no such commitment (Dowe 2000, ch. 1).

This construal of the task of delivering an account of causation has drawn criticism from a number of commentators. According to Koons, it threatens ‘to turn [the] metaphysical account into a watered-down version of more-or-less contemporary physical theory’. (Koons 2003, p. 244). But Hausman notes that since causation is not a technical concept in science, ‘[w]ithout some plausible connection to what ordinary people and scientists take to be causation, the conserved quantity theory would float free of both physics and philosophy.’ (Hausman 2002, p. 718, see also Garcia-Encinas 2004, p. 45) And McDaniel asks what could justify one in believing a putative ‘empirical analysis’? He adds that if an empirical analysis is not at least extensionally equivalent (in the actual world) to the true conceptual analysis, then what would be the point? (2002, p. 259).

Despite their denial of a primary need to respect common sense intuitions about the concept of causation, Salmon and Dowe do still want to say their account deals with everyday cases of causation. This again raises the question of translation. As Kim puts it, there is the ‘question of whether the [Dowe-Salmon] theory provides a way to “translate” causality understood in the [Dowe-Salmon] theory into ordinary causal talk and vice versa.’ (Kim 2001, p. 242, and see especially Hausman 1998, pp. 14–17, 2002, p. 719).

6.6 Objection 6: Worries about Reduction.

According to Dowe the relata in true ‘manifest’ (common sense) claims of causation must be translated to physical states of the sort discussed above (‘object a has a value q of a conserved quantity’) such that the manifest causal claim supervenes on some physical causation. Even for purely physical cases such as ‘chalking the ball’ this is a complicated matter, and it is not obvious that it can be carried through.

Even if this could be made to work in purely physical cases, there remain questions about mental causation, causation in history, and causation in other branches of science besides physics (Woodward 2003, pp. 355-6, Machamer, Darden and Craver 2000, p. 7, Cartwright 2004, p. 812). In any case, to suppose that the conserved quantity theory will deal with causation in other branches of science also requires commitment to a fairly thorough going reductionism, since clearly there is nothing in economics or psychology that could pass for a conservation law.

An alternative to such reductionism is the view developed by Nancy Cartwright, which we might call causal pluralism After rejecting the conserved quantity theory (along with a range of major theories of causation) as an account of a ‘monolithic’ causal concept, on the grounds that it cannot deal with cases in economics, Cartwright summarises her position:

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1. There is a variety of different kinds of causal laws that operate in a variety of different ways and a variety of different kinds of causal questions that we can ask.

2. Each of these can have its own characteristic markers; but there are no interesting features that they all share in common. (2004, p. 814, see also Hausman 2002, p. 723)

7. Related theories of causation

There is an increasing number of accounts of causation which are close relatives of the Process Theory, but which don't exactly fit the definition of a Process Theory given above. In this section we summarise some important theories that take causation to be the transfer or persistence of properties of a specific property, in particular, energy.

7.1. Aronson's transference theory

Aronson's theory is presented in three propositions:

1. In ‘A causes B,’ ‘B’ designates a change in an object, a change which is an unnatural one.2. In ‘A causes B,’ at the time B occurs, the object that causes B is in contact with the object

that undergoes the change.3. Prior to the time of the occurrence of B, the body that makes contact with the effect object

possesses a quantity (e.g., velocity, momentum, kinetic energy, heat, etc.) which is transferred to the effect object (when contact is made) and manifested as B. (1971: 422)

Proposition (1) refers to a distinction Aronson draws between natural and causal changes—causal changes are those that result from interactions with other bodies; natural changes are not causal, and come about according to the normal course of events, when things happen without outside interference. Thus internal changes, or developments, are not seen by Aronson as cases of causation. Proposition (2) is Hume's requirement that causation occurs only by contact, which rules out action at a distance. It also means that, strictly speaking, there is no indirect causation, where one thing causes another via some intermediate mechanism. All causation is direct causation.

Proposition (3) is the key notion in Aronson's theory. It appeals to the idea of a quantity, which is possessed by objects, and which may be possessed by different objects in turn, but which is always possessed by some object. The direction of transfer sets the direction of causation. For a critique of this theory see Earman (1976).

7.2. Fair's transference theory

In (1979) David Fair, a student of David Lewis, offers an account of causation similar in many respects to that of Aronson. Fair makes the claim that physics has discovered the true nature of causation: what causation really is, is a transfer of energy and/or momentum. This discovery is an empirical matter, and the identity is contingent. Fair presents his account as a program for a physicalist reduction of the everyday concept, and he doesn't claim to be able to offer a detailed account of the way energy transfer makes true the fact that, for example, John's anger caused him to hit Bill. A full account awaits, Fair says, a complete unified science (1979: 236).

Fair's program begins with the reduction of the causal relata found in ordinary language. Events, objects, facts, properties and so forth need to be redescribed in terms of the objects of physics. Fair introduces ‘A-objects’ and ‘B-objects,’ which manifest the right physical quantities, namely energy and momentum, and where the A-objects underlie the events, facts, or objects identified as causes in everyday talk, while the B-objects underlie those identified as effects. The physical quantities, energy and momentum, underlie the properties that are identified as causes or effects in everyday causal talk.

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The physically specifiable relation between the A-objects and the B-objects is the transfer of energy and/or momentum. Fair sees that the key is to be able to identify the same energy and/or momentum manifested in the effect as was manifested in the cause. This is achieved by specifying closed systems associated with the appropriate objects. A system is closed when no gross energy and/or momentum flows into or out of it. Energy and/or momentum transfer occurs when there is a flow of energy from the A-object to the B-object, which will be given by the time rate of change of energy and/or momentum across the spatial surface separating the A-object and the B-object.

Fair's reduction thus is:

A causes B iff there are physical redescriptions of A and B as some manifestation of energy or momentum or [as referring to] objects manifesting these, that is transferred, at least in part, from the A-objects to the B-objects. (1979: 236)

For one extended critique of Fair's theory see Dowe (2000: Ch 3).

7.3. Ehring's trope persistence theory

Douglas Ehring sets out a highly original theory of causation in his book Causation and Persistence (1997). Ehring takes the relata of causation to be tropes – i.e. non-repeating property instances. Causal connections involve the persistence of such tropes, and also their fission (partial destruction) and fusion. Trope persistence is endurantist, that is to say, tropes wholly exist at every time they exist, and that a particular trope at one time is strictly identical to itself at other times. Since tropes do not change they avoid the well-known problem for edurantists of temporary intrinsics.

Actually Ehring's theory has two parts. ‘Strong causal connection’ concerns trope persistence, and this is a symmetric matter. Causal priority on the other hand involves broader considerations including counterfactuals. Here are Ehring's definitions (following the summary in Ehring 2004):

Strong Causal Connection: Tropes P and Q, are strongly causally connected if and only if:

1. P and Q are lawfully connected, and either2. P is identical to Q or some part of Q, or Q is identical to P or some part of P, or3. P and Q supervene on tropes P′ and Q′ which satisfy (1) and (2).

Causal Priority: Ehring employs counterfactuals to define a relation of ‘being a condition of a causal connection’, and then he uses this relation, together with the symmetrical relation of causal connection, to define causal direction. (1997: 145, 146, 148, 149, 151, 179).

Putting these two together, we get:

Causation: Trope P at t causes trope Q at t′ iff either

A. P at t is strongly causally connected to Q at t′, and P at t is causally prior to Q at t′. orB. there is a set of properties (R1, …, Rn) such that P is a cause of R1, under clause (A), …, and Rn

is a cause of Q under clause (A).

Clause (B) is to allow for events connected by a chain of indirect causation. For discussion of Ehring's theory see Beebee (1998).

7.4. Other theories

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There are a number of notable and related theories of causation which space unfortunately forbids us to deal with in detail. The reader is encouraged to consult the references for details.

On Castaneda's (1980) transference theory of causation, ‘causity’, is the transmission of a physical element: energy, movement, charge. According to Bigelow, Ellis and Pargetter (1988) causation is the action of forces (see also Bigelow and Pargetter 1990), while for Heathcote (1989) causation is an interaction (as defined by a suitable quantum field theory). Collier (1999) develops the notion that causation is the transfer of information. Krajewski (1997) outlines several causal concepts including transfer of energy and the transfer of information. Kistler (1998, 2006) develops the trope persistence view in terms of conserved quantities. Reiber (2002) provides a conceptual analysis of causation in terms of property acquisition and transfer, and also gives references to many historical figures who hold a similar view. Finally, Chakravartty (2005) defines causal processes as systems of continuously manifesting relations between objects with causal properties and concomitant dispositions.

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Kant and Hume on Causality

First published Wed Jun 4, 2008; substantive revision Wed Dec 11, 2013

Kant famously attempted to “answer” what he took to be Hume's skeptical view of causality, most explicitly in the Prolegomena to Any Future Metaphysics (1783); and, because causality, for Kant, is a central example of a category or pure concept of the understanding, his relationship to Hume on this topic is central to his philosophy as a whole. Moreover, because Hume's famous discussion of causality and induction is equally central to his philosophy, understanding the relationship between the two philosophers on this issue is crucial for a proper understanding of modern philosophy more generally. Yet ever since Kant offered his response to Hume the topic has been subject to intense controversy. There is no consensus, of course, over whether Kant's response succeeds, but there is no more consensus about what this response is supposed to be. There has been sharp disagreement concerning Kant's conception of causality, as well as Hume's, and, accordingly, there has also been controversy over whether the two conceptions really significantly differ. There has even been disagreement concerning whether Hume's conception of causality and induction is skeptical at all. We shall not discuss these controversies in detail; rather, we shall concentrate on presenting one particular perspective on this very complicated set of issues. We shall clearly indicate, however, where especially controversial points of interpretation arise and briefly describe some of the main alternatives. (Most of this discussion will be confined to footnotes, where we shall also present further, more specialized details.)

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1. Kant's “Answer to Hume” 2. Induction, Necessary Connection, and Laws of Nature 3. Kant, Hume, and the Newtonian Science of Nature 4. Time Determination, the Analogies of Experience, and the Unity of Nature Bibliography

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1. Kant's “Answer to Hume”

In the Preface to the Prolegomena Kant considers the supposed science of metaphysics. He states that “no event has occurred that could have been more decisive for the fate of this science than the attack made upon it by David Hume” and goes on to say that “Hume proceeded primarily from a single but important concept of metaphysics, namely, that of the connection of cause and effect” (4, 257; 7). (See the Bibliography for our method of citation.) Over the next few pages Kant defends the importance of Hume's “attack” on metaphysics against common-sense opponents such as Thomas Reid, James Oswald, James Beattie, and Joseph Priestley (all of whom, according to Kant, missed the point of Hume's problem), and Kant then famously writes (4, 260; 10): “I freely admit that it was the remembrance of David Hume which, many years ago, first interrupted my dogmatic slumber and gave my investigations in the field of speculative philosophy a completely different direction.” Thus, it was Hume's “attack” on metaphysics (and, in particular, on the concept of cause and effect) which first provoked Kant himself to undertake a fundamental reconsideration of this (supposed) science.

Later, in §§ 27–30 of the Prolegomena, Kant returns to Hume's problem and presents his own solution. Kant begins, in § 27, by stating that “here is now the place to remove the Humean doubt from the ground up” (4, 310; 63); and he continues, in § 29, by proposing “to make a trial with Hume's problematic concept (his crux metaphysicorum), namely the concept of cause” (4, 312; 65). Kant concludes, in § 30, by stating that we are now in possession of “a complete solution of the Humean problem” (4, 313; 66)—which, Kant adds, “rescues the a priori origin of the pure concepts of the understanding and the validity of the general laws of nature as laws of the understanding, in such a way that their use is limited only to experience, because their possibility has its ground merely in the relation of the understanding to experience, however, not in such a way that they are derived from experience, but that experience is derived from them, a completely reversed kind of connection which never occurred to Hume” (ibid.). Thus, Kant's “complete solution of the Humean problem” directly involves him with his whole revolutionary theory of the constitution of experience by the a priori concepts and principles of the understanding—and with his revolutionary conception of synthetic a priori judgments.

Indeed, when Kant first introduces Hume's problem in the Preface to the Prolegomena he already indicates that the problem is actually much more general, extending to all of the categories of the understanding (4, 260; 10): “I thus first tried whether Hume's objection might not be represented generally, and I soon found that the concept of the connection of cause and effect is far from being the only one by which the understanding thinks connections of things a priori; rather, metaphysics consists wholly and completely of them. I sought to secure their number, and since this succeeded as desired, namely, from a single principle, I then proceeded to the deduction of these concepts, on the basis of which I was now assured that they are not derived from experience, as Hume had feared, but have sprung from the pure understanding.” Moreover, Kant soon explains, in § 5, how this more general problem (common to all the categories and principles of the understanding) is to be formulated: “How is cognition from pure

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reason possible?” (4, 275; 27), or, more specifically, “How are synthetic a priori propositions possible?” (4, 276; 28).

In the Introduction to the second (B) edition of the Critique of Pure Reason (1787), Kant follows the Prolegomena in formulating what he here calls “the general problem of pure reason” (B19): “How are synthetic a priori judgments possible?” And, as in the Prolegomena, Kant insists that the possibility of metaphysics as a science entirely depends on this problem (ibid.): “That metaphysics until now has remained in such a wavering state of uncertainty and contradictions is to be ascribed solely to the fact that this problem, and perhaps even the distinction between analytic and synthetic judgments, was not thought of earlier. Metaphysics stands or falls with the solution of this problem, or on a satisfactory proof that the possibility it requires to be explained does not in fact obtain.” Kant then immediately refers to “David Hume, who, among all philosophers, came closest to this problem”; and he suggests, once again, that Hume failed to perceive the solution because he did not conceive the problem in its “[full] generality, but rather stopped with the synthetic proposition of the connection of the effect with the cause (principium causalitatis)” (ibid.).

It is only in the second edition of the Critique that Kant gives such a prominent place to Hume and his “objection” to causality, serving to introduce what Kant now calls “the general problem of pure reason.” By contrast, the name of Hume does not appear in either the Introduction or the Transcendental Analytic in the first (A) edition (1781): it appears only in the Transcendental Doctrine of Method at the very end of the book, in a discussion of “skepticism” versus “dogmatism” in metaphysics (where Hume's skepticism about causation, in particular, is finally explicitly discussed). This is not to say, of course, that implicit references to Hume are not found earlier in the text of the first edition. Thus, for example, in a preliminary section to the Transcendental Deduction Kant illustrates the need for such a deduction with the concept of cause, and in both editions remarks (A91/B124): “Appearances certainly provide cases from which a rule is possible in accordance with which something usually happens, but never that the succession is necessary; therefore, a dignity pertains to the synthesis of cause and effect that cannot be empirically expressed at all, namely, that the effect does not merely follow upon the cause but is posited through it and follows from it.” But it is only in the second edition that Kant then goes on to mention “David Hume” explicitly, as one who attempted to derive the pure concepts of the understanding from experience (B127): “namely, from a subjective necessity arising from frequent association in experience—i.e., from custom—which is subsequently falsely taken for objective.” This striking difference between the two editions clearly reflects the importance of the intervening appearance of the Prolegomena.

Given the crucial importance of the Prolegomena in this respect, it is natural to return to Kant's famous remarks in the Preface to that work, where, as we have seen, Kant says that “it was the remembrance of David Hume which, many years ago, first interrupted my dogmatic slumber and gave my investigations in the field of speculative philosophy a completely different direction.” It is natural to wonder, in particular, about the precise years to which Kant is referring and the specific events in his intellectual development he has in mind. Here, however, we now enter controversial terrain, where there are basically two competing alternatives—both of which reflect the circumstance that Kant could read Hume only in German translation.

Kant might be referring, on the one hand, to the late 1750s to mid 1760s. A translation of Hume's Enquiry Concerning Human Understanding (originally published in 1748) appeared in 1755 and was widely read in Germany. Kant had almost certainly read this translation by the mid 1760s, by which time he himself expressed doubts about whether causal connections could be known by reason alone and even suggested that they were knowable only by experience. Or, on the other hand, Kant might be referring to the mid 1770s. After the Inaugural Dissertation appeared in 1770, Kant published nothing more until the first edition of the Critique in 1781. Meanwhile, a German translation of Beattie's Essay on the Nature and Immutability of Truth (originally published in 1770) appeared in 1772, where, in particular, Beattie quoted extensively from Book 1 of Hume's Treatise of Human Nature (originally published in 1739). Thus, in the famous

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“dogmatic slumber” passage, Kant might be referring either to the mid 1760s, when he then had a “remembrance” of reading the translation of Hume's Enquiry, or to the mid 1770s, when he then had a “remembrance” of reading translations from the Treatise.[1]

We prefer the first alternative. From this point of view, the decisive event to which Kant is referring is his reading of Hume's Enquiry (in translation) during the late 1750s to mid 1760s, and this event, we believe, is clearly reflected in two important writings of the mid 1760s: the Attempt to Introduce the Concept of Negative Magnitudes into Philosophy (1763) and Dreams of a Spirit-Seer Explained by Dreams of Metaphysics (1766).

In the first (1763) essay Kant introduces the distinction between “logical grounds” and “real grounds,” both of which indicate a relationship between a “ground” (cause or reason) and a “consequent” (following from this ground). Kant explains his problem as follows (2, 202; 239):

I understand very well how a consequent may be posited through a ground in accordance with the rule of identity, because it is found to be contained in [the ground] by the analysis of concepts. … [A]nd I can clearly comprehend this connection of the ground with the consequent, because the consequent is actually identical with part of the concept of the ground …. However, how something may flow from another, but not in accordance with the rule of identity, is something that I would very much like to have made clear to me. I call the first kind of ground a logical ground, because its relation to the consequent can be logically comprehended in accordance with the rule of identity, but I call the second kind of ground a real ground, because this relation indeed belongs to my true concepts, but the manner of this [relation] can in no way be estimated. With respect to such a real ground and its relation to the consequent, I pose my question in this simple form: how can I understand the circumstance that, because something is, something else is to be? A logical consequent is only posited because it is identical with the ground.

The fundamental problem with the relationship between a real ground and its consequent, therefore, is that the consequent is not identical with either the ground or a part of this concept—i.e., it is not “contained in [the ground] by the analysis of concepts.”

Thus, using his well-known later terminology (from the Critique and the Prolegomena), Kant is here saying that, in the case of a real ground, the relationship between the concept of the consequent (e.g., an effect) and the concept of the ground (e.g., a cause) is not one of containment, and the judgment that the former follows from the latter is therefore not analytic. Moreover, although Kant does not explicitly refer to Hume in the essay on Negative Magnitudes, he proceeds to illustrate his problem with an example (among others) of the causal connection in the communication of motion by impact (2, 202; 240): “A body A is in motion, another B is at rest in the straight line [of this motion]. The motion of A is something, that of B is something else, and, nevertheless, the latter is posited through the former.” Hume famously uses this example (among others) in the Enquiry to illustrate his thesis that cause and effect are entirely distinct events, where the idea of the latter is in no way contained in the idea of the former (EHU 4.9; SBN 29): “The mind can never possibly find the effect in the supposed cause, by the most accurate scrutiny and examination. For the effect is totally different from the cause, and consequently can never be discovered in it. Motion in the second billiard-ball is a quite distinct event from motion in the first; nor is there anything in the one to suggest the smallest hint of the other.” A few lines later Hume describes this example as follows (EHU 4.10; SBN 29): “When I see, for instance, a billiard-ball moving in a straight line towards another; even suppose motion in the second ball should by accident be suggested to me, as the result of their contact or impulse; may I not conceive, that a hundred different events might as well follow from the cause? … All these suppositions are consistent and conceivable.”

In Kant's second essay from this period, Dreams of a Spirit-Seer (1766), he goes further: he suggests a Humean solution to the problem he had posed, but did not solve, in the essay on Negative

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Magnitudes. Kant suggests, more specifically, that the relation between a real ground and its consequent can only be given by experience (2, 370; 356):

It is impossible ever to comprehend through reason how something could be a cause or have a force, rather these relations must be taken solely from experience. For the rule of our reason extends only to comparison in accordance with identity and contradiction. But, in so far as something is a cause, then, through something, something else is posited, and there is thus no connection in virtue of agreement to be found—just as no contradiction will ever arise if I wish to view the former not as a cause, because there is no contradiction [in the supposition that] if something is posited, something else is cancelled. Therefore, if they are not derived from experience, the fundamental concepts of things as causes, of forces and activities, are completely arbitrary and can neither be proved nor refuted.

This passage seems clearly to recall the main ideas in section 4, part 1 of Hume's Enquiry. After distinguishing between “relations of ideas” and “matters of fact,” and asserting that the former “are discoverable by the mere operation of thought” (EHU 4.1; SBN 25), Hume continues (EHU 4.2; SBN 25): “Matters of fact, which are the second objects of human reason, are not ascertained in the same manner; nor is our evidence of their truth, however great, of a like nature with the foregoing. The contrary of every matter of fact is still possible; because it can never imply a contradiction ….” Hume then explains that: “all reasonings concerning matters of fact seem to be founded on the relation of Cause and Effect” (EHU 4.4; SBN 26) and adds (EHU 4.6; SBN 27): “I shall venture to affirm, as a general proposition, which admits of no exception, that the knowledge of this relation is not, in any instance, attained by reasonings a priori; but arises entirely from experience, when we find that any particular objects are constantly conjoined with each other.” Finally (EHU 4.10; SBN 29): “And as the first imagination or invention of a particular effect, in all natural operations, is arbitrary, where we consult not experience; so must we also esteem the supposed tye or connexion between the cause and effect, which binds them together, and renders it impossible that any other effect could result from the operation of that cause.” Thus, although Kant does not explicitly mention Hume in Dreams of a Spirit-Seer, the parallels with Hume's Enquiry are striking indeed.[2]

Kant does not endorse a Humean solution to the problem of the relation between cause and effect in the critical period (beginning with the first edition of the Critique in 1781): he does not (as he had in Dreams of a Spirit-Seer) claim that this relation is derived from experience. Instead (as we have seen) Kant takes Hume's problem of causality to be centrally implicated in the radically new problem of synthetic a priori judgments. Yet the latter problem, in turn, clearly has its origin in Kant's earlier discussion (in the essay on Negative Magnitudes and Dreams of a Spirit-Seer) of the apparently mysterious connection between a real ground (or cause) and its consequent (or effect). Just as Kant had earlier emphasized (in these pre-critical works) that the consequent of a real ground is not contained in it, and thus does not result by “the analysis of concepts,” Kant now (in the critical period) maintains that the concept of the effect cannot be contained in the concept of the cause and, accordingly, that a judgment relating the two cannot be analytic. Such a judgment, in Kant's critical terminology, must now be synthetic—it is a judgment in which “the connection of the predicate with the subject … is thought without identity,” where “a predicate is added to the concept of the subject which is by no means thought in it, and which could not have been extracted from it by any analysis” (A7/B10–11). The crucial point about a synthetic a priori judgment, however, is that, although it is certainly not (as a priori) derived from experience, it nonetheless extends our knowledge beyond merely analytic judgments.

It therefore becomes clear why, in the Introduction to the second edition of the Critique, Kant says of the crucial problem of synthetic a priori judgments that “this problem, and perhaps even the distinction between analytic and synthetic judgments, was not thought of earlier,” and then explicitly names “David Hume, who, among all philosophers, came closest to this problem” (B19). It also becomes clear why, in the Preface to the Prolegomena, Kant explains Hume's problem as follows (4, 257; 7):

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Hume proceeded primarily from a single but important concept of metaphysics, namely, that of the connection of cause and effect … , and he challenged reason, which here pretends to have generated this concept in her womb, to give him an account of by what right she thinks that something could be so constituted that, if it is posited, something else must necessarily also be posited thereby; for this is what the concept of cause says. He proved indisputably that it is completely impossible for reason to think such a connection a priori and from concepts [alone] (for this [connection] contains necessity); but it can in no way be comprehended how, because something is, something else must necessarily also be, and how, therefore, the concept of such a connection could be introduced a priori.

Thus here, in the Prolegomena, Kant describes what he calls Hume's “challenge” to reason concerning “the connection of cause and effect” in precisely the same terms that he had himself earlier used, in the 1763 essay on Negative Magnitudes and the 1766 Dreams of a Spirit-Seer, to pose a fundamental problem about the relation of a real ground (as opposed to a logical ground) to its consequent.

What is most important, however, is the official solution to Hume's problem that Kant presents in § 29 of the Prolegomena. This solution depends on the distinction between “judgments of perception” and “judgments of experience” which Kant has extensively discussed in the preceding sections. In § 18 Kant introduces the distinction as follows (4, 298; 51):

Empirical judgments, in so far as they have objective validity, are judgments of experience; they, however, in so far as they are only subjectively valid, I call mere judgments of perception. … All of our judgments are at first mere judgments of perception: they are valid merely for us, i.e., for our subject, and only afterwards do we give them a new relation, namely to an object, and we intend that [the judgment] is supposed to be also valid for us at all times and precisely so for everyone else; for, if a judgment agrees with an object, then all judgments about the same object must also agree among one another, and thus the objective validity of the judgment of experience signifies nothing else but its necessary universal validity.

Then, in § 22, Kant emphasizes that the pure concepts of the understanding or categories function precisely to convert mere (subjective) perceptions into objective experience by effecting a “necessary unification” of them (4, 305; 58): “Therefore, the pure concepts of the understanding are those concepts under which all perceptions must first be subsumed before they can serve as judgments of experience, in which the synthetic unity of perceptions is represented as necessary and universally valid.”[3] Here is how Kant formulates his solution in § 29 (4, 312; 65):

In order to make a trial with Hume's problematic concept (his crux metaphysicorum), namely the concept of cause, first, there is given to me a priori, by means of logic, the form of a conditional judgment in general, namely, to use a given cognition as ground and the other as consequent. It is possible, however, that a rule of relation is found in perception which says that a given appearance is constantly followed by another (but not conversely); and this is a case for me to employ the hypothetical judgment and, e.g., to say: if a body is illuminated sufficiently long by the sun, then it becomes warm. Here, there is certainly no necessity of connection as yet, and thus [not] the concept of cause. However, I continue and say that, if the above proposition, which is merely a subjective connection of perceptions, is to be a judgment of experience, then it must be viewed as necessary and universally valid. But such a proposition would be: the sun is through its light the cause of heat. The above empirical rule is now viewed as a law—and, in fact, not as valid merely of appearances, but [valid] of them on behalf of a possible experience, which requires completely and thus necessarily valid rules.

All the elements from Kant's earlier discussion of causality in the essays on Negative Magnitudes and Dreams of a Spirit-Seer seem to be present here. Kant begins with the purely logical relation between ground and consequent. Since, in the case of the concept of cause, we are dealing with what Kant had earlier called a real ground, Kant holds that we need a synthetic rather than

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merely analytic connection between the two. The most obvious thought, which Hume had defended in the Enquiry (and, apparently following Hume, Kant himself had defended in Dreams of a Spirit-Seer) is that “experience” (in the Humean sense) is the basis for this connection in so far as one perception is found to be “constantly conjoined” with another. Now, however, in the critical period, Kant introduces a revolutionary new concept of “experience” which is explicitly opposed to mere constant conjunctions among perceptions in being “necessary and universally valid”—in particular, “experience is possible only by means of the representation of a necessary connection of perceptions” (B218).

In Kant's example from § 29 of the Prolegomena, then, we begin from a mere subjective “empirical rule”: that the perception of an illuminated stone is constantly followed by the perception of heat; and we then convert this “empirical rule” into an objective law according to which the very same relationship is now viewed as “necessary and universally valid.” This transformation is effected by the addition of the a priori concept of causality: “the sun is through its light the cause of heat.” It is in precisely this way, more generally, that the categories or pure concepts of the understanding relate to experience: “not in such a way that they are derived from experience, but that experience is derived from them, a completely reversed kind of connection which never occurred to Hume” (§ 30: 4, 313; 66).

We shall devote the rest of this article to clarifying Kant's solution and its relationship with Hume's conception of causation. For now, we simply note an important difficulty Kant himself raises in the Prolegomena. Whereas the concept of causality is, for Kant, clearly a priori, he does not think that particular causal laws relating specific causes with specific effects are all synthetic a priori—and, if they are not a priori, how can they be necessary? Indeed, Kant illustrates this difficulty, in a footnote to § 22, with his own example of the sun warming a stone (4, 305; 58):

But how does this proposition, that judgments of experience are supposed to contain necessity in the synthesis of perceptions, agree with my proposition, urged many times above, that experience, as a posteriori cognition, can yield only contingent judgments? If I say that experience teaches me something, I always mean only the perception that lies within in it, e.g., that heat always follows the illumination of the stone by the sun. That this heating results necessarily from the illumination by the sun is in fact contained in the judgment of experience (in virtue of the concept of cause); but I do not learn this from experience, rather, conversely, experience is first generated through this addition of the concept of the understanding (of cause) to the perception.

In other words, experience in the Humean sense teaches me that heat always (i.e., constantly) follows the illumination of the stone by the sun; experience in the Kantian sense then adds that: “the succession is necessary; … the effect does not merely follow upon the cause but is posited through it and follows from it” (A91/B124). But what exactly does this mean?

2. Induction, Necessary Connection, and Laws of Nature

Kant formulates a crucial distinction between “strict” and “comparative” universality in § II of the Introduction to the second edition of the Critique (B3–4):

Experience never gives its judgments true or strict, but merely assumed or comparative universality (through induction), so that, properly speaking, it must be formulated: so far as we have observed until now, no exception has been found to this or that rule. If, therefore, a judgment is thought with strict universality, i.e., so that no exception at all is allowed to be possible, then it is not derived from experience, but is valid absolutely a priori. Empirical universality is thus only an arbitrary augmentation of validity from that which is valid in most cases to that which is valid in all—as, e.g., in the proposition: all bodies are heavy. By contrast, where strict universality essentially belongs to a judgment, this [universality] indicates a special source of cognition for [the judgment], namely a faculty of a priori cognition. Necessity and strict universality are thus secure criteria of an a priori cognition, and also inseparably belong together.

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Kant then explicitly links this distinction to Hume's discussion of causality in the following paragraph (B5): “The very concept of cause so obviously contains the concept of a necessity of the connection with an effect and a strict universality of the rule, that the concept [of cause] would be entirely lost if one pretended to derive it, as Hume did, from a frequent association of that which happens with that which precedes, and [from] a thereby arising custom (thus a merely subjective necessity) of connecting representations.”[4] Moreover, in the second edition (as we have seen) Kant also goes on to name Hume explicitly, as one who attempted to derive the concept of causality “from a subjective necessity arising from frequent association in experience—i.e., from custom—which is subsequently falsely taken for objective” (B127). It appears, therefore, that Kant's discussion, in § 29 of the Prolegomena, of how, by the addition of the concept of cause, we convert a mere subjective “empirical rule” into an objective law (which is “necessary and universally valid”), is not only indebted to Hume for the insight that the connection between cause and effect is synthetic rather than analytic, it is also indebted to Hume's discussions of the problem of induction (in section 4, part 2 of the Enquiry) and of the idea of necessary connection (in section 7). Kant agrees with Hume that the idea of necessary connection is in fact an essential ingredient in our idea of the relation between cause and effect; Kant agrees, in addition, that, if all we had to go on were a purely inductive inference from observed constant conjunctions, the inference from comparative to strict universality would not be legitimate, and the presumed necessary connection arising in this way (i.e., from custom) would be merely subjective.

Section 4 of the Enquiry is entitled “Sceptical Doubts Concerning the Operations of the Understanding.” In part 1 of this section (as we have already seen) Hume maintains that the idea of the effect is never contained in the idea of the cause (in Kant's terminology, the relation is not analytic), and thus, according to Hume, it is never knowable a priori. We therefore need experience in the Humean sense in order to make any causal claims—that is, the observation of an event of one type A constantly followed by an event of another type B. Otherwise (as we have also seen) any event could follow any other (EHU 4.10; SBN 29): “And as the first imagination or invention of a particular effect, in all natural operations, is arbitrary, where we consult not experience; so must we also esteem the supposed tye or connexion between the cause and effect, which binds them together, and renders it impossible that any other effect could result from the operation of that cause.” Note that Hume is here supposing that, in our idea of the relation between cause and effect, the “tye or connexion … which binds them together” is necessary (“it is impossible that any other effect could result”). In the corresponding section of the Treatise, Book 1, part 3, section 2 (“Of probability; and of the idea of cause and effect”), Hume makes this completely explicit (T 1.3.2.11; SBN 77): “Shall we then rest contented with these two relations of contiguity and succession, as affording a compleat idea of causation? By no means. An object may be continuous and prior to another, without being consider'd as its cause. There is a NECESSARY CONNEXION to be taken into consideration; and that relation is of much greater importance, than any of the other two above-mention'd.”

In the Enquiry, section 4, part 2, Hume presents his famous skeptical argument concerning causation and induction. Since we need “experience” (i.e., the observation of constant conjunctions) to make any causal claims, Hume now asks (EHU 4.14; SBN 32): “What is the foundation of all conclusions from experience?” The conclusion from an experience of constant conjunction is an inference to what has not yet been observed from what has already been observed, and Hume finds an unbridgeable gap between the premise (summarizing what we have observed so far) and the (not yet observed) conclusion of this inference (EHU 4.16; SBN 34): “These two propositions are far from being the same, I have found that such an object has always been attended with such an effect, and I foresee, that other objects, which are, in appearance, similar, will be attended with similar effects.” Hume concludes that this inference has no foundation in the understanding—that is, no foundation in what he calls “reasoning.”[5] How does Hume arrive at this position?

All our inductive inferences—our “conclusions from experience”—are founded on the supposition that the course of nature is sufficiently uniform so that the future will be conformable to the

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past (EHU 4.21; SBN 37–38): “For all inferences from experience suppose, as their foundation, that the future will resemble the past …. If there be any suspicion, that the course of nature may change, and that the past may be no rule for the future, all experience becomes useless, and can give rise to no inference or conclusion.” Therefore, what Hume is now seeking, in turn, is the foundation in our reasoning for the supposition that nature is sufficiently uniform.

Section 4, part 1 of the Enquiry distinguishes (as we have seen) between reasoning concerning relations of ideas and reasoning concerning matters of fact and existence. Demonstrative reasoning (concerning relations of ideas) cannot establish the supposition in question, “since it implies no contradiction, that the course of nature may change, and that an object, seemingly like those which we have experienced, may be attended with different or contrary effects” (EHU 4.18; SBN 35). Moreover, reasoning concerning matters of fact and existence cannot establish it either, since such reasoning is always founded on the relation of cause and effect, the very relation we are now attempting to found in reasoning (EHU 4.19; SBN 35–36): “We have said, that all arguments concerning existence are founded on the relation of cause and effect; that our knowledge of that relation is derived entirely from experience; and that all our experimental conclusions proceed upon the supposition, that the future will be conformable to the past. To endeavour, therefore, the proof of this last proposition by probable arguments, or arguments regarding existence, must be evidently going in a circle, and taking that for granted, which is the very point in question.”[6]

Although Hume has now shown that there is no foundation for the supposition that nature is sufficiently uniform in reasoning or the understanding, he goes on, in the following section 5 of the Enquiry (“Skeptical Solution of these Doubts”), to insist that we are nonetheless always determined to proceed in accordance with this supposition. There is a natural basis or “principle” for all our arguments from experience, even if there is no ultimate foundation in reasoning (EHU 5.4–5; SBN 42–43):

And though [one] should be convinced, that his understanding has no part in the operation, he would nonetheless continue in the same course of thinking. There is some other principle, which determines him to form such a conclusion. This principle is CUSTOM or HABIT. For wherever the repetition of any particular act or operation produces a propensity to renew the same act or operation, without being impelled by any reasoning or process of the understanding; we always say, that this propensity is the effect of Custom. By employing that word, we pretend not to have given the ultimate reason of such a propensity. We only point out a principle of human nature, which is universally acknowledged, and which is well known by its effects. [7]

In section 7 of the Enquiry (“On the Idea of Necessary Connexion”), after rejecting the received views of causal necessity, Hume explains that precisely this custom or habit also produces our idea of necessary connection (EHU 7.28; SBN 75):

It appears, then, that this idea of a necessary connexion among events arises from a number of similar instances which occur of the constant conjunction of these events; nor can that idea ever be suggested by any one of these instances, surveyed in all possible lights and positions. But there is nothing in a number of instances, different from every single instance, which is supposed to be exactly similar; except only, that after a repetition of similar instances, the mind is carried by habit, upon the appearance of one event, to expect its usual attendant, and to believe that it will exist. This connexion, therefore, which we feel in the mind, this customary transition of the imagination from one object to its usual attendant, is the sentiment or impression, from which we form the idea of power or necessary connexion.

Thus, the custom or habit to make the inductive inference not only gives rise to a new idea of not yet observed instances resembling the instances we have already observed, it also produces a feeling of determination to make the very inductive inference in question. This feeling of determination, in turn, gives rise to a further new idea, the idea of necessary connexion, which has no resemblance whatsoever with anything we have observed. It is derived from an

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“impression of reflection” (an internal feeling or sentiment), not from an “impression of sensation” (an observed instance before the mind), and it is in precisely this sense, for Hume, that the idea of necessary connection is merely subjective. Hume emphasizes that this is a “discovery” both “new and extraordinary,” and that it is skeptical in character (EHU 7.28–29; SBN 76): “No conclusions can be more agreeable to scepticism than such as make discoveries concerning the weakness and narrow limits of human reason and capacity. And what stronger instance can be produced of the surprising ignorance and weakness of the understanding, than the present? For surely, if there be any relation among objects, which it imports to us to know perfectly, it is that of cause and effect.”

Kant agrees with Hume that neither the relation of cause and effect nor the idea of necessary connection is given in our sensory perceptions; both, in an important sense, are contributed by our mind. For Kant, however, the concepts of both causality and necessity arise from precisely the operations of our understanding—and, indeed, they arise entirely a priori as pure concepts or categories of the understanding. It is in precisely this way that Kant thinks that he has an answer to Hume's skeptical problem of induction: the problem, in Kant's terms, of grounding the transition from merely “comparative” to “strict universality” (A91–92/B123–124). Thus in § 29 of the Prolegomena, as we have seen, Kant begins from a merely subjective “empirical rule” of constant conjunction or association among our perceptions (of heat following illumination by the sun), which is then transformed into a “necessary and universally valid law” by adding the a priori concept of cause.

At the end of our discussion in section 1 above we saw that there is a serious difficulty in understanding what Kant intends here—a difficulty to which he himself explicitly calls attention. Kant does not think that the particular causal law that “the sun is through its light the cause of heat” is itself a synthetic a priori truth. Indeed, the very same difficulty is present in our discussion at the beginning of this section. For, what Kant is saying in § II of the second edition of the Introduction to the Critique is that necessity and strict universality are “secure criteria of an a priori cognition” (B4; emphasis added). More specifically (B3): “Experience in fact teaches us that something is constituted thus and so, but not that it cannot be otherwise. Hence, if … a proposition is thought together with its necessity, then it is an a priori judgment.” Yet, once again, Kant does not think that particular causal laws relating specific causes to specific effects are all (synthetic) a priori. Accordingly, when Kant provides examples of (synthetic) a priori cognitions in the immediately following paragraph, he cites the synthetic a priori principle of the Second Analogy of Experience (“All alterations take place in accordance with the law of the connection of cause and effect” [B232]) rather than any particular causal law (B4–5): “Now it is easy to show that there actually are such judgments in human cognition which are necessary and in the strictest sense universal, and therefore purely a priori. If one wants an example from the sciences, then one need only take a look at any of the propositions of mathematics. If one wants such an example from the most common use of the understanding, then the proposition that every alteration must have a cause can serve.”

On the basis of this important passage, among others, the majority of twentieth-century English-language commentators have rejected the idea that Kant has a genuine disagreement with Hume over the status of particular causal laws. One must sharply distinguish between the general principle of causality of the Second Analogy—the principle that every event b must have a cause a—and particular causal laws: particular instantiations of the claim that all events of type A must always be followed by events of type B. The former is in fact a synthetic a priori necessary truth holding as a transcendental principle of nature in general, and this principle is explicitly established in the Second Analogy. But the Second Analogy does not establish, on this view, that particular causal laws are themselves necessary. Indeed, as far as particular causal laws are concerned, the Second Analogy is in basic agreement with Hume: they (as synthetic a posteriori) are established by induction and by induction alone.[8]

It is indeed crucially important to distinguish between the general principle of causality Kant establishes in the Second Analogy and particular causal laws. It is equally important that

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particular causal laws, for Kant, are (at least for the most part) synthetic a posteriori rather than synthetic a priori. It does not follow, however, that Kant agrees with Hume about the status of synthetic a posteriori causal laws. On the contrary, Kant (as we have seen) clearly states, in § 29 of the Prolegomena (the very passage where he gives his official “answer to Hume”), that there is a fundamental difference between a mere “empirical rule” (heat always follows illumination by the sun) and a genuine objective law (the sun is through its light the cause of heat) arrived at by adding the a priori concept of cause to the merely inductive rule. Any law thus obtained is “necessary and universally valid,” or, as Kant also puts it, we are now in possession of “completely and thus necessarily valid rules.” In such cases (A91/B124): “The succession is necessary; … the effect does not merely follow upon the cause but is posited through it and follows from it. The strict universality of the rule is certainly not a property of empirical rules, which, through induction, can acquire nothing but comparative universality: i.e., extensive utility.” Therefore, it is by no means the case that Kant simply agrees with Hume that particular causal laws are grounded solely on induction and, accordingly, that the necessity we attribute to particular causal connections is merely subjective.

Similarly, the text of the Second Analogy is also committed to the necessity and strict universality of particular causal laws. If the general causal principle (that every event b must have a cause a) is true, then, according to Kant, there must also be particular causal laws (relating preceding events of type A to succeeding events of type B) which are themselves strictly universal and necessary.[9] Kant maintains that, when one event follows another in virtue of a causal relation, it must always follow “in accordance with a rule” (A193/B238). Moreover, the “rule” to which Kant is here referring is not the general causal principle, but rather a particular law connecting a given cause to a given effect which is itself strictly universal and necessary (A193/B238–239): “In accordance with such a rule, there must thus lie in that which precedes an event as such the condition for a rule according to which this event follows always and necessarily.” Kant insists on this point throughout the Second Analogy: “that which follows or happens must follow according to a universal rule from that which was contained in the previous state” (A200/B245), “in that which precedes the condition is to be met with under which the event always (i.e., necessarily) follows” (A200/B246), and so on. One cannot escape the burden of explaining the apparently paradoxical necessity and universal validity of particular (synthetic) a posteriori causal laws simply by distinguishing them from the general (synthetic) a priori causal principle.

What is the relationship, then, between the general causal principle of the Second Analogy and the particular causal laws whose existence, according to Kant, is required by the causal principle? What, more generally, is the relationship between the transcendental synthetic a priori principles of the understanding (including all three Analogies of Experience—compare the end of note 3 above—as well as the principles corresponding to the other categories) and the more particular synthetic a posteriori laws of nature involved in specific causal relationships governing empirically characterized events and processes? The relationship cannot be deductive; for, if one could deductively derive the particular causal laws from the transcendental principles of the understanding, then the former would have to be synthetic a priori as well.

Kant himself discusses this relationship extensively, beginning in the first edition version of the Transcendental Deduction (A126–128):

Although we learn many laws through experience, these are still only particular determinations of yet higher laws, among which the highest (under which all others stand) originate a priori in the understanding itself, and are not borrowed from experience, but must rather provide appearances with their law-governedness, and precisely thereby make experience possible … To be sure, empirical laws as such can in no way derive their origin from pure understanding—no more than the immeasurable manifold of appearances can be sufficiently comprehended from the pure form of sensibility. But all empirical laws are only particular determinations of the pure laws of the understanding, under which and in accordance with the norm of which they first become possible, and the appearances take on a lawful form—just as all appearances,

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notwithstanding the diversity of their empirical form, still must also always be in accordance with the condition of the pure form of sensibility [i.e., space and time].

The “pure laws of the understanding” (here and elsewhere) refers to the pure transcendental principles of the understanding characterizing what Kant calls “experience in general” or “nature in general.”

In the second edition version Kant makes essentially the same point, this time explicitly stating that the relationship in question is not deductive (B165):

The pure faculty of understanding, however, is not sufficient for prescribing to appearances a priori, through mere categories, any laws other than those which are involved in a nature in general, as the law-governedness of all appearances in space and time. Particular laws, because they concern empirically determined appearances, can not be completely derived therefrom, although they one and all stand under them. Experience must be added in order to become acquainted with the [particular laws] as such, but only the former laws provide a priori instruction concerning experience in general, and [concerning] that which can be cognized as an object of experience.

But what exactly does it mean for particular laws of nature to “stand under” the a priori principles of the understanding—that is, to be what Kant calls “particular determinations” of these principles? Once again, it will take more work fully to clarify this relationship, but we can meanwhile observe that it is precisely in virtue of the relationship in question that empirical causal connections—empirical causal laws of nature—count as necessary for Kant.

The necessity in question is characterized in Kant's official discussion of the category of necessity in the Postulates of Empirical Thought—the three principles corresponding to the categories of possibility, actuality, and necessity (A218–218/B265–266):

1. That which agrees with the formal conditions of experience (according to intuition and concepts), is possible.

2. That which coheres with the material conditions of experience (with sensation), is actual.3. That whose coherence with the actual is determined in accordance with the general

conditions of experience, is (exists as) necessary.

The “formal [or “general”] conditions of experience” include the forms of intuition (space and time), together with all the categories and principles of the understanding. The material conditions of experience include that which is given to us, through sensation, in perception. Kant is thus describing a three-stage procedure, in which we begin with the formal a priori conditions of the possibility of experience in general, perceive various actual events and processes by means of sensation, and then assemble these events and processes together—via necessary connections—by means of the general conditions of the possibility of experience with which we began.

In his detailed discussion of the third Postulate Kant makes it clear that he is referring, more specifically, to causal necessity, and to particular (empirical) causal laws (A226–8/B279–80): “Finally, as far as the third Postulate is concerned, it pertains to material necessity in existence, and not the merely formal and logical necessity in the connection of concepts. … Now there is no existence that could be cognized as necessary under the condition of other given appearances except the existence of effects from given causes in accordance with laws of causality. Thus, it is not the existence of things (substances), but only that of their state, about which we can cognize their necessity—and, indeed, from other states that are given in perception, in accordance with empirical laws of causality.” Note that, in this passage, Kant refers to “laws of causality” (in the plural) in the second quoted sentence, and “empirical laws of causality” (again in the plural) in the last sentence. Hence, he is here referring to particular causal laws (of the form every event of type A must always be followed by an event of type B)

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rather than the general principle of the Second Analogy (that every event b must have a cause a).[10]

In the Transcendental Deduction (as we have seen) Kant says that “all empirical laws are only particular determinations of the pure laws of the understanding, under which and in accordance with the norm of which they first become possible, and the appearances take on a lawful form” (A127–128). In the discussion of the third Postulate Kant says that we can cognize an effect as necessary on the basis of an empirical law relating it to its cause—where the effect's “connection with the actual is determined in accordance with the general conditions of experience” (A218/B266). Kant is suggesting, therefore, that the precise sense in which particular empirical laws themselves become necessary is that they, too, are “determined” in relation to actual perceptions “in accordance with the general conditions of experience” (where the latter, of course, essentially include the “pure laws of the understanding,” i.e., the principles).

Thus, in the example from § 29 of the Prolegomena, Kant begins from a mere “empirical rule” (that heat always follows illumination by the sun) and then proceeds to a “necessary and universally valid” law by adding the a priori concept of cause to this (so far) merely inductive rule. The very same three-stage procedure described by the three Postulates as a whole—in which we begin with the formal a priori conditions of the possibility of experience in general, perceive various actual events and processes by means of sensation, and then assemble these events and processes together (via necessary connections) by means of the a priori conditions of the possibility of experience—also results in “necessary and universally valid” empirical causal laws of nature (the sun is through its light the cause of heat) governing the events and processes in question.

3. Kant, Hume, and the Newtonian Science of Nature

In § 36 of the Prolegomena (after he has presented his official “answer to Hume” in § 29) Kant addresses the question of the relationship between particular empirical laws and the a priori principles of the understanding under the title “How is nature itself possible?” Nature in the material sense is “the totality of all appearances” given in space and time (4, 318; 69). Nature in the formal sense is “the totality of rules under which all appearances must stand if they are to be thought as connected in an experience” (4, 318; 70). In answering the question of how nature in the formal sense is possible Kant proceeds to distinguish between “empirical laws of nature, which always presuppose particular perceptions” and “the pure or universal laws of nature, which, without having a basis in particular perceptions, contain merely the conditions of their necessary unification in an experience” (4, 320; 71).

Yet (as we have seen) the empirical laws owe their status as “necessary and universally valid” to their relationship with the a priori “pure or universal” laws (principles) of the understanding. Moreover, Kant illustrates this situation with an example, which (as explained in the very brief § 37) “is to show, that laws that we discover in objects of sensible intuition, especially if they are cognized as necessary, are already taken by us to be such as the understanding has put there, even though they are otherwise similar in all respects to laws of nature that we attribute to experience” (4, 320; 72). The example (presented in the immediately following § 38) is a “physical law of mutual attraction, extending over the whole of material nature, whose rule is that it diminishes inversely with the square of the distances from every attracting point” (4, 321; 73). Thus, Kant illustrates his conception of the relationship between particular empirical laws and the a priori principles of the understanding with the Newtonian law of universal gravitation.[11]

In § VI of the Introduction to the second edition of the Critique, where Kant discusses the “general problem of pure reason” (“How are synthetic a priori judgments possible?”), Kant explains that “in the solution of [this] problem there is also conceived, at the same time, the possibility of the pure employment of reason in grounding and developing all sciences that contain a theoretical

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a priori cognition of objects, i.e., the answer to the questions: How is pure mathematics possible? How is pure natural science possible?” (B20). Kant illustrates his contention that propositions of “pure natural science” actually exist in a footnote (ibid.): “One need only attend to the various propositions that appear at the beginning of proper (empirical) physics, such as those of the permanence of the same quantity of matter, of inertia, of the equality of action and reaction, and so on, in order to be soon convinced that they constitute a pure (or rational) physics, which well deserves, as a science of its own, to be isolated and established in its entire extent, be it narrow or wide.”

Kant had just completed the latter task, in fact, in his Metaphysical Foundations of Natural Science, which had meanwhile appeared in 1786 (following the publication of the Prolegomena in 1783 and immediately preceding the publication of the second edition of the Critique in 1787). There Kant articulates what he calls “pure natural science” in four chapters corresponding, respectively, to the four headings of the table of categories (quantity, quality, relation, and modality). In the third chapter or Mechanics (corresponding to the three categories of relation: substance, causality, and community) Kant derives three “laws of mechanics” corresponding, respectively, to the three Analogies of Experience: the permanence or conservation of the total quantity of matter, the law of inertia, and the equality of action and reaction—which Kant describes as a law of “the communication of motion” (4, 544; 84). All these laws, Kant makes clear, are synthetic a priori propositions, demonstrated a priori and “drawn from the essence of the thinking faculty itself” (4, 472; 8).

For Kant, therefore, the laws of the Newtonian science of nature are of two essentially different kinds. Kant regards Newton's three “Axioms or Laws of Motion” presented at the beginning of the Principia as synthetic a priori truths—which Kant himself attempts to demonstrate a priori in the Metaphysical Foundations.[12] By contrast, Kant does not regard the inverse-square law of universal gravitation, which Newton establishes by a famous “deduction from the phenomena” in Book 3 of the Principia, as a synthetic a priori truth—and, accordingly, Kant does not attempt to demonstrate this law a priori in the Metaphysical Foundations. Nevertheless, Kant regards the synthetic a posteriori law of universal gravitation as “necessary and universally valid” in virtue of the way in which it is “determined” in relation to the “phenomena” by the synthetic a priori laws of pure natural science. And, since the latter, in turn, are “determined” from the a priori principles of the understanding, the a posteriori law of universal gravitation is thereby “determined” in relation to actual perceptions “in accordance with the general conditions of experience.”[13]

We shall return to Kant's conception of Newtonian natural science below, but we first want to discuss Hume's rather different debt to Newton. Hume, like virtually everyone else in the eighteenth century (including Kant), takes Newtonian natural science as his model, and, indeed, he attempts to develop his own “science of human nature” following Newton's example. Yet Hume learns a very different lesson from Newton than does Kant, based on Newtonian inductivism rather than Newtonian mathematical demonstrations. Contrasting Hume and Kant on this point greatly illuminates their diverging conceptions of causation and necessity.

To begin with, Hume does not consider Newton's “Axioms or Laws of Motion” as a priori in any sense (in Kant's terminology, neither analytic nor synthetic a priori). All of these laws, according to Hume, are simply “facts” inductively derived from (constant and regular) experience. Hume considers Newton's second law of motion (F = ma) in the Enquiry, section 4, part 1 (EHU 4.13; SBN 31): “Thus, it is a law of motion, discovered by experience, that the moment or force of any body in motion is in the compound ratio or proportion of its solid contents and its velocity … . Geometry assists us in the application of this law … ; but still the discovery of the law itself is owing merely to experience, and all the abstract reasonings in the world could never lead us one step towards the knowledge of it.”

One of Newton's main examples of the third law of motion is the communication of motion by impact or impulse.[14] Hume considers such communication of motion in the same section of the

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Enquiry (EHU 4.8; SBN 28–29): “We are apt to imagine, that we could discover these effects by the mere operation of our reason, without experience. We fancy, that were we brought, on a sudden, into this world, we would at first have inferred, that one billiard ball would communicate motion to another upon impulse; and that we needed not to have waited for the event, in order to pronounce with certainty concerning it. Such is the influence of custom, that, where it is strongest, it not only covers our natural ignorance, but even conceals itself, and seems not to take place, merely because it is found in the highest degree.”

Finally, in a footnote at the end of part 1 of section 7 (the section in the Enquiry devoted to the idea of necessary connection), Hume considers the law of inertia (EHU 7.25n16; SBN 73n1): “I need not examine at length the vis inertiae which is so much talked of in the new philosophy, and which is ascribed to matter. We find by experience, that a body at rest or in motion continues for ever in its present state, till put from it by some new cause; and that a body impelled takes as much motion from the impelling body as it acquires itself. These are facts. When we call this a vis inertiae, we only mark these facts, without pretending to have any idea of the inert power.” (Hume here puts the law of inertia and the communication of motion by impulse together, because both are consequences of a body's “inherent force [vis insita]” or “inert force [vis inertiae”] according to Newton's third definition preceding the Laws of Motion.[15]) It is clear, therefore, that Hume views all of Newton's laws of motion as inductively derived empirical propositions, which (deceptively) appear to be derived from reason simply because the constant and regular experience on which they are in fact based is so pervasive.

We believe that Hume's discussion of the communication of motion by contact or impulse shows his debt to Newton especially clearly. In section 7, part 1 of the Enquiry Hume is criticizing the inherited ideas of necessary connection. We believe that both here and in section 4, part 1, where he rejects any a priori demonstration of causality, Hume is centrally concerned with the conception of necessary connection articulated by the mechanical natural philosophy. This philosophy had taken the communication of motion by contact or impulse as the paradigm of an a priori rationally intelligible causal connection, to which all other instances of causal connection must be reduced. The reduction would take place by reducing all observable causal relationships to the motions and impacts of the tiny microscopic parts of bodies.[16]

In the view of contemporary mechanical philosophers, especially Huygens and Leibniz, Newton's conception of universal gravitation involved an entirely unintelligible action at a distance across empty space. Gravitation could only be acceptable, on their view, if it were explained, in turn, by vortices of intervening invisible matter whose tiny microscopic particles effected the apparent attraction of bodies via impulse. Although both Leibniz and Huygens accepted Newton's demonstration that the orbits of the satellites of the major astronomical bodies in the solar system obey the inverse-square law (the planets with respect to the sun, the moons of Jupiter and Saturn with respect to their planets, the earth's moon with respect to the earth), they rejected Newton's unrestricted generalization of this law to hold between all bodies (and all parts of bodies) whatsoever. For them, the inverse-square law could be accepted in astronomy only by taking the major bodies of the solar system as each being surrounded by vortices limited to the finite surrounding region of their satellites. The validity of the inverse-square law would thus be restricted to precisely such a finite region, so that it could not be extended arbitrarily far: the moons of Jupiter would accelerate towards Jupiter, for example, but neither Saturn nor the sun, for example, would experience such accelerations towards Jupiter.[17]

In the second (1713) edition of the Principia, in response to these doubts about the law of universal gravitation raised by mechanical philosophers, Newton adds an explicit principle of unrestricted inductive generalization—Rule 3—to a set of “Rules for the Study of Natural Philosophy” at the beginning of Book 3. Rule 3 states (Principia, 795): “Those qualities of bodies that cannot be intended and remitted [i.e. qualities that cannot be increased and diminished] and that belong to all bodies on which experiments can be made should be taken as qualities of all bodies universally.”[18] Then, in the explanation of this Rule, Newton depicts the hypotheses of the

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mechanical philosophy as in conflict with the method of inductive generalization that leads to the law of universal gravitation (Principia, 795–796): “For the qualities of bodies can be known only through experiments; and therefore qualities that square with experiments universally are to be regarded as universal qualities …. Certainly idle fancies ought not to be fabricated recklessly against the evidence of experiments, nor should we depart from the analogy of nature, since nature is always simple and ever consonant with itself.”

That the “idle fancies” in question include the hypotheses of the mechanical philosophers (such as the vortex hypothesis) is made perfectly clear and explicit in the passage from the General Scholium (also added to the second edition in 1713) where Newton famously says that he “feigns” no hypotheses (Principia, 943): “I have not as yet been able to deduce from phenomena the reason for [the] properties of gravity, and I do not feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this experimental philosophy, propositions are deduced from the phenomena and are made general by induction. The impenetrability, mobility, and impetus of bodies, and the laws of motion and the law of gravitation have been found by this method.”[19] Thus, Newton also makes it clear that gravity is (at least) as well grounded by induction as the favored properties of bodies singled out by the mechanical philosophers (impenetrability, motion, and impetus), all of which have been derived inductively from phenomena (a point he had earlier developed in the explanation of Rule 3).[20]

Hume (as we have seen) considers all the laws of motion—including the communication of motion by contact or impulse—as (merely) inductively derived general principles. Accordingly, Hume also unreservedly accepts universal gravitation and takes Newton's theory to articulate a fundamental law of nature completely on a par with all other inductively established laws (EHU 6.4; SBN 57): “There are some causes, which are entirely uniform and constant in producing a particular effect; and no instance has ever yet been found of any failure or irregularity in their operation. Fire has always burned, and water suffocated every human creature: The production of motion by impulse and gravity is an universal law, which has hitherto admitted of no exception.” For Hume, contrary to the mechanical philosophy, there is absolutely no asymmetry between the law of universal gravitation and the laws of impact with respect to their intrinsic intelligibility.[21]

There is an even more fundamental relationship between Hume's conception of the inductive method and Newton's Rule 3. In the explanation of this Rule (as we have seen) Newton takes the supposition that “nature is always simple and ever consonant with itself” to license the inductive generalizations made in accordance with the Rule. Similarly, Hume appeals, in the Enquiry, to the supposition that “the course of nature” does not change (EHU 4.21; SBN 37–38) or, equivalently, that “the future will be conformable to the past” (EHU 4.19; SBN 35–36). In the Treatise Hume formulates this supposition as the “principle, that instances, of which we have had no experience, must resemble those, of which we have had experience, and that the course of nature continues always uniformly the same” (T 1.3.6.4; SBN 89). Hume takes this supposition to license (in his own words, to provide the “foundation” for: compare note 5 above) all inductive inferences from observed constant conjunctions, just as Newton takes the supposition that “nature is always simple and ever consonant with itself” to license the applications of his Rule 3. It appears very likely, therefore, that Hume takes this Newtonian supposition as the model for his own principle of the uniformity of nature.[22]

Yet Hume raises radical skeptical doubts about this very principle. It has no foundation in reasoning: neither in demonstrative reasoning nor (on pain of circularity) in inductive reasoning itself. Nevertheless, as firmly based in custom or habit, it is a universal principle of the human mind. Moreover, it is also the foundation for the best available science of matters of fact—Newtonian inductive science—and for Hume's own inductive science (self-consciously following Newton) of human nature.[23] Thus, when Hume sets his radical skeptical doubts aside, the application of our foremost empirical scientific method (based on uniform constant conjunction) has normative

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force, and it thereby leads to the articulation of universal, exceptionless laws of nature which, as such, we are compelled to treat as necessary until experience teaches us otherwise (in accordance with Newton's Rule 4 in Book 3 of the Principia: see note 19 above).[24] It is because the idea of necessary connection, for Hume, arises from the application of the Newtonian inductive method that our projection of an inner feeling of determination onto nature does not merely reduce to a blind instinctual disposition, but amounts to a normative methodological standard in our best scientific understanding of nature.[25]

In the famous hypothesis non fingo passage from the General Scholium Newton characterizes his “experimental” method as follows (Principia, 943): “In this experimental philosophy, propositions are deduced from the phenomena and are made general by induction.” Hume focusses exclusively on the second, inductive, clause, and he thereby shows an especially deep insight into the fundamental difference between Newton's methodology and the purely deductive ideal of scientific knowledge represented by the mechanical philosophy. For Kant, by contrast, the dispute between Newton and the mechanical philosophers is now effectively over; and Kant concentrates instead on Newtonian mathematical demonstrations and the idea of “deduction from phenomena.” This comes out especially clearly in the Metaphysical Foundations of Natural Science, where Kant engages with some of the most important details of Newton's demonstration of the law of universal gravitation from the initial “phenomena” described at the beginning of Book 3 of the Principia. Kant shows especially deep insight into the way in which this argument is inextricably entangled, in turn, with the Newtonian mathematical conception of (absolute) space, time, and motion; and he thereby takes special pains to frame the explicitly inductive steps in Newton's argument within the a priori “special metaphysics” of nature expounded in the Metaphysical Foundations.[26]

The “phenomena” with which Book 3 of the Principia begins record the observed relative motions of the principal satellites in the solar system with respect to their primary bodies (the planets with respect to the sun, the moons of Jupiter and Saturn with respect to their planets, the earth's moon with respect to the earth). All of these satellites obey Kepler's laws (at the time often called “rules”) of orbital motion; and, appealing to his first law of motion (the law of inertia), Newton is able to derive purely mathematically that each of the satellites in question experiences an inverse-square acceleration directed towards it respective primary body. Moreover, the so-called “moon test” (developed in Proposition 4 of Book 3) shows that the inverse-square acceleration governing the moon's orbit is, when the distance in question approaches the surface of the earth, numerically equal to the constant acceleration of terrestrial gravity figuring in Galileo's law of fall. Newton concludes (by the first and second of his Rules for the Study of Natural Philosophy) that the (centripetal) force holding the moon in its orbit is the same force as terrestrial gravity.

The crucial inductive steps come next. Newton generalizes the result of the moon test to all the other satellites in the solar system: they, too, are held in their orbits by the same force of gravity (Proposition 5). Then (in Proposition 6) Newton concludes that all bodies whatsoever gravitate towards every primary body (including both Saturn and the sun towards Jupiter, for example); moreover, their weights, like those of terrestrial bodies, are proportional to their masses at equal distances from the primary body in question.[27] Finally (in Proposition 7), Newton applies the third law of motion to this last result to derive the law of universal gravitation itself: not only do all bodies whatsoever experience inverse-square accelerations (proportional to mass) towards every primary body in the solar system, but the primary bodies themselves experience inverse-square accelerations (proportional to mass) towards every other body (Jupiter towards its moons and all other planets, the earth towards its moon and all other planets, and so on). [28] Indeed, Newton here extends this universal conclusion to the parts of all bodies as well.[29]

Kant accepts Newton's law of gravitation in its full universal form—as a “physical law of mutual attraction, extending over the whole of material nature, whose rule is that it diminishes inversely with the square of the distances from every attracting point” (Prolegomena, § 38: 4, 321; 73). Moreover, Kant has no qualms at all about action at a distance, and he even attempts

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to demonstrate a priori (in the Metaphysical Foundations) that universal gravitation, as a manifestation of what he calls the “original” or “fundamental” force of attraction, must be conceived as an immediate action at a distance through empty space.[30] Kant also attempts to demonstrate his three “laws of mechanics” corresponding to Newton's three laws of motion as synthetic a priori truths, especially the crucially important third law (the equality of action and reaction).[31] Whereas Newton had devoted considerable effort to producing experimental evidence for this law (see note 14 above), Kant here ventures a rare criticism of Newton for not having the courage to prove it a priori.[32] Indeed, regarding this particular law as a synthetic a priori truth is central to Kant's reinterpretation of the Newtonian concepts of (absolute) space, time, and motion; for it is in virtue of his understanding of the equality of action and reaction that Kant is now able simply to define the center of gravity of the solar system (in which this principle necessarily holds) as an empirically determinable (provisional) surrogate for Newtonian absolute space.[33] Moreover, and for closely related reasons, Kant takes the universality of what he calls the “original” or “fundamental” force of attraction—that it proceeds from every part of matter to every other part to infinity—as another synthetic a priori truth demonstrable in “pure natural science.”[34]

Given this foundation in “pure natural science,” Kant then reconstructs Newton's “deduction from the phenomena” of the law of universal gravitation as follows. We begin, following Newton, from the observable “phenomena” described by Kepler's “rules.” These “phenomena,” in Kant's terminology, are so far mere “appearances [Erscheinungen],” which have not yet attained the status of “experience [Erfahrung].”[35] Then, again simply following Newton, we can use the law of inertia to derive (purely mathematically) inverse-square accelerations of their satellites directed towards every primary body in the solar system. Once we have done this, however, we can now, from Kant's point of view, frame all of Newton's explicitly inductive steps within the a priori “special metaphysics” of nature developed in the Metaphysical Foundations. By demonstrating a priori his three “laws of mechanics” corresponding to the three Analogies of Experience, Kant establishes that Newton's three “Axioms or Laws of Motion” are synthetic a priori truths (compare notes 12 and 31 above). Further, by identifying the accelerations in question as effects of what Kant calls the fundamental force of attraction, it now follows from Kant's “special metaphysics” of (material) nature that these accelerations must hold immediately between each part of matter and every other part of matter—and, accordingly, are also directly proportional to the mass.[36]

In the fourth chapter or Phenomenology of the Metaphysical Foundations Kant connects this reconstruction of Newton's argument with the modal categories of possibility, actuality, and necessity—the very categories which (as we saw at the end of the second section above) make it possible for initially merely inductive generalizations (à la Hume) to acquire the status of necessary laws. The first stage, where we simply record the “phenomena” described by Kepler's “rules” (as mere “appearances”: note 35 above), corresponds to the category of possibility. The second stage, where we say that we here have instances of “true” (as opposed to merely “apparent”) rotation by appealing to the law of inertia, corresponds to the category of actuality.[37] In the third stage, finally, we apply the equality of action and reaction to the true centripetal accelerations correlated with such true rotations (note 37 above); and all of them, in accordance with Kant's metaphysical “dynamical theory of matter,” must now be taken as extending universally to infinity from each attracting point (compare notes 34 and 36 above). The result is the law of universal gravitation, now seen as falling under the category of necessity. In this way, Kant's reconstruction of Newton's “deduction” of the law of universal gravitation from the initial Keplerian “phenomena” provides a perfect illustration of the three-step procedure, described in the Postulates of Empirical Thought, by which a mere “empirical rule” is transformed into a “necessary and universally valid” objective law. [38]

4. Time Determination, the Analogies of Experience, and the Unity of Nature

We have suggested that Kant's reconstruction of Newton's “deduction from the phenomena” of the law of universal gravitation in the Metaphysical Foundations of Natural Science is inextricably

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entangled with his reinterpretation of the Newtonian concepts of (absolute) space, time, and motion.[39] Indeed, Kant begins the Metaphysical Foundations by defining matter as “the movable in space”—and by introducing a distinction between absolute and relative space which is clearly derived from Newton's Scholium on space, time, and motion at the beginning of the Principia (see note 37 above). In Newton's words (Principia, 408–409): “Absolute space, of its own nature without reference to anything external, always remains homogeneous and immovable. Relative space is any movable measure or dimension of this absolute space.” In Kant's words (4, 480; 15): “Matter is the movable in space. That space which is itself movable is called material, or also relative space. That space in which all motion must finally be thought (and which is therefore itself absolutely immovable) is called pure, or also absolute space.”

It turns out, however, that Kant's own view, in sharp contrast to Newton's, is that “absolute space is in itself nothing and no object at all,” but signifies only an indefinite process of considering ever more extended relative spaces (4, 481–482; 16–17). Moreover, when Kant returns to this issue in the Phenomenology chapter (compare note 35 above), he states that “absolute space is therefore not necessary as the concept of an actual object, but only as an idea, which is to serve as the rule for considering all motion and rest therein merely as relative” (4, 560; 99). Kant's procedure for deriving “true motions” from “apparent motions” does not conceive true motions as taking place in an infinite empty absolute space (as in Newton), but views them as the product of an indefinitely extended process of empirical determination taking place within experience itself: we begin from our parochial perspective here on the surface of the earth, proceed (in accordance with the argument of Book 3 of Newton's Principia) to the center of gravity of the solar system, then proceed to the center of gravity of the Milky Way galaxy, and so on ad infinitum.[40]

Similarly, it is a central theme of the Analogies of Experience in the first Critique that “absolute time”—“time itself” (B219), “time for itself” (B225), or “time in itself” (B233)—is no actual object of perception. Hence, the three “modes of time” (duration, succession, and simultaneity) must all be determined in and through perceptible features of the appearances. Kant calls this procedure “time determination” (more precisely, “the determination of the existence of appearances in time”), and he sums up his view as follows (A215/B262):

These, then, are the three analogies of experience. They are nothing else but the principles for the determination of the existence of appearances in time with respect to all of its three modes, the relation to time itself as a magnitude (the magnitude of existence, i.e., duration), the relation in time as a series (successively), and finally [the relation] in time as a totality of all existence (simultaneously). This unity of time determination is thoroughly dynamical; that is, time is not viewed as that in which experience immediately determines the place of an existent, which is impossible, because absolute time is no object of perception by means of which appearances could be bound together; rather, the rule of the understanding, by means of which alone the existence of the appearances can acquire synthetic unity with respect to temporal relations, determines for each [appearance] its position in time, and thus [determines this] a priori and valid for each and every time.

For Kant, therefore, the temporal relations of duration, succession, and simultaneity cannot be viewed as pre-existing, as it were, in an absolute time subsisting prior to and independently of the procedures of our pure understanding for determining these relations within the appearances themselves. On the contrary, temporal relations as such are the products of an empirical construction whereby we objectively determine the appearances as objects of a unified experience by means of the a priori principles of the Analogies. Thus, just as Kant does not view the determination of true motions from apparent motions as taking place within an infinite empty absolute space, he also rejects Newtonian absolute time and replaces it, too, with a process of empirical determination taking place within experience itself.

Indeed, there is an intimate relationship between these two procedures for empirical determination—of time and of motion, respectively. At the very beginning of his famous Scholium Newton

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distinguishes between “true” and merely “apparent” time (Principia, 408): “Absolute, true, and mathematical time, in and of itself and of its own nature, without reference to anything external, flows uniformly and by another name is called duration. Relative, apparent, and common time is any sensible measure (whether accurate or nonuniform) of duration by means of motion: such a measure—for example, an hour, a day, a month, a year—is commonly used instead of true time.” Then, several pages later, Newton illustrates the difference between “absolute” and “relative” time with reference to the celestial motions studied in astronomy (Principia, 410):

In astronomy, absolute time is distinguished from relative time by the equation of common time. For natural days, which are commonly considered equal for the purpose of measuring time, are actually unequal. Astronomers correct this inequality in order to measure celestial motions on the basis of a truer time. It is possible that there is no uniform motion by which time may have an accurate measure. All motions can be accelerated and retarded, but the flow of absolute time cannot be changed. The duration or perseverance of the existence of things is the same, whether their motions are rapid or slow or null; accordingly, duration is rightly distinguished from its sensible measures and is gathered from them by means of an astronomical equation.

Newton is here referring to the standard astronomical procedure, already well-understood in ancient astronomy, whereby we correct the ordinary measure of time in terms of days, months, and years so as to obtain “sidereal” or mean solar time based on the motions of the sun relative to both the earth and the fixed stars.[41]

In the Refutation of Idealism added to the second edition of the Critique Kant argues that all empirical determination of time—including determination of the temporal relations among one's own inner states—ultimately depends on the perception of outer things, and, in particular, on the perception of motion in space (B277–278):

All empirical employment of our cognitive faculties in the determination of time fully agrees with this. It is not only that we can undertake all time determination only by the change of external relations (motion) in relation to the permanent in space (e.g., motion of the sun with respect to objects on the earth), but we also have nothing at all permanent, which could underlie the concept of a substance, as intuition, except merely matter, and even this permanence is not derived from outer experience, but is rather presupposed a priori as necessary condition of all time determination, and thus also [of] the determination of inner sense with respect to our own existence by means of the existence of outer things.

In emphasizing that only matter can instantiate the concept of substance here, Kant is alluding to the way in which the conservation of the total quantity of matter, in the Metaphysical Foundations, realizes the (transcendental) principle of the conservation of substance.[42] Moreover, Kant's language at B277–278 (we “undertake [vornehmen]” time determination by observing “motion of the sun with respect to objects on the earth”) thereby suggests a progressive empirical procedure in which we begin with our perspective here on earth, measure the duration of time by the apparent motion of the sun, and then proceed to correct this measure in light of our evolving astronomical knowledge.[43]

Yet for Kant, unlike Newton, this need for correction is not an indication of a pre-existing absolute time subsisting prior to and independently of our empirical procedures for determining temporal magnitudes from observable motions. It rather implies that empirically observable motions must be subject to a priori principles of the understanding (a priori rules of time determination) in order to count as fully objective experience within a unified, temporally determinate objective world. Applying the relevant principles of the understanding—the Analogies of Experience—therefore results in a sequence of successive corrections or refinements of our ordinary temporal experience, as the observable motions are progressively embedded within an increasingly precise and refined conception of temporality itself.

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In the Metaphysical Foundations, in particular, Kant articulates a specific realization of the Analogies of Experience in terms of the Newtonian theory of universal gravitation. Kant's three “laws of mechanics” (a version of the Newtonian laws of motion: compare notes 12 and 31 above) correspond to the three principles of the Analogies; the categories of substance, causality, and community are realized by the system of Newtonian massive bodies interacting with one another in the context of what Newton, in Book III of the Principia, calls the System of the World. The category of substance, that is, is realized by the conservation of the total quantity of matter (mass) in all interactions involving these bodies (compare note 42 above, together with the sentence to which it is appended); the category of causality is realized by the gravitational forces through which these interactions take place (in accordance with the law of inertia); and the category of community is realized by the circumstances that precisely these forces are everywhere mutually equal and opposite. The temporal relation of duration is thereby realized by the progressive empirical procedure by which we successively correct our ordinary measure of time in light of our evolving astronomical knowledge (compare note 43 above, together with the sentence to which it is appended).[44] The temporal relation of succession is realized by the deterministic evolution of the motions of the bodies (masses) in question described by the law of universal gravitation (according to which every later state of the system is uniquely determined by its earlier states).[45] The temporal relation of simultaneity, finally, is realized by the circumstance that gravitational forces instantaneously connect each body in the system with all other bodies.[46] It is in precisely this sense that the procedure of time determination Kant describes in the Analogies is intended to replace Newtonian absolute time.

We have now arrived at the most fundamental divergence between Kant and Hume concerning causation and induction. For Hume, the order of time is empirically given by the sequence of impressions and ideas (and associations among them) which in fact happen to appear before the mind. As Kant explains in the Second Analogy, however, such a sequence, from his point of view, is “merely something subjective, and determines no object, and can therefore in no way count as cognition of any object at all (not even in the appearance)” (A195/B240). For Kant, it is only the a priori concept of causality (requiring a necessary rule of connection between preceding and succeeding events) which can then transform a merely subjective temporal sequence into an objective one (ibid.):

If we thus experience that something happens, then we always presuppose thereby that something precedes on which it follows in accordance with a rule. For otherwise I would not say of the object that it follows, because the mere sequence in my apprehension, if it is not determined by means of a rule in relation to something preceding, justifies no sequence in the object. Therefore, it is always in reference to a rule, in accordance with which the appearances in their sequence (i.e., as they happen) are determined through the previous state, that I make my subjective synthesis (of apprehension) objective, and, it is solely under this presupposition that even the experience of something happening is possible.

It is for precisely this reason, Kant concludes, that mere induction alone cannot be the ground for objective causal connections—which presuppose both strict universality and necessity, and therefore must be grounded on a priori concepts and principles of the pure understanding (A195–196/B240–241):

It seems, to be sure, that this contradicts all remarks that have always been made concerning the course of the employment of our understanding, according to which we have only been first guided by the perception and comparison of many concurring sequences of events following on certain appearances to discover a rule, in accordance with which certain events always follow on certain appearances, and we have thereby been first prompted to make for ourselves the concept of cause. On such a basis this concept would be merely empirical, and the rule it supplies, that everything that happens has a cause, would be just as contingent as experience itself: its universality and necessity would then be only feigned and would have no true universal validity, because they would not be grounded a priori but only on induction.

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For Kant, the concept of cause cannot possibly arise from a mere repetition of resembling constant conjunctions (“concurring sequences of events following on certain appearances”) producing a merely subjective custom.[47] The procedure by which we apply the concept of cause to experience cannot be merely inductive in the Humean sense; it must rather involve a priori rules of the understanding through which we progressively determine the objective causal relations between appearances—and thereby determine the objective order of succession in time itself.[48]

Kant thus has a completely different perspective from Hume's concerning the uniformity of nature. For Hume, the principle of uniformity is a supposition implicit in all of our inductive inferences leading to the formulation of laws of nature. If this principle itself had a foundation in the understanding (in either a priori or a posteriori “reasoning”), then so would our inductive inferences from observed constant conjunctions to so far unobserved events. Yet the supposition in question—“that instances, of which we have had no experience, must resemble those, of which we have had experience, and that the course of nature continues always uniformly the same” (T 1.3.6.4; SBN 89)—cannot itself be justified by either demonstrative or inductive reasoning. In the former case it would have to be self-contradictory to imagine that the course of nature is not sufficiently uniform; in the latter the attempted justification would be viciously circular. The principle of uniformity, however, is firmly based in custom or habit, as a universal principle of the human mind, and it is also the foundation for the Newtonian inductive method—including Hume's own inductive science of the human mind. Although the principle thus has normative force in all our reasoning concerning matters of fact in both science and common life, it cannot ultimately legitimate the attribution of objective necessity to our inductively established laws of nature.[49]

Kant, in our view, is attempting to provide precisely such a grounding of objective necessity by means of the general principle of the Analogies of Experience (B218): “Experience is possible only by means of the representation of a necessary connection of perceptions.” More specifically, the Analogies of Experience provide an a priori conception of the unity and uniformity of experience playing the role, for Kant, of Hume's principle of the uniformity of nature. According to the Analogies we know a priori that nature in general must consist of interacting substances in space and time governed by universally valid and necessary causal laws determining the temporal relations (of duration, succession, and simultaneity) among all empirical events, and this articulated a priori conception of nature in general amounts to the knowledge that nature is, in fact, sufficiently uniform.[50]

We can only have objective experience of particular events, for Kant, in so far as we simultaneously construct particular causal relations among them step by step, and this is only possible, in turn, in so far as we presuppose that they are one and all parts of a unified and uniform experience of nature in space and time governed by the Analogies of Experience (together with the other principles of pure understanding). Moreover, since particular causal relations, for Kant, necessarily involve causal laws, all of our inferences from particular perceptions to universal causal laws of nature are grounded in synthetic a priori principles of pure understanding providing a synthetic a priori conception of the unity and uniformity of nature in general. Hume was correct, therefore, that the principle of the uniformity of nature governs all of our inductive causal inferences; and he was also correct that this principle is not and cannot be analytic a priori. What Hume did not see, from Kant's point of view, is that the merely comparative universality of inductive generalization can indeed be overcome by transforming initially merely subjective “empirical rules” into truly objective and necessary “universal laws” in accordance with synthetic but still a priori principles of the unity of nature in general.[51]

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Primary Sources

Kant

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Citations from Kant's works, except for the Critique of Pure Reason, are by volume and page numbers of the Akademie edition of Kant's gesammelte Schriften (Berlin, 1902—); the Critique of Pure Reason is cited by the standard A and B pagination of the first (1781) and second (1787) editions respectively. Although all translations from Kant's writings are our own, we follow the reference to the Akademie edition (except in the case of the Critique of Pure Reason) with references to the translations in the now standard Cambridge Edition of the Works of Immanuel Kant, as follows:

Critique of Pure Reason, translated and edited by Paul Guyer and Allen W. Wood (Cambridge: Cambridge University Press, 1997).

Prolegomena to Any Future Metaphysics, translated and edited by Gary Hatfield, revised edition (Cambridge: Cambridge University Press, 2004).

Metaphysical Foundations of Natural Science, translated and edited by Michael Friedman (Cambridge: Cambridge University Press, 2004).

Theoretical Philosophy, 1755–1770, translated and edited by David Walford, in collaboration with Ralf Meerbote (Cambridge: Cambridge University Press, 1992). This volume contains translations of Kant's pre-critical writings, including Attempt to Introduce the Concept of Negative Magnitudes into Philosophy (1763) and Dreams of a Spirit-Seer Explained by Dreams of Metaphysics (1766).

Hume

Citations from Hume's A Treatise of Human Nature (abbreviated as T) are from the David Fate Norton and Mary J. Norton edition (New York: Oxford University Press, 2000), and thus include book, part, section, and paragraph numbers; we also add the corresponding page numbers in the L. A. Selby-Bigge second edition (abbreviated as SBN), with revised text and notes by P. H. Nidditch (Oxford: Oxford University Press, 1978).

Citations from Hume's An Enquiry concerning Human Understanding (abbreviated as EHU) are from the Tom L. Beauchamp edition (New York: Oxford University Press, 1999), and thus include section and paragraph numbers; we also add the corresponding page numbers in Enquiries concerning Human Understanding and concerning the Principles of Morals, edited by L. A. Selby-Bigge, third edition (abbreviated as SBN), with revised text and notes by P. H. Nidditch (Oxford: Oxford University Press, 1975).

Locke

Citations from Locke's An Essay concerning Human Understanding are from the Peter H. Nidditch edition (Oxford: Oxford University Press, 1975), and include the Roman numerals of the book and chapter, followed by the Arabic numeral of the section.

Newton

Citations from Newton's Principia are to The Principia: Mathematical Principles of Natural Philosophy, translated and edited by I. Bernard Cohen and Anne Whitman, assisted by Julia Budenz (Berkeley and Los Angeles: University of California Press, 1999), and are given in the form (Principia, page numbers).

Citations from Newton's Opticks are to Opticks: or A Treatise of the Reflections, Refractions, Inflections & Colours of Light, based on the fourth edition, London 1730 (New York: Dover, 1979), and are given in the form (Opticks, page numbers).

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The relevant secondary literature is vast. We confine ourselves to English-language literature and, more specifically, to the works cited in the main text. These works can be consulted, in turn, for extensive references to other secondary literature.

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Philosophy (Cambridge: Cambridge University Press). Allison, H. E. (2004) Kant's Transcendental Idealism, revised and enlarged edition (New

Haven: Yale University Press). Allison, H. E. (2008) Custom and Reason in Hume: A Kantian Reading of the First Book of the

Treatise (Oxford: Oxford University Press). Baier, A. (1991) A Progress of Sentiments (Cambridge, Mass.: Harvard University Press). Beauchamp, T. L. & Rosenberg, A. (1981) Hume and the Problem of Causation (Oxford:

Oxford University Press). Beck, L. W. (1978) “A Prussian Hume and a Scottish Kant,” in Essays on Kant on Hume (New

Haven: Yale University Press), pp. 111–129. Bird, G. (1973) Kant's Theory of Knowledge (New York: Humanities Press). Buchdahl, G. (1969) Metaphysics and the Philosophy of Science (Oxford: Basil Blackwell). Buchdahl, G. (1974) “The Conception of Lawlikeness in Kant's Philosophy of Science,” in L. W.

Beck, ed., Kant's Theory of Knowledge (Dordrecht: Reidel), pp. 128–150. De Pierris, G. (2001) “Hume's Pyrrhonian Skepticism and the Belief in Causal Laws,” Journal of

the History of Philosophy 39: 351–383. De Pierris, G. (2002) “Causation as a Philosophical Relation in Hume,” Philosophy and

Phenomenological Research 64: 499–545. De Pierris, G. (2006) “Hume and Locke on Scientific Methodology: the Newtonian Legacy,”

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Kegan Paul). Friedman, M. (1992a) “Causal Laws and the Foundations of Natural Science,” in P. Guyer, ed.,

The Cambridge Companion to Kant (Cambridge: Cambridge University Press), pp. 161–199. Friedman, M. (1992b) Kant and the Exact Sciences (Cambridge, Mass.: Harvard University

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Friedman, M. (2013) Kant's Construction of Nature: A Reading of the Metaphysical Foundations of Natural Science (Cambridge: Cambridge University Press).

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Princeton University Press). Kemp Smith, N. (1941) The Philosophy of David Hume (London: MacMillan). Koyré, A. (1968) Newtonian Studies (London: Chapman and Hall). Kuhn, T. (1957) The Copernican Revolution: Planetary Astronomy and the Development of

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