on the impossibility of a unitary pure logic in husserl

8/9/2019 On the Impossibility of a Unitary Pure Logic in Husserl

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On the Impossibility of a Unitary Pure Logic::Axiomatic Closure and Categorial Intuition

Rowan G. Tepper

1

Husserlian phenomenology has as its ideal limit, in the mathematical sense, in the

sache selbstof phenomenal experience. This is to say that Husserls task in the Logical

Investigations,would be to account for the structure and logic evident in lived experience by

means of which we may know the world. The complete achievement of this pure logic

deduced from experience would, in principle, exhaust the phenomena of experience in the

sense of demonstrating a unified theory of logic corresponding to the unified manifold of

experience, leaving no phenomenon inexplicable in terms of this totalized pure logic. This is

the first criterion of the completeness of Husserls phenomenology. Implicit in this first

criterion is a second. This implied criterion, namely, that a logic that is essentially divergent

from a pure phenomenological logic, would of necessity collapse into non-sense under the

first and foremost, through the weight of its own internal contradictions, as well as

discrepancies between the expression logical laws and lived experience. This is to say that

Husserl argues from the pure Idea of Theory that corresponding to the manifold of the real

there must be a comprehensive unitary theory containing all of the basic laws expressed in

the manifold of experience. My argument here stems from these two criteria. That is,

without complicating the matter further, as I will shortly, subjective experience is at once

irreducibly qualitative in nature (accentuating the necessity of Husserls intuitive method)

and more importantly, subjective experience is in principle inexhaustible. Furthermore, if we

introduce the Kantian noumenal object beyond subjective phenomenal experience,

subjective experience becomes inexhaustible to the second degree. I will argue that

phenomenological analysis, and a forterioriall analysis of experience is an interpretation of


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said experience and further, subjective experience itself is an interpretation of the Kantian

sache selbst. The existence of experiences and facts that cannot be assimilated into a logical

schema, when taken in the context of an understanding of analysis and experience, a la

Nietzsche, as essentially interpretive, it is then implied that other interpretive and therefore

logical and conceptual schemata are not only possible but demonstrablyconcretelypossible by

virtue of these unassimilable facts and experiences.

These facts and experiences that defy logical or conceptual explanation abound.

Husserls counter-argument here would be that these facts and experiences are merely those

which science has not yetbeen able to assimilate. However, this counterargument reveals

Husserls positivistic underlying assumptions, which he does not question until The Crisis of

European Sciences and Transcendental Phenomenology. The most central presupposition that

Husserl bears is a form positivism itself, i.e. the faith in the progressive nature of science and

its infinite capacity for the assimilation of unassimilated facts and experiences. This is the

very presupposition of philosophy and science that first came under attack two decades prior

by Nietzsche and some time after with the critiques of Horkheimer and Adorno on one

hand and Heidegger on the other. That which cannot properly be knownwithin Husserls

phenomenology is precisely the object of their interest; henceforth in this paper I will adopt

Adornos term for this unassimilated supplement: the non-identical. This assumption

essentially means that despite the pretensions to a purely phenomenological derivation of the

logic of knowledge, at some point, this logic is taken as complete and a fait accompli and is

assumed to be capable of assimilating all experience without further (significant)

modification.

A difficulty of the first order is found in Husserls strong assertion of logical

universalism and the axiomatic structure of logic. He writes:


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There will be a definite, ordered procedure which will enable us to construct thepossible forms of theories, to survey their legal connections, and to pass from one toanother by varying their basic determining factors etc. There will be universalpropositions, if not for the forms of theory generally, then at least for forms oftheory belonging to defined classes, which will govern the legal connection, the

transformation and the mutual interchange of these forms.

1

Because logic, thus conceived would axiomatic, Goedels proof of the essential

incompleteness of axiomatic systems would seem to render Husserls totalizing inclination,

in principle, impossible. However, this would merely open the closure of the system of logic.

This would not in itself demonstrate the essential fungibility of logical systems; what it would

demonstrate is that in any given system there is (in the strong sense of an Es gibt) a non-

identical, indeterminate, non-assimilable part. However, it is interesting to note that Goedels

incompleteness theorem also states that in any given system, there are statements that, while

true, are indemonstrable. These statements, which while true in terms of a correspondence-

epistemology, are indemonstrable in a consistency-based epistemology. This is precisely the

state of all phenomenological data while the epocheis in place in Husserls later work,

however, at this stage, the logical indemonstrability of these phenomenologically valid data

within the hypothetically closed system of logic is irreducibly at odds with their phenomenal

character. The later introduction of the phenomenological reduction was an inventive means

to circumvent the difficulties presented by this disconnect between consistency and

correspondence. Although Husserls reduction predates Goedels proof, it is indubitable that

Husserl had an intimation of this problem in his introduction of the reduction.

Husserls later introduction of the reduction can be read as an acknowledgment of

the inexhaustibility of lived experience, which permitted him to maintain the monolithic

status of logic while providing a means for phenomenology to supplement this logic by

1 Edmund HusserlLogical Investigations, Volume 1 , Translated by J.N. Findlay, Edited by Dermot Moran

(2001: Routledge, London and New York), pg. 155


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adding, as needed, axioms derived from phenomenological data. In fact, this interpretation

of the introduction of the reduction is suggested in the closing section of the Prolegomena,

in which Husserl writes ofempirical sciencethat both the theory and facts of the empirical

sciences are always only probable and are informed by their very explanation: We state with

such facts, they are taken as given; all that we want is to explain them. But when we rise to

the explanatory hypotheses and after deduction, verification and perhaps repeated

modification, accept them as probably laws, the facts themselves do not remain quite

unchanged; they too change as the process of knowledge proceeds.2 However, the

intervention of the reduction is a radical departure from Husserls position in the Logical

Investigations, with which we are concerned, namely that logic is notan empirical or empirically

informed science, but is rather nomological, purely and simply. Husserl is bound by his

conception of philosophy as an exact science and logic as a purely nomological, or

theoretical one with a normative function in opposition to logical technology. This

conception forces him, at the conclusion of the Prolegomena to claim the status of a unitary

universal for phenomenologically purified logic.

Let us here follow Husserls argument in favor of the universality and unitarynature of pure logic in view of his conclusion that:

pure logic covers the ideal conditions of the possibility of science in general in the mostgeneral manner. It must, however, be noted that logic so regarded does not include, asa special case, the ideal conditions ofempirical science in general ideal laws do notdetermine the unity of the empirical sciences merely in the form of the laws ofdeductive unity, since empirical science cannot be reduced merely to its theories. 3

Correspondingly:we must conclude that there must be ideal elements and laws even in the field of empiricalthinking, in the sphere of probabilities. In these thepossibilityof empirical science ingeneral, of the probable knowledge of the real, has its a prioribasis. This sphere ofpure laws does not relate to the Idea of Theory of to the more general Idea of truth,but to the Idea of the Empirical Unity of Explanation, the Idea of Probability. This

2 Ibid, pg 1603 Ibid, pg. 160


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yields us a second great foundation of logical technology, which is included in thefield of pure logic in a sense to which corresponding width must be given.4

Thus, the distinctions established at the outset between logic conceived normatively and as

technology as well as that between logic as a theoretical and practical science are born out

through the distinction between the theoretical and empirical sciences with the ultimate

result being a strong distinction between logic as the condition of possibility (or condition of

existence) for the real and logic that is empirically informed. The former is a closed

axiomatic system grounded in the Idea of Truth whereas the latter is an open system

grounded in the Idea of Probability.

However, from the beginning of Husserls argument in the concluding chapter of the

Prolegomena this is a distinction that is only accessible through means of abstraction. The

aforementioned distinctions correspond closely to the distinction between truths and things,

the interconnections of which form the two rudimentary forms of unity given to us. Husserl

writes Both sorts of unity are given to us, and can only by abstraction be thought apart, in

judgment, or, more precisely, in knowledge the unity of objectivity, on the one hand, and of

truth on the other.5 According to Husserl, the interconnections of truth and the

interconnection of things are both given a prioritogether, however, without the two being

identical. Rather, the interconnections of truths differ from the interconnection of things,

which are truly in the former; this at once appears in the fact that truths which old of truths

do not correspond with truths that hold of the things posited in such truths.6 Truth is the

ideal correlate of the transient subjective act of knowledge, as standing opposed in its unity

to the unlimited possible acts of knowing and of knowing individuals.7 Thus, the things of

4 Ibid, pg. 1615 Ibid, pg. 1456 Ibid, pg. 144-57 Ibid, pg. 145


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experience in their known interconnections form a ground of truth and its interconnections,

because the act of knowing gives us both the object and truth.

Truth is then given in the act of knowledge, but is notthe known. It is rather the

universal to which the result of the act corresponds. Husserl continues that scientific

knowledge as a subset of knowledge in general is grounded knowledge, which thus implies

that necessity is likewise predicated of scientific knowledge, which then implies knowledge

of the law governed validity of the state of affairs in question. [And] To see a state of affairs

as a matter of lawis to see its truth as necessarily obtaining, and to have knowledge of theground of

the state of affairsor of its truth8 Truths then differentiate into individualor contingent

truths and general truths, which are context-independent and the truths to which Husserl

would ascribe the strong sense of the term and with which he is exclusively concerned. That

which is of foremost import here is that knowledge that is scientific implicates the laws

governing its validity, and thus interconnections of things known yield interconnections of

truth, which then yield the laws governing their validity. Due to the irrefutable validity of

grounded acts of knowing, these laws of validity are also laws of existence. Thus a formal

connection between grounded knowledge of the lifeworld and the logical laws governing the

experience of knowing is established. Husserl continues to write:

The proof of general laws necessarily leads to certain laws which in their essence, i.e.intrinsically, and not merely subjectively or anthropologically, are not furtherprovable. The systematic unity of the ideally closed sum total of laws resting on onebasic legality as their final ground, an arising out of it through systematic deduction,is the unity of a systematically complete theory. This basic legality may here consist of one

basic law or a conjunction ofhomogeneousbasic laws.

9

Although in the next section, Husserl differentiates normative science from theoretical and

empirical science, normative science definitively implies a theoretical basis as its standard for

8 Ibid, pg. 1469 Ibid.


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normative judgment. Furthermore, in this section, he differentiates the categories of essential

and extra-essential principle of unity. We must bear in mind that unity is originally given in

the form of the interconnection of truths and the interconnections of things, which is the

unity of the world of experience. In view of distinguishing individual sciences preparatory to

the hypothesis of a general science and its corresponding manifold, Husserl asserts that the

essential unity of the truths of a science is a unity of explanation, which means, therefore,

theoreticalunity, which means homogeneous unity of legal base, and, lastly, homogeneous unity

of explanatory principles.10 This unity defines nomological or theoretical science in opposition

to empirical or descriptive science, which is concerned with truths whose content relates to

one and the same individual object, or to one and the same empirical genus,11 whose unity is a posteriori,

extra-essential and subject to revision as technology. These latter unities of science contain

essential, ideal laws, which do not exhaust them.12 This assertion is, in itself, problematic by

virtue of the fact that nomological unity is an explanatory unity not established by the

explanation. Thus, a theoretical science explains the facts of an empirical science, however

different its mode of unity may be.

Leaving aside this difficulty for a moment, we continue in following Husserls

argument. In section sixty-five of the Prolegomena, Husserl discusses the grounding of

knowledge and science in terms of Kantian conditions of possibility. This step becomes self

evident if we reflect upon the answer demanded in the question On what ground? We are

asking for the reasons that a state of affairs is. A state of affairs is, following Kants

demonstration of the unreality of the predicate being, only if it is already possible. Thus, in

seeking the grounds of theory and knowledge, Husserl is seeking the unity of objective

10 Ibid, pg. 14711 Ibid. pg. 14812 Come back to this


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legality: [falling], therefore, under the concept of theoretical unity.13 This legality, the

conditions of possibility for theory and by implication, existence, consists of

Idealconditions for the possibility of knowledge of two sorts. They are either noetic

conditions which have their grounds, a priori, in the Idea of Knowledge as such,without any regard to the empirical peculiarity of human knowledge or they arepurelylogicalconditions, i.e. they are grounded purely in the content of ourknowledge.14

However, he continues that the noetic conditions as opposed to logically objective

conditions, are no more than such modifications of the insights, the laws which pertain to

the pure content of knowledge, as render them fruitful for the criticism and for practical,

logical normativity.15 This is to say that the noetic laws have their ground as well in the

content of knowledge, yet are one degree removed, such that they do not hold in so far as

we have insight into them, but we can only have insight into them in so far as they hold. 16

Thus the categories of the noetic and the logical are circularly related, in so far as they

ground one another. Theory must be logically justified, and logic must have theoretical

grounds that a priorimake it possible. This circular construction forces Husserl to starkly

delimit the field of theory with which he is concerned to systematic theories which has their roots

in the essence of theory, with an a priori, theoretical, nomological science which deals with the ideal essence of

science as such, and which accordingly has parts relating to systematic theories whose empirical,

anthropological aspect it excludes.17 Thus, it is a meta-theory at which Husserl aims. Pure

logic would thus be a meta-logic, a logic divorced of its origins in lived experience by virtue

not of abstraction, but through abstraction arriving at the ultimate laws governing theory and

logic as such as conditions of possibility of science, theory and factical experience.

13 Ibid, pg. 14914 Ibid, pg. 149-5015 Ibid. pg 15016 Ibid.17 Ibid, pg 152


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Husserl goes on in the next three sections to programmatically set out the tasks of a

pure logic, the first of which being to establish the primitiveconcepts which make possible

the interconnected web of knowledge as seen objective, and particularly the web of theory

the concepts which constitute the Idea of unified theory, or with concepts which are

connected with these through ideal laws.18Theseprimitiveconcepts include the concepts:

Concept, Proposition, Truth etc. as well as the connective forms such as conjunction,

disjunction, hypothetical linkage, etc. as well as what he terms laws of complication.

Additionally ideal categories of meaning, the categories of Aristotelian pedigree are included

here as formal objective category. These concepts and categories must then be examined in

terms of their phenomenological origin and essence. This is achieved only byintuitive

representationof the essence in adequate Ideation, or, in the case of complicated concepts,

through knowledge of the essentiality of the elementary concepts present in them, and of the

concepts of their forms of combination.19 We shall return to the method of intuition cited

here. (in 2)

The second task asserted of pure logic consists in

the search for the lawsgrounded in the two above classes of categorial concepts,which do not merely concern possible forms of complication and transformationbut rather the objective validityof the formal structures which thus arise: on the onehand, the truth or falsity ofmeaningsas such, purely on the basis of their categorialformal structure, on the other hand (in relation to their objectivecorrelates), the beingand not being of objects as such, of states of affairs as such, again on the basis oftheir pure, categorial form

All the laws here belonging lead to a limited number ofprimitive or basic laws

[emphasis mine], which have their immediate roots in our categorial concepts. Theymust, in virtue of their homogeneity, serve to base an all-comprehensive theory,which will contain the separate theories as relatively closed elements in itself.20

18 Ibid, pg. 15319 Ibid, pg. 15420 Ibid.


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This is the strongest assertion of universality yet put forth for pure logic. The focus of our

critique once again lies in the presupposition that the number of primitive, basic laws are

indeed limited by virtue of the finitude of the number of irreducible categorial concepts.

Thus, in reference to this task, our argument will proceed on two paths: an examination of

this supposed irreducibility and one of the nature of the finitude of the categorial concepts.

With the third task of pure logic and the introduction of the concept of the

manifold, Husserl will elevate pure logic to the status of a meta-logic, which would

supposedly subsume an alternate logical system by both accounting for its own incompletion

and making possible the transformation between it and any other logical system without the

necessity of detour through the lifeworld and subjective acts of knowledge.

Pure logic would be, for Husserl a meta-science, a meta-theory, which deals a priori

with the essential sorts (forms) of theories and the relevant laws of relation all of this taken together

[as] a more comprehensive science of theory in general.21 Thus, pure logic is, in fact, the

axiomatic system that would account for the forms which theory may take and the

transformations and interrelations possible between these theories, through universal

propositions rather than by virtue of their objective connectedness.22 As with all sciences,

to this axiomatic, pure logic, corresponds what Husserl refers to as a manifold in the

mathematical sense, that is The objective correlateof the concept of a possible theory, definite

only in respect of form, is the concept of a possible field of knowledge over which a theory of this form

will preside It is accordingly a field which is uniquely and solely determined by falling under

a theory of such a form, whose objects are such as to permit ofcertainassociations which fall

under certain basic laws of this or that determinateform.23Thus, what Husserl refers to as a

21 Ibid, pg. 15522op cit.23 Ibid, pg. 156


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general theory of manifoldsdefines the possible theories and their respective fields and the laws

of their interrelations. This is, so to speak, to construct a meta-theory that accounts for all

theories as well as their objective correlates, which would necessarily constitute the lifeworld

as such.

If such a meta-theory as pure logic is possible, then its objective correlate would be

the manifold which encompasses the entirety of the real. There would be no remainder

either on the level of theory or on the level of the manifold. Apparent lacunae would be

referred to a law of relation that prohibits simultaneous perception of two theoretical

schemata in the manner of a Gestalt image in which it is impossible to simultaneously view

the image in both cognitive interpretations. These differing interpretations would be, in

Husserls view, analogous to the illusion of multiple logical systems or multiple geometries.

However, we would be remiss if we were to accept this as proof that such a pure logic is

possible and that such a logic constitutes a closed system. Husserl, however, cites a different

example in his argument. He writes:

if we mean by space the categorial form of world-space, and, correlatively, bygeometry the categorical theoretic corm of geometry in the ordinary sense, thenspace falls under a genus, which we can bound by laws, of pure categoriallydeterminate manifolds, in regard to which it is natural to speak of space in a yetmore extended sense. Just so, geometric theory falls under a corresponding genus oftheoretically interrelated theory-forms determined in purely categorical fashion,which in a correspondingly extended sense can be called geometries of thesespatial manifolds. At any rate, the theory ofn-dimensional spaces forms atheoretically closed piece of the theory of theory in the sense above defined. Thetheory of a Euclidean manifold of three dimensions is an ultimate ideal singular inthis legally interconnected series ofa priori, purely categorical theoretic forms (formal

deductive systems). This manifold itself is related to our space, i.e. space in theordinary sense, as its pure categorical form, the ideal genus of which the latterrepresents so to say an individual singular rather than a specific difference.24

Thus Husserls argument boils down to this: pure logic as a meta-theory accounts at once for

all theories and their interrelations; any lacunae are merely indications of a law-governed

24 ibid, pg. 158


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relation between differing theories or levels of theory, each a relatively closed system

together constitutive of the meta-theoretical absolutely closed system of primitive categories

and relations.

2

I. Three Weak Points

In light of the foregoing considerations in terms, the task at hand, i.e. the

demonstration of the possibility of alternate logical systems obtains clear conditions for its

own possibility. Namely, through the introduction of the concept of the manifold and the

designation of pure logic as a set of rudimentary propositions governing the transformation

of theory and manifold within the meta-theory-manifold, Husserl has effectively admitted of

alternate logical constructions, which, however, are subsumed by recourse to metatheoretical

laws of transformation. Analogous to the notion of spatial curvature permitting the

transformation of space-like manifolds into one another, are these rudimentary laws that

subsume alternate logical constructions into the meta-logic of pure logic. Thus, Husserl

supposes that the lifeworld itself would constitute the corresponding manifold to pure

logical theory. Thus our task becomes more difficult. Not only must the possibility of

alternate logical systems be demonstrated but also their incapacity of propositional

translation into customary logical systems. The difficulty is heightened by the fact that an

alternate logic would of necessity either be absolutely closed (an impossibility) or part of a

meta-theory of its own (an unpalatable choice by virtue of its proximity to Husserls

universalism).

This dilemma can only be avoided if such an alternate theory defines a manifold other

than that of pure logic. This can be achieved only through undermining the universalistic

claim of Husserls argument for pure logic as a meta-theory. The weak points in Husserls


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argument, in order of increasing fruitfulness for our purpose are as follows: (a) the essential

impossibility of closure for axiomatic systems except through constraints which are extra-

essential under Husserls schema; (b) the questionable status of the primitive categories and

transformations; and most importantly (c) the somewhat circular relationship between

knowledge and things, truths and facts and the similar relationship between theoretical and

empirical science. It is (c) with which we will primarily concern ourselves, but before thus

proceeding, the first two will be briefly addressed.

First, although Husserls logic claims a far larger domain than the mathematical field

to which Goedels theorems strictly apply, their principles can be applied to it. This is to say

that because Husserls conception of pure logic is an axiomatic one, it is sufficiently formal,

whereas its corresponding field of applicability is not. The results thus yielded by the

application of Goedels theorems to Husserls logic consist in the admission that un-

assimilable facts will arise and that the corresponding knowledge will be true, but not

demonstrable (not necessarilyforming part of the meta-theory) and not yet having

corresponding laws of appearance and explanation, and that ifthe meta-theory is to be

augmented by axioms that account for the appearance of non-assimilated facts, the meta-

theory can be raised to another degree of abstraction (if the departure is radical enough,

otherwise it simply gains in complexity).

To address our second weak point in Husserls argument, we briefly note that most

categorial unities have multiple modalities that are subsumed in the concept of the category.

Substance, time and possession for example have multiple modalities, yet the a prioristatus

of the category is unchallenged by these modalities. These modalities are subsumed and

explained in terms of manifestation or expression. However, the apriority of the category is

not thereby brought into question. Of essential import here is that an interpretive choice


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determined the number and types of categorial objects, rather than an inherent apriority of

the category.

However, this second point will be addressed more fully in the course of the third.

The original givenness of the categories of thought is, according to Husserls account of

categorial intuition, a givenness of a higher order than the givenness of both mere sensuous

intuitions and categorial forms. This is set out in great clarity in section fifty-eight of the

Sixth Investigation. In this account intuition, consisting both of perception and imagination,

constitutes an ascension from lived-through perception of the real to the level of universal

categorial forms. It must be noted that while the universal categorial forms are founded

upon sensuous intuitions of lived-through experience; by means of an intermediate step and

a shift of objects of intuition, Husserl sets up this structure such that the universal categorial

forms do not refer back to or demand illustration from the lived-through experience which

serves as its foundation. Thus, when the level of universal categorial forms is attained, no

empirical verification is necessary or possible. It is with this structural formulation and its

associated problems that we proceed to the heart of my argument.

II.The Problem of Categorial Intuition

Before continuing, it would be particularly fruitful to recall the fundamental position

at which I have aimed, this time in the form of Husserls dismissal of this position. Husserl

writes:

It would further be possible to demonstrate ad nauseeumthe absurdity involved inconsidering thepossibilityof an illogical course of the world in signitive thought,thereby making this possibilityhold, and destroying in one breath, so to say, the lawswhich make this or any other possibility hold at all. We could also point out that acorrelation with perceivability, meanability and knowability, is inseparable from thesense of being in general, and that the ideal laws, therefore, which pertain to these


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possibilities in specie, can never be set aside by the contingent content of what itselfhappens to be at the moment.25

Furthermore, in the preceding section, Husserl advances the proposition that the universal

categorial forms constitute laws of thought in the strong sense, that they are absolutely

independent of contingent empirical reality yet related to empirical reality in a mode

altogether different from that of the signitive.A forteriori, he writes that An understanding

governed by other than the purely logical laws would be an understanding without

understanding.26 And as such, the universal categorial forms, such as conjunction,

disjunction, aggregate, totality, etc. are pure in the same sense as pure logic, and more

importantly in the freedom of categorial union and formation it still has its law-governed limits

How else could we speak of categorialperceptionand intuition, if nay conceivable matter could

be put into any conceivable form, and the underlying straightforward intuitions therefore

permitted themselves to be arbitrarily combined with categorial characters?27 And thus his

argument continues to its terminus in the assertion that while we may think any relation,

only particular relations can serve as foundational.

Husserls argument here distills to the following: that all categorial intuitions are

founded (whether or not they are foundational for further intuitions) in sensuous intuitions

(which are then founded in lived experience), and being forms of intuition (the concept of

which subsumes both perception and imagination) they must, in principle, be perceptible.

Thus, for categorial forms and a forteriori, universal categorial forms, which do not conform

to legal limitations must have as their condition of possibility some directly imperceptible

and unimaginable basis. Husserl then proceeds to make the rather questionable statement

25 Edmund Husserl,Logical Investigations Volume Two , Translated by J.N. Findlay, Edited by Dermott

Moran (New York and Lodon: Routledge, 2001), pg 31726 Ibid, pg 31527 Ibid, pg 309


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that nothing exists that cannot be perceived.28 Thus, if the entirety of the real is in

principle perceptible or imaginable, then this perceived world provides, in a sense, the

absolute ground of categorial forms and also grounds the law-governed limitations of the

same.

We may conclude this summation by pointing out that in section fifty-nine, Husserl

specifies this governing legality [as] the intuitive counterpart of the grammatical legality

of pure logic29 and that this governing legality

determines what variations in any given categorial forms there can be in relation to the samedefinite, but arbitrarily chosen, matter.They circumscribe the ideally closed manifoldof the rearrangements and transformations of categorial forms on the basis of

constant, selfsame matter [and that] The ideal conditions of categorial intuition ingeneral are the conditions of the possibility of the objects of categorial intuition, and of thepossibility ofcategorial objects simpliciter.30[boldface emphasis mine]

For now we must content ourselves to note that Husserl situates these laws of

transformation on precisely the same level as the laws or pure logic, while at the same time

retaining a distinction between the two corresponding to the distinction established between

acts of intuition and signification. It will be seen that this distinction is crucial to Husserl and

must be retained at all costs in order to avoid a circularity generated in the use of the

constituted legality in the constitution of the same, i.e. the elementary logical laws needed to

establish the intuition of universal categories are not constituted thereby but are rather

presupposed. The point worth noting is that the pure grammatical laws, being signitive and

lacking intuitive fullness, may yield constructions that are impossible. Thus, in this case, the

intuitive dimension serves to limit the signitive. It must also be noted that these laws which,

like those of pure logic, define a manifold that determines the legal transformations that may

serve as foundational.

28 Ibid, pg 30929 Ibid, pg 30430 Ibid, pg 311


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At this juncture, the preceding may seem disjointed and meandering. However, it is

precisely at this point where we may begin to clarify the difficulties inherent in Husserls use

of categorial intuition to obtain universally valid laws of thought. It is left ambiguous the

precise relation these laws of thought bear to the laws of pure logic. Moreover, it is left

unclear whether the laws governing the transformations and relations of categorial intuitions

are subsumed under the rubric of pure logic or constitute a wholly separate sphere. It is my

interpretation that the laws of transformation and relation constitute a subsidiary or parent

sphere to that of pure logic, while the universal categorial forms constitute those laws of

pure logic that pertain to the intuitive as opposed to the signitive. Most importantly, here we

must examine the structure and process of categorial intuition as outlined in chapter seven

of the Sixth Investigation.

At the conclusion to the abovementioned chapter, Husserl outlines the structure of

categorial intuition. In this structure, there are at least three levels, the first being that of the

un-reflected, straightforward intuition in which the intuited object is the same as the

intended object in its fullness. Husserls example here is that of a perceived house. At this

level, the intuited object is the house in its particularity At the next level, that of categorial

representation, the perception of this house gives way to the perception of the house in its

generality, that ofhouseness. The percept is at this level is the same as the last, but rather than

being addressed straightforwardly the concept ofhousenessis abstracted. Thus the perception

of a house yields the categorial form of House. At the third level, that of categorial intuition

as such, the percept is no longer the house naively pointed out in the first, but rather the

perception ofthis percept. Thus, intuition only truly becomes categorial and relatively

independent of its foundations at the level of reflection. Husserls argument is that by

reflectively objectifiying the preceding level, i.e. by taking for its percept not the house but


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the perception of the house, categorial intuition severs its inherent grounding in lived-

through reality by biting its own tail; it derives from the forms derived from foundational

intuitions. The categorially intuited forms are forms arising out of the forms, and not out of

the matters31 and thereby attain independence and universality in a two step process.

That which is important here is the fact that as a second degree abstraction from

straightforward intuition, categorially intuited forms and contents are no longer dependent

upon straightforward intuition by virtue of referring back the ideal contents and forms

yielded in categorial representation. These intuited forms of the third order, i.e. the results of

categorial intuitions operation upon the objectified representation, e.g. unity, plurality,

relation, concept, etc. are then purein the sense that they contain no sensuous concept in their whole

theoretical fabric,32 despite being founded originally in straightforward intuition. Thus, logical

operators, connectives, etc. are all given in the second degree of categorial intuition, thus

constituting the basic logical forms of pure logic and its law-governed legality.

III. Arguments

The problem that results is twofold, that is on one hand, this would seem to

subsume pure logic under the aegis of categorial intuition, while on the other, introducing an

even higher level of abstraction that also constitutes logical laws. That is, the aforementioned

laws of transformation and relation between categorially intuited objects, i.e. the laws

governing the transformations and relations between the categories of being and time, e.g.

coming into and passing out of being is governed by temporal laws, would only be possible

on the addition of another level of abstraction over the level of categorial intuition. It would

31 Ibid, pg 30432 Ibid, pg 307


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seem that an endless series of abstractions is possible in this structure (although higher order

structures become increasingly hard to conceptualize).

Furthermore, this apparent subsuming of pure logic to its constitution in categorial

intuition leads to a blurring in the distinction between the logico-grammatical laws of

signitive acts and the logic of intuitive acts beyond the hierarchical ambiguity of pure logic

and categorial intuition. That is, the logico-grammatical laws of signitive acts owe their

existence and possibility to categorial intuition and as such should not admit of the

thinkability of the impossible or illogical. If this were not trouble enough, Husserls assertion

of the absolute perceptability of the entirety of the real has become problematic due to

advances in physics. Many qualities and particles of the subatomic level are directly

imperceptible, only indirectly perceptible through statistical observation. These particles and

characteristics such as photons and electron spin must be observed statistically in order to

render them perceptible on the macroscopic level. All of the methods of quantum physics

rest on statistical observation. This is of crucial import: statistical observation serves as the

matrix of translation between quantum and classical physics, serving the same function as

curvature in space-like manifolds. Doubly important is the fact that on one hand, these

statistical measures are meant to eliminate logical contradictions such as photons

simultaneous behavior as both wave and particle or the absolute abstraction of the concept

of electron spin, while on the other doing so imperfectly. I say imperfectly because of recent

experimental demonstration ofsome sort of information transferexceeding the speed of light

between two entangled photons in an experimental re-creation of the Einstein-Podolsky-

Rosen Gedankenexperiment. Moreover, the most probable interpretation of these results is not

the invalidation of the limiting quality of the velocity of light, but rather the hypothesis of


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absolutely imperceptible mechanisms by which these correlated particles know the state of

the other.33

In this situation we are compelled to admit of the absolutely imperceptible whose

imperceptibility is guaranteed by laws governing relations and transformations on the

quantum level, which have no applicability in any other frame of reference (Heisenbergs

Uncertainty Principle governs the degree to which a particle may be known!). Further, we

also must regard the manifolds of quantum physics and classical physics as radically different

owing to the difficulties emerging from attempts at their correlation (the statistical method

sets absolute limits to the possibility of correlation and unification). This is to say that with

reference to modern physics, two distinct logical systems apply, one in which our and

Husserls logics apply, the other in which these logical forms radically do not apply. Even

more difficulty emerges from the Husserlian standpoint when it becomes clear that on the

quantum level, the elementary concept of the State of Affairs no longer applies, if only

because its modification alters less than applying it to the quantum level in which in a given

state of affairs the principles of identity and non-contradiction break down, along with

concepts such as unity, totality, state, etc. are altered or absolutely not applicable.

Thus physics has been deprived of a unitary manifold. If we are to use the term

physics henceforth, without qualification, this would effectively posit physics as such as a

meta-discipline subsuming the laws of quantum and classical physics and reconstituting a

unified manifold. Otherwise, the concept physics would simply be the juxtaposition of two

heterogeneous systems unified only in their common aim of describing the behavior of the

physical world. Both are in principle possible, the first demonstrating the incompletion of

33 Rowan G. Tepper The Experimental Demonstration of Quantum Mechanical Non-Locality and its

Consequences for Philosophy, May 2004, Goucher College/Johns Hopkins University.

Valerio scarani, Wolfgang Tittel, Hugo Zbinden, Nicolas Gisin The speed of quantum information and the

preferred frame analysis of experimental data. In Physics Letters A 276 (2000) 1-7.


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the two axiomatic systems a laGoedel, the second demonstrating the irreconcilable

heterogeneity of two logical systems.

It is the second possibility that I prefer. In this alternative, with two logical systems

differently applicable based upon the scale and nature of their domains, it is implicit that the

straightforward intuitive acts refer to a condition beyond their phenomenal object, i.e. scale

in order to determine which logical system is to be constituted in subsequent acts of

categorial abstraction and intuition. On a purely speculative level, were knowing entities to

exist on the quantum mechanical scale, the applicable laws of logic would be entirely alien to

ours. It must be noted that contraHusserls argument in section sixty-five, this speculative

hypothesis does not run afoul of the signtive-intuitive dichotomy; the foundational acts for

the constitution of this other world are accounted for and radically different from ours, and

furthermore do not require recourse to facticity to demonstrate quite simply, at a certain

point in scale the laws abruptly change. As foundational acts are present, so are founded

acts, witness the development of the laws of quantum theory, and as such independent,

universal categorial forms may emerge that differ from ours, i.e. perception is no longer a

passive act that leaves its object unchanged in reality, rather perception is an action which

necessarily disturbs and changes the object being perceived.

If this second alternative is denied, we are left with a contradiction that compels us

to higher levels of abstraction, to a meta-physics if you will, which on the level of pure logic

either implies the existence of a higher-order meta-logic or an incompleteness in its

constitutive axiomatic system. This approach has the advantage of retaining the unitary

status of logic, but only provisionally and, as it were, on credit. Faith in this approach implies

a positivistic faith in the progress of scientific capabilities and our capacity for knowing. Its

disadvantage is its provisional quality and its foundation on a positivistic faith that one day a


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openness. This is to say that accepting apriority and self-evidence on faith amounts to

abandoning the monolithic nature, if not the entire method of categorial intuition, essentially

opening it to the criticism of arbitrariness. The act that, as Husserl writes in section forty-

five, fulfills the categorial intention in the same manner as the sensuous no longer need be

categorial intuition, it might as well be the arbitrary grammatical structure of a natural

language or metaphor.

It would seem that of the alternatives presented for these dilemmas, Husserl would

be greatly inclined to opt for the alternatives that preserve the hypothetical Univocity of

logic to the manifold of the real at the expense of greater conceptual complexity, greater

abstraction and a theoretically open axiomatic system that may be closed by exhausting the

sum total of the phenomena of the real. However, this option is problematic at very least.

Due to the interpenetration of the signitive and the intuitive and their situation on the same

level of abstraction, albeit interrelated such that only the intuitive may constitute the signitive

and not vice versa, i.e. in expression they occupy the same theoretical level. Thus, with

reference to our final characterizations of pure logic in 1 the interpenetrating spheres of the

intuitive and the signitive constitute and neither are they closed systems or different levels of

theory. Thus the lacunae evident in logic and its correspondence to its correlated manifold

cannot be ascribed to incompatibilities between closed systems or differing levels of

signification and intuition. Moreover, the incompatibilities in physical systems mentioned

earlier demonstrates real lacunae both in transformation and relations between levels of the

real, which are not mirrored in logic and which cannot be accounted for on the theoretical

level in Husserls preferred alternative exceptby recourse to a positivistic faith in the

unlimited progress of science that will one day come up against the limits of the totality of

the real.


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IV. Conclusion

Little remains to be added. Husserl is forced the difficult alternatives of preserving

the unitary status of logic at the expense of opening the system to an unlimited increase in

complexity and levels of abstraction, while at the same time requiring both assumed a priori

logical primitives and a positivistic faith in scientific progress. The other set of alternatives,

on the basis of phenomena such as the disjunction between the quantum and classical

physical laws from which an alternative system of logic arises, implies at least one other

possiblelogical system.

According to Goedels Incompleteness Theorem, any axiomatic system can only be

closed by means of an axiom that is un-demonstrable within the system itself. In the case of

Euclidean geometry this axiom is that which states that space is in fact not curved. Given

this axiom the system of Euclidean geometry is closed; this axiom is implicit in all axioms of

the system. For classical physics this axiom is that which states that physical laws are

discernible directly through observation, i.e. scientifically assisted sense-experience. This is

true of all axiomatic systems that refer to reality. So it is with Husserls pure logic. He

attempts closure through the phenomenological appeal to the world as it appears. However,

this closure is doomed to failure in so far as phenomenal reality always exceeds the grasp of

conceptualization. Husserl lacks a means by which this remainder can be eliminated. Only

through his later insertion of the phenomenological reduction does Husserl escape this

difficulty, in essence through the abandonment of his strong claim of universality and

axiomaticity. Categorial intuition was no silver bullet for his difficulties; rather it became, for

Husserl, his soft underbelly.

on the impossibility of a unitary pure logic in husserl

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