IlluminationismFrom Wikipedia, the free encyclopedia

Contents

1 Conceptualism 11.1 Conceptualism in scholasticism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Modern conceptualism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3 Conceptualism and perceptual experience . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.4 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 Dialetheism 32.1 Motivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.1.1 Dialetheism resolves certain paradoxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.1.2 Dialetheism and human reasoning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.1.3 Apparent dialetheism in other philosophical doctrines . . . . . . . . . . . . . . . . . . . . 42.1.4 Dialetheism may be a more accurate model of the physical world . . . . . . . . . . . . . . 4

2.2 Formal consequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.3 Advantages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.4 Criticisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.5 Examples of True Contradictions that Dialetheists Accept . . . . . . . . . . . . . . . . . . . . . . 52.6 Modern Dialetheists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.7 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.8 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.9 Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.10 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3 Epilogism 73.1 Epilogism in popular culture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73.2 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73.3 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

4 Illuminationism 84.1 Early history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84.2 Iranian school of Illuminationism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94.3 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114.4 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

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4.5 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124.6 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

5 Logical holism 135.1 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

6 Panlogism 146.1 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

7 Polylogism 157.1 Types of polylogism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

7.1.1 Proletarian logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157.1.2 Racialist polylogism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

7.2 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167.3 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

8 Preintuitionism 178.1 The introduction of natural numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178.2 The principle of complete induction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178.3 Arguments over the excluded middle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188.4 Other Pre-Intuitionists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188.5 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

9 Ultrafinitism 199.1 Main ideas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199.2 People associated with ultrafinitism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199.3 Complexity theory based restrictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209.4 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209.6 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209.7 Text and image sources, contributors, and licenses . . . . . . . . . . . . . . . . . . . . . . . . . . 21

9.7.1 Text . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219.7.2 Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219.7.3 Content license . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Chapter 1

Conceptualism

For the postmodern art movement, see conceptual art.

Conceptualism is a philosophical theory that explains universality of particulars as conceptualized frameworks sit-uated within the thinking mind.[1] Intermediate between nominalism and realism, the conceptualist view approachesthe metaphysical concept of universals from a perspective that denies their presence in particulars outside of themind’s perception of them.[2]

1.1 Conceptualism in scholasticism

The evolution of late scholastic terminology has led to the emergence of Conceptualism, which stemmed from doc-trines that were previously considered to be nominalistic. The terminological distinction was made in order to stressthe difference between the claim that universal mental acts correspond with universal intentional objects and theperspective that dismissed the existence of universals outside of the mind. The former perspective of rejection ofobjective universality was distinctly defined as Conceptualism.Peter Abélard was a medieval thinker whose work is currently classified as having the most potential in representingthe roots of conceptualism. Abélard’s view denied the existence of determinate universals within things, proposingthe claim that meaning is constructed solely by the virtue of conception.[3] William of Ockham was another famouslate medieval thinker who had a strictly conceptualist solution to the metaphysical problem of universals. He arguedthat abstract concepts have no fundamentum outside the mind, and that the purpose they serve is the construction ofmeaning in an otherwise meaningless world.[4]

In the 17th century conceptualism gained favour for some decades especially among the Jesuits: Hurtado deMendoza,Rodrigo de Arriaga and Francisco Oviedo are the main figures. Although the order soon returned to the more realistphilosophy of Francisco Suárez, the ideas of these Jesuits had a great impact on the contemporary early modernthinkers.

1.2 Modern conceptualism

Conceptualism was either explicitly or implicitly embraced by most of the early modern thinkers like René Descartes,John Locke or Gottfried Leibniz – often in a quite simplified form if compared with the elaborate Scholastic the-ories. Sometimes the term is applied even to the radically different philosophy of Kant, who holds that universalshave no connection with external things because they are exclusively produced by our a priori mental structures andfunctions.[5] However, this application of the term “conceptualism” is not very usual, since the problem of universalscan, strictly speaking, be meaningfully raised only within the framework of the traditional, pre-Kantian epistemology.

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1.3 Conceptualism and perceptual experience

Though separate from the historical debate regarding the status of universals, there has been significant debate re-garding the conceptual character of experience since the release of Mind and World by John McDowell in 1994.[6]McDowell’s touchstone is the famous refutation that Wilfrid Sellars provided for what he called the “Myth of theGiven”—the notion that all empirical knowledge is based on certain assumed or 'given' items, such as sense data.[7]Thus, in rejecting the Myth of the Given, McDowell argues that perceptual content is conceptual “from the groundup”, that is, all perceptual experience is a form of conceptual experience. Put differently, there are no “bare” or“naked” sense data that serve as a foundation for all empirical knowledge—McDowell is not a foundationalist aboutperceptual knowledge.A clear motivation of conceptualism, in this sense, is that the kind of perception that rational creatures like humansenjoy is unique in the fact that it has conceptual character. McDowell explains his position in a recent paper as:

I have urged that our perceptual relation to the world is conceptual all the way out to the world’simpacts on our receptive capacities. The idea of the conceptual that I mean to be invoking is to beunderstood in close connection with the idea of rationality, in the sense that is in play in the traditionalseparation ofmature human beings, as rational animals, from the rest of the animal kingdom. Conceptualcapacities are capacities that belong to their subject’s rationality. So another way of putting my claimis to say that our perceptual experience is permeated with rationality. I have also suggested, in passing,that something parallel should be said about our agency.[8]

McDowell’s conceptualism, though rather distinct (philosophically and historically) from conceptualism’s genesis,shares the view that universals are not “given” in perception from outside of the sphere of reason. Particular objectsare perceived, as it were, already infused with conceptuality stemming the spontaneity of the rational subject herself.

1.4 See also• Problem of universals

• Pierre Abélard

• Conceptual art

• Lyco art (Lyrical Conceptualism), term coined by artist Paul Hartal

• Philosophical realism

• Conceptual architecture

1.5 References[1] See articles in Strawson, P. F. and Arindam Chakrabarti (eds.), Universals, concepts and qualities: new essays on the

meaning of predicates. Ashgate Publishing, 2006.

[2] “Conceptualism.” The Oxford Dictionary of Philosophy. Simon Blackburn. Oxford University Press, 1996. Oxford Ref-erence Online. Oxford University Press. 8 April 2008.

[3] “Aune, Bruce. “Conceptualism.” Metaphysics: the elements. U of Minnesota Press, 1985. 54.

[4] “Turner, W. "William of Ockham." The Catholic Encyclopedia. Vol. 15. New York: Robert Appleton Company, 1911.27 Oct. 2011

[5] “De Wulf, Maurice. "Nominalism, Realism, Conceptualism." The Catholic Encyclopedia. Vol. 11. New York: RobertAppleton Company, 1911. 27 Oct. 2011

[6] McDowell, John (1994). Mind and World. Cambridge: Harvard University Press. ISBN 978-0-674-57610-0.

[7] “Wilfrid Sellars”. Retrieved 2013-05-24.

[8] McDowell, J. (2007). “What Myth?". Inquiry 50 (4): 338–351. doi:10.1080/00201740701489211.

Chapter 2

Dialetheism

Dialetheism is the view that some statements can be both true and false simultaneously. More precisely, it is thebelief that there can be a true statement whose negation is also true. Such statements are called “true contradictions",dialetheia, or nondualisms.Dialetheism is not a system of formal logic; instead, it is a thesis about truth that influences the construction of aformal logic, often based on pre-existing systems. Introducing dialetheism has various consequences, depending onthe theory into which it is introduced. For example, in traditional systems of logic (e.g., classical logic and intuitionisticlogic), every statement becomes true if a contradiction is true; this means that such systems become trivialist whendialetheism is included as an axiom. Other logical systems do not explode in this manner when contradictions areintroduced; such contradiction-tolerant systems are known as paraconsistent logics.Graham Priest defines dialetheism as the view that there are true contradictions.[1] JC Beall is another advocate; hisposition differs from Priest’s in advocating constructive (methodological) deflationism regarding the truth predicate.[2]

2.1 Motivations

2.1.1 Dialetheism resolves certain paradoxes

The Liar’s paradox and Russell’s paradox deal with self-contradictory statements in classical logic and naïve settheory, respectively. Contradictions are problematic in these theories because they cause the theories to explode—ifa contradiction is true, then every proposition is true. The classical way to solve this problem is to ban contradictorystatements, to revise the axioms of the logic so that self-contradictory statements do not appear. Dialetheists, on theother hand, respond to this problem by accepting the contradictions as true. Dialetheism allows for the unrestrictedaxiom of comprehension in set theory, claiming that any resulting contradiction is a theorem.[3]

2.1.2 Dialetheism and human reasoning

Ambiguous situations may cause humans to affirm both a proposition and its negation. For example, if John standsin the doorway to a room, it may seem reasonable both to affirm that John is in the room and to affirm that John is notin the room.Critics argue that this merely reflects an ambiguity in our language rather than a dialetheic quality in our thoughts; ifwe replace the given statement with one that is less ambiguous (such as “John is halfway in the room” or “John is inthe doorway”), the contradiction disappears. The statements appeared contradictory only because of a syntactic play;here, the actual meaning of “being in the room” is not the same in both instances, and thus each sentence is not theexact logical negation of the other: therefore, they are not necessarily contradictory.The inadequacy of dialetheism to model human thoughts is shown by the appearance of cognitive dissonances whenfacing real contradictions.

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2.1.3 Apparent dialetheism in other philosophical doctrines

The Jain philosophical doctrine of anekantavada— non-one-sidedness— states that[4] all statements are true in somesense and false in another. Some interpret this as saying that dialetheia not only exist but are ubiquitous. Technically,however, a logical contradiction is a proposition that is true and false in the same sense; a proposition which is true inone sense and false in another does not constitute a logical contradiction. (For example, although in one sense a mancannot both be a “father” and “celibate”, there is no contradiction for a man to be a spiritual father and also celibate;the sense of the word father is different here. In another example, although at the same time George W. Bush cannotboth be President and not be President, he was President from 2001-2009, but was not President before 2001 or after2009, so in different times he was both President and not President.)The Buddhist logic system namedCatuṣkoṭi similarly implies that a statement and its negationmay possibly co-exist.[5][6]

Graham Priest argues in Beyond the Limits of Thought that dialetheia arise at the borders of expressibility, in a numberof philosophical contexts other than formal semantics.

2.1.4 Dialetheism may be a more accurate model of the physical world

This is a new area of study, so ideas are only just coming to light, but dialetheism allows the possibility that naturalthings may have contradictory properties. Whether Wave–particle duality is one such case is not established, but it isa possibility Are there non-semantic dialethia

2.2 Formal consequences

In some logics, we can show that taking a contradiction p ∧ ¬p as a premise (that is, taking as a premise the truth ofboth p and ¬p ), we can prove any statement q . Indeed, since p is true, the statement p∨q is true (by generalization).Taking p ∨ q together with ¬p is a disjunctive syllogism from which we can conclude q . (This is often called theprinciple of explosion, since the truth of a contradiction makes the number of theorems in a system “explode”.)Because dialetheists accept true contradictions, they reject that logic alone can prove anything at all because anythingat all is possible. According to dialetheists, evidence is always needed, and we cannot conclude anything for certainoutside of our own immediate experiences, which cannot be described perfectly with words.

2.3 Advantages

The proponents of dialetheism mainly advocate its ability to avoid problems faced by other more orthodox resolutionsas a consequence of their appeals to hierarchies. Graham Priest once wrote “the whole point of the dialetheic solutionto the semantic paradoxes is to get rid of the distinction between object language and meta-language”.[1]

There are also dialetheic solutions to the sorites paradox.

2.4 Criticisms

One important criticism of dialetheism is that it fails to capture something crucial about negation and, consequently,disagreement. Imagine John’s utterance of P. Sally’s typical way of disagreeing with John is a consequent utterance of¬P. Yet, if we accept dialetheism, Sally’s so uttering does not prevent her from also accepting P; after all, P may be adialetheia and therefore it and its negation are both true. The absoluteness of disagreement is lost. The dialetheist canrespond by saying that disagreement can be displayed by uttering "¬P and, furthermore, P is not a dialetheia”. Again,though, the dialetheist’s own theory is his Achilles’ heel: the most obvious codification of "P is not a dialetheia” is¬(P & ¬P). But what if this itself is a dialetheia as well? One dialetheist response is to offer a distinction betweenassertion and rejection. This distinction might be hashed out in terms of the traditional distinction between logicalqualities, or as a distinction between two illocutionary speech acts: assertion and rejection. Another criticism is thatdialetheism cannot describe logical consequences because of its inability to describe hierarchies.[1]

2.5. EXAMPLES OF TRUE CONTRADICTIONS THAT DIALETHEISTS ACCEPT 5

2.5 Examples of True Contradictions that Dialetheists Accept

According to dialetheists, there are some truths that can only be expressed in contradiction. Some examples include:The only certain knowledge we have outside of our immediate experience is that there is no certain knowledge outsideof our immediate experience.“All statements are false” is a true statement.“There are no absolutes” is an absolute.According to dialetheists, these statements are not derived from logic (which they say is false), but are instead de-scriptions of experience.

2.6 Modern Dialetheists

Many modern Zen Buddhists are dialetheists. They use the term nondualism to refer to true contradictions.

2.7 See also• Problem of future contingents

• Leibniz's compossibility

• Liar paradox

• Doublethink

• Trivialism

2.8 References[1] Whittle, Bruno. “Dialetheism, logical consequence and hierarchy.” Analysis Vol. 64 Issue 4 (2004): 318–326.

[2] Jc Beall in The Law of Non-Contradiction: New Philosophical Essays (Oxford: Oxford University Press, 2004), pp. 197–219.

[3] Transfinite Numbers in Paraconsistent Set Theory (Review of Symbolic Logic 3(1), 2010), pp. 71-92..

[4] Matilal, Bimal Krishna. (1998), “The character of logic in India” (Albany, State University of New York press), 127-139

[5] http://www.iep.utm.edu/nagarjun/#H2

[6] ed : Ganeri, J. (2002), “The Collected Essays of Bimal Krishna Matilal: Mind, Language and World” (Oxford UniversityPress), 77-79

2.9 Sources• Frege, Gottlob. “Negation.” Logical Investigations. Trans. P. Geach and R. H Stoothoff. New Haven, Conn.:Yale University Press, 1977. 31–53.

• Parsons, Terence. “Assertion, Denial, and the Liar Paradox.” Journal of Philosophical Logic 13 (1984): 137–152.

• Parsons, Terence. “True Contradictions.” Canadian Journal of Philosophy 20 (1990): 335–354.

• Priest, Graham. In Contradiction. Dordrecht: Martinus Nijhoff (1987). (Second Edition, Oxford: OxfordUniversity Press, 2006.)

• Priest, Graham. “What Is So Bad About Contradictions?" Journal of Philosophy 95 (1998): 410–426.

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2.10 External links• Francesco Berto and Graham Priest. Dialetheism. In the Stanford Encyclopedia of Philosophy.

• JC Beall UCONN Homepage

• (Blog & ~Blog)

• Dialethiesm Web Page

• Kabay on dialetheism and trivialism (includes both published and unpublished works)

Chapter 3

Epilogism

Epilogism is a style of Inference invented by the ancient Empiric school of medicine. It is a theory-free methodof looking at history by accumulating fact with minimal generalization and being conscious of the side effects ofmaking causal claims (See also Causal inference). Epilogism is an inference which moves entirely within the domainof visible and evident things, it tries not to invoke unobservables. It is tightly knit to the famous “tripos of medicine”.See also Doctrines of the Empiric school.

3.1 Epilogism in popular culture

Epilogism is discussed as a way of viewing history in The Black Swan (Taleb book) by Nassim Nicholas Taleb.

3.2 See also• Transduction (machine learning)

3.3 External links• http://bmcr.brynmawr.edu/2004/2004-12-20.html

• repository.kulib.kyoto-u.ac.jp/dspace/bitstream/2433/24239/1/nishimura.pdf

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Chapter 4

Illuminationism

Illuminationism is a doctrine according to which the process of human thought needs to be aided by divine grace. It isthe oldest and most influential alternative to naturalism in the theory of mind and epistemology.[1] It was an importantfeature of ancient Greek philosophy, Neoplatonism, medieval philosophy, and in particular, the Illuminationist schoolof Islamic philosophy.

4.1 Early history

Socrates says in The Apology that he had a divine or spiritual sign that began when he was a child. It was a voicethat turned him away from something he was about to do, although it never encouraged him to do anything. Apuleiuslater suggested the voice was of a friendly demon [2] and that Socrates deserved this help as he was the most perfectof human beings.The early Christian philosopher Augustine (354 – 430) also emphasised the role of divine illumination in our thought,saying that “The mind needs to be enlightened by light from outside itself, so that it can participate in truth, because itis not itself the nature of truth. You will light my lamp, Lord [3] and “You hear nothing true from me which you havenot first told me.[4] Augustine’s version of illuminationism is not that God gives us certain information, but rathergives us insight into the truth of the information we received for ourselves.

If we both see that what you say is true, and we both see that what I say is true, then where do we seethat? Not I in you, nor you in me, but both of us in that unalterable truth that is above our minds.[5]

Augustine’s theory was defended by Christian philosophers of the later Middle Ages, particularly Franciscans suchas Bonaventura and Matthew of Aquasparta. According to Bonaventura:

Things have existence in the mind, in their own nature (proprio genere), and in the eternal art. So thetruth of things as they are in themind or in their own nature – given that both are changeable – is sufficientfor the soul to have certain knowledge only if the soul somehow reaches things as they are in the eternalart.[6]

The doctrine was criticised by John Pecham and Roger Marston, and in particular by Thomas Aquinas, who deniedthat in this life we have divine ideas as an object of thought, and that divine illumination is sufficient on its own,without the senses. Aquinas also denied that there is a special continuing divine influence on human thought. Peo-ple have sufficient capacity for thought on their own, without needing “new illumination added onto their naturalillumination”.[7]

The theory was defended by Henry of Ghent. Henry argued against Aquinas that Aristotle’s theory of abstractionis not enough to explain how we can acquire infallible knowledge of the truth, and must be supplemented by divineillumination. A thing has two exemplars against which it can be compared. The first is a created exemplar whichexists in the soul. The second is an exemplar which exists outside the soul, and which is uncreated and eternal. But nocomparison to a created exemplar can give us infallible truth. Since the dignify of man requires that we can acquiresuch truth, it follows that we have access to the exemplar in the divine mind.[8]

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4.2. IRANIAN SCHOOL OF ILLUMINATIONISM 9

Socrates

Henry’s defence of illuminationism was strongly criticised by the Franciscan theologian Duns Scotus, who arguedthat Henry’s version of the theory led to scepticism.

4.2 Iranian school of Illuminationism

Influenced by Avicennism and Neoplatonism, the Persian[9][10][11][12] or Kurdish,[13][14][15][16] philosopher Shahabal-Din Suhrawardi (1155–1191), who left over 50 writings in Persian and Arabic, founded the school of Illumination.He developed a version of illuminationism (Persian اشراق حكمت hikmat-i ishrāq, Arabic: الإشراق حكمة ḥikmat al-ishrāq). The Persian and Islamic school draws on ancient Iranian philosophical disciplines,[17][18] Avicennism (IbnSina’s early Islamic philosophy), Neoplatonic thought (modified by Ibn Sina), and the original ideas of Suhrawardi.In his Philosophy of Illumination, Suhrawardi argued that light operates at all levels and hierarchies of reality (PI,97.7–98.11). Light produces immaterial and substantial lights, including immaterial intellects (angels), human andanimal souls, and even 'dusky substances’, such as bodies.[19]

10 CHAPTER 4. ILLUMINATIONISM

Augustine

Suhrawardi’s metaphysics is based on two principles. The first is a form of the principle of sufficient reason. Thesecond principle is Aristotle’s principle that an actual infinity is impossible.[20]

None of Suhrawardi’s works were translated into Latin, and so he remained unknown in the Latin West, although hiswork continued to be studied in the Islamic East.[21]

4.3. SEE ALSO 11

4.3 See also• Augustine• Bonaventure• Henry of Ghent• Duns Scotus• Iranian philosophy• Early Islamic philosophy• Light (theology)• Mulla Sadra• Enlightenment (spiritual)

4.4 Notes[1] Stanford Encyclopedia of Philosophy

[2] De deo Socratis, XVII–XIX)

[3] Confessions IV.xv.25

[4] Confessions X.ii.2

[5] Confessions XII.xxv.35

[6] De scientia Christi, q.4 resp

[7] Summa theologiae 1a2ae 109.1c

[8] A Companion to Philosophy in the Middle Ages, ed. Gracia and Noone

[9] John Walbridge, “The leaven of the ancients: Suhrawardī and the heritage of the Greeks”, State University of New YorkPress, 1999. Excerpt: “Suhrawardi, a 12th-century Persian philosopher, was a key figure in the transition of Islamic thoughtfrom the neo-Aristotelianism of Avicenna to the mystically oriented philosophy of later centuries.”

[10] Seyyed Hossein Nasr, “The need for a sacred science”, SUNY Press, 1993. Pg 158: “Persian philosopher Suhrawardi refersin fact to this land as na-kuja abad, which in Persian means literally utopia.”

[11] Matthew Kapstein, University of Chicago Press, 2004, “The presence of light: divine radiance and religious experience”,University of Chicago Press, 2004. pg 285:"..the light of lights in the system of the Persian philosopher Suhrawardi”

[12] Hossein Ziai. Illuminationsim or Illuminationist philosophy, first introduced in the 12th century as a complete, reconstructedsystem distinct both from the Peripatetic philosophy of Avicenna and from theological philosophy. in: Encyclopaedia Iranica.Volumes XII & XIII. 2004.

[13] R. Izady, Mehrdad (1991). The Kurds: a concise handbook.

[14] Kamāl, Muḥammad (2006). Mulla Sadra’s transcendent philosophy.

[15] =C. E. Butterworth, M. Mahdi, The Political Aspects of Islamic Philosophy, Harvard CMES Publishers, 406 pp., 1992,ISBN 0-932885-07-1 (see p.336)

[16] M. Kamal, Mulla Sadra’s Transcendent Philosophy, p.12, Ashgate Publishing Inc., 136 pp., 2006, ISBN 0-7546-5271-8(see p.12)

[17] Henry Corbin. The Voyage and the Messenger. Iran and Philosophy. Containing previous unpublished articles and lecturesfrom 1948 to 1976. North Atlantic Books. Berkeley, California. 1998. ISBN 1-55643-269-0.

[18] Henry Corbin. The Man of Light in Iranian Sufism. Omega Publications, New York. 1994. ISBN 0-930872-48-7.

[19] Philosophy of Illumination 77.1–78.9

[20] Philosophy of Illumination 87.1–89.8

[21] Marcotte, Roxanne, “Suhrawardi”, The Stanford Encyclopedia of Philosophy (Summer 2012 Edition), Edward N. Zalta(ed.), URL = <http://plato.stanford.edu/archives/sum2012/entries/suhrawardi/>.

12 CHAPTER 4. ILLUMINATIONISM

4.5 Further reading• Suhrawardi and the School of Illumination by Mehdi Amin Razavi

• Islamic Intellectual Tradition in Persia by Seyyed Hossein Nasr

4.6 External links• Stanford Encyclopedia of Philosophy, Divine Illumination

• Encyclopedia Britannica, Epistemology (philosophy)

• Augustine Stanford Encyclopedia of Philosophy

• Duns Scotus Stanford Encyclopedia of Philosophy

• suhrawardi Stanford Encyclopedia of Philosophy

• Illuminationist philosophy

Chapter 5

Logical holism

Logical holism is the belief that the world operates in such a way that no part can be known without the whole beingknown first.

5.1 See also• The doctrine of internal relations

• Holography

1. In optics:holography

2. In metaphysics:holonomic brain theory, holographic paradigm and The Holographic Universe (MichaelTalbot’s book)

Proponents: Michael Talbot, David Bohm, Karl H. Pribram

• 1. In quantum mechanics:holographic principle (the conjecture that all of the information about the realities in a volumeof space is present on the surface of that volume)

Proponents: Gerard 't Hooft, Leonard Susskind, John A. Wheeler

13

Chapter 6

Panlogism

In philosophy, panlogism is a Hegelian doctrine that holds that the universe is the act or realization of Logos.[1][2]According to the doctrine of panlogism, logic and ontology are the same study.[3]

6.1 References[1] “Dagobert D. Runes, Dictionary of Philosophy, 1942” Retrieved September 1, 2009

[2] “Panlogism” at the free dictionary Retrieved September 1, 2009

[3] “Panlogism” at About.com Retrieved September 1, 2009

14

Chapter 7

Polylogism

Polylogism is the belief that different groups of people reason in fundamentally different ways (coined from Greekpoly=many + logos=logic).[1] The term is attributed to Ludwig von Mises,[2] who claimed that it described Marxismand other social philosophies.[3] In the Misesian sense of the term, a polylogist ascribes different forms of “logic” todifferent groups, which may include groups based on race,[1][4] gender, class, or time period.

7.1 Types of polylogism

A polylogist would claim that different groups reason in fundamentally different ways: they use different “logics”for deductive inference. Normative polylogism is the claim that these different logics are equally valid. Descriptivepolylogism is an empirical claim about different groups, but a descriptive polylogism need not claim equal validity fordifferent “logics”.[5] That is, a descriptive polylogist may insist on a universally valid deductive logic while claimingas an empirical matter that some groups use other (incorrect) reasoning strategies.An adherent of polylogism in the Misesian sense would be a normative polylogist. A normative polylogist mightapproach an argument by demonstrating how it was correct within a particular logical construct, even if it wereincorrect within the logic of the analyst. AsMises noted “this never has been and never can be attempted by anybody.”

7.1.1 Proletarian logic

The term 'proletarian logic' is sometimes taken as evidence of polylogism.[6] This term is usually traced back to JosephDietzgen in his 11th letter on logic.[7][8] Dietzgen is the now obscure philosophical monist of the 19th century whocoined the term 'dialectical materialism' and was praised by communist figures such as Karl Marx and V. I. Lenin.[9]His work has received modern attention primarily from the philosopher Bertell Ollman. As a monist, Dietzgen insistson a unified treatment of mind and matter. As Simon Boxley puts it, for Dietzgen “thought is as material an eventas any other”. This means that logic too has “material” underpinnings. (But note that Dietzgen’s “materialism” wasexplicitly not a physicalism.)

7.1.2 Racialist polylogism

Racialist polylogism is often identified with the Nazi era. It has been proposed that the ferment around Einstein’stheory of relativity is an example of racialist polylogism. Some of the criticisms of relativity theory were mixedwith racialist resistance that characterized the physics as an embodiment of Jewish ideology. (For example, NobelPrize winner Philipp Lenard claimed scientific thought was conditioned by “blood and race”, and he accused WernerHeisenberg of teaching "Jewish physics".[10]) However this appears to be an argument ad hominem, not polylogism.Modern examples of supposed racialist polylogism are generally misleading. For example, US Supreme Court JusticeSotomayor has been accused of racialist polylogism for suggesting that a “wise Latina” might come to different legalconclusions than a white male. Although generally given the interpretation that life experience can influence one’sability to understand the practical implications of a legal argument, some commentators suggested that Sotomayorsupported the idea that Latinas have a unique “logic”.[11][12]

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16 CHAPTER 7. POLYLOGISM

7.2 References[1] Percy L. Greaves Jr. (1974). “Glossary, Panphysicalism - Pump-priming”. Mises Made Easier. Retrieved 2011-01-13.

[2] Perrin, Pierre (2005). “Hermeneutic economics: Between relativism and progressive polylogism”. Quarterly Journal ofAustrian Economics 8 (3). pp. 21–38. doi:10.1007/s12113-005-1032-3.

[3] Ludwig von Mises. “Chapter 3, Section 1”. Human Action (PDF) (1996 ed.). pp. 72–75.

[4] Alexander Moseley (2002). A Philosophy of War. Algora Publishing. p. 239. ISBN 978-1-892941-94-7.

[5] Roderick Long. “Anti-Psychologism in Economics: Wittgenstein and Mises” (PDF).

[6] " “Polylogism”.

[7] Emmett, Dorothy (1928). “Joseph Dietzgen: The Philosopher of Proletarian Logic”. Journal of Adult Education 3. pp.26–35.

[8] The Positive Outcome of Philosophy; Letters on Logic, Especially Democratic Proletarian Logic.

[9] A Dictionary of Marxist thought

[10] Joseph W. Bendersky (2000). A history of Nazi Germany: 1919-1945. p. 140.

[11] Rich Lowry. “How Sotomayor Misspoke”.

[12] Peter Wehner. “Judge Sotomayor, in Her Own Words”.

• Boxley, Simon, (2008), Red, Black andGreen: Dietzgen’s PhilosophyAcross theDivide. http://www.anarchist-studies-network.org.uk/documents/Conference%20Papers/Simon%20Boxley.doc

• Ollman, B. (1976) Alienation: Marx’s Conception of Man in Capitalist Society, Cambridge: Cambridge Uni-versity Press

• Ollman, B. (2003a) Dance of the Dialectic: Steps in Marx’s Method, Chicago: University of Illinois Press

• Ollman, B. (2003b) ‘Marx’s Dialectical Method is more than a Mode of Exposition: A Critique of SystematicDialectics’ in Albritton, R. & Siloulidis, J. (Eds.) NewDialectics and Political Economy, Basingstoke: PalgraveMacmillan

• Perrin, Pierre, “Hermeneutic economics: Between relativism and progressive polylogism”, Quarterly Journalof Austrian Economics, Volume 8, Number 3, 21-38, doi:10.1007/s12113-005-1032-3

7.3 External links• Theory and History by Ludwig von Mises, for an exposition.

Chapter 8

Preintuitionism

In themathematical philosophy, the pre-intuitionistswere a small but influential group who informally shared similarphilosophies on the nature of mathematics. The term itself was used by L. E. J. Brouwer, who in his 1951 lectures atCambridge described the differences between intuitionism and its predecessors:

Of a totally different orientation [from the “Old Formalist School” of Dedekind, Cantor, Peano,Zermelo, andCouturat, etc.] was the Pre-Intuitionist School, mainly led by Poincaré, Borel and Lebesgue.These thinkers seem to have maintained a modified observational standpoint for the introduction ofnatural numbers, for the principle of complete induction [...] For these, even for such theorems aswere deduced by means of classical logic, they postulated an existence and exactness independent oflanguage and logic and regarded its non-contradictority as certain, even without logical proof. For thecontinuum, however, they seem not to have sought an origin strictly extraneous to language and logic.

8.1 The introduction of natural numbers

The Pre-Intuitionists, as defined by Brouwer, differed from the Formalist standpoint in several ways, particularly inregard to the introduction of natural numbers, or how the natural numbers are defined/denoted. For Poincaré, thedefinition of a mathematical entity is the construction of the entity itself and not an expression of an underlyingessence or existence.This is to say that no mathematical object exists without human construction of it, both in mind and language.

8.2 The principle of complete induction

This sense of definition allowed Poincaré to argue with Bertrand Russell over Giuseppe Peano’s axiomatic theory ofnatural numbers.Peano’s fifth axiom states:

• Allow that; zero has a property P;

• And; if every natural number less than a number x has the property P then x also has the property P.

• Therefore; every natural number has the property P.

This is the principle of complete induction, which establishes the property of induction as necessary to the system.Since Peano’s axiom is as infinite as the natural numbers, it is difficult to prove that the property of P does belong toany x and also x+1. What one can do is say that, if after some number n of trials that show a property P conserved inx and x+1, then we may infer that it will still hold to be true after n+1 trials. But this is itself induction. And hencethe argument is a vicious circle.From this Poincaré argues that if we fail to establish the consistency of Peano’s axioms for natural numbers withoutfalling into circularity, then the principle of complete induction is not provable by general logic.

17

18 CHAPTER 8. PREINTUITIONISM

Thus arithmetic and mathematics in general is not analytic but synthetic. Logicism thus rebuked and Intuition is heldup. What Poincaré and the Pre-Intuitionists shared was the perception of a difference between logic and mathematicswhich is not a matter of language alone, but of knowledge itself.

8.3 Arguments over the excluded middle

It was for this assertion, among others, that Poincaré was considered to be similar to the intuitionists. For Brouwerthough, the Pre-Intuitionists failed to go as far as necessary in divesting mathematics from metaphysics, for they stillused principium tertii exclusi (the "Law of excluded middle").The principle of the excluded middle does lead to some strange situations. For instance, statements about the futuresuch as “There will be a naval battle tomorrow” do not seem to be either true or false, yet. So there is some questionwhether statements must be either true or false in some situations. To an intuitionist this seems to rank the law ofexcluded middle as just as unrigorous as Peano’s vicious circle.Yet to the Pre-Intuitionists this is mixing apples and oranges. For them mathematics was one thing (a muddledinvention of the human mind (aka. synthetic)), and logic was another (analytic).

8.4 Other Pre-Intuitionists

The above examples only include the works of Poincaré, and yet Brouwer named other mathematicians as Pre-Intuitionists too; Borel and Lebesgue. Other mathematicians such as Hermann Weyl (who eventually became disen-chanted with intuitionism, feeling that it places excessive strictures on mathematical progress) and Leopold Kroneckeralso played a role - though they are not cited by Brouwer in his definitive speech.In fact Kronecker might be the most famous of the Pre-Intuitionists for his singular and oft quoted phrase, “Godmade the natural numbers; all else is the work of man.”Kronecker goes in almost the opposite direction from Poincaré, believing in the natural numbers but not the law ofthe excluded middle. He was the first mathematician to express doubt on non-constructive existence proofs. That is,proofs that show that something must exist because it can be shown that it is “impossible” for it not to.

8.5 External links• Logical Meanderings - a brief article by Jan Sraathof on Brouwer's various attacks on arguments of the Pre-Intuitionists about the Principle of the Excluded Third.

• Proof And Intuition - an article on themany varieties of knowledge as they relate to the Intuitionist and Logicist.

• Brouwer’s Cambridge Lectures on Intuitionism - Wherein Brouwer talks about the Pre-Intuitionist School andaddresses what he sees as its many shortcomings.

Chapter 9

Ultrafinitism

In the philosophy of mathematics, ultrafinitism, also known as ultraintuitionism, strict-finitism, actualism, andstrong-finitism is a form of finitism. There are various philosophies of mathematics that are called ultrafinitism.A major identifying property common among most of these philosophies is their objections to totality of numbertheoretic functions like exponentiation over natural numbers.

9.1 Main ideas

Like other strict finitists, ultrafinitists deny the existence of the infinite set N of natural numbers, on the grounds thatit can never be completed.In addition, some ultrafinitists are concerned with acceptance of objects in mathematics that no one can constructin practice because of physical restrictions in constructing large finite mathematical objects. Thus some ultrafinitistswill deny or refrain from accepting the existence of large numbers, for example, the floor of the first Skewes’ number,which is a huge number defined using the exponential function as exp(exp(exp(79))), or

eee79 .

The reason is that nobody has yet calculated what natural number is the floor of this real number, and it may noteven be physically possible to do so. Similarly, 2 ↑↑↑ 6 (in Knuth’s up-arrow notation) would be considered only aformal expression which does not correspond to a natural number. The brand of ultrafinitism concerned with physicalrealizability of mathematics is often called actualism.Edward Nelson criticized the classical conception of natural numbers because of the circularity of its definition. Inclassical mathematics the natural numbers are defined as 0 and numbers obtained by the iterative applications of thesuccessor function to 0. But the concept of natural number is already assumed for the iteration. In other words, toobtain a number like 2 ↑↑↑ 6 one needs to perform the successor function iteratively, in fact exactly 2 ↑↑↑ 6 times to0.Some versions of ultrafinitism are forms of constructivism, but most constructivists view the philosophy as unworkablyextreme. The logical foundation of ultrafinitism is unclear; in his comprehensive survey Constructivism inMathematics(1988), the constructive logician A. S. Troelstra dismissed it by saying “no satisfactory development exists at present.”This was not so much a philosophical objection as it was an admission that, in a rigorous work of mathematical logic,there was simply nothing precise enough to include.

9.2 People associated with ultrafinitism

Serious work on ultrafinitism has been led, since 1959, by Alexander Esenin-Volpin, who in 1961 sketched a programfor proving the consistency of ZFC in ultrafinite mathematics. Other mathematicians who have worked in the topicinclude Doron Zeilberger, Edward Nelson, and Rohit Jivanlal Parikh. The philosophy is also sometimes associatedwith the beliefs of Ludwig Wittgenstein, Robin Gandy, and J. Hjelmslev.

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20 CHAPTER 9. ULTRAFINITISM

Shaughan Lavine has developed a form of set-theoretical ultra-finitism that is consistent with classical mathematics.[1]Lavine has shown that the basic principles of arithmetic such as “there is no largest natural number” can be upheld,as Lavine allows for the inclusion of “indefinitely large” numbers. [2]

9.3 Complexity theory based restrictions

Other considerations of the possibility of avoiding unwieldy large numbers can be based on computational complexitytheory, as in Andras Kornai's work on explicit finitism (which does not deny the existence of large numbers[3]) andVladimir Sazonov's notion of feasible number.There has also been considerable formal development on versions of ultrafinitism that are based on complexity theory,like Samuel Buss's Bounded Arithmetic theories, which capture mathematics associated with various complexityclasses like P and PSPACE. Buss’s work can be considered the continuation of Edward Nelson's work on PredicativeArithmetic as bounded arithmetic theories like S12 are interpretable in Raphael Robinson's theory Q and thereforeare predicative in Nelson's sense. The power of these theories for developing mathematics is studied in BoundedReverse Mathematics as can be found in the works of Stephen A. Cook and Phuong The Nguyen. However theseresearches are not philosophies of mathematics but rather the study of restricted forms of reasoning similar to ReverseMathematics.

9.4 Notes[1] http://plato.stanford.edu/entries/philosophy-mathematics/

[2] http://plato.stanford.edu/entries/philosophy-mathematics/

[3] http://kornai.com/Drafts/fathom_3.html

9.5 References• Ésénine-Volpine, A. S. (1961), “Le programme ultra-intuitionniste des fondements des mathématiques”, In-finitistic Methods (Proc. Sympos. Foundations of Math., Warsaw, 1959), Oxford: Pergamon, pp. 201–223, MR0147389 Reviewed by Kreisel, G.; Ehrenfeucht, A. (1967), “Review of Le Programme Ultra-Intuitionniste desFondements des Mathematiques by A. S. Ésénine-Volpine”, The Journal of Symbolic Logic (Association forSymbolic Logic) 32 (4): 517, doi:10.2307/2270182, JSTOR 2270182

• Lavine, S., 1994. Understanding the Infinite, Cambridge, MA: Harvard University Press.

9.6 External links• Explicit finitism by Andras Kornai

• On feasible numbers () by Vladimir Sazonov

• “Real” Analysis Is A Degenerate Case Of Discrete Analysis by Doron Zeilberger

• Discussion on formal foundations on MathOverflow

• History of constructivism in the 20th century by A. S. Troelstra

• Predicative Arithmetic by Edward Nelson

• Logical Foundations of Proof Complexity by Stephen A. Cook and Phuong The Nguyen

• Bounded Reverse Mathematics by Phuong The Nguyen

• Reading Brian Rotman’s “Ad Infinitum…” by Charles Petzold

9.7. TEXT AND IMAGE SOURCES, CONTRIBUTORS, AND LICENSES 21

9.7 Text and image sources, contributors, and licenses

9.7.1 Text• Conceptualism Source: https://en.wikipedia.org/wiki/Conceptualism?oldid=664401327 Contributors: Stevertigo, Andres, Hyacinth,

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• Epilogism Source: https://en.wikipedia.org/wiki/Epilogism?oldid=649984280 Contributors: Kjetil1001, AshLin, Gregbard, Ariconte,FrescoBot and ChrisGualtieri

• Illuminationism Source: https://en.wikipedia.org/wiki/Illuminationism?oldid=675598956 Contributors: Michael Hardy, Skysmith, Ben-der235, Woohookitty, BD2412, DVdm, Wavelength, Fram, Jagged 85, Beetstra, Texas Dervish, Iridescent, Gregbard, Cydebot, NickNumber, Jarkeld, Anoushirvan, Flyer22, Tomas e, Ernobe, Johnuniq, Editor2020, Addbot, Yobot, Ptbotgourou, Jim1138, Materialsci-entist, ChildofMidnight, Omnipaedista, Hadrien, DivineAlpha, Antenor81, Pollinosisss, Sideways713, John Watkins LLD, Wikipelli,Donner60, Polisher of Cobwebs, Hame fan harif, ClueBot NG, Tniggs16, Widr, Helpful Pixie Bot, BG19bot, Whitjr, Bokan995, JoshuaJonathan, Billy Ockham, Edward Buckminster, Rizwah, Babitaarora, JaconaFrere, Jayasonn, Shawwaliwali1212, Jesusislovejesusislife,Lolz1233456, Iogreshrekmlg, Kartoflerne and Anonymous: 21

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22 CHAPTER 9. ULTRAFINITISM

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