Theories of deduction 1From Wikipedia, the free encyclopedia

Contents

1 Anti-psychologism 11.1 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2 Conceptualism 22.1 Conceptualism in scholasticism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.2 Modern conceptualism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.3 Conceptualism and perceptual experience . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.4 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

3 Conventionalism 43.1 Linguistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43.2 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43.3 Philosophy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43.4 Legal Philosophy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53.6 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

4 Dialetheism 64.1 Motivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

4.1.1 Dialetheism resolves certain paradoxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64.1.2 Dialetheism may accurately model human reasoning . . . . . . . . . . . . . . . . . . . . . 64.1.3 Apparent dialetheism in other philosophical doctrines . . . . . . . . . . . . . . . . . . . . 64.1.4 Dialetheism may be a more accurate model of the physical world . . . . . . . . . . . . . . 7

4.2 Formal consequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74.3 Advantages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74.4 Criticisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74.5 Examples of True Contradictions that Dialetheists Accept . . . . . . . . . . . . . . . . . . . . . . 74.6 Modern Dialetheists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84.7 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84.8 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

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4.9 Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84.10 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

5 Epilogism 105.1 Epilogism in popular culture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105.2 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105.3 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

6 Fictionalism 116.1 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116.2 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116.3 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

7 Formalism (philosophy) 127.1 Religion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127.2 Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127.3 Criticism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

7.3.1 Art criticism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127.3.2 Literary criticism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

7.4 The arts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137.4.1 Poetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137.4.2 Film . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

7.5 Intellectual method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137.6 Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147.7 Anthropology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

8 Illuminationism 158.1 Early history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158.2 Iranian school of Illuminationism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168.3 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188.4 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188.5 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198.6 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

9 Inferential role semantics 209.1 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209.2 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

10 Logical atomism 2110.1 Origin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2110.2 Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2110.3 Differences between Russells and Wittgensteins atomism . . . . . . . . . . . . . . . . . . . . . . 2210.4 Influence and decline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2210.5 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

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10.6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2210.7 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

11 Logical holism 2411.1 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

12 Logicism 2512.1 Origin of the name logicism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2512.2 Intent, or goal, of Logicism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2612.3 Epistemology behind logicism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2712.4 The Logistic construction of the natural numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

12.4.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2912.4.2 The definition of the natural numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3012.4.3 Criticism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

12.5 The unit class, impredicativity, and the vicious circle principle . . . . . . . . . . . . . . . . . . . . 3512.5.1 A solution to impredicativity: a hierarchy of types . . . . . . . . . . . . . . . . . . . . . . 3712.5.2 Gdels criticism and suggestions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

12.6 Neo-logicism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3912.7 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3912.8 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3912.9 Annotated bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4112.10External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

13 Mental model theory of reasoning 4313.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4313.2 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

14 Modal fictionalism 4414.1 Strong Fictionalism about Possible Worlds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4414.2 Timid Fictionalism about Possible Worlds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4414.3 Objections and Criticisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4414.4 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4514.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

15 Object theory 4615.1 The genetic versus axiomatic method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4615.2 Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4715.3 Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4715.4 Tacit assumptions, tacit knowledge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4715.5 A formal system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4815.6 Informal theory, object theory, and metatheory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4815.7 Expansion of the notion of formal system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

15.7.1 Well-formed objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

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15.7.2 Undefined (primitive) objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4915.7.3 Axioms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

15.8 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5015.9 Footnotes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5015.10References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5015.11External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

16 Panlogism 5116.1 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

17 Polylogism 5217.1 Types of polylogism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

17.1.1 Proletarian logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5217.1.2 Racialist polylogism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

17.2 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5317.3 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

18 Preintuitionism 5418.1 The introduction of natural numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5418.2 The principle of complete induction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5418.3 Arguments over the excluded middle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5518.4 Other Pre-Intuitionists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5518.5 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

19 Psychologism 5619.1 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5619.2 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5619.3 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

20 Ramism 5820.1 Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5820.2 Opposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5820.3 Placing Ramism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5920.4 Disciplines and demarcations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6020.5 Ramist laws and method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6020.6 Ramism in Cambridge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6120.7 Ramism in Herborn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6120.8 In literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6120.9 Ramists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

20.9.1 Danish . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6220.9.2 Dutch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6220.9.3 Scottish . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6220.9.4 English . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

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20.9.5 French . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6220.9.6 German . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6320.9.7 Hungarian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6320.9.8 Scottish . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6320.9.9 Swedish . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6320.9.10 Swiss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6320.9.11Welsh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

20.10Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6320.11Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6720.12External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

21 Self-verifying theories 6821.1 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6821.2 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

22 Semantic theory of truth 6922.1 Origin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6922.2 Tarskis theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6922.3 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7022.4 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7022.5 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7022.6 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

23 Sophism 7223.1 Etymology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7223.2 Sophists of ancient Greece . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

23.2.1 Sophists and democracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7423.3 Sophists and education . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7423.4 Modern usage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7423.5 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7423.6 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7523.7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7623.8 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

24 Supervaluationism 7724.1 Example abstraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7724.2 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7724.3 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7724.4 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

25 Trivialism 7925.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

25.1.1 Etymology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

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25.1.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8025.1.3 Taxonomy of trivialisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

25.2 Arguments against trivialism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8025.2.1 Aristotle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8025.2.2 Priest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

25.3 Arguments for trivialism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8125.3.1 Argument from possibilism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8125.3.2 Paradoxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

25.4 Philosophical implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8125.4.1 Comparison to skepticism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8125.4.2 Impossibility of action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

25.5 Advocates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8225.5.1 Jainism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8225.5.2 Azzouni . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8225.5.3 Anaxagoras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

25.6 Anti-trivialism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8225.7 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8325.8 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8325.9 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8425.10External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

26 Ultrafinitism 8526.1 Main ideas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8526.2 People associated with ultrafinitism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8526.3 Complexity theory based restrictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8626.4 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8626.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8626.6 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

27 Unifying theories in mathematics 8727.1 Historical perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8727.2 Mathematical theories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8727.3 Geometrical theories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8727.4 Through-axiomatisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8827.5 Bourbaki . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8827.6 Category theory as a rival . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8827.7 Uniting theories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8827.8 Reference list of major unifying concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8927.9 Recent developments in relation with modular theory . . . . . . . . . . . . . . . . . . . . . . . . . 8927.10Isomorphism conjectures in K-theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9027.11See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9027.12Text and image sources, contributors, and licenses . . . . . . . . . . . . . . . . . . . . . . . . . . 91

CONTENTS vii

27.12.1 Text . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9127.12.2 Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9327.12.3 Content license . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

Chapter 1

Anti-psychologism

In logic, anti-psychologism is a theory about the nature of logical truth, that it does not depend upon the contentsof human ideas but exists independent of human ideas. The term was coined by Gottlob Frege (the most famousanti-psychologist of logic), and has been the centre of an important debate in early phenomenology and analyticalphilosophy, closely related to the internalism and externalism debate in logic and epistemology.The rival thesis, psychologism, is not widely held amongst logicians, but it does have some high-profile defenders, forexample Dov Gabbay.Edmund Husserl was an important proponent of anti-psychologism, and this trait passed on to other phenomenolo-gists, such as Martin Heidegger, whose doctoral thesis was meant to be a refutation of psychologism. They sharedthe argument that, because the proposition no-p is a not-p is not logically equivalent to It is thought that 'no-p is anot-p'", psychologism does not logically stand. Psychologism was criticized in logic also by Charles Sanders Peirce[1]whose fields included logic, philosophy, and experimental psychology,[2] and generally in philosophy by MauriceMerleau-Ponty who held the chairs of philosophy and child psychology[3] at Sorbonne in France.

1.1 Notes[1] Peirce attacked the idea, held by some logicians at that time, that rationality rests on a feeling of logicality, rather than on

fact. See the first of Peirces 1903 Lowell Institute Lectures What Makes a Reasoning Sound?", Essential Peirce v. 2, pp.242-257. See also the portion of Peirces 1902 Minute Logic published in Collected Papers v. 2 (1931), paragraphs 1819and 3943. Peirce held that mathematical and philosophical logics precede psychology as a special science and that theydo not depend on it for principles.

[2] Peirce (sometimeswith Joseph Jastrow) investigated the probability judgments of experimental subjects, pioneering decisionanalysis. He and Jastrow wrote On Small Differences in Sensation,Memoirs of the National Academy of Sciences (1885),3, 73-83, presented 17 October 1884, reprinted in Collected Papers v. 7, paragraphs 2135. Classics in the History ofPsychology. Eprint.

[3] Reynolds, Jack (as last updated 2005), Maurice Merleau-Ponty (19081961)", Internet Encyclopedia of Philosophy.Eprint.

1.2 References Vladimir Bryushinkin. Metapsychologism In The Philosophy Of Logic. Proc. Logic and Philosophy of Logic,20th World Congress in Philosophy, 2000.

Dov Gabbay and John Woods. The New Logic. In Journal of the Interest Group in Pure and Applied Logic,Volume 9(2). Oxford, 2000.

1.3 External links Anti-psychologism at PhilPapers

1

https://en.wikipedia.org/wiki/Logichttps://en.wikipedia.org/wiki/Theoryhttps://en.wikipedia.org/wiki/Logical_truthhttps://en.wikipedia.org/wiki/Gottlob_Fregehttps://en.wikipedia.org/wiki/Mathematical_logichttps://en.wikipedia.org/wiki/Phenomenology_(philosophy)https://en.wikipedia.org/wiki/Analytical_philosophyhttps://en.wikipedia.org/wiki/Analytical_philosophyhttps://en.wikipedia.org/wiki/Internalism_and_externalismhttps://en.wikipedia.org/wiki/Epistemologyhttps://en.wikipedia.org/wiki/Psychologismhttps://en.wikipedia.org/wiki/Dov_Gabbayhttps://en.wikipedia.org/wiki/Edmund_Husserlhttps://en.wikipedia.org/wiki/Martin_Heideggerhttps://en.wikipedia.org/wiki/Logical_equivalencehttps://en.wikipedia.org/wiki/Charles_Sanders_Peircehttps://en.wikipedia.org/wiki/Maurice_Merleau-Pontyhttps://en.wikipedia.org/wiki/Maurice_Merleau-Pontyhttps://en.wikipedia.org/wiki/Sorbonnehttps://en.wikipedia.org/wiki/Charles_Sanders_Peirce_bibliography#Lectures_by_Peircehttps://en.wikipedia.org/wiki/Charles_Sanders_Peirce#EPhttps://en.wikipedia.org/wiki/Charles_Sanders_Peirce#CPhttps://en.wikipedia.org/wiki/Classification_of_the_sciences_(Peirce)https://en.wikipedia.org/wiki/Joseph_Jastrowhttps://en.wikipedia.org/wiki/Bayesian_probabilityhttps://en.wikipedia.org/wiki/Decision_analysishttps://en.wikipedia.org/wiki/Decision_analysishttps://en.wikipedia.org/wiki/Charles_Sanders_Peirce_bibliography#CPhttp://psychclassics.yorku.ca/Peirce/small-diffs.htmhttp://www.iep.utm.edu/merleau/http://www.bu.edu/wcp/Papers/Logi/LogiBryu.htmhttp://www3.oup.co.uk/igpl/Volume_09/Issue_02/pdf/Gabbay.pdfhttp://philpapers.org/s/Anti-psychologismhttps://en.wikipedia.org/wiki/PhilPapers

Chapter 2

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 theminds perception of them.[2]

2.1 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 Ablard was a medieval thinker whose work is currently classified as having the most potential in representingthe roots of conceptualism. Ablards 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 Surez, the ideas of these Jesuits had a great impact on the contemporary early modernthinkers.

2.2 Modern conceptualism

Conceptualism was either explicitly or implicitly embraced by most of the early modern thinkers like Ren 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.

2

https://en.wikipedia.org/wiki/Conceptual_arthttps://en.wikipedia.org/wiki/Nominalismhttps://en.wikipedia.org/wiki/Philosophical_realismhttps://en.wikipedia.org/wiki/Universality_(philosophy)https://en.wikipedia.org/wiki/Peter_Ab%C3%A9lardhttps://en.wikipedia.org/wiki/William_of_Ockhamhttps://en.wikipedia.org/wiki/Jesuithttps://en.wikipedia.org/wiki/Francisco_Su%C3%A1rezhttps://en.wikipedia.org/wiki/Ren%C3%A9_Descarteshttps://en.wikipedia.org/wiki/John_Lockehttps://en.wikipedia.org/wiki/Gottfried_Leibnizhttps://en.wikipedia.org/wiki/Immanuel_Kanthttps://en.wikipedia.org/wiki/A_priori_and_a_posteriorihttps://en.wikipedia.org/wiki/Epistemology

2.3. CONCEPTUALISM AND PERCEPTUAL EXPERIENCE 3

2.3 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]McDowells touchstone is the famous refutation that Wilfrid Sellars provided for what he called the Myth of theGiventhe 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 ornaked sense data that serve as a foundation for all empirical knowledgeMcDowell 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 worldsimpacts 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 subjects 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]

McDowells conceptualism, though rather distinct (philosophically and historically) from conceptualisms 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.

2.4 See also Problem of universals

Pierre Ablard

Conceptual art

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

Philosophical realism

Conceptual architecture

2.5 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): 338351. doi:10.1080/00201740701489211.

https://en.wikipedia.org/wiki/John_McDowellhttps://en.wikipedia.org/wiki/Wilfrid_Sellarshttps://en.wikipedia.org/wiki/Foundationalismhttps://en.wikipedia.org/wiki/Problem_of_universalshttps://en.wikipedia.org/wiki/Pierre_Ab%C3%A9lardhttps://en.wikipedia.org/wiki/Conceptual_arthttps://en.wikipedia.org/wiki/Lyco_arthttps://en.wikipedia.org/wiki/Philosophical_realismhttps://en.wikipedia.org/wiki/Conceptual_architecturehttp://www.newadvent.org/cathen/15636a.htmhttps://en.wikipedia.org/wiki/Catholic_Encyclopediahttp://www.newadvent.org/cathen/11090c.htmhttps://en.wikipedia.org/wiki/International_Standard_Book_Numberhttps://en.wikipedia.org/wiki/Special:BookSources/978-0-674-57610-0http://plato.stanford.edu/entries/sellars/https://en.wikipedia.org/wiki/Digital_object_identifierhttps://dx.doi.org/10.1080%252F00201740701489211

Chapter 3

Conventionalism

Conventionalism is the philosophical attitude that fundamental principles of a certain kind are grounded on (explicitor implicit) agreements in society, rather than on external reality. Although this attitude is commonly held withrespect to the rules of grammar, its application to the propositions of ethics, law, science, mathematics, and logic ismore controversial.

3.1 Linguistics

The debate on linguistic conventionalism goes back to Plato's Cratylus and the Mms philosophy of KumrilaBhaa. It has been the standard position of modern linguistics since Ferdinand de Saussure's l'arbitraire du signe, butthere have always been dissenting positions of phonosemantics, recently defended byMargaret Magnus and VilayanurS. Ramachandran.

3.2 Geometry

The French mathematician Henri Poincar was among the first to articulate a conventionalist view. Poincar's use ofnon-Euclidean geometries in his work on differential equations convinced him that Euclidean geometry should notbe regarded as a priori truth. He held that axioms in geometry should be chosen for the results they produce, not fortheir apparent coherence with human intuitions about the physical world.

3.3 Philosophy

Conventionalism was adopted by logical positivists, chiefly AJ Ayer and Carl Hempel, and extended to both mathe-matics and logic. To deny rationalism, Ayer sees two options for empiricism regarding the necessity of the truth offormal logic (and mathematics): 1) deny that they actually are necessary, and then account for why they only appearso, or 2) claim that the truths of logic and mathematics lack factual content - they are not truths about the world -and then explain how they are nevertheless true and informative.[1] John Stuart Mill adopted the former, which Ayercriticized, opting himself for the latter. Ayers argument relies primarily on the analytic/synthetic distinction.The French philosopher Pierre Duhem espoused a broader conventionalist view encompassing all of science. Duhemwas skeptical that human perceptions are sufficient to understand the true, metaphysical nature of reality and arguedthat scientific laws should be valued mainly for their predictive power and correspondence with observations.

3.4 Legal Philosophy

Conventionalism, as applied to legal philosophy, provides a justification for state coercion. It is one of the three rivalconceptions of law constructed by American legal philosopher Ronald Dworkin in his work Laws Empire. The othertwo conceptions of law are legal pragmatism and law as integrity.

4

https://en.wikipedia.org/wiki/Philosophyhttps://en.wikipedia.org/wiki/Grammarhttps://en.wikipedia.org/wiki/Ethicshttps://en.wikipedia.org/wiki/Sciencehttps://en.wikipedia.org/wiki/Platohttps://en.wikipedia.org/wiki/Cratylus_(dialogue)https://en.wikipedia.org/wiki/M%C4%ABm%C4%81%E1%B9%83s%C4%81https://en.wikipedia.org/wiki/Kum%C4%81rila_Bha%E1%B9%AD%E1%B9%ADahttps://en.wikipedia.org/wiki/Kum%C4%81rila_Bha%E1%B9%AD%E1%B9%ADahttps://en.wikipedia.org/wiki/Linguisticshttps://en.wikipedia.org/wiki/Ferdinand_de_Saussurehttps://en.wikipedia.org/wiki/L%2527arbitraire_du_signehttps://en.wikipedia.org/wiki/Phonosemanticshttps://en.wikipedia.org/wiki/Margaret_Magnushttps://en.wikipedia.org/wiki/Vilayanur_S._Ramachandranhttps://en.wikipedia.org/wiki/Vilayanur_S._Ramachandranhttps://en.wikipedia.org/wiki/Mathematicianhttps://en.wikipedia.org/wiki/Henri_Poincar%C3%A9https://en.wikipedia.org/wiki/Non-Euclidean_geometrieshttps://en.wikipedia.org/wiki/Euclidean_geometryhttps://en.wikipedia.org/wiki/A_priori_and_a_posteriorihttps://en.wikipedia.org/wiki/Axiomshttps://en.wikipedia.org/wiki/Logical_positivismhttps://en.wikipedia.org/wiki/Alfred_Jules_Ayerhttps://en.wikipedia.org/wiki/Carl_Hempelhttps://en.wikipedia.org/wiki/Rationalismhttps://en.wikipedia.org/wiki/Empiricismhttps://en.wikipedia.org/wiki/John_Stuart_Millhttps://en.wikipedia.org/wiki/Analytic-synthetic_distinctionhttps://en.wikipedia.org/wiki/Philosopherhttps://en.wikipedia.org/wiki/Pierre_Duhemhttps://en.wikipedia.org/wiki/Legal_philosophyhttps://en.wikipedia.org/wiki/Ronald_Dworkinhttps://en.wikipedia.org/wiki/Law%2527s_Empirehttps://en.wikipedia.org/wiki/Legal_pragmatismhttps://en.wikipedia.org/wiki/Law_as_integrity

3.5. REFERENCES 5

According to conventionalism as defined by Dworkin, a communitys legal institutions should contain clear socialconventions relied upon which rules are promulgated. Such rules will serve as the sole source of information for allthe community members because they demarcate clearly all the circumstances in which state coercion will and willnot be exercised.Dworkin nonetheless has argued that this justification fails to fit with facts as there are many occasions wherein clearapplicable legal rules are absent. It follows that, as he maintained, conventionalism can provide no valid ground forstate coercion. Dworkin himself favored law as integrity as the best justification of state coercion.One famous criticism of Dworkins idea comes from Stanley Fish who opines that Dworkin, like the Critical LegalStudies movement, Marxists and adherents of feminist jurisprudence, was guilty of a false 'Theory Hope'. Fishclaims that such mistake stems from their mistaken belief that there exists a general or higher 'theory' that explainsor constrains all fields of activity like state coercion.Another criticism is based on Dworkins assertion that positivists claims amount to conventionalism. H. L. A. Hart,as a soft positivist, denies such claim as he had pointed out that citizens cannot always discover the law as plain matterof fact. It is however unclear as to whether Joseph Raz, an avowed hard positivist, can be classified as conventionalistas Raz has claimed that law is composed exclusively of social facts which could be complex, and thus difficult tobe discovered.In particular, Dworkin has characterized law as having the main function of restraining states coercion. Nigel Sim-monds has rejected Dworkins disapproval of conventionalism, claiming that his characterization of law is too narrow.

3.5 References[1] Ayer, Alfred Jules. Language, Truth and Logic, Dover Publications, Inc.: New York. 1952. p. 73.

The Internet Encyclopedia of Philosophy entry on Henri Poincar

Pierre Duhem. Notes by David Huron

Mary Jo Nye, The Boutroux Circle and Poincares Conventionalism, Journal of the History of Ideas, Vol. 40,No. 1. (Jan. - Mar., 1979), pp. 107120.

3.6 See also phonosemantics

true name

Kumarila Bhatta

https://en.wikipedia.org/wiki/Convention_(norm)https://en.wikipedia.org/wiki/State_coercionhttps://en.wikipedia.org/wiki/State_coercionhttps://en.wikipedia.org/wiki/Law_as_integrityhttps://en.wikipedia.org/wiki/Stanley_Fishhttps://en.wikipedia.org/wiki/Critical_Legal_Studieshttps://en.wikipedia.org/wiki/Critical_Legal_Studieshttps://en.wikipedia.org/wiki/Marxistshttps://en.wikipedia.org/wiki/Feminist_jurisprudencehttps://en.wikipedia.org/wiki/H._L._A._Harthttps://en.wikipedia.org/wiki/Joseph_Razhttps://en.wikipedia.org/wiki/Nigel_Simmondshttps://en.wikipedia.org/wiki/Nigel_Simmondshttps://en.wikipedia.org/wiki/Language,_Truth_and_Logichttp://www.iep.utm.edu/p/poincare.htm#H4http://music-cog.ohio-state.edu/Music829C/Notes/Duhem.htmlhttp://links.jstor.org/sici?sici=0022-5037%2528197901%252F03%252940%253A1%253C107%253ATBCAPC%253E2.0.CO%253B2-Ghttps://en.wikipedia.org/wiki/Phonosemanticshttps://en.wikipedia.org/wiki/True_namehttps://en.wikipedia.org/wiki/Kumarila_Bhatta

Chapter 4

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 Priests in advocating constructive (methodological) deflationism regarding the truth predicate.[2]

4.1 Motivations

4.1.1 Dialetheism resolves certain paradoxes

The Liars paradox and Russells paradox deal with self-contradictory statements in classical logic and nave settheory, respectively. Contradictions are problematic in these theories because they cause the theories to explodeifa 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]

4.1.2 Dialetheism may accurately model human reasoning

Ambiguous situations may cause humans to affirm both a proposition and its negation. For example, if John stands inthe 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 ourthoughts; if we replace the given statement with one that is less ambiguous (such as John is halfway in the room orJohn is in the doorway), the contradiction disappears.

4.1.3 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;

6

https://en.wikipedia.org/wiki/Statement_(logic)https://en.wikipedia.org/wiki/Negationhttps://en.wikipedia.org/wiki/Contradictionhttps://en.wikipedia.org/wiki/Nondualismhttps://en.wikipedia.org/wiki/Formal_systemhttps://en.wikipedia.org/wiki/Truthhttps://en.wikipedia.org/wiki/Logical_consequencehttps://en.wikipedia.org/wiki/Classical_logichttps://en.wikipedia.org/wiki/Intuitionistic_logichttps://en.wikipedia.org/wiki/Intuitionistic_logichttps://en.wikipedia.org/wiki/Trivialisthttps://en.wikipedia.org/wiki/Principle_of_explosionhttps://en.wikipedia.org/wiki/Paraconsistent_logichttps://en.wikipedia.org/wiki/Graham_Priesthttps://en.wikipedia.org/wiki/Deflationismhttps://en.wikipedia.org/wiki/Liar_paradoxhttps://en.wikipedia.org/wiki/Russell%2527s_paradoxhttps://en.wikipedia.org/wiki/Na%C3%AFve_set_theoryhttps://en.wikipedia.org/wiki/Na%C3%AFve_set_theoryhttps://en.wikipedia.org/wiki/Principle_of_explosionhttps://en.wikipedia.org/wiki/Axiom_schema_of_specification#Unrestricted_comprehensionhttps://en.wikipedia.org/wiki/Set_theoryhttps://en.wikipedia.org/wiki/Theoremhttps://en.wikipedia.org/wiki/Jainhttps://en.wikipedia.org/wiki/Anekantavada

4.2. FORMAL CONSEQUENCES 7

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 namedCatukoi 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.

4.1.4 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 Waveparticle duality is one such case is not established, but it isa possibility Are there non-semantic dialethia

4.2 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 pq 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.

4.3 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.

4.4 Criticisms

One important criticism of dialetheism is that it fails to capture something crucial about negation and, consequently,disagreement. Imagine Johns utterance of P. Sallys typical way of disagreeing with John is a consequent utterance ofP. Yet, if we accept dialetheism, Sallys 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 dialetheists 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]

4.5 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.

https://en.wikipedia.org/wiki/Buddhisthttps://en.wikipedia.org/wiki/Catu%E1%B9%A3ko%E1%B9%ADihttps://en.wikipedia.org/wiki/Graham_Priesthttps://en.wikipedia.org/wiki/Wave%E2%80%93particle_dualityhttp://www.dialetheism.org/dialetheism/index.php?title=Dialetheism:Dialetheism/non-semantichttps://en.wikipedia.org/wiki/Principle_of_explosionhttps://en.wikipedia.org/wiki/Sorites_paradoxhttps://en.wikipedia.org/wiki/Negationhttps://en.wikipedia.org/wiki/Achilles%2527_heelhttps://en.wikipedia.org/wiki/Logical_assertionhttps://en.wikipedia.org/wiki/Logical_qualityhttps://en.wikipedia.org/wiki/Logical_qualityhttps://en.wikipedia.org/wiki/Illocutionary_forcehttps://en.wikipedia.org/wiki/Speech_actshttps://en.wikipedia.org/wiki/Logical_assertion

8 CHAPTER 4. DIALETHEISM

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.

4.6 Modern Dialetheists

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

4.7 See also

Problem of future contingents

Leibniz's compossibility

Liar paradox

Doublethink

Trivialism

4.8 References

[1] Whittle, Bruno. Dialetheism, logical consequence and hierarchy. Analysis Vol. 64 Issue 4 (2004): 318326.

[2] Jc Beall in The Law of Non-Contradiction: New Philosophical Essays (Oxford: Oxford University Press, 2004), pp. 197219.

[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

4.9 Sources

Frege, Gottlob. Negation. Logical Investigations. Trans. P. Geach and R. H Stoothoff. New Haven, Conn.:Yale University Press, 1977. 3153.

Parsons, Terence. Assertion, Denial, and the Liar Paradox. Journal of Philosophical Logic 13 (1984): 137152.

Parsons, Terence. True Contradictions. Canadian Journal of Philosophy 20 (1990): 335354.

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): 410426.

https://en.wikipedia.org/wiki/Zenhttps://en.wikipedia.org/wiki/Nondualismhttps://en.wikipedia.org/wiki/Contradictionshttps://en.wikipedia.org/wiki/Problem_of_future_contingentshttps://en.wikipedia.org/wiki/Gottfried_Wilhelm_Leibnizhttps://en.wikipedia.org/wiki/Compossibilityhttps://en.wikipedia.org/wiki/Liar_paradoxhttps://en.wikipedia.org/wiki/Doublethinkhttps://en.wikipedia.org/wiki/Trivialismhttp://www.iep.utm.edu/nagarjun/#H2https://en.wikipedia.org/wiki/Gottlob_Fregehttps://en.wikipedia.org/wiki/Terence_Parsonshttps://en.wikipedia.org/wiki/Graham_Priesthttps://en.wikipedia.org/wiki/Graham_Priest

4.10. EXTERNAL LINKS 9

4.10 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)

http://plato.stanford.edu/entries/dialetheism/https://en.wikipedia.org/wiki/Stanford_Encyclopedia_of_Philosophyhttp://homepages.uconn.edu/~jcb02005/http://blogandnot-blog.blogspot.com/http://dialetheism.org/http://www.paulkabay.com/

Chapter 5

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.

5.1 Epilogism in popular culture

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

5.2 See also Transduction (machine learning)

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

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

10

https://en.wikipedia.org/wiki/Inferencehttps://en.wikipedia.org/wiki/Empiric_schoolhttps://en.wikipedia.org/wiki/Inductive_reasoning#Types_of_inductive_reasoning%2523Causal_inferencehttps://en.wikipedia.org/wiki/Unobservablehttps://en.wikipedia.org/wiki/Empiric_school#Doctrineshttps://en.wikipedia.org/wiki/The_Black_Swan_(Taleb_book)https://en.wikipedia.org/wiki/Nassim_Nicholas_Talebhttps://en.wikipedia.org/wiki/Transduction_(machine_learning)http://bmcr.brynmawr.edu/2004/2004-12-20.html

Chapter 6

Fictionalism

Fictionalism is the view in philosophy according to which statements that appear to be descriptions of the worldshould not be construed as such, but should instead be understood as cases of make believe, of pretending totreat something as literally true (a useful fiction). Two important strands of fictionalism are modal fictionalismdeveloped by Gideon Rosen, which states that possible worlds, regardless of whether they exist or not, may be a partof a useful discourse, and mathematical fictionalism advocated by Hartry Field, which states that talk of numbers andother mathematical objects is nothing more than a convenience for doing science. Also in meta-ethics, there is anequivalent position called moral fictionalism (championed by Richard Joyce). Many modern versions of fictionalismare influenced by the work of Kendall Walton in aesthetics.Fictionalism consists in at least the following three theses:

1. Claims made within the domain of discourse are taken to be truth-apt; that is, true or false.

2. The domain of discourse is to be interpreted at face valuenot reduced to meaning something else.

3. The aim of discourse in any given domain is not truth, but some other virtue(s) (e.g., simplicity, explanatoryscope).

6.1 See also Nancy Cartwright

Philosophy of color

6.2 Further reading Balaguer, Mark (1998). Platonism and Anti-Platonism in Mathematics. Oxford: Oxford University Press.ISBN 978-0-19-514398-0.

Kalderon, Mark (2005). Moral Fictionalism. Oxford: Clarendon Press. ISBN 978-0-19-927597-7.

6.3 External links Fictionalism in the Philosophy of Mathematics article in the Internet Encyclopedia of Philosophy

Modal Fictionalism entry by Daniel Nolan in the Stanford Encyclopedia of Philosophy, 2007-12-11

Fictionalism entry by Matti Eklund in the Stanford Encyclopedia of Philosophy, 2007-03-30

Mathematical fictionalism entry by Mark Balaguer in the Stanford Encyclopedia of Philosophy, 2008-04-22

11

https://en.wikipedia.org/wiki/Philosophyhttps://en.wikipedia.org/wiki/Modal_fictionalismhttps://en.wikipedia.org/wiki/Gideon_Rosenhttps://en.wikipedia.org/wiki/Possible_worldshttps://en.wikipedia.org/wiki/Philosophy_of_mathematics#Fictionalismhttps://en.wikipedia.org/wiki/Hartry_Fieldhttps://en.wikipedia.org/wiki/Meta-ethicshttps://en.wikipedia.org/wiki/Richard_Joyce_(philosopher)https://en.wikipedia.org/wiki/Kendall_Waltonhttps://en.wikipedia.org/wiki/Domain_of_discoursehttps://en.wikipedia.org/wiki/Truth-apthttps://en.wikipedia.org/wiki/Nancy_Cartwright_(philosopher)https://en.wikipedia.org/wiki/Philosophy_of_colorhttps://en.wikipedia.org/wiki/International_Standard_Book_Numberhttps://en.wikipedia.org/wiki/Special:BookSources/978-0-19-514398-0https://en.wikipedia.org/wiki/International_Standard_Book_Numberhttps://en.wikipedia.org/wiki/Special:BookSources/978-0-19-927597-7http://www.iep.utm.edu/mathfict/https://en.wikipedia.org/wiki/Internet_Encyclopedia_of_Philosophyhttp://plato.stanford.edu/entries/fictionalism-modalhttps://en.wikipedia.org/wiki/Stanford_Encyclopedia_of_Philosophyhttp://plato.stanford.edu/entries/fictionalismhttps://en.wikipedia.org/wiki/Stanford_Encyclopedia_of_Philosophyhttp://plato.stanford.edu/entries/fictionalism-mathematicshttps://en.wikipedia.org/wiki/Stanford_Encyclopedia_of_Philosophy

Chapter 7

Formalism (philosophy)

The term formalism describes an emphasis on form over content or meaning in the arts, literature, or philosophy.A practitioner of formalism is called a formalist. A formalist, with respect to some discipline, holds that there is notranscendent meaning to that discipline other than the literal content created by a practitioner. For example, formalistswithin mathematics claim that mathematics is no more than the symbols written down by the mathematician, whichis based on logic and a few elementary rules alone. This is as opposed to non-formalists, within that field, who holdthat there are some things inherently true, and are not, necessarily, dependent on the symbols within mathematicsso much as a greater truth. Formalists within a discipline are completely concerned with the rules of the game, asthere is no other external truth that can be achieved beyond those given rules. In this sense, formalism lends itselfwell to disciplines based upon axiomatic systems.

7.1 Religion

Formalism in religion means an emphasis on ritual and observance over their meanings. Within Christianity, the termlegalism is a derogatory term that is loosely synonymous to religious formalism.

7.2 Law

Main article: Legal formalism

Formalism is a school of thought in law and jurisprudence which assumes that the law is a system of rules thatcan determine the outcome of any case, without reference to external norms. For example, formalism animates thecommonly heard criticism that judges should apply the law, not make it. To formalisms rival, legal realism, thiscriticism is incoherent, because legal realism assumes that, at least in difficult cases, all applications of the law willrequire that a judge refer to external (i.e. non-legal) sources, such as the judges conception of justice, or commercialnorms.

7.3 Criticism

In general in the study of the arts and literature, formalism refers to the style of criticism that focuses on artistic orliterary techniques in themselves, in separation from the works social and historical context.

7.3.1 Art criticism

Main article: formalism (art)

12

https://en.wikipedia.org/wiki/Artshttps://en.wikipedia.org/wiki/Literaturehttps://en.wikipedia.org/wiki/Philosophyhttps://en.wikipedia.org/wiki/Mathematicshttps://en.wikipedia.org/wiki/Axiomatic_systemhttps://en.wikipedia.org/wiki/Ritualhttps://en.wikipedia.org/wiki/Religious_observancehttps://en.wikipedia.org/wiki/Legalism_(theology)https://en.wikipedia.org/wiki/Legal_formalismhttps://en.wikipedia.org/wiki/Jurisprudencehttps://en.wikipedia.org/wiki/Formalism_(art)

7.4. THE ARTS 13

General speaking, formalism is the concept which everything necessary in a work of art is contained within it. Thecontext for the work, including the reason for its creation, the historical background, and the life of the artist, isnot considered to be significant. Examples of formalist aestheticians are Clive Bell, Jerome Stolnitz, and EdwardBullough.

7.3.2 Literary criticism

Main article: formalism (literature)

In contemporary discussions of literary theory, the school of criticism of I. A. Richards and his followers, traditionallythe New Criticism, has sometimes been labelled 'formalist'. The formalist approach, in this sense, is a continuationof aspects of classical rhetoric.Russian formalism was a twentieth century school, based in Eastern Europe, with roots in linguistic studies and alsotheorising on fairy tales, in which content is taken as secondary since the tale 'is the form, the princess 'is the fairy-taleprincess.

7.4 The arts

7.4.1 Poetry

In modern poetry, Formalist poets may be considered as the opposite of writers of free verse. These are only labels,and rarely sum up matters satisfactorily. 'Formalism' in poetry represents an attachment to poetry that recognises anduses schemes of rhyme and rhythm to create poetic effects and to innovate. To distinguish it from archaic poetry theterm 'neo-formalist' is sometimes used.See for example:

The Formalist, a literary magazine (now defunct) for formalist poetry

New Formalism, a movement within the poetry of the United States.

7.4.2 Film

Main article: Formalist film theory

In film studies, formalism is a trait in filmmaking, which overtly uses the language of film, such as editing, shotcomposition, camera movement, set design, etc., so as to emphasise graphical (as opposed to diegetic) qualities ofthe image. Strict formalism, condemned by realist film theorists such as Andr Bazin, has declined substantially inpopular usage since the 1950s, though some more postmodern filmmakers reference it to suggest the artificiality ofthe film experience.Examples of formalist filmsmay include ResnaissLast Year atMarienbad and Parajanov'sThe Color of Pomegranates,

7.5 Intellectual method

Formalism can be applied to a set of notations and rules for manipulating them which yield results in agreementwith experiment or other techniques of calculation. These rules and notations may or may not have a correspondingmathematical semantics. In the case no mathematical semantics exists, the calculations are often said to be purelyformal. See for example scientific formalism.

https://en.wikipedia.org/wiki/Clive_Bellhttps://en.wikipedia.org/wiki/Jerome_Stolnitzhttps://en.wikipedia.org/wiki/Edward_Bulloughhttps://en.wikipedia.org/wiki/Edward_Bulloughhttps://en.wikipedia.org/wiki/Formalism_(literature)https://en.wikipedia.org/wiki/Literary_theoryhttps://en.wikipedia.org/wiki/I._A._Richardshttps://en.wikipedia.org/wiki/New_Criticismhttps://en.wikipedia.org/wiki/Rhetorichttps://en.wikipedia.org/wiki/Russian_formalismhttps://en.wikipedia.org/wiki/Fairy_talehttps://en.wikipedia.org/wiki/Free_versehttps://en.wikipedia.org/wiki/The_Formalisthttps://en.wikipedia.org/wiki/New_Formalismhttps://en.wikipedia.org/wiki/Poetry_of_the_United_Stateshttps://en.wikipedia.org/wiki/Formalist_film_theoryhttps://en.wikipedia.org/wiki/Film_studieshttps://en.wikipedia.org/wiki/Editinghttps://en.wikipedia.org/wiki/Composition_(visual_arts)https://en.wikipedia.org/wiki/Graphicalhttps://en.wikipedia.org/wiki/Diegetichttps://en.wikipedia.org/wiki/Realism_(arts)https://en.wikipedia.org/wiki/Andr%C3%A9_Bazinhttps://en.wikipedia.org/wiki/Last_Year_at_Marienbadhttps://en.wikipedia.org/wiki/Sergei_Parajanovhttps://en.wikipedia.org/wiki/The_Color_of_Pomegranateshttps://en.wikipedia.org/wiki/Scientific_formalism

14 CHAPTER 7. FORMALISM (PHILOSOPHY)

7.6 Mathematics

Main article: Formalism (mathematics)

In the foundations of mathematics, formalism is associated with a certain rigorous mathematical method: see formalsystem. In common usage, a formalism means the out-turn of the effort towards formalisation of a given limited area.In other words, matters can be formally discussed once captured in a formal system, or commonly enough withinsomething formalisable with claims to be one. Complete formalisation is in the domain of computer science.Formalism also more precisely refers to a certain school in the philosophy of mathematics, stressing axiomatic proofsthrough theorems, specifically associated with David Hilbert. In the philosophy of mathematics, therefore, a formalistis a person who belongs to the school of formalism, which is a certain mathematical-philosophical doctrine descendingfrom Hilbert.

7.7 Anthropology

In economic anthropology, formalism is the theoretical perspective that the principles of neoclassical economics canbe applied to our understanding of all human societies.

https://en.wikipedia.org/wiki/Formalism_(mathematics)https://en.wikipedia.org/wiki/Foundations_of_mathematicshttps://en.wikipedia.org/wiki/Formal_systemhttps://en.wikipedia.org/wiki/Formal_systemhttps://en.wikipedia.org/wiki/Formalisationhttps://en.wikipedia.org/wiki/Computer_sciencehttps://en.wikipedia.org/wiki/Philosophy_of_mathematicshttps://en.wikipedia.org/wiki/Axiomhttps://en.wikipedia.org/wiki/Theoremhttps://en.wikipedia.org/wiki/David_Hilberthttps://en.wikipedia.org/wiki/Philosophy_of_mathematicshttps://en.wikipedia.org/wiki/Economic_anthropologyhttps://en.wikipedia.org/wiki/Neoclassical_economics

Chapter 8

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.

8.1 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] Augustines 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]

Augustines 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 Aristotles 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]

15

https://en.wikipedia.org/wiki/Doctrinehttps://en.wikipedia.org/wiki/Divine_gracehttps://en.wikipedia.org/wiki/Naturalism_(philosophy)https://en.wikipedia.org/wiki/Theory_of_mindhttps://en.wikipedia.org/wiki/Epistemologyhttps://en.wikipedia.org/wiki/Greek_philosophyhttps://en.wikipedia.org/wiki/Neoplatonismhttps://en.wikipedia.org/wiki/Medieval_philosophyhttps://en.wikipedia.org/wiki/Islamic_philosophyhttps://en.wikipedia.org/wiki/Socrateshttps://en.wikipedia.org/wiki/Apology_(Plato)https://en.wikipedia.org/wiki/Apuleiushttps://en.wikipedia.org/wiki/Augustinehttps://en.wikipedia.org/wiki/Franciscanhttps://en.wikipedia.org/wiki/Bonaventurehttps://en.wikipedia.org/wiki/Matthew_of_Aquaspartahttps://en.wikipedia.org/wiki/John_Pechamhttps://en.wikipedia.org/wiki/Roger_Marstonhttps://en.wikipedia.org/wiki/Thomas_Aquinashttps://en.wikipedia.org/wiki/Henry_of_Ghenthttps://en.wikipedia.org/wiki/Abstraction

16 CHAPTER 8. ILLUMINATIONISM

Socrates

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

8.2 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 (11551191), who left over 50 writings in Persian and Arabic, founded the school of Illumination.He developed a version of illuminationism (Persian hikmat-i ishrq, Arabic: ikmat al-ishrq). The Persian and Islamic school draws on ancient Iranian philosophical disciplines,[17][18] Avicennism (IbnSinas 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,97.798.11). Light produces immaterial and substantial lights, including immaterial intellects (angels), human andanimal souls, and even 'dusky substances, such as bodies.[19]

https://en.wikipedia.org/wiki/Socrateshttps://en.wikipedia.org/wiki/Duns_Scotushttps://en.wikipedia.org/wiki/Scepticismhttps://en.wikipedia.org/wiki/Avicennismhttps://en.wikipedia.org/wiki/Neoplatonismhttps://en.wikipedia.org/wiki/Persiahttps://en.wikipedia.org/wiki/Kurdish_peoplehttps://en.wikipedia.org/wiki/Shahab_al-Din_Suhrawardihttps://en.wikipedia.org/wiki/Shahab_al-Din_Suhrawardihttps://en.wikipedia.org/wiki/Persian_languagehttps://en.wikipedia.org/wiki/Arabic_languagehttps://en.wikipedia.org/wiki/Iranian_philosophyhttps://en.wikipedia.org/wiki/Avicennahttps://en.wikipedia.org/wiki/Avicennahttps://en.wikipedia.org/wiki/Early_Islamic_philosophyhttps://en.wikipedia.org/wiki/Neoplatonismhttps://en.wikipedia.org/wiki/Angel

8.2. IRANIAN SCHOOL OF ILLUMINATIONISM 17

Augustine

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

None of Suhrawardis 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]

https://en.wikipedia.org/wiki/Augustinehttps://en.wikipedia.org/wiki/Principle_of_sufficient_reasonhttps://en.wikipedia.org/wiki/Actual_infinityhttps://en.wikipedia.org/wiki/Latin_West

18 CHAPTER 8. ILLUMINATIONISM

8.3 See also Augustine

Henry of Ghent

Duns Scotus

Iranian philosophy

Early Islamic philosophy

Light (theology)

Mulla Sadra

Enlightenment (spiritual)

8.4 Notes[1] Stanford Encyclopedia of Philosophy

[2] De deo Socratis, XVIIXIX)

[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: Suhraward 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] Kaml, Muammad (2006). Mulla Sadras 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 Sadras 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 77.178.9

[20] Philosophy of Illumination 87.189.8

[21] Marcotte, Roxanne, Suhrawardi, The Stanford Encyclopedia of Philosophy (Summer 2012 Edition), Edward N. Zalta(ed.), URL = .

https://en.wikipedia.org/wiki/Augustinehttps://en.wikipedia.org/wiki/Henry_of_Ghenthttps://en.wikipedia.org/wiki/Duns_Scotushttps://en.wikipedia.org/wiki/Iranian_philosophyhttps://en.wikipedia.org/wiki/Early_Islamic_philosophyhttps://en.wikipedia.org/wiki/Light_(theology)https://en.wikipedia.org/wiki/Mulla_Sadrahttps://en.wikipedia.org/wiki/Enlightenment_(spiritual)http://plato.stanford.edu/entries/illumination/https://books.google.com/books?id=I9mr6OgLjBoC&pg=PA160&dq=Suhrawardi+Kurd&hl=en&ei=-pExTqiiKsXHtAakudjoBg&sa=X&oi=book_result&ct=result&resnum=7&ved=0CEUQ6AEwBg#v=snippet&q=Suhrawardi&f=falsehttp://books.google.no/books?id=EwB7Zo7lVp0C&pg=PA12&dq=Suhrawardi+was+a+Kurdish&hl=no&ei=a1MtTubqK8vIsga9wr33Dw&sa=X&oi=book_result&ct=result&resnum=1&ved=0CDAQ6AEwAA#v=onepage&q=Suhrawardi%2520was%2520a%2520Kurdish&f=falsehttps://en.wikipedia.org/wiki/Special:BookSources/0932885071https://en.wikipedia.org/wiki/Special:BookSources/0754652718https://en.wikipedia.org/wiki/Special:BookSources/1556432690https://en.wikipedia.org/wiki/Special:BookSources/0930872487http://plato.stanford.edu/archives/sum2012/entries/suhrawardi/

8.5. FURTHER READING 19

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

Islamic Intellectual Tradition in Persia by Seyyed Hossein Nasr

8.6 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

https://en.wikipedia.org/wiki/Seyyed_Hossein_Nasrhttp://plato.stanford.edu/entries/illumination/http://www.britannica.com/EBchecked/topic/190219/epistemology/59974/St-Augustinehttp://plato.stanford.edu/entries/augustinehttp://plato.stanford.edu/entries/duns-scotus/http://plato.stanford.edu/entries/suhrawardihttp://www.muslimphilosophy.com/ip/rep/H054.htm

Chapter 9

Inferential role semantics

Inferential role semantics (also conceptual role semantics, functional role semantics, procedural semantics)is an approach to the theory of meaning that identifies the meaning of an expression with its relationship to other ex-pressions, typically its inferential relations with other expressions. Proponents include Robert Brandom,[1][2] GilbertHarman,[3] Paul Horwich, andNed Block.[4] Inferential role semantics originated in the later work of LudwigWittgen-stein.Inferential role semantics is sometimes contrasted to truth-conditional semantics. Jerry Fodor coined the term in-ferential role semantics in order to criticise it as a holistic (i.e. essentially non-compositional) approach to the theoryof meaning.The approach is related to accounts of proof-theoretic semantics in the semantics of logic which associate meaningwith the reasoning process.

9.1 References[1] Pragmatism and Inferentialism

[2] Brandom, Robert (2000). Articulating Reasons: An Introduction to Inferentialism. Harvard University Press. p. 230.ISBN 0-674-00158-3.

[3] "(Nonsolipsistic) Conceptual Role Semantics by Gilbert Harman

[4] Conceptual Role Semantics by Ned Block

9.2 External links Conceptual Role Semantics entry in the Internet Encyclopedia of Philosophy

20

https://en.wikipedia.org/wiki/Robert_Brandomhttps://en.wikipedia.org/wiki/Gilbert_Harmanhttps://en.wikipedia.org/wiki/Gilbert_Harmanhttps://en.wikipedia.org/wiki/Paul_Horwichhttps://en.wikipedia.org/wiki/Ned_Blockhttps://en.wikipedia.org/wiki/Ludwig_Wittgensteinhttps://en.wikipedia.org/wiki/Ludwig_Wittgensteinhttps://en.wikipedia.org/wiki/Truth-conditional_semanticshttps://en.wikipedia.org/wiki/Jerry_Fodorhttps://en.wikipedia.org/wiki/Proof-theoretic_semanticshttps://en.wikipedia.org/wiki/Formal_semantics_(logic)http://johnmacfarlane.net/pragmatism-inferentialism.pdfhttps://en.wikipedia.org/wiki/International_Standard_Book_Numberhttps://en.wikipedia.org/wiki/Special:BookSources/0-674-00158-3http://www.nyu.edu/gsas/dept/philo/courses/concepts/NonSolips.htmlhttp://www.nyu.edu/gsas/dept/philo/faculty/block/papers/ConceptualRoleSemantics.htmlhttp://www.iep.utm.edu/conc-rolhttps://en.wikipedia.org/wiki/Internet_Encyclopedia_of_Philosophy

Chapter 10

Logical atomism

Logical atomism is a philosophical belief that originated in the early 20th century with the development of analyticphilosophy. Its principal exponents were the British philosopher Bertrand Russell, the early work of his Austrian-bornpupil and colleague Ludwig Wittgenstein, and his German counterpart Rudolf Carnap.The theory holds that the world consists of ultimate logical facts (or atoms) that cannot be broken down anyfurther. Having originally propounded this stance in his Tractatus Logico-Philosophicus, Wittgenstein rejected it inhis later Philosophical Investigations.The name for this kind of theory was coined in 1918 by Russell in response to what he called "logical holism"i.e.,the belief that the world operates in such a way that no part can be known without the whole being known first. Thisbelief is commonly called monism, and in particular, Russell (and G. E. Moore) were reacting to the absolute idealismdominant then in Britain.

10.1 Origin

The term was first coined in a 1911 essay by Russell. However, it became widely known only when Russell gave aseries of lectures in 1918 entitled The Philosophy of Logical Atomism. Russell was much influenced by LudwigWittgenstein, as an introductory note explicitly acknowledges.Russell and Moore broke themselves free from British Idealism which, for nearly 90 years, had dominated Britishphilosophy. Russell would later recall in My Mental Development[1] that with a sense of escaping from prison, weallowed ourselves to think that grass is green, that the sun and stars would exist if no one was aware of them.

10.2 Principles

Russell referred to his atomistic doctrine as contrary to the tier of the people who more or less follow Hegel (PLA178).The first principle of logical atomism is that the World contains facts. The facts are complex structures consistingof objects (Particulars). This he defines as objects relations in terms of atomic facts "(PLA 199) is a fact, eitherfrom an object with a simple property or from different objects, in relation to each other more easily. In addition,there are judgments (Beliefs), which are in a relationship to the facts, and by this relationship either true or false.According to this theory, even ordinary objects of daily life are apparently complex entities. According to Russell,words like this and that are used to denote particulars. In contrast, ordinary names such as Socrates actually aredefinitive descriptions. In the analysis of Plato talks with his pupils, Plato needs to be replaced with somethinglike the man who was the teacher of Aristotle.In 1905, Russell had already criticized Alexius Meinong, whose theories led to the paradox of the simultaneousexistence and non-existence of fictional objects. This theory of descriptions was crucial to logical atomism, as Russellbelieved that language mirrored reality.

21

https://en.wikipedia.org/wiki/Analytic_philosophyhttps://en.wikipedia.org/wiki/Analytic_philosophyhttps://en.wikipedia.org/wiki/Bertrand_Russellhttps://en.wikipedia.org/wiki/Ludwig_Wittgensteinhttps://en.wikipedia.org/wiki/Rudolf_Carnaphttps://en.wikipedia.org/wiki/Tractatus_Logico-Philosophicushttps://en.wikipedia.org/wiki/Philosophical_Investigationshttps://en.wikipedia.org/wiki/Logical_holismhttps://en.wikipedia.org/wiki/Monismhttps://en.wikipedia.org/wiki/G._E._Moorehttps://en.wikipedia.org/wiki/Absolute_idealismhttps://en.wikipedia.org/wiki/Alexius_Meinong

22 CHAPTER 10. LOGICAL ATOMISM

10.3 Differences between Russells and Wittgensteins atomism

At the time Russell delivered his lectures on logical atomism, he had lost contact with Wittgenstein. After World WarI, Russell met with Wittgenstein again and helped him publish the Tractatus Logico Philosophicus, Wittgensteinsown version of Logical Atomism.AlthoughWittgenstein did not use the expression Logical Atomism, the book espouses most of Russells logical atom-ism except for Russells Theory of Knowledge (T 5.4 and 5.5541). By 1918 Russell had moved away from thisposition. Nevertheless, the Tractatus differed so fundamentally from the philosophy of Russell that Wittgensteinalways believed that Russell misunderstood the work.The differences relate to many details, but the crucial difference is in a fundamentally different understanding of thetask of philosophy. Wittgenstein believed that the task of philosophy was to clean up linguistic mistakes. Russell wasultimately concerned with establishing sound epistemological foundations. Epistemological questions such as howpractical knowledge is possible did not interest Wittgenstein. Wittgenstein investigated the limits of the world andlater on meaning.ForWittgenstein, metaphysics and ethics were nonsensical, though he did not mean to devalue their importance in lifeby describing them in this way. Russell, on the other hand, believed that these subjects, particularly ethics, thoughbelonging not to philosophy nor science and of possessing an inferior epistemological foundation, were of certaininterest.

10.4 Influence and decline

The immediate effect of the Tractatus was enormous, particularly by the reception it received by the Vienna Circle.However, it is now claimed by many contemporary analytic philosophers, that the Vienna Circle misunderstoodcertain sections of the Tractatus. The indirect effect of the method, however, was perhaps even greater long-term,especially on Logical Positivism. Like Russell, Wittgenstein eventually rejected Logical Atomism. This rejectionculminated in the posthumously published book, Philosophical Investigations.

10.5 See also

G. E. Moore

Logical positivism

Philosophy of language

Logic

Ordinary language philosophy

Theory of descriptions

On Denoting

10.6 References[1] Russell B, (1944) My Mental Development, in Schilpp, Paul Arthur: The Philosophy of Betrand Russell, New York,

Tudor, 1951, pp 3-20

10.7 External links

Russells Logical Atomism entry in the Stanford Encyclopedia of Philosophy

Logical atomism at PhilPapers

https://en.wikipedia.org/wiki/World_War_Ihttps://en.wikipedia.org/wiki/World_War_Ihttps://en.wikipedia.org/wiki/Tractatus_Logico_Philosophicushttps://en.wikipedia.org/wiki/Vienna_Circlehttps://en.wikipedia.org/wiki/Analytic_Philosophyhttps://en.wikipedia.org/wiki/Tractatus_Logico_Philosophicushttps://en.wikipedia.org/wiki/Logical_Positivismhttps://en.wikipedia.org/wiki/Philosophical_Investigationshttps://en.wikipedia.org/wiki/G._E._Moorehttps://en.wikipedia.org/wiki/Logical_positivismhttps://en.wikipedia.org/wiki/Philosophy_of_languagehttps://en.wikipedia.org/wiki/Logichttps://en.wikipedia.org/wiki/Ordinary_language_philosophyhttps://en.wikipedia.org/wiki/Theory_of_descriptionshttps://en.wikipedia.org/wiki/On_Denotinghttp://plato.stanford.edu/entries/logical-atomismhttps://en.wikipedia.org/wiki/Stanford_Encyclopedia_of_Philosophyhttp://philpapers.org/browse/logical-atomismhttps://en.wikipedia.org/wiki/PhilPapers

10.7. EXTERNAL LINKS 23

Logical atomism at the Indiana Philosophy Ontology Project

Russells Metaphysics entry in the Internet Encyclopedia of Philosophy

Peter Schulte: Bertrand Russell: Philosophie des Logischen Atomismus

Kevin Klement: Russells Logical Atomism

Ian Proops: Wittgensteins Logical Atomism

Jeff Speaks: Russell on logical constructions and logical atomism, McGill University 2004

https://inpho.cogs.indiana.edu/idea/676https://en.wikipedia.org/wiki/Indiana_Philosophy_Ontology_Projecthttp://www.iep.utm.edu/russ-met/https://en.wikipedia.org/wiki/Internet_Encyclopedia_of_Philosophyhttp://wwwhomes.uni-bielefeld.de/pschulte/pla-seminar.htmlhttp://plato.stanford.edu/entries/logical-atomism/http://plato.stanford.edu/entries/wittgenstein-atomism/http://www.nd.edu/~jspeaks/mcgill/370/winter2004/russell-atomism.htm

Chapter 11

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.

11.1 See also The doctrine of internal relations

Holography

1. In optics:holography

2. In metaphysics:holonomic brain theory, holographic paradigm and The Holographic Universe (MichaelTalbots 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

24

https://en.wikipedia.org/wiki/Holismhttps://en.wikipedia.org/wiki/Doctrine_of_interna