Reflections on methodology II: Philosophy of science (Hirzel, 2011)
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Reflections on methodology belongs to a serious of propaedeutics in the context of the research dissertation Principles of Liberty by Tabea Hirzel (2015). Reflections on methodology II gives an overview about the most relevant logical theories, especially dilemma's in syllogism's propositional calculus, known as logical tetralemma or Catuṣkoṭi.
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Reflections on methodology II: Philosophy of science (Hirzel, 2011)
- 1. Reflections on Methodology II Philosophy of Science Doctoral Candidate: Tabea Hirzel Program: Doctorate of Diplomacy/ Political Economy University: SMC University, Zug, Switzerland Date: 12.30.2011
- 2. Catuṣkoṭi (central problem in dharmic logic) • Not (Both P and Not- P) • Not (Neither P nor Not-P) • Not (Not- P) • Not (P) P Not-P Both P and Not-P Neither P nor Not-P 4 P in positive configuration (black) 4 P in negative configuration (white) 1 2 3 4 9 Superposition (Śūnyatā)© Tabea Hirzel 2
- 3. 3 levels of science Define «reality» (factual truth, what) • define the limitations in all details Understand the meaning of «reality» • Explain the reasons for doubt Transform reality • Manifest certainty © Tabea Hirzel 3
- 4. Comparison of schools Goal (why) Reason is Mean (how) What is searched Givens Foundatio n 1. Positivism Find truth Calculation Define reality through testing of hypoteses (which lead to certainty): hypothetical propositions Prediction constants (empirical certainty) External reality (objects) 2. Critical theory Underst and the world Dialiectics Find meaning through doubt which leads to personal appreciation of reality: axiomatic propositions (a priori) Apodictic knowledge (logical certainty) Existential being (objects + subjects) 3. Ontological turn (OOO) Becomi ng Tansform reality through encounters which transforming yourself Totality of being (objects + subjects + eternal being) © Tabea Hirzel 4
- 5. Categories of being (1) Action (liberty, totality, God) (2) External universal being (God) (3) Existential being (4) objects (5) time (6) space (7) energy (8) matter (9) subjects (10) subjectivity Kant’s view on space and time © Tabea Hirzel 5
- 6. Aristotle categories © Tabea Hirzel 6
- 8. Syllogism: Dilemmas in propositional calculus Problems Actuality Reality Certainity Totality Arguments Apodictic- epideictic Formatted- unformatted implicit.- explicit Propositions Under any (all) valuation s Logic, propositional logic, Boolean algebra; modal logic Tautological Necessari ly true p;⊤; T; 1 Contradictions Necessari ly untrue ⌐p;⊥; F; 0 Possible Could have been true ⌐□⌐; ◊ Contingent Neither true nor untrue ⌐ (p ᴧ ⌐p) © Tabea Hirzel 8
- 9. Theories of logic Logic Dialectical logic Informal logic Natural language (fallacies) Formal logic Symbolic logic (mathematical) Predicate logic First-order-logic Second-order-logic Higher-order-logic Type theory (formal system) Propositional logic Zeroth-order-logic ZOL with axiom schema (Peano) ZFC Etc. Mathematical logic model theory semantics proof theory set theory recursion theory Syllogism (Aristotle) Modal logic Infinitary logic Ω-logic (set theory) Intuitionistic logic (without law of the excluded middle) Algebraic logic Boolean algebras Heyting algebras Cylindric algebras © Tabea Hirzel 9
- 10. Systems of logic Unification logic Formal logic Dialectical logic Transcend ental logic Process logic Forms of thought Objective & Subjective Subjective Objective Subjective Content of though Objective & Subjective none Objective Objective Laws of though Give-and- Receive law Law of Identity and law of Contradicti on Dialectical method Transcend ental method Standard of thought Structure of the original image none none none Characteris tics Theory of collation Theory of form Theory of reflection Theory of synthesis Source: http://www.unification-thought.org/eut/eut10.html © Tabea Hirzel 10
- 11. Laws of thought (formal logic) Kant & Aristotle Symbolic Formal Implies i) The Law of Identity p ⊃ q A ≡ A A is A A flower is a flower A flower is a plant identity of thought Categorical thinking ii) The Law of Contradiction p. – p A ⌐ (⌐ A) A is not (not A) A plant is not an animal iii) The Law of the Excluded Middle (Leibnitz) P V -p (¬A) ⊕ A B is either A or not-A something is and is not iv) The Law of Sufficient Reason ⇒ x = 2 ⇒ x2 If a rose is a flower and a flower is a plant then a rose is a plant. © Tabea Hirzel 11
- 12. Propositional logic Definition Aspects Concept A concept is a general representation (or idea) through which the essential characteristics of a thing are grasped. Intension, extension Specific (supordinate), generic (superordinated) The qualities, or properties, common to a certain concept are called the intension of that concept. A set of things to which a certain concept is applied is called the extension of that concept Categories: the highest generic concepts. Intension: all cognitive being is personal being. Extension: open, possibly human, animal, plants, universe, certainly not totality (liberty, God). Judgement Is a proposition, an affirmation or denial of a relation among certain concepts subject, predicate, and copula (S-P) The object to which a thinking is directed is the subject; the predicate describes its content; and the copula connects the two Inference © Tabea Hirzel 12
- 13. i) substance ii) quantity iii) quality iv) relation v) place vi) time vii) position viii) condition ix) action x) passivity Aristotle Kant © Tabea Hirzel 13
- 14. 12 Kinds of Judgements (Kant) Universal judgment (Quantity) Every S is P Particular judgment (quantity) Some S is P Singular judgment This S is P Affirmative judgment (quality) S is P Negative judgment (quality) S is not-P Infinite judgment (quality) S is not-P Relation Categorical Judgment S is P Hypothetical Judgment If A is B, C is D Disjunctive judgment A is either B or C Modality Problematic judgment S may be P Assertoric judgment S is in fact P Apodeictic judgment S must be P © Tabea Hirzel 14
- 15. Chris Jones (2012). 21st Century Kant: Learning to Frame Knowledge Anew (w/ help from Aristotle & Wittgenstein). http://sourcepov.com/2012/01/22/21stc-kant-convergence/ © Tabea Hirzel 15
- 20. Forms of judgement (Kant) Code Universal categorical S is P Universal affirmative Every S is a P. A Universal negative No S is a P E Particular affirmative Some S is a P I Particular negative Some S is not a P O distributedundistributed vs. PS P Universal Affirmative judgment S P Universal Negative judgment © Tabea Hirzel 20
- 21. Inference Conclusion s Propositions Premises (already known propositions) Inference Amount of premises (propositions) Methodology Types Deduction direct 1 indirect 1+1 Syllogism Cathegorical 1+1 Syllogism Hypothetical 1+1 Syllogism Disjunctive 1+1 Syllogism dilemma 1+1+1+n Induction Application of syllogism Propositional calculus Calculus Analogy Phenomenology Empirics Analogy The method by which one attempts to reach a general assertion from a number of observed particular facts is called inductive inference, or induction. It is regarded as an application of the syllogism. Analogy refers to the inference through which, based on similarities, other particular phenomena are inferred from known particular phenomena. © Tabea Hirzel 21
- 22. Categorical syllogism Man is mortal. Major premise «mortal» has the greatest extension. M is P. Socrates is a man. Minor premise «Socrates» has the smallest extension. S is M. Therefore, Socrates is mortal. Conclusion The extension of "man" is between the two; therefore, it is called the "middle term. Therefore, S is P. P= major term S= minor term M= middle term © Tabea Hirzel 22
- 23. Is possible (true) fallacy of illicit minor In a syllogism the minor term being unduly distributed. … because in natural science rules the "principle of uniformity in nature" (= all phenomena in the natural world have the same form) and because the "law of causality“ (= there are always cause and effect) fallacy of undistributed middle In a syllogism the middle term is not distributed … but the conclusion has merely the value of probability If the middle concept is distributed (that is, if all the necessary conditions for the premise to be true are given), the conclusion becomes certain. © Tabea Hirzel 23
- 24. God’s thinking: universal definitions and laws of reality (Hegel) Logic (Idea) of Being Quality Being Being Nothing Becoming Determinate Being Being-for- Itself Quantity Measure of Essence Essence Appearance Actuality of Notion Subjective notion Objective notion Idea Life Cognition Absolute Idea ⌐ Logic (Nature) © Tabea Hirzel 24
- 25. Nature Mechanics Physics Organics © Tabea Hirzel 25
- 26. Hegel’s System © Tabea Hirzel 26
- 27. Returning Nature of Hegel’s Dialectic © Tabea Hirzel 27
- 28. Symbolic Logic i) Negation «not p»; ⌐p; ii) Disjunction «p or q»; p V q iii) Conjunction «p and q»; p - q iv) Implication «if p then q»; p ⊃ q v) Equivalence «p equals q»; ≡ © Tabea Hirzel 28
- 30. Hume’s Fork © Tabea Hirzel 30
- 31. The Personhood Puzzle http://www.webpages.uidaho.edu/ngier/103/kant.htm © Tabea Hirzel 31
- 32. History • Aristotle (384 BC – 322 BC): Realist theory of categories ; Intelligible universals extending across all domains; Central role of organisms • Medieval scholastics: Aquinas, Scotus, Ockham, … (1200 – 1600): Aristotelianism as philosophia perennis; Common panscientific ontology and controlled vocabulary (Latin) • Descartes (1596 – 1650): Sceptical doubt initiates subversion of metaphysics, rise of epistemology; Central role of mind; Dualism of mind and matter • Kant (1724 – 1804): Reality is unknowable; Metaphysics is impossible; We can only know the quasi-fictional domains which we ourselves create • Brentano (1838 – 1917): Rediscovery of Aristotle; Methods of philosophy and of science are one and the same • Husserl (1859 – 1938): Inventor of formal ontology as a discipline distinct from formal logic; Showed how philosophy and science had become detached from the ‘life world’ of ordinary experience © Tabea Hirzel 32
- 33. History II • Wittgenstein 1 (ca. 1910 – 1918): Bases ontology on formal logic in reductionistic atomism • Vienna Circle (1922 – ca. 1938) -Schlick, Neurath, Gödel, Carnap, Gustav Bergmann …:Centrality of logic to philosophy; Construction of philosophy from either physics or sensations as base • Wittgenstein 2 (ca. 1930 – 1951): Centrality of language and of language games; Metaphysics = language goes on holiday • British Ordinary Language philosophy: Philosophical problems to be solved by the study of the workings of language; Speech Act Theory (J. L. Austin, 1911-1960) • Quine (ca. 1930 – 1951): Ontological commitment (study not: what there is, but: what sciences believe there is when logically formalized) • Analytical metaphysics (from ca. 1980): Chisholm, Lewis, Armstrong, Fine, Lowe, … beginnings of a rediscovery of metaphysics as first philosophy • Ontologic turn in philosophy © Tabea Hirzel 33
- 34. Four phases of Philosophy • First cycle (rapid progress): ThalesAristotles; Stoicism & Epicurianism; Pyrrho, Eclectics; Neo-Pythagoreans, Neo-platonists. • Second cycle (practical interest): up to Aquinas; Scotism; Ockham, Nominalists; Lull, Nicholas of Cusa. • Third cycle (scepticism): Bacon, Locke; Rationalists; Hume, Reid; Berkley, Kant, German Idealism. • Fourth Continental cycle (mysticism): Brentano, Polish school; Husserl; Heidegger; Derrida and the French. • Fourth Analytic cycle (mysticism): Frege, Wittgenstein 1, Russell; Vienna Circle; Wittgenstein 2, Quine; Rortry. • Fifth cycle: Analytical Metaphysics, Rediscovery of Aristotle; Ontology © Tabea Hirzel 34
- 35. Each cycle starts with a rediscovery of Aristotle: From the 3rd cycle marked by invention of new disciplines: 3. Empirical natural science; 4. Psychology, logic © Tabea Hirzel 35
- 39. https://www.brocku.ca/MeadProject/Bergson/Bergson_1 911b/Bergson_1911_03.html Henri Bergson’s Matter and Mind. Chapter 3 Bergson’s Cone of Memory http://www.unification-thought.org/neut/Neut01.html © Tabea Hirzel 39
- 41. Whitehead (continued) © Tabea Hirzel 41
- 42. Tahlil: Lā 'Ilāha 'Il-lal-lāhu http://www.untiredwithloving.org/papillon.html © Tabea Hirzel 42
- 44. The Tantalizing ‘Gap’ in Kant’s System http://staffweb.hkbu.edu.hk/ppp/ksp2/KCR11.htm Tjurunga © Tabea Hirzel 44
- 46. OOO Object oriented ontology http://bebereignis.blogspot.com.es/2011/01 /some-problems-with-object-oriented.html © Tabea Hirzel 46
- 47. Graham Harman’s Quadruple Object http://www.zero-books.net/books/quadruple-object-the http://philosophyinatimeoferror.com/2012/06/27/speculative-realism-and-real- time/ © Tabea Hirzel 47
- 48. Bernhard Bolzano © Tabea Hirzel 48
- 49. Process Philosophy Source: Adelheid Mers 2013 © Tabea Hirzel 49
- 51. Interactive Iteration http://www.celta.paris-sorbonne.fr/forum/viewtopic.php?pid=68 © Tabea Hirzel 51
- 53. Formal Ontology http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0104- 65002003000300005 © Tabea Hirzel 53
- 55. Lacan’s famous Borromean knots http://larvalsubjects.wordpress.com/2009/12/08/borromean-knots-ooo-and- social-and-political-theory/ © Tabea Hirzel 55
- 56. Barry Smith http://ontology.buffalo.edu/smith/articles/menger.html We might represent the a priori relations between such species (relations of de re necessitation) in diagrammatic form as follows, employing links connecting broken to solid walls of adjacent frames to represent relations of one-sided dependence between the entities concerned: © Tabea Hirzel 56
- 57. Gene Ontology (GO) Parent Term Child Regulation + ve regulation - Ve regulation is a part of regulates + ve regulates - ve regulates © Tabea Hirzel 57
- 58. Aristotle’s Metaphysics • The world is organized via types/universals/categories which are hierarchically organized • Linnaean Hierarchy: species-genus hierarchy; as inference machine © Tabea Hirzel 58
- 59. From Species to Genera animal bird canary can sing is yellow has wings can fly has feathers has skin moves eats breathes species-genus hierarchy as inference machine 59 © Tabea Hirzel
- 60. From Species to Genera animal bird canary can sing is yellow has wings can fly has feathers has skin moves eats breathes fish has fins can swim has gills 60 © Tabea Hirzel
- 61. animal bird canary From Species to Genera can sing is yellow has skin moves eats breathes has wings can fly has feathers species-genus hierarchy as inference machine X 61 © Tabea Hirzel
- 62. Species-genus trees can be represented also as map-like partitions If Aristotelian realism is right, then such partitions, when correctly built are transparent to the reality beyond 62 © Tabea Hirzel
- 63. Aristotle’s Metaphysics is focused on objects (things, substances, organisms) • The most important universals in his ontology are substance universals • cow man rock planet • which pertain to what a thing is at all times at which it exists 63 © Tabea Hirzel
- 64. For Aristotle, the world contains also accidents • which pertain to how a thing is at some time at which it exists: • = what holds of a substance per accidens red hot suntanned spinning 64 © Tabea Hirzel
- 65. Different partitions may represent cuts through the same reality which are skew to each other 65 Perspetivalism © Tabea Hirzel
- 66. Not all need be structured in substance-accident terms – perhaps there are pure process levels, perhaps there are levels structured as fields 66 Perspectivalism © Tabea Hirzel
- 67. From Species to Genera animal bird canary can sing is yellow has wings can fly has feathers has skin moves eats breathes fish has fins can swim has gills ostrich has long thin legs is tall can‘t fly y 67 © Tabea Hirzel
- 68. From Species to Genera animal bird canary can sing is yellow has wings can fly has feathers has skin moves eats breathes fish has fins can swim has gills ostrich has long thin legs is tall can’t fly y 68 © Tabea Hirzel
- 69. Different partitions may capture reality in ways which involve different degrees of vagueness 69 Perspectivalism © Tabea Hirzel
- 70. hard vs. soft categories • Kantianism: we constitute/shape (empirical) reality in such a way that it corresponds to our categories • Aristotelianism: reality in itself is messy, but our categories fit nonetheless 70 © Tabea Hirzel
- 71. Concepts vs. categories • on the Kantian reading species are concepts, which we bring to reality • on the Aristotelian reading the world itself exhibits a species-genus structure independently of how we conceive it and we do our best to map this structure in our representations 71 © Tabea Hirzel
- 72. Basic Formal Ontology (BFO) Continuant Occurrent (Process) Independent Continuant Dependent Continuant ..... ..... ........72 © Tabea Hirzel