A Priori Knowledge: Analytic? Synthetic A Priori (again) Is All A Priori Knowledge Analytic?

A Priori Knowledge: Analytic? Synthetic A Priori (again) Is All A Priori Knowledge Analytic?

Recap A Priori Knowledge Knowledge independent of experience Kant: necessary and universal A Posteriori Knowledge Knowledge by experience Kant: contingent and at best comparatively universal Analytic Propositions 1) Predicate contained within the subject 2) Denial contradictory Synthetic Propositions 1) Predicate lies outside the subject 2) Denial not contradictory

Three Types of Knowledge? 1. Synthetic A Posteriori Contingent, known by experience E.g. this chair is blue, all bodies are heavy 2 Analytic A Priori Necessary, known by analysis of concepts (or meanings) E.g. all bachelors are unmarried men 3. Synthetic A Priori Necessary, known by faculty of a priori intuition Knowledge of truths about the world or reality Kant: empirical reality, as opposed to transcendental reality E.g. 7+5=12, internal angles of a triangle add up to 180

A Priori Intuition? A priori reasoning fallible? Made mistakes in past, so perhaps in future? A priori reasoning cannot be calibrated? Experience? But can this (dis)confirm a priori beliefs? (Cf. Ayer, p. 101 and lecture 16) How can we have knowledge of reality independent of experience? Perceptual beliefs causally related to the facts How are a priori beliefs related to the facts? Transcendental idealism? Platonism?

(Digression: Kitcher) 1) S knows that p iff S knows that p and S s belief that p was produced by a process which is an a priori warrant for it 2) a is an a priori warrant for S s belief that p iff a is process such that, whatever S s experience: Some process of the same type could produce in S a belief that p That process would warrant S in believing that p If it were to produce in S a belief that p then p A version of reliablism: S knows that p iff S s belief is formed by a reliable belief forming mechanism

Ayer, Language, Truth and Logic Empiricist: all (factual) knowledge from experience Verificationist: the meaning of statement is determined by its verification conditions Statement meaningful iff there is some observation that allows you to determine whether statement is true or false Meaningful: statements about physical objects, science Meaningless: metaphysics, theology, ethics (cf. emotivism) Note: verificationism a form of empiricism No synthetic a priori knowledge Kant: How is metaphysics possible? (Preface, Critique) Ayer: The Elimination of Metaphysics (Chapter 1)

Ayer: A Priori Knowledge Of necessary truths, so not from experience Cf. Kant: Experience teaches us that a thing is so and so, but not that it cannot be otherwise (p. 143) Of analytic truths, so not about the world Tautologies: true in virtue of meaning of the words Devoid of factual content, but not meaningless They simply record our determination to use words in a certain fashion (p. 112) No synthetic a priori, so no a priori intuition

Verificationism Strong verification: too restrictive E.g. Ants will never inherit the earth, atoms exist Weak verification: too permissive E.g. God exists is perhaps in principle verifiable Is verification theory of meaning meaningful? What observation would allow us to determine truth or falsity of principle: A statement is meaningful iff there is some observation that allows you to determine whether statement is true or false?

Maths: Analytic? it is possible for symbols to be synoymous without having the same intensional meaning for anyone (Ayer p. 104) Intension = meaning, or sense (distinguish: intention) Contrasts with extension = reference, or what its true of Hesperus, Phosperus : different intension, same extension Mathematical propositions synthetic according to Kant s first criterion 12 not contained within 7+5 but analytic according to his second criterion: 7+5 = 12 is necessarily true, so 7+5 12 is a contradiction

New Knowledge? If both are tautologies, why does all unmarried men are unmarried differ from 91 x 79 = 7189? Former is obvious, latter is not Phenomenology of maths: seems like discovery Ayer: The power of logic and mathematics to surprise us depends, like their usefulness, on the limitations of reason (p. 114) Not all tautologies are obvious E.g. It is not the case that not all unmarried men are bachelors but is this acceptable?

Knowledge of Meaning? Analytic truths are true in virtue of meaning, but how can we know facts about meaning? Reductive: analytic truths reducible to logical truths by substitution of synonyms E.g. all bachelors are unmarried men all unmarried men are unmarried men ( p)(p p) But how do we know (a priori) truths of logic? Non-reductive: how does a priori knowledge of meaning differ from a priori intuition?

Apsychologistic Says nothing about psychological processes that cause a priori beliefs S knows a priori that p iff S believes that p and p is analytically true Can t distinguish belief that p from knowledge that p Can t distinguish believing that p for good and bad reasons (Cf. Kitcher, A Priori Knowedge, p. 22) Compare: S knows that p iff S believes that p and p is true. (Cf. Ayer, The Right to Be Sure (Week 1), from The Problem of Knowledge (1956).)

Recap Synthetic A Priori Knowledge (again) Is All A Priori Knowledge Analytic?