A priori knowledge A priori: knowledge that does not require (sense) experience to be known to be true (v. a posteriori) It is not a claim that no experience was necessary to arrive at the claim, but that none is needed to prove it.
Analytic and synthetic propositions An analytic proposition is true or false in virtue of the meanings of the words. –Not all analytic propositions are obvious: In five days’ time, it will have been a week since the day which was tomorrow three days ago. A synthetic proposition is one that is not analytic, i.e. it is true not in virtue of the meanings of the words, but in virtue of the way the world is.
Rationalism v. empiricism Rationalism: we can have substantive a priori knowledge of how things stand outside the mind. –Substantive knowledge is knowledge of a synthetic proposition. Trivial knowledge is knowledge of an analytic proposition. Empiricism: we cannot.
Empiricism on a priori knowledge For any area of knowledge, either –Knowledge is possible, but empirical, not a priori –Knowledge is possible and a priori, but analytic Hume: we can only know ‘relations of ideas’ (analytic and a priori) and ‘matters of fact’ (synthetic and a posteriori) Ayer’s verification principle: all meaningful statements are either analytic or empirically verifiable
Locke: religion and morality Knowledge of God and moral knowledge is ‘ demonstrable ’ and ‘ self-evident ’ We know that we exist (synthetic) and that something cannot come from nothing (analytic). So something must always have existed, and everything else which exists must have come from this (analytic). As we have knowledge and intelligence, we may deduce that this original being is a knowing intelligence (analytic). From our knowledge of the existence and nature of God, and of ourselves as creations of God, we can deduce what our moral duties are.
Hume’s response Locke’s analytic truths are, in fact, unjustified assumptions. To deny an analytic truth is a contradiction in terms, e.g. ‘some bachelors are married’. But it is not a contradiction to deny that something exists, e.g. that God does not exist. So analytic truths can’t tell us what exists.
Kant and mathematics Kant argued that mathematics is a priori, but synthetic Most empiricists argue it is analytic - we don’t allow true mathematical claims (2 x 5 = 10) to be false, they are true by definition So maths is a roundabout, complicated way of saying A = A
Metaphysics Kant: a priori synthetic truths are about the way experience must be for us, e.g. ‘Nothing can be coloured in different ways at the same time in the same part’ –If this is analytic, it is made true by rules of language. But is this the (arbitrary) source of how we experience things?
Rational intuition? How could we gain knowledge of ‘metaphysical’ truths? ‘Reason’ But how does ‘reason’ work here? What is rational ‘intuition’ into how things are? Is it reliable?