The Synthetic a Priori
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Empiricist philosophies of mathematics - Wittgenstein and non-cognitivism
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This rejects the view that mathematical knowledge is knowledge at all. It maintains that we do not have a conscious or cognitive grasp of the truth of mathematics, and that all our understanding of mathematics is expressed by the use of mathematical processes. This view rejects the Kantian concepts of distinctions between a priori and a posteriori, and between the analytic and synthetic as based on a false theory of meaning. This philosophy appears to the interpretation of mathematics offered by Wittgenstein. Diagrammatically, this philosophy refuses to classify mathematics as knowledge, and therefore does not place it into the scheme of synthetic/analytic a posteriori/a priori judgments.
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Contents of
The Synthetic a Priori
1 Empiricism, Platonism, Innate Ideas and the A Priori
2 Analytic a priori
3 Kant and the synthetic a priori
4 Compound (molecular) and atomic sentences
5 Logically atomic sentences and the philosophy of logical atomism
6 Complex sentences and attitudes
7 Subject and predicate, individual and property
8 Synthetic and analytic, definitions offered by Kant
9 A priori and a posteriori
10 The synthetic a priori in Kant - the Critique of Pure Reason
11 Kant, The Critique of Pure Reason, the self and transcendental apperception
12 Empiricist philosophies of mathematics - conventionalism (formalism)
13 Empiricist philosophies of mathematics - the empiricism of J.S. Mill
14 Hybrid empiricist philosophies of mathematics
15 Empiricist philosophies of mathematics - Wittgenstein and non-cognitivism
16 A.J. Ayer and conventionalism - his reply to Kant
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