The Synthetic a Priori
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Kant, The Critique of Pure Reason, the self and transcendental apperception
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If Kant is correct then empiricism is false. Furthermore, there is an obvious question that would arise. If we have knowledge of mathematics and that knowledge applies to the real world, and yet we cannot gain that knowledge by looking or experiencing that world, how is this possible? Kant writes, "How are a priori synthetic judgements possible?" His work, The Critique of Pure Reason, gives his answer. We will only sketch it in here. Like Plato, Kant seeks to draw metaphysical conclusions regarding the nature of the soul from his theory of knowledge. He calls the soul the "self" in order to distinguish his conception of it from the Cartesian conception of it as a substance. Whilst the self exists, it is not a substance. He calls his argument the "transcendental deduction". He writes, for example, "We cannot have any kind of knowledge, nor would we be able to connect and form a unity of one kind of knowledge with another, without that unity of consciousness which comes before all the content of our intuitions, and without which the representation of objects would not be possible. I shall call this pure original unchanging consciousness the transcendental apperception." The abiding and unchanging 'I' (pure apperception) is the correlative of everything that is presented to us, and it would not be possible that we should become conscious of any representation without it. All consciousness … belongs in truth to an all-embracing pure apperception. What this means is that according to Kant the self, which is the true seat of our identity, is not to be found in the world. It comprises a pure consciousness that is always present when we experience anything. This, however, does not quite answer the question he posed: how is synthetic a priori knowledge possible? His answer to that question is expressed in the following quotation. "The order and regularity of appearances, which is what we call nature, is created by ourselves. We could never find them in appearances were it not the case that we, or the nature of our minds, had originally supplied them." In order to make the world intelligible to us, the mind unconsciously structures all experiences so as to conform to a certain order and regularity. Mathematics describes that structure. The structure does not come from the experiences and hence cannot be derived from it either; the structure is supplied by the mind itself, and hence the mind can form conclusions about that structure independently of particular experience.
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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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