A Priori Synthetic Judgements

Judgements can be either a priori or a posteriori in terms of origin, that is, depending on whether they precede or succeed empirical experience (a distinction which also marks the difference between necessary and contingent truths); and analytic or synthetic in terms of content, depending on whether they contain elements internal or external to the faculty of reason. Kant determines the latter by means of a subject-copula-predicate relation: the predicate term in an analytic judgment never contains anything more than what is already contained in the subject term, while the predicate term in a synthetic judgment will always be in excess of its subject term. An analytic judgement, therefore, elucidates the subject term by making clear some particular aspect of it that had been there all along, while a synthetic judgment adds something to reason that is not already inherent in it.

Kant gives the following example: 

‘If I say, for instance, All bodies are extended, then this is an analytic judgement, I need not go beyond the concept which I connect to the body in order to find that extension is connected to it. To find that predicate, I only need to analyse the concept, that is, become conscious of the manifold that I always think in it. The judgment is therefore analytic. But if I say, All bodies are heavy, the predicate is something quite different from what I think in the mere concept of a body in general. The addition of such a predicate therefore yields a synthetic judgement’. Another way of putting this is to assert that analytic judgements are subject to the logical law of non-contradiction, while synthetic judgements are not. An illuminating, yet infrequently cited description of this distinction is Kant's claim that judgments are analytic only if their truth is 'based entirely on the principle of [non]contradiction', while judgments are synthetic only 'under the condition that an intuition underlies the concept of their subject'. 
- Kant, Critique of Pure Reason, A7-A8; B11-B12

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