Notes on Kant’s Introduction to The Critique of Pure Reason

“Experience teaches us, to be sure, that something is constituted thus and so, but not that it could not be otherwise. First, then, if a proposition is thought along with its necessity, it is an a priori judgement; … Second: Experience never gives its judgements true or strict but only assumed and comparative universality (through induction), so properly it must be said: as far as we have yet perceived, there is no exception … Necessity and strict universality are therefore secure indications of an a priori cognition” (B 3–4).

“he focuses on apriority as applied to warrants rather than propositions, and limits himself to a sufficient condition only. Universality and explicit necessity turn out to be criteria for apriority in the sense of providing sufficient condition for there being at least some important a priori element in the best kinds of warrant for the claim.”⁶

“In all judgements in which the relation of a subject to the predicate is thought… this relation is possible in two different ways. Either the predicate B belongs to the subject A as something that is (covertly) contained in this concept A; or B lies entirely outside the concept A, though to be sure it stands in connection with it. In the first case I call the judgement analytic, in the second synthetic. Analytic judgements are thus those in which the connection of the predicate is thought through identity, but those in which this connection is thought without identity are to be called synthetic judgements. One could also call the former judgements of clarification, and the latter judgements of amplification, since through the predicate the former do not add anything to the concept of the subject, but only break it up by means of analysis into its component concepts, which were already thought in it (though confusedly); while the latter on the contrary add to the concept of the subject a predicate that was not thought in it at all, and could not have been extracted from it through any analysis” (A 6–7/B 10).

“… that connection is constrained by reciprocity; if B is contained in A, then A must fall under B, and further, it must contain whatever B contains and exclude whatever B excludes, lest their contents and extensions come apart. But even elementary arithmetic truth requires contents and extensions to part company in just this way. Consider Kant’s example, “7 + 5 = 12”: if <12> is supposed to be contained in the sum concept, <7 + 5>, then <7 + 5> must exclude whatever <12> does, including, presumably, <5> and <7> (since 12 ≠ 5 and 12 ≠ 7). But now, since it permits only the one type of affirmative connection, containment analyticity affords no way of explaining the relation <7 + 5> bears to <7> and <5>, and thus it fails to express the relation among the three numbers that is essential to the content of the arithmetic proposition.”¹⁰

“in a latter explaining his position to his disciple Johann Schultz, where he considers propositions like “3 + 5 = 2 × 4” (Correspondence, 10: 554–8). Here the failure of reciprocity is fully transparent, since it is obviously wrong to attribute the same content to the concepts, which involve different operations on different numbers, but the judgement is nevertheless true because the terms on each side “determine the same object” falling under them — that is, the magnitude to which they apply (Correspondence, 10: 555).”¹¹



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