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Single Idea 5203

[filed under theme 12. Knowledge Sources / A. A Priori Knowledge / 5. A Priori Synthetic ]

Full Idea

From the fact that one can think of the sum of seven and five without necessarily thinking of twelve, it by no means follows that the proposition '7+5=12' can be denied without self-contradiction.

Gist of Idea

We can think of 7 and 5 without 12, but it is still a contradiction to deny 7+5=12

Source

comment on Immanuel Kant (Critique of Pure Reason [1781]) by A.J. Ayer - Language,Truth and Logic Ch.4

Book Ref

Ayer,A.J.: 'Language, Truth and Logic' [Penguin 1974], p.104

A Reaction

Kant's claim that arithmetic was synthetic always looked glib and dubious, and this pinpoints an objection very nicely. It appears that the great Kant has confused his epistemology with his ontology.

The 26 ideas with the same theme [a priori knowledge which refers to the external world]:

3342 Seeing that only one parallel can be drawn to a line through a given point is clearly synthetic a priori [Kant, by Benardete,JA]
20943 Kant bases the synthetic a priori on the categories of oneness and manyness [Kant, by Bowie]
5402 Kant showed that we have a priori knowledge which is not purely analytic [Kant, by Russell]
5203 We can think of 7 and 5 without 12, but it is still a contradiction to deny 7+5=12 [Ayer on Kant]
5527 That a straight line is the shortest is synthetic, as straight does not imply any quantity [Kant]
5528 That force and counter-force are equal is necessary, and a priori synthetic [Kant]
5529 The real problem of pure reason is: how are a priori synthetic judgments possible? [Kant]
5537 That two lines cannot enclose a space is an intuitive a priori synthetic proposition [Kant]
5546 Are a priori concepts necessary as a precondition for something to be an object? [Kant]
5558 7+5=12 is not analytic, because 12 is not contained in 7 or 5 or their combination [Kant]
5624 We possess synthetic a priori knowledge in our principles which anticipate experience [Kant]
3726 The categorical imperative is a practical synthetic a priori proposition [Kant]
16916 A priori synthetic knowledge is only of appearances, not of things in themselves [Kant]
9225 Hegel reputedly claimed to know a priori that there are five planets [Hegel, by Field,H]
23500 My main problem is the order of the world, and whether it is knowable a priori [Wittgenstein]
23479 The Tractatus aims to reveal the necessities, without appealing to synthetic a priori truths [Wittgenstein, by Morris,M]
23501 There is no a priori order of things [Wittgenstein]
2619 Whether geometry can be applied to reality is an empirical question outside of geometry [Ayer]
2513 We don't have a clear enough sense of meaning to pronounce some sentences meaningless or just analytic [Katz]
2794 Knowing that a cow is not a horse seems to be a synthetic a priori truth [Dancy,J]
3341 Logical positivism amounts to no more than 'there is no synthetic a priori' [Benardete,JA]
3344 Assertions about existence beyond experience can only be a priori synthetic [Benardete,JA]
3345 Appeals to intuition seem to imply synthetic a priori knowledge [Benardete,JA]
3349 If we know truths about prime numbers, we seem to have synthetic a priori knowledge of Platonic objects [Benardete,JA]
3887 Maybe our knowledge of truth and causation is synthetic a priori [Scruton]
3876 If my team is losing 3-1, I have synthetic a priori knowledge that they need two goals for a draw [PG]