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What are some specific synthetic a priori truths according to Kant?

Kant’s so-called ‘synthetic a priori’ truths are really just deep analytic truths.

He regards all truths of arithmetic (with exception of ‘1+1=2’ and ‘1=1’ and the like) as synthetic a priori, and puts all of geometry (with similar qualifications) in the same category.

The truth of the matter is that all of these supposedly ‘synthetic’ truths are non-obvious analytic (purely conceptual) truths.

But since you asked—’straight line shortest distance between two points’, ‘7+5=12’, ‘circle=closed planar figure of uniform curvature’: if it’s non-empirical and reasonably non-obvious, Kant says that it is ‘synthetic a priori’—which reflects his utter failure to understand the concept of analyticity.

The relevant fact is that there are no synthetic a priori truths. There are deep analytic truths—some of them a priori, some of them not—but no synthetic ones.

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