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From what I understand in the context of Western philosophy René Descartes famous statement "I think therefore I am" is an example of sythetic a priori. Descartes was a rationalist and this statement is a very famous point of evidence toward rationalism.

Are there any more classic examples of sythentic a priori believed by Descartes or other Western Philosophers?

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    Could you perhaps share a bit more of the context of your question? Generally, 'list questions' are frowned upon on StackExchange. Perhaps you could reformat the question in some way? See the tour and the help center for more information. – Keelan Jan 17 '15 at 21:00
  • I have updated the question, I wasn't looking for an exhaustive list just additional statements or views held by other western philosophers similarly "famous" or "classical" to the claim made by Descartes. Preferably backed up with evidence would be more accepted on Stack Exchange. – user2497792 Jan 17 '15 at 21:09
  • Why would you understand "I think, therefore I am" as a synthetic a priori? How are you defining that term? – virmaior Feb 17 '15 at 0:24
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Kant is the most famous defenser of synthetic a priori. He believed math axioms (of geometry...), or the principle of causality belong to this category. They are constitutive of our experience rather than known by experience (we need them in order to know anything). They are synthetic rather than analytic because their negation is not absurd, yet they are true of the world (according to Kant). Basically any metaphysical principle which is not rooted in experience can be said to belong to this category. Of course, all this is not uncontroversial (empiricists typically deny that the category exists. We now know that Euclid's axioms are not true of physical space).

  • It's worth adding that Euclids axioms are true locally; which I think is the point of Kants 'observers' perspective; that we directly observe only locally. – Mozibur Ullah Mar 19 '15 at 10:34
  • Perhaps in approximation, but not strictly speaking. – Quentin Ruyant Mar 19 '15 at 20:05

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