Q&A: Synthetic A Priori
Synthetic A Priori
Question
Hi,
One of the examples I found online to explain Kant’s synthetic a priori is geometrical truths.
Take, for example, a triangle, where the definition of a triangle is a shape with 3 sides. That is analytic because it is rooted in the definition of a triangle. After that they say that the property of a triangle, namely that its angles add up to 180 degrees, is synthetic because it is not rooted in the definition of a triangle, and yet it is necessary and universal—and therefore this geometrical truth is both synthetic and a priori. Q.E.D.
My question is about the second claim, that the sum of the angles in a triangle being 180 is synthetic because it is not rooted in the definition of a triangle as a shape with 3 sides. Why can’t one say that the property of the sum of the angles in a triangle defines the triangle exactly the same way as its having 3 sides does? True, we do not notice this property at first the way we identify the number of its sides, but still I do not see any fundamental difference between the two claims. The definition of a triangle is a shape with 3 sides, and also a shape whose angles sum to 180. If so, it seems that this is not really synthetic a priori.
Thank you
Answer
Hello,
The description you gave is apparently taken from Kant himself, who argued that an arithmetic proposition like 5+7=12 is synthetic a priori. In my opinion this is an analytic claim, and the same is true regarding the sum of the angles in a triangle.
I agree. It seems pretty trivial to understand that these claims are analytic and not synthetic. Do you think Kant didn’t know that?