eli5: how do synthetic judgments a priori work in maths and physics?

Question

eli5: how do synthetic judgments a priori work in maths and physics?

In: 1

Answer 1

Since you can’t ‘expirience’ math all math except maybe the number 1 is a priori. But you can make judgments about mathematical things that are not already part of the terms you use. An analytical judgement would be that a triangle has three angles. What a synthetic judgment would be is a bit controversial in philosophy still but could be things like pi or a²+b²=c².