Q&A: Kant and the Synthetic A Priori
Originally published:
This is an English translation (via GPT-5.4). Read the original Hebrew version.
Kant and the Synthetic A Priori
Question
Hello Rabbi,
Why do you think that arithmetic propositions (7+5=12) are not synthetic a priori?
Answer
Because there is a valid logical way to get from the definitions of the numbers, addition, and equality to that proposition.
Discussion on Answer
You’re just playing around here without adding anything. To say that something is logically necessary means that its negation is a contradiction. So what have you gained here?
Okay, but the claim that *in the real world* 5+7 oranges are 12 oranges is necessarily synthetic.
That is, given the definitions the proposition is analytic, but the fit between the definition and reality is indeed synthetic.
Kant argues that the test for whether a proposition is analytic is the principle of contradiction, meaning that denying the judgment produces a self-contradiction. Let’s illustrate:
"My uncle is not my relative" — how would we check whether this sentence is analytic? We see that there is a contradiction here, since it is like saying: my relative is not my relative. Now let’s try doing this with mathematics:
7+5=12 — let’s try Kant’s own test: 7+5/=12 — contradiction!(?)
Is that what the Rabbi means? Is my argument correct?