I have already read several posts on this topic but I have some other questions.
- According to Kant,
5 + 7 = 12
is synthetic a priori judgement. I want to know what the judgement really is. Is it
5 + 7 = 12, or
5 + 7 (which is judged to be 12) ? If it's the first case, we have to know 5 concepts (5,+,7,=,12) to determine if the judgement is true.
- Kant says, nothing allows us to know 5 + 7 equals 12 without synthetic judgement. But that depends on how we see the word "concept". The number "5" has no meaning if it's not in a context (real number, etc.), and in real number context, we have axioms to know 5 + 7 = 12 (by ++ operator). We can't separate "+" and "5" in different contexts. For example, in a strong-type language, there is meaningless to add a float and an integer.