I have done some reading around Kant's idea of splitting knowledge into synthetic and analytic. I don't understand why does this split matter, knowledge could be split in other way by different criteria - not only by channel of acquisition and its check for truthfulness in statement itself.
Why split it like that, what benefit does it bring if you split this way? Why does it matter?
The issue has a long and debated tradition in modern philosophy since Kant; see The Analytic/Synthetic Distinction.
Against it, see at least the position of Willard van Orman Quine and his famous rejection of the distinction in “Two Dogmas of Empiricism” (1951).
The distinction is related to :
The problem of accounting for mathematical knowledge [...] one of the oldest and hardest problems in Western philosophy. It is easy enough to understand: ordinarily we acquire knowledge about the world by our senses. [...] mathematics does not seem to be known on the basis of experience.
Mathematicians don't do experiments in the way that chemists, biologists or other “natural scientists” do. They seem simply to think, at most with pencil and paper as an aid to memory. In any case, they don't try to justify their claims by reference to experiments: “Twice two is four” is not justified by observing that pairs of pairs tend in all cases observed so far to be quadruples.
But how could mere processes of thought issue in any knowledge about the independently existing external world? [...] Here's where the analytic seemed to many to offer a more promising alternative.
But the "proposed" solution it's far from being definitive...
