The synthetic a priori

I somewhat regret having been so perfunctory in my discussion of Kant in my book on the history of modern philosophy. 

I've been making up for that lately on Quora, posting repeatedly on matters Kantian. 

Here I am getting all pedantic full throttle when another Quora denizen asked the meaning and significance of the phrase "synthetic a priori." 

---------------- 

There are two different dichotomies involved. First, for Kant, (following Hume here), some propositions are synthetic and others are analytic. Roughly speaking, synthetic propositions refer to the objective world, whereas analytic propositions describe the concepts/tools that I may use to grapple with the world. In other words, if we think of knowing-the-world as watching a football game, then synthetic means “about the game and its outcome,” whereas analytic means “about what counts as a ‘point’ and what counts as a ‘win’ etc.”

Secondly, taking from thinkers like Leibniz, Kant sees some knowledge as innate (inborn, hardwired) and other knowledge as learned. Innate is also called a priori and learned is called a posteriori.

So knowledge is “synthetic” and “a priori”... if it consists of knowledge about the external world, AND it is innate.

This matters for Kant because he sees a priori knowledge as more secure than the learned stuff. He wants us to have SECURE knowledge of the objective world, and at the same time he wants to know HOW we can have such knowledge.

Quick examples? “The Vikings beat the Cowboys because they had more points at the end of the game.” That is analytic. It doesn’t tell us anything about the game, it tells us about our concepts — about what we mean when we say one team has defeated another.

“The Vikings beat the Cowboys because they had a superior offensive line, which gave their QB a lot of time to pass.”

That may be true or false, but it is definitely synthetic, it DOES purport to tell me about the game. And it is a posteriori — acquired from a careful viewing of the game, and perhaps of earlier games in the same season by both teams, a study of the QB's pass completion percentages in various "pressured" circumstances, etc. 

Hume had said in effect that all knowledge is of these two sorts. The only certain sort of knowledge doesn’t tell us about the game, only about our words for it. The flip side of that is that the knowledge that does tell us about the game is always going to be uncertain — in this case, there may always have been something my study of the game tapes has missed that would change that interpretation of the outcome.

Kant isn’t happy with Hume’s view. He wants a form of knowledge that is about the game AND can be certain. Something synthetic a priori. Does it exist?

His answer is “Yes, but…” or “Yes, in a sense.” Yes we have synthetic a priori knowledge, but it isn’t knowledge of the most real world, the noumenal world. We have synthetic a priori knowledge of things like tables, sunsets, and football games.

Example: we know of the world that contains such things and events that “every event has a cause.” There is SOME reason or perhaps some congeries of reasons why the Vikings won! Of that we can be certain.

Why are we certain of that? Because we are experiencing this world — it would be impossible for us to experience it unless it had certain features — unless it was the sort of world in which events have causes, game outcomes have reasons.

But notice a corollary of that reasoning. If we deduce the validity of the synthetic a priori from our ability to experience the world, then there is an element of subjectivity about the whole phenomenal world. We can postulate another deeper world that we do NOT experience, the really real, the Noumenal. As to THAT world, we have no knowledge at all, and we must take everything on faith.

Okay this answer was longwinded. But I hope it helped. And it is a lot less longwinded than Kant’s own treatment.