Thursday, November 01, 2007


I don't have my copy of Critique of Pure Reason at hand, so what follows won't be sourced or complete. I really need to read the relevant parts again.

Kant says that 7 + 5 = 12 is synthetic a priori. I've been reflecting on why exactly that is. To compare: "the sum of the interior angles of a triangle is 180 degrees" is also synthetic. It's synthetic because the pure concept (I hate using that word here, but bear with me) "triangle" is defined as "three-sided figure." At this point, the properties of a triangle are purely analytic. In order to get to the (true) synthetic judgment that the angles sum to 180 degrees, one has to "immerse" the pure concept in space. Thus, what makes a synthetic judgment about mathematics synthetic is that it has been applied to space or time (the two forms of empirical intuition). Synthetic judgments in physics must, if I recall, add the twelve concepts in addition to intuition in order to become real. Again, I need the source to confirm that.

So what intuition is involved in "7 + 5 = 12"? There are two choices - space or time. I suspect time, if anything, is the relevant form of intuition, and this may confirm the interpretation of Kant that claims that time is represented, when we think about it, as some sort of counting. That is, event 2 follows event 1 as the number 2 follows the number 1.

This is nothing but a sloppy pseudo-brainstorm about Kantianism, which I hope to perfect over the weekend. Stay tuned.


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