Comment on Open thread, August 4 - 10, 2014

Wed, 06 Aug 2014 00:10:23 GMT

Take, for example, the proposition: "Two straight lines cannot enclose a space, and with these alone no figure is possible," and try to deduce it from the conception of a straight line and the number two; or take the proposition: "It is possible to construct a figure with three straight lines," and endeavour, in like manner, to deduce it from the mere conception of a straight line and the number three. All your endeavours are in vain, and you find yourself forced to have recourse to intuition, as, in fact, geometry always does.

Geometry, nevertheless, advances steadily and securely in the province of pure a priori cognitions, without needing to ask from philosophy any certificate as to the pure and legitimate origin of its fundamental conception of space.

I agree that Kant doesn't seem to have ever considered non-euclidean geometry, and thus can't really be said to be making an argument that space is flat. If we could drop an explanation of general relativity, he'd probably come to terms with it. On the other hand, he just assumes that two straight lines can only intersect once, and that this describes space, which seems pretty much what he was accused of.

Discuss