Kant expresses the cosmological ideas as four distinct antinomies, or pairs of seemingly contradictory metaphysical propositions. They are:
(1) The claim that the world has a definite beginning and end vs. the claim that the world is infinite
(2) The claim that all things are made up of simple, indestructible, indivisible parts vs. the claim that everything is composite and infinitely divisible
(3) The claim that we can act in accordance with our own free will vs. the claim that everything we do is determined by nature
(4) The claim that there are necessary causes vs. the claim that nothing is necessary and everything is contingent
None of these claims can be verified in experience, and so we are tempted to think that they deal not with appearances but with things in themselves. Reason by itself seems capable of proving either side of each antinomy. Rather than come down on one side or the other, Kant proceeds to show how each antinomy results from a misunderstanding of the matter being discussed.
One gathers the impression from what is here, that Kant's not terribly compelling, or plausible, whatever his historical importance. I think this is debatable.
About the claim that is made here, that Frege was the first to point out that geometry is not synthetic a priori. Well, this implies that indeed, geometry is not synthetic a priori. However, Some believe that Frege was wrong. I'll note that I'm also reading, here, about how this position 'was given a boost by Einstein's relativity..' That is to say, that Einstein's relativity<... Read more→
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