Can anybody advise me reading on how contemporary philosophy treats Kant"s antinomies?
In particular, I am curious, what is the attitude of analytic philosophy to the idea that human intellect inevitably comes to contradictions when analyzing problems like "whether the world has a beginning in time?", or "...is limited as regards space?"
My sense is that contemporary analytic philosophers only mine Kant for interesting arguments and resources useful to their projects. In that respect, they are not going to put much weight in the antinomies for at least two reasons.
First, the antinomies build on Kant's complicated apparatus of knowledge whereby we don't have access to the ding-an-sich (thing in itself) but only receive representations rendered under space and time as the forms of sensibility and turned into objects by the categories of our understanding (of which Kant believes there are exactly 12). It is largely in light of features of this account of understanding that Kant is in the bind on the four antinomies so it's not really interesting if you don't accept that picture of knowledge.
To give just one example, the third antinomy is the one that gets the most contemporary writing, because it relates directly to Kant's moral philosophy (or maybe I write about it because I know the most about that particular topic). Kant thinks Hume is right and there's no freedom to be found in the world we can know. Instead, everything happens by natural necessity. At the same time, Kant's understanding of morality requires that rational beings pick their actions. But we cannot know this on his picture, so Kantian reason is stuck in a bind.
Second, as miners rather than system followers, their goals would be just to look at how the argument is interesting. So these arguments will come up briefly in places like mereology or philosophy of religion but not taken to be authorities -- only interesting problems that come up if you accepts conditions similar to Kant.
