chuck, your best bet is to hunker down and go through the two big books. i will say, however, two things, in response to you and to ravi. Jeffery Fisher
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First, Jeff. Yes your right about the necessity of reading Badiou. But jeus my apartment is full of books I've started but haven't finished. The other thing is I am not really mounting a critique of Badiou. I was presenting a sketch of how I conceive the idea that math is ontology. I was being as sincere as I could get, mostly in support of the idea, just reconceptualized.
This kind of philosophy is very tough to do and to follow.
Now for Chris. I think most philosophies don't start with either space or time, but start with some logical assertion. That way they skip the problem of a concrete ontology. If you pick something that also has a concrete or physical analog you have to back pedal and justify it with some logical sounding argument. Heidegger (I think) want to concretize an ontology through subjective experience, or through an analysis of the phenomenology of mind. The dynamic nature of conscienousness is its experience in or as time.
Now in my philosophy of mathematics, the concept of time is developed as a concept of the real number system as used in physics, counting and what have you. In the deeper philosophical sense our concept of time is intimate linked with the concept of Measure as in set of measure X. Space on the other is given a mathematical form as geometry or topology.
Also there is an external motivation. I want to get to a theory of mind that can be used in empirical studies of the mind that can also be extended to animals. While us and furries both share spacetime in a 3-d eucidean space, it is a lot easier to account for the similarities of mind between us and animals if you convert over to space constructions and studies. It is a lot more difficult to account for some similarity of mind between us, if we have to start with the nature of the phenomenon given to conscieousness in the sense of a time like experience. We damn well know animals navigate space. We don't necessarily know they experience pain or what we might mean by that.
So that is another of my excuses for starting with some ontology of space.
There is yet another issue. We know our world hasn't changed its physics, so we share that with all our past ancestors and the animals and plants. So that forms a constant against an ever changing relativity of views, thoughts, theories, etc.Space is one of those constants with lots of physics associated with it.
CG