Ken, Lacan, and group theory

Thu Nov 4 09:09:38 PST 1999

Absolutely nothing. But I got fascinated by the idea that the structuralists in the early sixties were using groups as the underlying form to their theories. Piaget was probably the only one who knew what he was doing, since he had started off with a degree in the philosophy of science and probably had to take the courses. Ecco also might.

In any event, I started off a post on quark theory to show that this theory is developed from a combination of elementary groups and partitions, built up by direct product and sum operators (SU(2), SU(3)). I have to wonder how much of that Sokal knows or cares about. And, even if he does at least know these forms, does he understand how artifical they are? I mean, does he realise that given some arbitrary collection of elements, you can construct a group out them? That this construction will have symmetries as built-in features and that these will seem to be a discovered 'sense' to this arbitrary collection?


Hmmmm ... I thought the original post was very interesting and even understood most of it (I even spotted the mistake, sort of, but assumed that the reason I couldn't see how to get 1111 and 0000 from paths was that I was being brainless).

But don't these results all come from the huge degree of generality of group theory, which in turn is a result of the high degree of abstraction? If you start introducing any degree of intensional content (and certainly if you start having "T" and "F" referring to true and false rather than to formal properties), then I wonder whether you can still make the assumptions necessary to get one theory to be a subgroup of another.

I didn't understand why "scientific truth" was represented as the truth table for a conjunction operator, and would be grateful to anyone who could explain why.

I also seem to remember that any truth table can be generated by repeated use of either the "nand" or the "nor" operator, so the underlying symoblic logic might be even simpler?



Any way, it was fun to do.

Chuck Grimes

(PS. There was at least one mistake in that other post. If you make the triangle and label the vertices and center (00) (10) (11) (01), you have to count the points twice to complete all sixteen. For example the center with one path out is (00 01). But the center itself has to be counted by itself (00 00) also.)





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