> > Well the basic problem here is that it's a little difficult to discern > what the author is complaining about in set theory. Sets of properties > are perfectly useful. However typical set theory definitions which run > along the lines of a "set of all points which . . ." do turn out to be > a joke because they invariably rely on various geometric assumptions > regarding figures such as planes, lines, etc. > ~v~~
My suspicion is that the objection is to the idea of applying operations which are valid for finite sets to infinite sets and arriving at conclusions which challenge conventional wisdom. For example it was recently pointed out that permutations of N result in a demonstration that there exist uncountable bijections. Another example is Cantor's theory of transfinite induction. One can reasonably ask if any of these findings are meaningful.
I'm told by some that the Löwenheim-Skolem theorem will do all kinds of wonderful things for me. The theorem depends upon Cantor's findings. Now, if I take the time to truly understand this stuff, will I simply be led down the primrose path? -- Nil conscire sibi