Gerry Myerson wrote: > In article <email@example.com>, > "Peter Webb" <firstname.lastname@example.org> wrote: > > >>"Gerry Myerson" <email@example.com> wrote in message >>news:gerry-D682F9.firstname.lastname@example.org... >> >>>In article <email@example.com>, >>>"Gene Ward Smith" <firstname.lastname@example.org> wrote: >>> >>> >>>>I didn't see any signs, as far as I had gotten, that he even knows >>>>anything about modern set theory. Does he? >>> >>>I don't know. >>> >>>I reject astrology, even though I don't know anything about modern >>>astrology (I don't even know if there is such a thing). I reject >>>"creation science" and "intelligent design," even though I haven't >>>read any recent writings of their advocates. I don't have to; I >>>know where they're going, and I know they're never going to get >>>anywhere useful, going in that direction. >>> >>>I personally don't put set theory in the same category as astrology >>>or creation science. >> >>Doesn't this undermine your whole analogy? Why didn't you pick an orthodox >>theory like Evolution, Special Realtivity or Plate Techtonics as being the >>theory he is attacking? (Set theory is every bit as well accepted as any of >>these other topics). Because he looks less of a crank if you compare him to >>attacking astrology than him attacking (say) the Theory of Evolution, even >>though this is a much closer analogy? > > > In its day, phlogiston was a well-accepted theory. Alchemy was orthodox. > So was spontaneous generation. Bright people, not cranks, spent > a lot of time and effort trying to prove the parallel postulate. > It's not unknown in the history of science, even of mathematics, > for very good people to do a lot of work that makes later generations > scratch their heads and say, why did they go down that blind alley? > why did they even bother to think about those things? > > It may be wrong to say that today's set theorists are yesterday's > phlogiston theorists - but is it crankish? > > Evolution - I've read statements along the lines of, "nothing in modern > biology makes sense, without evolution." I've never read anything like, > "nothing in modern mathematics makes sense, without ZFC." I read (and > write) papers of mathematical research all the time that go on for pages > and never mention ZFC, or large cardinals, or anything else that I > recognize as coming from modern set theory. I think the analogy between > evolution and set theory is overstated. > > >>Doesn't it worry you that a professional mathematician can write a paper on >>set theory (that has "caused a bit of discussion in some logic circles") and >>you can't tell from the paper if he actually "knows anything about modern >>set theory" ? > > > If you haven't already guessed it, I know very little about modern set > theory myself. It shouldn't be surprising that I can't tell whether > someone else does.
I cannot claim to have a great knowledge of what modern set theory is about myself. They just don't talk about it much at the conferences I attend. The odd talk on the subject that I have seen has subjects like what kind of cardinals we might expect between aleph-null and the continuum, given that the continuum is not well ordered. I have to say it really does come across like the old theological debates about how many angels could fit on a pinhead.
When, in another post, I said that mathematics should try to get its ideas about reality, I certainly did not mean that every mathematician should call the physics or economics department before embarking on a course of research. But it does require using a bit of common sense and taste in deciding whether a course of research is worth pursuing, and from time to time reassessing these decisions.
For example, it seems absolutely clear to me that investigation of polynomials on finite fields is well grounded in reality. Maybe someone else disagrees, but there is going to be some concensus. Another example - funding agencies might feel that there is not much future in investigating Banach spaces that are not isomorphic to their hyperplanes.
We have no idea whether the axioms of set theory are going to hold up. It makes sense to investigate mathematical pursuits that have some connection with the world around us, even if that connection is philosophical or metaphorical in its nature. This does not preclude that a few people should be allowed to explore the weird stuff (or whoever wants to in their spare time) because you never know what is going to be useful (and useful in this context does not mean how many dollars it is going to make). But some math areas are clearly drying up, and set theory is one of them.