"Gerry Myerson" <firstname.lastname@example.org> wrote in message news:email@example.com... > In article <firstname.lastname@example.org>, > "Peter Webb" <email@example.com> wrote: > >> "Gerry Myerson" <firstname.lastname@example.org> wrote in message >> news:gerry-D682F9.email@example.com... >> > In article <firstname.lastname@example.org>, >> > "Gene Ward Smith" <email@example.com> 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? >
A poor analogy. Theories about the physical world are largely evaluated on the basis of their predicitive capacity, and it is on this basis that these theories have been proved wrong. Mathematics is based upon other crietria, including consistency and the ability to generate interesting theorems. Beleiving in phogiston was not crankish in the 17th century, but maintaining that you can't bisect an angle with a straightedge and compass is most certainly crankish - about as crankish as maintaining that the computable reals are uncountable.
> 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. > > -- > Gerry Myerson (firstname.lastname@example.org) (i -> u for email)
I'm no expert either, but lets go back to a quote from before:
---------- Most mathematicians reading this paper suffer from the impression that the `computable real numbers' are countable, and that they are not complete. As I mention in my recent book, this is quite wrong. Think clearly about the subject for a few days, and you will see that the computable real numbers are not countable , and are complete. Think for a few more days, and you will be able to see how to make these statements without any reference to `infinite sets', -------------------
The proof that computable numbers are countable (using the standard definition of computable numbers) takes about 3 lines. In typical crank style, he simply states that this result is false for reasons that are obvious if you think about it. Like the fact that the human eye must have been designed and not evolved is "obvious if you think about it".
If I saw a posting entitled "Evoloution: Should you believe", attacking evolution as "a religion" with an "anointed priesthood" talking "mumbo-jumbo" (all his words), and with chapter headings like "Why genes are a joke" (OK, his chapter heading is "Why Reals are a joke"), decrying the "academy" for "consistent refusal to get serious about the foundational aspects of the subject", saying that key basic beliefs about biology are wrong (without stating the reason), making basic mistakes about the subject, and then blaming the biological establishment for allowing false theories like evolution to be taught, I would treat it as another crank post.
If, however, this person signed their posts as "Assoc Professor of Biology, UNSW", published his opinions on the UNSW web site, and somewhat pompously invited responses from "microbiologists and biochemists", then I think the guy is fair game.
I do wonder how many of his students bought his new book proving that the computable reals are uncountable, and whether they know more about set theory as a result.