Stupid Spin and False Advertising
I normally enjoy posts in the blog "On the Fence": but I don't enjoy posts that just get it wrong.And J. Kelly Nestruck just gets it flatly wrong in the post "Math joins the postmodern world".
Let us start with the title, which suggests a level of relativism few mathematicians would buy into (I speak as a reformed one, now working on other things, but always caring about mathematics). The sole evidence for the post is a New Scientist article titled, "Mathematical proofs getting harder to verify". The substance of the article does not go beyond asserting that exhaustive searches in some proofs are being handed off to computers - and the proofs include the algorithms used. This is, to start with, old news, and actually a pretty incremental deivation from mathematical history. Proofs always need verification, and it can fail for all sorts of reasons; there is no major change in principle in allowing the refutation of a computer search to refute a purported proof.
Postmodern? How? This just seems silly and glib. Does Nestruck have the vaguest idea what this all really means?
posted by Alan Adamson @ 7:08 PM
7 Comments:
No idea. Have not read that sort of stuff in 20 years. Might start doing it again when I retire. I did just do a scan of the reviews and discussions of these books and saw nothing new compared to 20 years ago when I cared a lot about this. None of it seems to bear in any significant way on this silly idea of postmodernism as somehow impinging on current understandings of mathematics. Mathematicians almost always experience their work as Platonists, which is in no way to suggest they need such a clear-cut philosophy in the end. But the use of search eliminations by computer in proofs is no major step. It is harder to check, but no principles change. Exactly as the original article said, which in no way invited broader inferences.
Well if postmodernism remains a fashion when I reach retirement, perhaps I may choose to read them. But the original article that started this chain had nothing to do with postmodernism, simply with new tools being used in mathematical proofs. And I've never found much content in what I've consumed so far as 'postmodernism'.
I'd say constructed in a very disciplined way. But I don't think that means the outcomes are arbitrary. Lawson's book sounds interesting - I shall look out for it. I have nothing against any of the books suggested - I'm just not terribly interested in the philosophy of mathematics at the moment.
Bensonbear, you are waking dormant demons. :-) And certainly raising the tone of discussion on my blog! Thanks!
Goedel was a strong Platonist, who believed the subject matter of mathematics was 'out there', which is ironical, given the ways his incompeteness theorem is cited often to support relativistic views. I have always considered it a bulwark in the Platonist defence. When I actually 'did' mathematics, the experience was profoundly Platonist - one was trying to trick the world into showing some new side. I certainly always understood that the body of known mathematics was constructed by the vast community of us over time who had worked on it. This is not to say it was simply invented in some arbitrary manner. And I find it hard to believe, knowing the rigorous discipline on what gets counted as interesting and valuable content, that this body of 'literature' (I am being a bit provocative) that is mathematics, is very dependent on our biology or our 'social context' or 'politics'.
I think what troubles me about much of what I read from 'postmodernists' is that there is a poor appreciation of how hard it is to 'know' something, and how valuable. You point out the fundamental contradiction in the positions they espouse, and this is one reason I expect the whole movement will just go away in due course.
All I see in it is a skepticism less sophisticated than Hume's, and then claims of authority based, given their skepticism, on nothing of any importance.
I'll follow you a bit of the way but not very far - as I said, I don't find this really an attractive activity.
I think there is enormous circumstantial evidence (the best our limited systems will ever get) that PA is consistent. We have not found a problem with it. Moreover, we have managed to achieve a great deal on its basis (yes much engineering depends on this stuff, and that engineering works robustly).
You will have to explain Aristotelian realism vs. strong realism to me - I have no idea what the distinction is.
And yes I agree hte reason Lakoff and Hersh don't have this problem is that their whole universe has vansihed under them and there is no longer any basis for discussion.
I am afraid I do not see what any of this has to do with theories of evolution.
What's the problem with finite creature conceiving and understanding infinite notions? Is that not part of what things like the Peano axioms are for?
Why should we not accept that our knowledge is always partial?
What is the technical problem you see?
I was, yes, mostly being glib.
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