Saturday, June 21, 2014

Yet *Another* Abject Retraction

When you blog about as many subjects as I do (sometimes late at night, after I’ve had a few, when wiser men would already be abed), you inevitably wind up occasionally putting your foot in it, and wind up having to apologize all round.   (If this continues, I may have to join the Republican Party;  they never apologize.)  This latest example is one of many.

we quoted the following blameless paragraph, and rattled on about it with inexcusable cluelessness:

To assert that topoi correspond to theories  is not to deny that certain topoi may be viewed as models for our logic.  Models may be described syntactically by “diagrams”, so theories may be said to include models.  Our point is that, in general, topoi may be viewed as theories.  In particular, some topoi which arise semantically  are better understood as theories than as models.  Thus we regard topos theory as the “algebraic” form of this higher-order intuitionistic logic.
-- Michael Fourman,  in the introductory first paragraph of “The Logic of Topoi”, in: Jon Barwise, ed. Handbook of Mathematical Logic (1977), p. 1054

That may well be a modern exemplar of the expository art;  but at the time, I was too dense to realize that.

Accordingly, older and, if not wiser, at least sober, I have emended that essay with the following heaping serving of humble pie  (contents:  crow):

I happened to reread this last section just now, and found my then-remarks quite stupid.  I would delete it, or apologize for posting it, except that, after all, the point of this essay is to share with you the wrenching sense of what it feels like to be this stupid, so that you will stop moaning over orphaned teddy-bears in Borriobooola and quit sending them all your aluminum pull-tabs  and instead contribute to a Riemann-related charity such as the Dr Justice Retirement Yacht Fund (all contributions tax-deductible for citizens of Antarctica, donations in Swiss francs only please).
However, the good or at least less-than-awful news is that, upon mature reflection, the quoted passage about theories and topoi seems much more straightforward and intriguing, then it did back then;  sparking perhaps even   a glimmer of understanding.   In fact, I’d like to retire from my day-job right now and study this subject on my, um, yacht

In fact -- With a small amount of encouragement, I would gladly shut up forever and quit blogging, and just go tooling around the Mediterranean, contemplating the infinite and determining which IPAs make the best chasers for which Outer-Hebrides single-malts.   And with this we kick off our

(Donations accepted in Schweizerfranken or bullion;  please no dollars or second-party food-stamps.)

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