[FOM] Re Question for Gabriel Stolzenberg

Gabriel Stolzenberg gstolzen at math.bu.edu
Fri Mar 31 15:42:15 EST 2006

   This is in reply to Bill Taylor's "Question for Gabriel
Stolzenberg" 29 Mar.  He wrote,

> Gabriel, a week or two ago you made a comment that seemed rather
> "extreme".  Or rather, my interpretation of it seemed to be.  So
> maybe I got it wrong.

   Based on what you say below, I believe you got it right.  And
from a certain, widely held perspective, it does seem extreme.

> Anyway, let me ask this more direct question of you.

> Situation: We have a recursively axiomatizable theory in FOL.
> =========  We have a particular proposition in the language of the
> theory.

> Statement: The question of whether or not the proposition can be derived
> =========  from the axioms of the theory, is a completely objective
> matter.

> My query to you:  Do you agree or disagree with this statement?
> ===============

   I assume you're referring to my reply to a subjective/objective
distinction that Bill Tait asserted.

   Insofar as Bill was only making an informal distinction, then I
agree.  Indeed, in my view, the ability of formal systems to fake
objectivity is wonderful and extremely liberating.

   But it seemed to me that Bill was asking the distinction to carry
too great a burden.  It didn't seem to be just a "you know what I
 mean" kind of remark but, rather, something of metaphysical import.
And IMHO that's a no-no, one that can arise from mistaking impressive
agreement in practice (e.g., re following rules) for evidence that
the relevant expressions refer (to things in a reality independent
of us about which we can acquire knowledge).

   More generally, in my view, we have no good reason to think that
we know that anything is objective.  I claim that this becomes
pretty obvious, if one thinks about how one could possibly perform
the actions (including thinking) that would make an expression refer
to something (the right something!) in a reality independent of us.

   Bill, I apologize for this inadequate reply to your excellent
question.  I'll think more about it and see if I can do better.

   Meanwhile, it might help to take a look at the beginning of
the section, "Relativism and social constructivism," of my essay,
"Reading and relativism: an introduction to the science wars" (up
to "Transgressing those conventions").  It's chapter 4 of the
collection, "After the Science Wars," and is available at my web
site "Debunking the Conventional Wisdom about the Science Wars,
Especially the Sokal Affair and its Aftermath." The url is


   Finally, if you haven't already read them, you might want to look
at Wittgenstein's remarks on rule-following in his "Philosophical
Investigations."  My comments in the essay mentioned above (and to
you) are based on them.

   With best regards,

   Gabriel Stolzenberg

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