[FOM] "argument from authority in disguise" (reply to Eray Ozkural)

Gabriel Stolzenberg gstolzen at math.bu.edu
Sun Mar 5 18:26:36 EST 2006

   In "Re: intuitions of logic in Chicago and Cambridge" Feb 27,
Eray Ozkural begins by quoting from my message of the same date.

> >   It goes like this.  I say something like, "How do you know that
> > 'P or not P' is true?"  The immediate response is, "Well, suppose
> > not.  Then we'd have a contradiction.  So it's true."

> This sounds as if they are trying to use the principle of
> non-contradiction to prove the principle of the excluded middle.

   I agree.  And, of course, it doesn't work.  All it gives is
not not (P or not P).  and to go from this to (P or not P), they
need something like [(P or not P) or not(P or not P)].  I.e., a
case of LEM.

   (If I remember rightly, in "Language, Truth and Logic," A. J. Ayer
says something like "Every proposition is either true or false or,
WHAT IS THE SAME THING, a proposition cannot be both true and false.")

> [Concerning your remarks about intuition]

> The problem with those claims from intuition is that there is no such
> thing as the most reliable or the most intelligent intuition or an
> intuition of the highest authority (i.e., many such claims are usually
> argument from authority in disguise). Some posters have claimed that
> some "facts" are immediately obvious. That would usually mean
> they see the "perception" of those "facts" as an intelligence test.

   "Argument from authority in disguise" seems an excellent way to
put it.  Eray, you sound as if you've thought very seriously about
these things.  Have you considered writing about them?  To my mind,
these things badly need saying and I have rarely heard them said.

> The arguments from intuition have caused a lot of problems in
> philosophy. Tim Williamson had rightly criticized such appeals to
> intuition in philosophy:
> http://www.philosophy.ox.ac.uk/faculty/members/docs/intuit3.pdf

   Thanks for the reference.  I'm definitely going to look at it.

   By the way, my own biggest problem with "the authority" of
intuition is not in the foundations of mathematics but in the way
certain (most?) philosophers talk about reason and rationality.
They, in effect, block the infinite regress for justification by
the assumption that they (and so long as we agree with them, we)
are endowed by their creator with certain infallible intuitions
that magically certify their reasoning.  And that they know which
ones they are!  How do they know that they know this?  Let me show
you my way of breaking a regress.  Goodbye.

   Gabriel Stolzenberg

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