[FOM] Wittgenstein Inspired Skepticism
tchow at alum.mit.edu
Mon Feb 27 17:50:58 EST 2017
Thomas Klimpel wrote:
> I have the impression that the tacit consensus is rather that Turing
> machines successfully nail down what is meant by rule following.
I won't quibble with that.
> However, this doesn't mean that there would be a consensus that this
> solves all problems related to language and meaning. And I cannot see
> why mathematics should be free of vagueness iff Kripkenstein is silly.
> The ontological commitments of mathematics (and set theory) seem to go
> further than the mere existence of Turing machines (or the existence
> of a bedrock non-vague system of syntactic rules).
Certainly, what you say about going beyond Turing machines is true, but
what I was implicitly referring to was the tendency of mathematicians to
retreat to Turing machines if you push their backs to a wall. That is,
if we were to challenge a mathematician with the examples of vagueness
that some other FOMers have mentioned, the mathematician would probably
say something like this, "Well, yes, there is some vagueness, but that
involves just the informal part of doing mathematics in practice. In
the end, the permanent results of mathematical research are encapsulated
in formal proofs of theorems, and there is no vagueness there."
Vagueness and strong ontological commitments are tolerated because there
is a tacit understanding that there is a common bedrock to which we can
all retreat if disagreements threaten to become severe. (It is not
unlike physicists' reaction to probing questions about quantum
mechanics---they will, if pressed, point out that everyone agrees on how
the calculations should go and what the experimental predictions of the
theory are, even if there is disagreement about Copenhagen or Everett or
pilot waves or whatever.)
> If it would really show that, than it would indeed be a major
> achievement. But then it should be clarified how it is different from
> the skeptic denying any possibility to communicate meaning at all.
As I said, I believe that there is a spectrum or continuum of commitment
levels. The skepticism that you're referring to here is targeted at an
even more fundamental level. What's different about Kripkenstein is
that it's targeted precisely at the level (i.e., rule-following) that
mathematicians instinctively retreat to, as I explained above. That is,
Kripkenstein argues that even if you accept the possibility of certain
basic communication capabilities, there is still a barrier to surmount
if you want to be able to follow rules.
More information about the FOM