[FOM] Wittgenstein Inspired Skepticism

[W.Taylor at math.canterbury.ac.nz]

Quoting tchow <tchow at alum.mit.edu>:

> (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.)

I don't think the comparison is really apt.  In Deutsch's philosophy
of science he regards (in simplified form) the true purpose of science,
including quantum physics, as being not MERELY the prediction of results
and testing them, but also that of EXPLANATION of the topic, that is,
"what there is, what it does, and how, and why".

In quantum physics, there is Everett and/or pilot waves that do this,
(I can hardly call Copenhagen an "explanation"), and they lie well
outside the mechanistic/mathematical/predictive aspects.  But in math,
the mechanistic substrate, Turing machines (or more generally combinatoric
math), is not a mere predictive add-on (or foundation if that is one's
teleological preference), but an intrinsic part of the topic itself.
No further superstrate or explanation is needed.  Math is its own
explanation.  OC there may be explanation needed for its applications,
but that is science again, not math proper.

> 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.

I understand that this is the main thrust of the argument you make,
and it is a good thing to point out, as you have said.  But I'm still
not convinced that there is any "gap" between Kripkenstein's radical
skepticism about rule-following, and the allegedly even more radical
skepticism about meaning at large.

The rule-following argument as first presented could easily be seen
as a mere semantic skepticism.  The case was presented as an alien
being presented with a rule for generating a sequence, then claiming
not to understand the very simple (Turing-like) explanation.

"Not to understand" - this clearly indicates a fully semantic problem.
One need say nothing about N, or addition at large, or binary operations,
or any such "complex" matters, in order to tell the alien what is to be done.
If the alien persists in his "silliness", there is nothing we can do except
shrug and walk away declaring he has a semantic dissonance!  Not in any
way different (that I can see) from his learning all about botany and
then claiming not to understand what an elm tree was!

The alien's appearing to have a "quad" operation that breaks at 57
(and his claim that it's ours that does), is no more convincing than
Goodman's "paradox" about grue and bleen.

Bill Taylor


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