[FOM] Wittgenstein

[Dean Buckner]

Harvey:


*DID LW WRITE ANYTHING THAT CAN AT LEAST BE REASONABLY INTERPRETED AS
BEING SIGNIFICANT FOR THE FOUNDATIONS OF MATHEMATICS? IF SO, EXACTLY
WHAT?*

In Tractatus 6.02 he develops a formalistic theory of number in about half a
page.  John Mayberry (in his book, discussed in other postings) describes
this as a "farrago".

My main source is the end of "Philosophical Grammar", which is about half a
book on set theory, Skolem's Theorem, recursion and other matters.  Happy to
quote, but Harvey asked for no quotes.  W.'s view is that set theory is
fundamentally a mistake, which if true has clear significance for f.o.m.

>is LW a major force in nominalism and related views?

"Nominalism" is strictly speaking a medieval school of philosophy.  Let's
say "existential conservative".  Then yes, very much so.  But, as with
politics, there are huge varieties.

As to W. a major force, it's more a legacy.  However, Ray Monk is writing a
book on f.o.m.

>Roughly speaking, as I understand it, this [nominalism] is the view that
only
>objects which have been named are legitimate items of discourse.
>Quantifiers should range only over objects which have been named.

Not really.  Shorten it to "Quantifiers should range only over objects".  At
the heart of all Wittgensteinian thought is the idea of the _category
error_, subsequently popularised by Ryle. This is to read what is in fact a
distinction between linguistic categories, as though it were a distinction
between things.  There is in human nature (and particularly in philosophers
nature) a mistaken, but inevitable tendency to"look for a substance whenever
one sees a substantive".  (For example, to look in the meaning of "the
number of unicorns is zero" for something named by "the number of unicorns",
"zero" &c).





Dean Buckner
London
ENGLAND

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