[lit-ideas] Re: quintessential frege in three quotes--explain why
- From: Henninge@xxxxxxxxxxx (Richard Henninge)
- To: <lit-ideas@xxxxxxxxxxxxx>
- Date: Mon, 16 Aug 2004 13:12:15 +0200
Subject: [lit-ideas] quintessential frege in three quotes--explain why.
Robert Paul's answers follow the original three quotes:
> (1) A scientist can hardly meet with anything more undesirable than to
have the
> foundations give way just as the work is finished. I was put in this
position by a letter from Mr. Bertrand Russell when the work was nearly
through the press.
> Grundgesetze der Arithmetik (1903)
1. From the preface or the introduction to the Grundgesetze: Frege's report
of
his own reaction upon learning from Russell of the paradox of class
membership.
The paradox showed that Frege's Rule V was untenable, and his project of
establishing mathematics on a foundation of logic was doomed.
(Addendum from a second post:) I now realize that this could not be right,
for the Grundgesetze was published
in two volumes, and Russell's discovery wasn't acknowledged until Volume II
was
about to go to press. So this would be from an appendix or a postscript to
it.
For the moment this quote interests me the least. It is to be expected that
on a philosophy website in the UK Russell's humiliation of Frege would take
top billing in the three quintessential Frege quotes. But Wittgenstein, who
was in communication with and visited Frege before he went to England and
met Russell, effectively drove Russell from the
logico-philosophico-mathematical roost he'd clumb (sic) on the rungs of his
paradox. Within a decade of their first encounter, Russell could scarcely
understand his fledgling philosopher and had abandoned his own projects for
establishing the logical foundations of mathematics.
If there is a "paradox of class membership," this is a sign or a symptom
that indicates there is something "sick" about classes, about sets, about
set theory in general. Sets or classes are not exact enough, one-to-one
enough, correspondent enough to be included among the "non-sensible
something"s that Frege introduces in the next quote, and which come
remarkably close to the notion of forms/objects that Wittgenstein elaborates
in the Tractatus. We were discussing just this point--Wittgenstein's objects
in the Tractatus--earlier this year, wherein I maintained that this concept
of the "object as form" prefigured the later Wittgenstein in the
Philosophical Investigations. Again--at the basis of it all seems to be a
continuation of the very insight that Frege expresses in these next two
quotes. What drove Russell crazy about Wittgenstein may have owed a lot to
how much Wittgenstein had taken the Fregean project to heart (despite
Frege's rather gruffly confused--and one sees why--reception of the
Tractatus) and in a sense *continued* it.
> (2) Having visual impressions is, of course, necessary for seeing things,
but it is not
> sufficient. What must be added is not anything sensible. And it is
precisely this that
> unlocks the outer world for us; for without this non-sensible something,
each of us
> would remain locked up in his inner world.
2. A sentence from some work or letter in which Frege is intent on denying
the
truth of 'psychologism,' i.e. he is intent on denying that human psychology
plays any role in logic or mathematics).
>
I don't think that's the point at all in this quote. The point goes much
further toward the private language arguments in the later Wittgenstein. Can
you feel my pain? Can you know my tree? Can we communicate about anything?
Remaining "locked up" in one's "inner world" is no joke for Frege, but he
felt, with Wittgenstein, that the way out of the solipsistic dilemma was to
establish the dimensions, the boundaries, the field made up of these
"non-sensible something"s that *is* the outer world for us. Robert knows my
problem with Strawson. Maybe it's my grand problem with Anglo-Saxon or
UK-based philosophy, Kantianism, etc. Even Hawking. The "outer world" is too
much taken for granted, unquestioned, unchallenged--even by as much a
Kantian as Strawson. The extent to which the so-called outer world is forced
to sing to the tune of these Fregean-Wittgensteinian non-sensible
form-objects, that this "mathematical" agreement among language users
essentially provides to grounds for objectivity itself, has not yet been
*kapiert*. And that's why...
> (3) Every good mathematician is at least half a philosopher, and every
good philosopher is at least half a mathematician.
>
3. Self-evident.
Well, I don't know. Do we all have fits about what numbers really are?
Wittgenstein and Frege seem to be saying that if you can't reduce
"everything that is the case" to physics (mathematical formulae), your just
doing metaphysics--the bad, non-scientific metaphysics Kant was trying to
reform. The picturing theory in the Tractatus (everything that can be
pictured can be pictured clearly--mathematically, logically) may have
collapsed for the same reason Frege's theory collapsed. The question is: Is
the collapse ultimate and final or a pseudo-collapse surmountable by the
rescuing evolution of Wittgenstein's thought?
> Richard Henninge
> University of Mainz
------------------------------------------------------------------
To change your Lit-Ideas settings (subscribe/unsub, vacation on/off,
digest on/off), visit www.andreas.com/faq-lit-ideas.html
Other related posts:
