Math as God

Tue Nov 20 14:59:27 CST 2007

Your third paragraph is a nice summary of positivism. As for reduction to 
"simpler, describable objects," propositions about the world are ultimately 
about the simples, and the propositions are names for the objects (simples) 
in the world. You capture most of this in your first paragraph. One reason 
he was so focused on numbers, mathematics, and logic, is his concern about 
the foundations of the three. LW took Russell's contradiction in set theory 
as undermining the three topics mentioned in the previous sentence. Are you 
familiar with truth tables? Wittgenstein created them in the T L-p.

I agree that the earlier and later Wittgenstein are more similar than is 
commonly assumed. The early language game in the Investigations, five red 
apples, can be interpreted as a Tractarian sort of reduction--though I don't 
think he meant it to be. Do you know the quote from St. Augustine that is 
the opening section of the Investigations? St. A.'s claims about learning 
language applies only to nouns. He, at least implicitly, criticizes the 
Tractatus.

One short tale. John Wisdom, one of Wittgenstein's protégés at Cambridge, 
remarked to a prof teaching the Tractatus (1976), "I thought we were done 
with all that." He clearly thought that the Tractatus a source of 
unimportant, deep philosophical puzzles.

Page

----- Original Message ----- 
From: "Jordan Harp" <jordanharp at gmail.com>
To: "Page" <page at quesnelbc.com>; <pynchon-l at waste.org>
Sent: Tuesday, November 20, 2007 6:15 AM
Subject: Re: Math as God

> No, you have it exactly right. I mean "express" as in say.
> Wittgenstein does an interesting thing with ontology in the Tractatus.
> His rules, of course, are that the world consists of facts, which are
> really states of affairs, particular arrangements of simple objects.
> Something is an object only if it can be reduced to a set of simpler,
> describable objects, right?
>
> It took me a while to figure out why he spent so long going on about
> logic, operations, and numbers, but I think I know what's going on. He
> talks about number is basically a formal concept that can be conceived
> of using only to concept of an operation.  As in, "You take this null
> set, this nothing, and apply an operation to it, and now you have a
> once-operated null. Now apply the operation again to that, and the
> difference between your new product that your input is that it has
> been operated on another time. As you move through the sequence of the
> first null set, to the once-operated set, to the twice-operated set,
> you apprehend a patter--a formal property. I think the key here is
> that he does this without objects.  It may well be that people see one
> rock, then another, and form the concept of two, but he explains how
> the object is not necessary for the apprehension of a formal property.
>
> This all ties into the mystical, and I think it's because formal
> properties of the world are mystical. That is, an attempt to say
> anything about the world in general, to "make an object" of the world,
> is an attempt to speak of the mystical.  So it is nonsense.  The key
> being that no one has the vantage point to "see the world as a limited
> whole" and communicate that to someone else. This is because science
> cannot "stand outside the world" and measure in relation to (whatever
> isn't the world?). Anyway, the argument is coming from the perspective
> that you can't talk about things science can't measure, because no one
> would be able to verify what exactly you are referring to.
>
> So universal laws are mystical (ethics, metaphysics, logic). But
> Wittgenstein clearly believes that logic describes the rules of the
> universe.  But he talked about it for a whole book in order to
> convince us to reject that kind of talk.  That doesn't mean we can't
> see formal properties or patterns in the world, "feel the world as a
> limited whole," have religious believes, what have you. Wittgenstein
> did his whole life. But it just means we may as well not talk about
> those things because we our vocabulary is referring to "things" that
> cannot be picked out like a rock or a tree can.
>
> Anyway, from what I can tell, I think you're right on. The mystical
> doesn't exist in the sense of being an object in the world. If
> anything the mystical involves something at the level of the subject
> in its experience of the world, something that cannot be spoken of.
>
> Interesting aside, now that my email is this long: I think early and
> late Witt. are closer than usually believed. He later criticizes his
> earlier work, but he did not like what the logical positivists of the
> Vienna Circle did with the Tractatus, either.
>
> Jordan
>
> On Nov 19, 2007 9:53 PM, Page <page at quesnelbc.com> wrote:
>>
>>
>> Thanks, Jordan. You are correct. LW did consider the unsayable to be
>> mystical (T L-p 6.45). But it is a very particular sense of mysticism. I 
>> am
>> not sure how to read your last comment, but if you mean that the mystical
>> exists whether or not we can sensibly express it, I am not sure you are
>> correct. If it were sayable, it would be "in the world," and necessarily 
>> not
>> mystical. Or do you mean something else by "express it?" I do think LW is
>> important to TRP, possibly the later W. more than the earlier W.
>>
>> Anyone have any ideas? I'm struggling.
>>
>> Page
>>
>> ----- Original Message -----
>>
>> From: Jordan Harp
>> To: pynchon-l at waste.org
>>
>>
>> Sent: Monday, November 19, 2007 1:52 PM
>> Subject: Re: Math as God
>>
>> You're right here, but the Tractatus does evince Wittgenstein's 
>> mysticism.
>> It's in a proposition just prior that says something like "There are 
>> things
>> that can be known that cannot be said." That is the mystical, and it's 
>> there
>> whether or not one can sensible express it.
>>
>> Jordan
>>
>>
>> On 11/18/07, Page <page at quesnelbc.com> wrote:
>> > Thanks for the nice summary of Hegel. However, Schuyler (your reference
>> > below) makes a mistake in his reading of the Tractatus. He refers to
>> > proposition 7--the final proposition of the Tractatus, "Whereof one 
>> > cannot
>> > speak, thereof one must remain silent"--and claims it evinces
>> Wittgenstein's
>> > mysticism. We cannot speak about things like aesthetics or ethics 
>> > because
>> > sentences one cannot map on to the world of facts--proposition 1 of the
>> > Tractatus, "The world is everything that is the case"--is, literally
>> > nonsense (non-sense). The nonsense is based on Wittgenstein's logical
>> > atomism, not on his purported mysticism.
>> >
>> > If you really want to make your brain hurt, contemplate (the fact that)
>> one
>> > of the propositions of the Tractatus (sorry, I do not have the 
>> > reference
>> in
>> > front of me) is the claim that anyone who understands the Tractatus 
>> > will
>> > realize that every proposition in it is false.
>> >
>> > [Two stories about Wittgenstein. At some point Russell asked G.E. Moore
>> what
>> > he thought of Wittgenstein's intelligence. Moore replied, "I think he 
>> > is
>> > [roughly] exceedingly bright. Russell: Why? Moore: Because he is the 
>> > only
>> > student at my lectures who looks puzzled; On another occasion Russell
>> asked
>> > Moore if he thought L.W. was a genius. Moore replied that he did but 
>> > that
>> > Cambridge ought to give him a Ph.D. anyway.]
>> >
>> > Page
>> >
>> > ----- Original Message -----
>> > From: < robinlandseadel at comcast.net>
>> > To: <pynchon-l at waste.org>
>> > Sent: Friday, November 16, 2007 3:09 PM
>> > Subject: Math as God
>> >
>> >
>> > > Please bear with me as I explain Hegel's philosophy.
>> > > Excuse me, stumbled on this while searching for an answer to:
>> > > "Well, What Dooooooo you believe in---MR.. RUSSELL!?!?!?
>> > >
>> > > RUSSELL, WITTGENSTEIN, AND LINGUISTIC ANALYSIS
>> > > Grant Schuyler
>> > >
>> > > Please bear with me as I explain Hegel's philosophy.
>> > >
>> > > Hegel thought that Geist (German, "mind" or "spirit"; thought of not
>> only
>> > > as a mental faculty or abstract force but almost as a person) had
>> advanced
>> > > through the successive cultures of history growing more and more
>> > > conscious, self-conscious, and rational. This process had culminated 
>> > > in
>> > > Geist's realization as what Hegel called the Absolute Idea (Geist in
>> > > another guise, perhaps as God). God or the Absolute Idea had realized
>> > > itself as the best contemporary, that is, the best 1820s European,
>> > > philosophy and political culture. By implication, the philosophers,
>> > > philosophy, and political and cultural systems of Hegel's time were 
>> > > the
>> > > best that had ever existed, the realization of complete liberty, and 
>> > > the
>> > > goal of all history. And the philosophic method of the philosophers 
>> > > of
>> > > Hegel's time -- reason (Verstand), was somehow superior (it was 
>> > > implied)
>> > > to the method of thinking used by ordinary people and scientists. In
>> > > contrast to philosophical reason, these lesser beings used the (by 
>> > > impl!
>> > > ication
>> > > inferior) mental faculty most philosophers since Locke call
>> understanding
>> > > (Vernunft).
>> > >
>> > > "A tidy system it was," said Russell in 1959. "Once we [Moore and
>> himself]
>> > > applied rigorous logic to Hegel, he became fragmentary and puerile."
>> > >
>> > > Having rejected Hegelian absolute idealism, Russell looked for a new
>> basis
>> > > on which to have the absolutely certain knowledge of the world that
>> Hegel
>> > > had believed his philosophic system delivered.
>> > >
>> > > Russell thought that one might discover the basis of certainty in
>> > > mathematics
>> > >
>> > > http://home.ca.inter.net/~grantsky/wittgenstein.html
>> > >
>> > >
>> > >
>> > > --
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>> > >
>> >
>> >
>>
>>
>>
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