[Wittrs] Re: RFM, yellow cover
- From: kirby urner <kirby.urner@xxxxxxxxx>
- To: Wittrs@xxxxxxxxxxxxxxx
- Date: Sun, 9 Aug 2009 09:43:32 -0700
> You can get RFM in Gigapedia:
> http://ifile.it/qk6pv7f/wittgenstein_06_remarks_on_the_foundation_of_mathematics.rar
>
> Regards,
> Gerardo.
>
That's excellent Gerardo! Thank you.
So here's that quote:
"""
The mathematical problems of what is called foundations
are no more the foundation of mathematics for us than
the painted rock is the support of a painted tower.
"""
pg. 378
Here are some other tidbits...
My task is, not to talk about (e.g.) Gödel's proof, but to by-pass it. (pg 383)
However queer it sounds, my task as far as concerns Gödel's proof
seems merely to consist in making clear what such a proposition as:
"Suppose this could be proved" means in mathematics. (pg. 388-89)
One does not learn to obey a rule by first learning the use of the
word "agreement". Rather, one learns the meaning of "agreement" by
learning to follow a rule. (pg 405)
We say: "If you really follow the rule in multiplying, you must all
get the same result." Now if this is only the somewhat hysterical way
of putting things that you get in university talk, it need not
interest us overmuch. It is however the expression of an attitude
towards the technique of calculation, which comes out everywhere in
our life. The emphasis of the *must* corresponds only to the
inexorableness of this attitude both to the technique of calculating
and to a host of related techniques. The mathematical Must is only
another expression of the fact that mathematics forms concepts. And
concepts help us to comprehend things. They correspond to a particular
way of dealing with situations. (pg 431) -- compare with
investigation of "inexorable" on pg. 82
Here's that all import "machine analogy" (comparing to rule following,
the inexorability of logic):
"""
If we know the machine, everything else, that is its movement, seems
to be already completely determined.
"We talk as if these parts could only move in this way, as if they
could not do anything else."
How is this--do we forget the possibility of their bending, breaking
off, melting, and so on? Yes; in many cases we don't think of that at
all. We use a machine, or the picture of a machine, to symbolize a
particular action of the machine. For instance, we give someone such a
picture and assume that he will derive the movement of the parts from
it. (Just as we can give someone a number by telling him that it is
the twenty-fifth in the series 1, 4, 9, 16, ....)
"The machine's action seems to be in it from the start" means: you are
inclined to compare the future movements of the machine in
definiteness to objects which are already lying in a drawer and which
we then take out.
But we do not say this kind of thing when we are concerned with
predicting the actual behavior of a machine. Here we do not in general
forget the possibility of a distortion of the parts and so on.
We do talk like that, however, when we are wondering at the way we can
use a machine to symbolize a given way of moving -- since it can also
move in quite different ways.
Now, we might say that a machine, or the picture of it, is the first
of a series of pictures which we have learned to derive from this one.
But when we remember that the machine could also have moved
differently, it readily seems to us as if the way it moves must be
contained in the machine-as-symbol far more determinately than in the
actual machine. As if it were not enough here for the movements in
question to be empirically determined in advance, but they had to be
really--in a mysterious sense--already present. And it is quite true:
the movement of the machine-as-symbol is predetermined in a different
sense from that in which the movement of any given actual machine is
predetermined.
"""
Kirby
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