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Topic: Then answer to Frege's two objections to formalism.
Replies: 17   Last Post: Apr 9, 2013 7:56 AM

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 Zaljohar@gmail.com Posts: 2,665 Registered: 6/29/07
Re: Then answer to Frege's two objections to formalism.
Posted: Apr 7, 2013 6:39 AM
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On Apr 5, 2:25 pm, Zuhair <zaljo...@gmail.com> wrote:
> I just want to argue that
>
> "Mathematics is analytic processing fictional or real"
>

An objection that may be raised is that this definition would open the
door wide for all kinds of non mathematical terms to cash in. like for
example:

Julius Caesar is Julius Caesar

This is not generally thought of being a mathematical statement, while
with the above definition it is.

My answer is that the above statement IS mathematical, albeit so
weakly so.

Anyhow it is desirable to get rid of those non mathematical terms by
simply using a context in which the only words appearing in the
analytic statements are those of the constants of the rule following
game, while other components of the statement would be filled with
SYMBOLS that may stand for Any object, i.e. variables. So for example
"X is X" would be acceptable statement

Also Y is not X implies X is not Y

Y or X implies X or Y

Y and X implies Y

(Y implies X and X implies Z) implies (Y implies Z)

So the above statements has words with certain meaning assigned to
them by the rule following game, i.e. constants of the game, while
other parts are composed of symbols ranging over any object (i.e. have
no specified referents). And all of them are analytically true
according to the rules of the game.

Those kinds of analytic statements are to be called Symbolic analytic
statements or simply FORMAL analytic statements.

Mathematics can be defined as FORMAL analytic statements fictional or
real.

(notice that NOTHING in the definition of FORMAL pre-suppose
mathematics, I'm speaking of the word FORMAL as how it is explained
above)

However I don't like that, I prefer to call that FORMAL mathematics.
And I'll keep the term Mathematics reserved to cover all Analytic
statements fictional or real.

One may say that there are non analytic aspects in mathematical
discussions like for example those about justification of certain
axiomatic systems, those are clearly non analytic, and most are a
priori synthetic relying on intuitions and the alike, however those
parts I maintain as being outside of mathematics albeit having
connections to mathematics, much like pharmacy and clinical medicine I
explained in earlier messages in this thread.

Zuhair

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