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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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Posts: 2,665
Registered: 6/29/07
Re: Then answer to Frege's two objections to formalism.
Posted: Apr 7, 2013 8:51 AM
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On Apr 7, 1:39 pm, Zuhair <> wrote:
> On Apr 5, 2:25 pm, Zuhair <> 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

much like pharmacology and clinical medicine


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