
Re: Then answer to Frege's two objections to formalism.
Posted:
Apr 7, 2013 6:39 AM


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 presuppose 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

