
Re: Then answer to Frege's two objections to formalism.
Posted:
Apr 7, 2013 8:51 AM


On Apr 7, 1:39 pm, Zuhair <zaljo...@gmail.com> wrote: > 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
much like pharmacology and clinical medicine
Zuhair

