On Apr 5, 5:22 pm, fom <fomJ...@nyms.net> wrote: > On 4/5/2013 8:47 AM, Zuhair 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" > > Zuhair, > > In the link > > http://plato.stanford.edu/entries/existence/#FreRusExiNotProInd > > you can find the argument for the descriptivist theory of > names used to address the question of negative existentials. > > In the link > > http://plato.stanford.edu/entries/logic-free/ > > you will find the statement that classical logic presupposes > equivalence between denotation and existence. This comes > from the influence of Russellian description theory > and the analysis of negative existential statements. > > This presuppostion is embraced in the axioms for first-order > logic given by > > Ax(P(x)) -> P(t) > > P(t) -> Ex(P(x)) > > The link on free logic will explain how it differs from > classical first-order logic in relation to names and > existential import.
No problem at all, all of those are just variants of assumptive fictional reality (as far as first order logic is concerned, or free logic), that has nothing to do with mathematics per se, all mathematics has to do with is the CONSEQUENCES of those assumptions according to fictional assumed rules of logical inference, so it is of the kind of If-The-Ism. There is no commitment to any of those assumptions per se, there is only an assumptive record that has consequences and it is those consequences in relation to those assumptions that are the Analytics concerned with those methods that mathematics is concerned with. All what is in the links you've referred to is just changing the rules of the game we are to follow all made in a fictional world. All of those are not matters that mathematics is ought to be concerned with, they are indeed philosophical matters, but as said not mathematical.