On Jan 11, 7:16 pm, Zuhair <zaljo...@gmail.com> wrote: > Lets say that a real r is finitely definable iff there is a predicate > P that is describable by a Finitary formula that is uniquely satisfied > by r. > > Formally speaking: > > r is finitely definable <-> Exist P for all y. (P(y) <-> y=r) > > where of course P(y) is a Finitary formula. > > Of course NOT all reals are finitely definable in the above manner. > This is an obvious corollary of Cantor's arguments of uncountability > of reals. > > Also it is obvious that we have only COUNTABLY many finitely definable > reals. > > Other kinds of reals can be "infinitely" definable, this can be > achieved in a language that encounters infinitely long strings of > symbols, and many known first order languages are of that sort and > they are proven to be consistent and even supportive of a proof > system.
MODUS PONENS would not be able to make a single deduction.
This is where Mathematics went to Fairy land.
*CONTINUOUS LOGIC* Ask FRED THE FAGGOT HERE!
Take the powerset of ANYTHING (even True/False formula) and just like the POWERSET(N) makes the continuous REALS! You get CONTINOUS LOGIC FORMULA! <<<< ???
If you can REASON about infinitary formula THEN you already have an alternate finite representation for them.