On 12/7/2013 3:27 PM, WM wrote: > Am Samstag, 7. Dezember 2013 21:42:05 UTC+1 schrieb fom: > > >> >>> If Goedel was wrong, then ZF is wrong. If Goedel was right, then it will never be clear whether ZF is right. >> >>> >> >>> So or so, your yes is unfounded. >> >>> >> >> >> >> You forget the goal of Hilbert's program. > > Hilbert's program has be shown untenable by Goedel.
Not at all. For one thing, Goedel's proof relies upon recursive definition in the arithmetical sense applied to grammatical constructs. There are other ways of thinking mathematically.
For another thing, why should metamathematical research be restricted by Hilbert's opinion?
His decision to pursue arithmetization is motivated by the opinions he had in relation to his work in geometry. Frege did far more significant work in logic, and, the distinction between their views corresponds precisely to the distinction Kant draws in his distinction between general logic and transcendental logic. Hilbert's views are compatible with general logic, but the more difficult problems which allowed Frege to develop his compositional logic derive from Kant's program of transcendental logic.
Frege turned to geometry. And, when Hilbert let the cat out of the bag by admitting 'intuitive arithmetic' into metamathematics, he certainly opens the possibility for anyone intelligent enough to apply 'intuitive geometry' in the guise finite geometries to do so.
Combinatorial block designs are finite incident structures, and, many of them relate to one another recursively.
>> >> >> >> And, you forget that mathematics is not just arithmetic. > > ZFC is mainly arithmetic.
Yes, THANKS TO CANTOR'S GENIUS FOR ARGUING THAT IT IS SUCH. IT IS SO NICE TO SEE HOW MUCH YOU ACTUALLY AGREE WITH HIM.
But, what is within a theory is not what constitutes the metamathematical metatheory.
As always, I have complied with the constraints far more closely than others would take the time to discover.
>> >> >> >> Also, your decision to be ignorant of modern mathematics >> >> probably makes you incapabble of considering what I >> >> wrote. > > You commnitted an error as even every modern mathematican can tell you. >