Re: If WM,JJ,LV, PO, and RF all left,

george wrote:
file this under "careful what you wish for". Seriously, if all the
cranks all left, would we have
ANYthing left to talk about?!? Much as I would count it a victory if
they ALL JUST GAVE UP (with all this BULL***), what would we have TO
BE RIGHT *about*, if it weren't for them?

Hi,

George, please, not all who wander are lost.

Sure, I argue that ZF is inconsistent, in terms of its axiomatization of infinity as a finite literal.

For example, quantifying over sets in ZFC, nominally "a" and for many "the" set theory, doesn't describe a set, there is no universally true predicate in ZFC, or else it would describe a construct inconsistent with ZFC's axiomatization of regularity. Yet, that denies what the axioms of ZFC claim to purport about the objects of the domain of discourse.

I'm not an ultrafinitist nor do I say that infinite sets have the same "size", where I generally describe comparisons in terms of certain prototypically natural sets. While that may be so, I do argue that there is a particular function that bijects the naturals and the unit interval of reals, and that it preserves ordering, in obviously a non-standard construction of real numbers. I call it EF, and say that n < m <=> EF(n) < EF(m). Such a construct would be obvious and probably expected in terms of methods of exhaustion and drawing lines up through, basically, the era of generally sound formalizations of the standard open topology of the real numbers in analysis of Cauchy, Dedekind, Weierstrass, and etcetera, if not necessarily so through the abandonment of that particularly natural structure, where I can promote it via reference to well-esteemed canon.

Also, I claim to be sincere and not a crank. Also, you can read through many dozens of arguments I have presented, for example over the past years, and in many you might even find glimmers of insight into what should be the actual goal of a (would-be) research logician: progress.

Also, there's only one theory with no axioms.

Thanks,

Ross F.




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