On 4/11/2013 5:19 AM, Dan wrote: > On Apr 11, 2:31 am, fom <fomJ...@nyms.net> wrote: >> On 4/9/2013 11:27 AM, Dan wrote: >> >>> Anyway, may be a little off topic, I found this paper >>> interesting ,even though I don't agree with everything it says : >>> http://arxiv.org/abs/0905.1675 >> >> Ok. >> >> I am about halfway through. It seems like >> much of the rest will be verifying the >> relations for working with reals. >> >> So, what parts do you find problematic? > > I haven't really got the time to look at it comprehensively . > Basically, minimal logic seems to be a bit to extreme.
I have worked so hard to understand classical logic that I sort of like the idea of weaker logics.
> Also , I'd take > a different approach : namely , consider the "base logic" of the > universe classical, and add modalities that can behave as different > 'sub-logics' namely, intuitionistic logic . (Something along the lines > of "?" where "(?a ) or (?(not a))" doesn't hold .
I do not know what operator you put here. My reader is not resolving the symbol. I will guess that it is necessitation.
It seems to me that one is unlikely to get any predicativist author to accept a modal mathematics. Hilbert is supposed to have said that that which is not contradictory exists. And, I know that Leibniz viewed existents in terms of possible existence (as an epistemic reality of what is not known). These views would undoubtedly be tolerant of a mathematical framework that had a modal character. Individual existence is now expanded to the existence of consistent *systems*. So, either a possible worlds semantics or a counterpart semantics would be the unifying principle.
Predicativism seems to be just the opposite. There the effort seems to be directed at a single, necessary mathematics that is secured in order to be used for justificational purposes in other fields.
> Even if we hold that "CH or (not CH)" is valid , we needn't "complete > the universe" with any one of the two . That has consequences, of > course , for the modalities : something along the lines of "(not > ( ?CH ) ) and (not ( ?(not CH) ) )" should be able to be proven > valid .
No. Nothing should be established concerning any independent questions except with regard to possible worlds alternatives.
Add different modalities to represent the various aspect of > epistemology (constructability, enumerability ,etc.) .
That is sort of what there is now. It does not stop anyone from arguing over "right" and "wrong" principles.
It is curious. In Aristotle, there is an entire book devoted to demonstrative science. However, "essential definition" is bound with "substance". In the book on dialectical argumentation from common beliefs, he writes that one use of dialectic is for the debate of what constitutes the principles and essential definitions of demonstrative science.
He was probably conceding to the human nature that he witnessed with that little tidbit of philosophy -- if you can't agree, you engage in nothing more than rhetoric.
> Thus we can stop obsessing about things that we can't know (especially > of things that we know we can't know ) .
I have a book with numerous classical papers on semantics.
The editor's introduction begins by applauding how the modern era has vanquished epistemology in favor of semantics. Frege, Russell, and others replaced the "essence"/"substance" relationship with the "truth"/"existence" relationship in their work on denotation for negative existentials. So, I do not think the obsessing on that count is going anywhere either.
I will chalk that one up to human nature too.
> These things, of course , should be of no significant consequence, for > if they were, the consequence in itself would allow us to deduce their > "platonic" truth or falsity . To put it shortly : if the existence of > God (pick one definition) would be of no consequence, then, perhaps we > might still have theists and atheists, but it would be a meaningless > distinction. > Once concept I've been able to find who's truth or falsity is of no > consequence is "superdeterminism" : > http://en.wikipedia.org/wiki/Superdeterminism >
There are many who would like quantum mechanics to account for some sort of compatibilsm between physical laws and free will. It is a hard question.