The End of an Era - That of The Natural Numbers
in [Math]
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From: Aatu Koskensilta on 4 Jun 2010 12:10 stevendaryl3016(a)yahoo.com (Daryl McCullough) writes: > In article <87ljau98q0.fsf(a)dialatheia.truth.invalid>, Aatu Koskensilta says... > >>What's at issue is not any argument you've presented, but rather your >>baffling and bizarre claim that every formula is true in a model with >>empty domain. > > I think he said that every formula is *false* in a model with empty > domain. Not that that makes much difference. You're right, of course. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Aatu Koskensilta on 4 Jun 2010 12:11 "Jesse F. Hughes" <jesse(a)phiwumbda.org> writes: > Aatu Koskensilta <aatu.koskensilta(a)uta.fi> writes: > >> What's at issue is not any argument you've presented, but rather your >> baffling and bizarre claim that every formula is true in a model with >> empty domain. > > No, it's the equally baffling and bizarre claim that every formula is > *false* in a model with empty domain. You're absolutely right. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Nam Nguyen on 4 Jun 2010 22:44 Aatu Koskensilta wrote: > "Jesse F. Hughes" <jesse(a)phiwumbda.org> writes: > >> Aatu Koskensilta <aatu.koskensilta(a)uta.fi> writes: >> >>> What's at issue is not any argument you've presented, but rather your >>> baffling and bizarre claim that every formula is true in a model with >>> empty domain. >> No, it's the equally baffling and bizarre claim that every formula is >> *false* in a model with empty domain. > > You're absolutely right. Is this supposed to be "too-many-notes" joke, from Emperor Joseph II criticizing Mozart's work: "don't take it too hard ... there are simply too many notes, that's all. Just cut a few and it will be perfect"? "Claim" here is just conclusion that people arrive at _from argument_ which in turn consists of hypothesis, knowledge and rules of certain reasoning framework. If in "any argument [a poster has] presented" is NOT an issue, then why on Earth should we care about whether or not the conclusion sounds "baffling and bizarre" to one man's ears? Since when would all the mathematical, logic conclusions in these fora must pass the Koskensilta "baffling-and-bizarre" test, to be correct? And the other 2 guys (Jesse and Daryl) didn't say anything except uttering yes-man-like statements like "Yes your highness, you can never be wrong, there were simply too many notes", like Salieri? And these people's reasoning is supposed to be a shining light, illuminating examples how arguments should be different from cranks? [I just couldn't believe what I read here!]
From: Nam Nguyen on 4 Jun 2010 23:22 Aatu Koskensilta wrote: > Nam Nguyen <namducnguyen(a)shaw.ca> writes: > >> Suppose someone says to you "Marshall you're not couch potato", would >> you think they "mean" you aren't a couch or aren't a potato? > > Uh, come again? Like you, Marshall had the idea some mathematical truths must be absolutely true because they must be so "ordinary", so "evident" that exemplifying them otherwise would be nothing but an act of a crackpot. And the example he thought would be illuminating this mathematical reasoning issue is the following _non-mathematical_ potato-chip analogy. (Well, I'm generous here because he even denied it's analogy: somehow he believed this "potato chip" truth is a mathematical truth that no one could find another context in which it's false!) Marshall wrote: > You know what a potato chip is, right? And you know > who you are, right? So if I say "Nam Nguyen is not > a potato chip" then that is a true statement. I countered by saying "potato chip" could be considered as a call-sign for a group of people therefore whether or not one is or isn't a "potato chip" would depend on if the person is in that group, at least as a matter of abstraction, which mathematics is. What he didn't realize even is that even if I know perfectly what he meant by that truth, there are still different contexts, in the realm of abstraction, in which the statement would be interpreted as false. His "true" context (however real it might be) _is just another context_ in this case. My "Marshall you're not couch potato" is another counter example, illustrating his misconception. You can't tell the truth or falsehood of the statement, unless you relativize it in a context: should that be interpreted literally, or figuratively? Even if say it's interpreted figuratively, is the person in question a "lazy" person sitting in the couch all day watching TV? etc... Do yo understand the issue now?
From: Nam Nguyen on 5 Jun 2010 00:06
Aatu Koskensilta wrote: > Nam Nguyen <namducnguyen(a)shaw.ca> writes: > >> (Be careful here: you might run into conflict with Aatu's belief that >> logic is just a branch of mathematics, or that logic provability can >> be guided [or even "dictated"] by the mathematics of the naturals, >> iirc). > > There's nothing controversial in the observation that mathematical logic > is a branch of mathematics. Just like that, huh? So what happens if others believe the idea mathematical logic is a branch of mathematics is at the very least controversial? Would such a countering belief be dismissed? Or would they be as "correct" as your belief? And in such case, what does it mean for 2 negating concepts to both be correct, as far as reasoning is concerned? > The view that "logic provability" can be > "guided" or "dictated" by the "mathematics of the naturals" that you > ascribe to me I can't make anything of. That's nothing more than a quick "glossing over" terminologies in a post, that could be re-phrased. What was meant there is the knowledge of mathematics (arithmetic) of the naturals has been used to "assert/dictate" conclusions about provability that even the very means of provability (rules of inference) couldn't do. For example, can you PA's consistency using inference rules only? Doesn't you school of thought believe that we could use the naturals to prove PA's consistency? |