'When Are Relations Neither True Nor False?
in [Math]
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From: Marshall on 4 Apr 2010 21:49 On Apr 4, 6:12 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote: > > It wouldn't be a surprise if we learn there were those who would > defend physics against SR to the bitter end. This is somewhat off-topic, and I may be misreading you, but am I to understand from this sentence that you are of the opinion that special relativity is somehow incorrect, or not the best currently available theory? Marshall
From: Marshall on 4 Apr 2010 22:05 On Apr 4, 9:33 am, Nam Nguyen <namducngu...(a)shaw.ca> wrote: > Marshall wrote: > > On Apr 2, 5:32 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote: > >> Let me put to rest the idea we know enough about the natural numbers, > >> to prove important thing such as the consistency of PA. I'll do that > >> by pointing out the existence of a specific unknown natural number. > > > Why do you think the existence of a specific unknown number > > should have anything to do with consistency? > > Because they (the syntactical proof of consistency and collectively > many formulas about this unknown natural) both connote the same thing > in meta level: impossibility of syntactical proof. If you can't prove > a certain formula related to this number, you can forget about proving > a consistency, syntactically speaking. Both of these sentences are just a restatement of the position that I asked you for support of. My question is not, do you consider a proof of consistency of PA and the existence of an unknown natural number to be mutually incompatible. You have clearly stated so. Rather, my question is WHY do you see them as mutually incompatible. Is this some theorem of which I am unaware? If so, can you provide a reference? Or is it some theorem that you yourself have proved? If so, can you provide the proof for our inspection? Is it only *syntactic* consistency proof that are so affected? What about model-theoretic proofs of consistency. I seem to recall that you do not accept them, but I could be wrong. Does this mutual incompatibility generalize, or is it something specific to the natural numbers? > [Imho, it could be said the the later epitomizes the impossibility of > the former]. Can you explain how? > That aside, it's actually my position that it's impossible to > to syntactically prove a consistency: simply because the rules > of inference won't let us do that; hence it's a _delusion_ that > we could have any "sort of thing" that we could "accept as a > proof of consistency"! > [That's why I'd would be surprised if in the past I had said something > that has caused you to think there be a criteria to accept a proof > of inconsistency]. As far as I am aware, you have not given the conditions under which you would consider the consistency of a theory to be proven. As far as proving INconsistency, I was not under the impression that you disagreed with the usual method of deriving a contradiction. For the sake of completeness and clarity, and because I suspect you meant "consistency" above where you typed "inconsistency" would you clarify if/how you consider it possible to prove a theory inconsistent. Marshall
From: Nam Nguyen on 5 Apr 2010 00:12 Marshall wrote: > On Apr 4, 6:12 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote: >> It wouldn't be a surprise if we learn there were those who would >> defend physics against SR to the bitter end. > > This is somewhat off-topic, and I may be misreading you, > but am I to understand from this sentence that you are > of the opinion that special relativity is somehow incorrect, > or not the best currently available theory? No it's not off the topic: I was using SR as analogy to the anti-natural-number position some might have held (including me in this case). I I didn't mean at all SR is incorrect. In It wouldn't be a surprise if we learn there were those who would defend physics against SR to the bitter end. I think there are those today who'd similarly defend "the natural numbers" foundation in mathematical logic - to the bitter end - even though to no avail. > > > Marshall >
From: Nam Nguyen on 5 Apr 2010 00:14 Please disregard this post. I accidentally sent it when I was just editing it. Thanks. Nam Nguyen wrote: > Marshall wrote: >> On Apr 4, 6:12 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote: >>> It wouldn't be a surprise if we learn there were those who would >>> defend physics against SR to the bitter end. >> >> This is somewhat off-topic, and I may be misreading you, >> but am I to understand from this sentence that you are >> of the opinion that special relativity is somehow incorrect, >> or not the best currently available theory? > > No it's not off the topic: I was using SR as analogy to the > anti-natural-number position some might have held (including > me in this case). I I didn't mean at all SR is incorrect. In > > > It wouldn't be a surprise if we learn there were those who would > defend physics against SR to the bitter end. I think there are those > today who'd similarly defend "the natural numbers" foundation in > mathematical logic - to the bitter end - even though to no avail. > >> >> >> Marshall >>
From: Nam Nguyen on 5 Apr 2010 00:19
Marshall wrote: > On Apr 4, 6:12 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote: >> It wouldn't be a surprise if we learn there were those who would >> defend physics against SR to the bitter end. > > This is somewhat off-topic, and I may be misreading you, > but am I to understand from this sentence that you are > of the opinion that special relativity is somehow incorrect, > or not the best currently available theory? No it's not off the topic: I was using SR as analogy to the anti-natural-number position some might have held (including me in this case). Also, I didn't mean at all SR is incorrect. By "defend physics against SR" I meant there were people in the past who would defend the then "current" physics at the time when SR was introduced. |