The End of an Era - That of The Natural Numbers
in [Math]
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From: Marshall on 12 Jun 2010 16:19 On Jun 12, 12:52 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote: > Marshall wrote: > > > But I think it's safe for you to ignore any criticisms of mine > > Of course, I didn't ignore it; I refuted it that there would be > another context where your "potato chip" statement would be false, > in the realm of mathematical abstraction, remember? Yes, but maybe in a different context, the words you wrote are actually a proof that what I said was true! You can't ignore that possibility, can you? Maybe what you've been saying to me all along has been high praise! Wow, that was nice of you! > Since then have you had another either better or really more technical > example of a FOL absolute formula-truth? y=y Marshall
From: Nam Nguyen on 12 Jun 2010 17:11 Marshall wrote: > On Jun 12, 12:52 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote: >> Marshall wrote: >> >>> But I think it's safe for you to ignore any criticisms of mine >> Of course, I didn't ignore it; I refuted it that there would be >> another context where your "potato chip" statement would be false, >> in the realm of mathematical abstraction, remember? > > Yes, but maybe in a different context, the words you wrote > are actually a proof that what I said was true! You can't > ignore that possibility, can you? Sure. In the context of your own dream that is. > > Maybe what you've been saying to me all along has > been high praise! Wow, that was nice of you! As well in your dream you'd hear me saying "you're welcomed!" (But there's also such thing called the reality though!) > > >> Since then have you had another either better or really more technical >> example of a FOL absolute formula-truth? > > y=y Why is "y=y" better or more technical than "x=x" in this argument?
From: Marshall on 12 Jun 2010 18:20 On Jun 12, 2:11 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote: > Marshall wrote: > > On Jun 12, 12:52 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote: > >> Marshall wrote: > > >>> But I think it's safe for you to ignore any criticisms of mine > >> Of course, I didn't ignore it; I refuted it that there would be > >> another context where your "potato chip" statement would be false, > >> in the realm of mathematical abstraction, remember? > > > Yes, but maybe in a different context, the words you wrote > > are actually a proof that what I said was true! You can't > > ignore that possibility, can you? > > Sure. In the context of your own dream that is. So now you have a context in which I've proven you wrong. Now can you find a context where you're not a potato chip? > > Maybe what you've been saying to me all along has > > been high praise! Wow, that was nice of you! > > As well in your dream you'd hear me saying "you're welcomed!" > (But there's also such thing called the reality though!) Right! Reality is the context in which x=x is always true. But there are other contexts! > >> Since then have you had another either better or really more technical > >> example of a FOL absolute formula-truth? > > > y=y > > Why is "y=y" better or more technical than "x=x" in this argument? y=y is actually *less* technical than x=x. But I thought you'd find it easier to work with. It's certainly different, isn't it? Marshall
From: Nam Nguyen on 12 Jun 2010 19:02 Marshall wrote: > On Jun 12, 2:11 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote: >> Marshall wrote: >>> On Jun 12, 12:52 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote: >>>> Marshall wrote: >>>>> But I think it's safe for you to ignore any criticisms of mine >>>> Of course, I didn't ignore it; I refuted it that there would be >>>> another context where your "potato chip" statement would be false, >>>> in the realm of mathematical abstraction, remember? >>> Yes, but maybe in a different context, the words you wrote >>> are actually a proof that what I said was true! You can't >>> ignore that possibility, can you? >> Sure. In the context of your own dream that is. > > So now you have a context in which I've proven you wrong. > Now can you find a context where you're not a potato chip? > > >>> Maybe what you've been saying to me all along has >>> been high praise! Wow, that was nice of you! >> As well in your dream you'd hear me saying "you're welcomed!" >> (But there's also such thing called the reality though!) > > Right! Reality is the context in which x=x is always true. > But there are other contexts! > > >>>> Since then have you had another either better or really more technical >>>> example of a FOL absolute formula-truth? >>> y=y >> Why is "y=y" better or more technical than "x=x" in this argument? > > y=y is actually *less* technical than x=x. But I thought you'd > find it easier to work with. It's certainly different, isn't it? > > > Marshall
From: Daryl McCullough on 12 Jun 2010 19:51
Nam Nguyen says... > >Daryl McCullough wrote: >> Nam Nguyen says... >>> >>> (And didn't I post about A = B and C to counter any claim contrary >>> to what I've stating?) >> >> Yes, you said, essentially, that you are personally using a >> definition of truth in a model that relates to the definition >> everyone else uses in the following way: >> >> true_nam(M,Phi) = true_everyone-else(M,Phi) and nonempty(M) >> >> What everyone else is saying is that the second clause serves >> no purpose whatsoever. > >I don't know much about "everyone else" Well, I do... >but your statement "the second clause serves no purpose >whatsoever" has violated the fundamental basis of Tarski's >"factuality" vested in set-membership. (Assuming the >2nd clause being "nonempty(M)"). Your statement has basically discarded >Tarski's concept of truth! First, I don't believe that's true. Second, if it were, I couldn't care less. The additional clause is stupid. If Tarski insisted on it (which I'm sure he didn't), then Tarski did something stupid. Tarski is dead now, so he can't actually say whether he meant to make that stupid claim, or not, but it doesn't actually matter. There is a coherent notion of "truth in a model" that can be extended to models with empty domain in a sensible way. If Tarski couldn't figure out how to do it correctly, then so much the worse for Tarski. >In fact S. (Shoenfield) did allude to the 2nd clause in "We want to >define a formula A to be valid in M if all the meanings of A are true >in M", pg. 18. "All the meanings of A are true" requires the relevant >pM be non-empty hence U itself can't be empty! No, it doesn't, but I don't actually care what Shoenfield or Tarski said. What I care about is having a non-stupid definition of "truth in a model" that applies to models with empty domain. The definition that you are insisting follows Tarski or Shoenfield is a pointless definition, and I don't accept it. You want to propose that we use some particular definition of truth in the model with empty domain, say *why* you want to use that definition. Is there any point? Arguing that Tarski did it is no good, unless you can reproduce Tarski's reasoning for doing it that way. -- Daryl McCullough Ithaca, NY |