The End of an Era - That of The Natural Numbers
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From: William Hughes on 1 Jun 2010 07:17 On Jun 1, 2:08 am, Nam Nguyen <namducngu...(a)shaw.ca> wrote: > Isn't [William Hughes] > the one who uttered this idiotic rambling? > > > From now on a sentence is true iff I say it is true. > > The question is who is to be master, that is all. > Someone needs to bone up on their Lewis Carroll [Hint, Humpty Dumpty, Through the Looking Glass, google is your friend]. The point (which you clearly missed) is that if you are allowed to redefine ordinary words at will, then communication becomes impossible. There is no sensible meaning of "true" under which you are a potato chip. (No, using the name "potato chip" does not make you a potato chip). You can, of course, insist there is a meaning one can assign to true under which "I am a potato chip" is true. But if you do so, anything you say becomes meaningless. - William Hughes
From: Daryl McCullough on 1 Jun 2010 08:04 Nam Nguyen says... >> I wonder why you think a logic that calls some true >> sentences false is a useful logic. > >Because you haven't been able to _technically & successfully_ >demonstrate a formula truth is absolute. The formula "Ax x=x" is true in every model, including the empty model. -- Daryl McCullough Ithaca, NY
From: Alan Smaill on 1 Jun 2010 08:19 Nam Nguyen <namducnguyen(a)shaw.ca> writes: > Daryl McCullough wrote: >> Nam Nguyen says... >>> William Hughes wrote: >>>> On May 31, 3:08 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote: >>>> >>>> >>>>> Iow, a formula being true or false here is being being true or false >>>>> in the context of tautology or a contradiction. >>>> True or false in a tautology is very different from true or >>>> false in a contradiction. >>> You just didn't carefully read what I say here. (Note my "or" was used >>> 3 times!) >>> >>>> And since no model has a contradiction, >>> But it could have an empty U and empty predicates and in which >>> case all formulas are interpreted to be false. >> >> That's wrong. In the usual semantics for first-order logic, >> a formula is interpreted to be false if and only if its negation >> is interpreted as true. > > Sigh. I don't know why people just don't understand simple things! > Why should we care about the word "usual" here, for crying out loud. You claim that your notion of model is equivalent to Shoenfield's notion. Yet Shoenfield follows Tarski's truth definition: the negation of a formula is true in a structure if and only if the formula is false in the structure. By all means don't do the usual thing -- but don't then claim that what you have is faithful to Shoenfield and Tarski. -- Alan Smaill
From: Marshall on 1 Jun 2010 10:35 On May 31, 10:08 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote: > Marshall wrote: > > On May 31, 8:27 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote: > >> Marshall wrote: > >>> On May 31, 3:20 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote: > >>>> Marshall wrote: > >>>>> Factual set membership?! But you're still claiming that every > >>>>> formula in an empty model is false, even when the formula > >>>>> says that factual set membership shows a predicate is empty. > >>>> If this is where you got confused and not understand my explanation > >>>> then that's easy to fix. In the post about "A df= (B and C)", May 29th, > >>>> I had: > >>>> > Note in FOL the individuals of an U and U itself are off-limit > >>>> > to FOL expressibility: in the sense that they're of the kind > >>>> > of unformalized entities that we can only have a priori and > >>>> > that if we try to formalize them what we've formalized just > >>>> > aren't they. Iow, B is _not_ FOL expression. > >>> The above paragraph doesn't say anything about set membership, > >>> or address my point in any way. > >> It does. > > > OK, it says *something* about set membership, but it doesn't > > address the relevant issue about set membership. > > > I'll just quote someone else who said it plainly and succinctly: > > >> Your claim is that for a model with an empty universe > >> There is no x such that x is blue > >> is false. > > >> No matter how you get to it, the fact remains > >> that this claim is absurd. > > >> - William Hughes > > > Your claim is factually incorrect, false, wrong, absurd. > > Isn't he the one who uttered this idiotic rambling? > > > From now on a sentence is true iff I say it is true. > > The question is who is to be master, that is all. No, it was YOU that said that. Recall that during the VN war, people ate potato chips and watched the movie Top Gun. They also used code names. Therefore anyone can be anything! In conclusion, your ideas about set membership are wrong. But take heart, because they are also right! There is no such thing as a true statement. I know all of this because you told me so. > > I wonder why you think a logic that calls some true > > sentences false is a useful logic. > > Because you haven't been able to _technically & successfully_ > demonstrate a formula truth is absolute. So once you concluded that I couldn't demonstrate a FOL formula that was true in all models, you decided to develop a logic that would assign false to some true sentences. Makes as much sense as the other stuff you are saying. > Let me remind you: we're talking about mathematical abstraction. Are we? Perhaps there is another context in which FOL formulas are REALLY different kinds of fruit. So in another context, you and I have been discussing recipes for mixed fruit drinks. Hey, this is fun! Marshall
From: Aatu Koskensilta on 1 Jun 2010 15:56
Marshall <marshall.spight(a)gmail.com> writes: > In fact, it seems to me that if there is a simple frontrunner reason > for studying logic at all, it is just exactly to *avoid* doing this > sort of thing. But perhaps that's just my imperialist, narrowly > utilitarian view. I am sure Jesse or Aatu or someone like that will > correct me if I'm wrong here. I'll correct you even when you're right. My generosity knows no bounds! -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus |