The End of an Era - That of The Natural Numbers
in [Math]
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From: William Hughes on 31 May 2010 15:00 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. And since no model has a contradiction, true or false in a contradiction does not apply to model theoretic truth.
From: Nam Nguyen on 31 May 2010 15:14 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. > true or false in a contradiction does not apply to model > theoretic truth. My memory isn't 100% perfect. Where did I say that? Iirc, I think it's your guys who'd believe that truth or falsehood in tautolgy, contradiction should be applied to model truth or falsehood!
From: William Hughes on 31 May 2010 15:47 On May 31, 4:14 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote: > But it could have an empty U and empty predicates and in which > case all formulas are interpreted to be false. Only if you interpret as false a formula that says there is no element in U. Nothing you can say will make this less absurd. - William Hughes
From: Marshall on 31 May 2010 15:56 On May 31, 11:40 am, Nam Nguyen <namducngu...(a)shaw.ca> wrote: > > Good grief. Don't you have a better analogy? I wasn't making an analogy. I was making a true statement. You are not a potato chip. This is not a statement that is true in some narrow technical sense. It's just true, period. Are you seriously unable to comprehend what a true statement is? That boggles my mind. > > Well, actually, I don't really want to know your position > > better, because I'm confident that you position is fatally > > flawed. One reason that I'm so confident is because > > your approach leads you to label as false some true > > statements. > > If you first had a "serious" question for your opponent and now > you don't want to hear your opponent's explanation just because > you have some kind of "confidence" it's flaw, then how could > people take you serious the next time you say you'd be serious > about anything? (As if you had any seriousness in making logical > arguments here to begin with!). I don't want to hear my "opponent's" explanation of some completely different thing, no. I was just curious as to why you thought you were doing something useful when you were developing a logic that classifies true statements as false. If you want to answer that question, I'm interested. If you want to ruminate on how Godel thought this or that, then I'm not. I'm interested in some things and not in others. Is that somehow unclear? Marshall
From: Nam Nguyen on 31 May 2010 16:21
Daryl McCullough wrote: > Nam Nguyen says... > > Because you are very confused. For one thing, you have a paranoid > belief that you have "opponents". All you have is helpful people > who are trying to get you unconfused. Oh no. You might just don't remember the conversations. The following conversation between Marshall and I on May 13 actually precipitated this part of the thread about truth (or falsehood) as perceived in x=x. Marshall wrote (May 13): > On May 13, 7:13 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote: >> ... the fact that nobody could have a single example of a _FOL_ >> absolute (formula) truth. > x=x > > Anyway, this whole discussion was over the question of whether > x=x is true. I would say, to be picky, that it is not true, but > it is valid. Whatever the reason you have when saying x=x "is not true" is a direct contradiction with Marshall's belief (if not with Aatu's and Jesse's as well), in the original challenge I brought up above about showing any "absolute (formula) truth". There seems to be 3 sides now: - The relative side (my side) which states there's no "absolute (formula) truth". - Marshall's et al belief x=x is true in all contexts. - Your side: x=x is NOT true (in all contexts). I already defended my position with Tarski's definition via factual set membership (viz a viz empty and non-empty predicates). The other 2 sides still have yet to reconcile with each other, before I could even see why my relativity view is in any danger. (As for "validity", I _only_ meant the validity of reasoning via rules of inference which I thought you were referring to). |