True, but not provable
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From: Nam Nguyen on 20 Apr 2010 23:01 James Burns wrote: > Nam Nguyen wrote: >> James Burns wrote: >>> Nam Nguyen wrote: > >>>> But that wasn't the case. And, at least by the essence of Tarksi's >>>> concept of truth, if there's no context for saying a statement is >>>> true, there's no sense for saying the statement is true. >>> >>> For you, apparently it goes without saying that there is no context. >> >> You're so vague here: "there is no context" for what? > > Try to think of something that you have recently been saying > has no context, something that I have been saying does have > context. That is what I am referring to here. > > I know, I could just say what I am referring to here. > It would be easier for me, and certainly clearer for you. > > But, if you really can't tell what I am referring to, > then, what ever is going on here, it is not communication. > That seems important for us to realize. > >>> I am disputing that, so it is a little disturbing that you >>> continue to treat the lack of context as though everyone >>> agrees on that point. >> >> Huh? I don't follow what you're trying to say. The main reason why >> people make argument is usually because they don't agree on certain >> point. Why is that becoming "disturbing" to you and "everyone"? > > I agree: you do not follow what I am saying. > > It is not disturbing that you and I disagree. > > It is disturbing (to me -- I do not speak for anyone else) > that you ignore the fact that you and I disagree. > > Your argument from Tarski's concept of truth takes as > given that a particular sentence, "2+2=5" as used by Peter > Webb upthread, has no context. I say there is context. > You continue to argue from Tarski's concept of truth > as though I had said nothing. That is what is disturbing. > > It is not true that you have said nothing about the context > of Peter Webb's use of "2+2=5". You remarked at one point > that PW did not specify which model of L(PA) he used in > making his remark, from which you concluded that "2+2=5" > made no sense in this case. After this, you went back > to treating the lack of context of "2+2=5" as settled. > I have tried to make it clear that it is not settled. > You don't seem to have noticed. > > I will be honest: I do not know what "models of L(PA)" > is supposed to do with the context of "2+2=5". OK. There are only 2 NGs in the thread: "sci.logic" and "alt.philosophy". I'm going to be frank and say that I don't care much about "alt.philosophy" and so if our conversations have been based on some kind of "alt.philosophy" then perhaps it's my mistake I didn't warn others that that's not my interest. With that caveat then as far as at least "sci.logic" is concerned, the formula "2+2=5" is just that: a well-formed-formula that has NO intrinsic meaning or truth value. It'd mean anything you'd like for it to mean and its truth value is entirely up to you to choose what model of L(PA) you'd prefer! So if you, or PW, claim "2+2=5" is true - or false - a context MUST necessarily be given. Now by convention, a "context" should be already assumed: the natural numbers is the standard model of PA. My point though, which you seem to have missed, is since that context is bogus, in the sense we really don't know what the natural numbers are, then the "context" is as good as there's no (valid) context. And without a valid truth-context talking about the truth or falsehood of "2+2=5" is nonsensical. But "2+2=5" is still a formula and if you want to give it a meaning that you'd like you still can do that. But _semantic is not truth_. Take your own example about the statement: (1) "My neighbor's dog barked all night" For the sake of argument, suppose you take your neighbor to a court with that complain but your neighbor made a counter claim to the judge: (2) "My dog didn't bark at night" Now I'm sure the judge did understand what (1) and (2) _mean_, but _which truth_ would he believe in - without some _context_ of evidence? I hope I've explained well enough that you'd now understand that "My neighbor's dog barked all night" and "2+2=5" don't have intrinsic truth or falsehood, as far as FOL is concerned. > It is possible that I am too ignorant for you to waste your > time on. *HOWEVER*, we are talking about "2+2=5" here! > I find it flatly unbelievable that I do not know what > that means. AND, if I didn't know what "2+2=5" meant, then > I would be even less capable than I am of knowing what > models of L(PA) were and how they are intended to > interact with Tarski's concept of truth. > > What seems more likely to me is that you have somehow > reversed the order of something (I am not sure what). > The idea that I need to understand models of L(PA) in > order for me to understand "2+2=5" is as crazy as > insisting that I must climb Mount Everest before I > will be able to climb the staircase in my house. Again nobody has said nobody would understood the meaning (semantic) of "2+2=5". Your mistake is you've equated semantic to truth. The two are _NOT_ the same, as far as mathematical reasoning is concerned.
From: Nam Nguyen on 20 Apr 2010 23:06 Nam Nguyen wrote: > > Again nobody has said nobody would understood the meaning > (semantic) of "2+2=5". Your mistake is you've equated > semantic to truth. > > The two are _NOT_ the same, as far as mathematical reasoning is > concerned. Iow, uttering a meaningful statement is not necessarily proclaiming a truth or making a lie. Naturally.
From: Nam Nguyen on 20 Apr 2010 23:15 John Jones wrote: > Nam Nguyen wrote: >> >> It's truth - not semantic - that's the issue here. I might >> know what "My neighbor's dog barked all night" well, but how >> could I be so sure it wasn't an audio file being played by >> their naughty kids, for example? > > But now you are just changing the goalposts. Why do you say that? What were my original goalposts and what have they changed to? > You have made a bigger > situation out of the smaller situation on which your original premise of > knowledge was based. I have no clue what you're talking about.
From: Nam Nguyen on 20 Apr 2010 23:22 John Jones wrote: > > It doesn't matter what model is being used. If it doesn't follow the > model then it is not a manifestation of the model. This is idiotic babbling. How did you go from "If it doesn't follow the model then it is not a manifestation of the model." to the conclusion "It doesn't matter what model is being used."?
From: John Jones on 20 Apr 2010 23:52
Nam Nguyen wrote: > John Jones wrote: >> Nam Nguyen wrote: >>> >>> It's truth - not semantic - that's the issue here. I might >>> know what "My neighbor's dog barked all night" well, but how >>> could I be so sure it wasn't an audio file being played by >>> their naughty kids, for example? >> >> But now you are just changing the goalposts. > > Why do you say that? What were my original goalposts and what > have they changed to? > >> You have made a bigger situation out of the smaller situation on which >> your original premise of knowledge was based. > > I have no clue what you're talking about. I meant that you made a conclusion from a statement such as "my dog barked all night" from a set of statements that INCLUDED "my dog barked all night". You introduced a new scenario, not a related one. |