True, but not provable
in [Logic]
|
Prev: EINSTEIN KNICKER ELASTIC GOOD FOR SAGGING KNOCKERS
Next: AT commands dial, accept, and manipulate voice and data calls.
From: John Jones on 20 Apr 2010 20:18 Michael Gordge wrote: > On Apr 17, 4:07 pm, "Peter Webb" > <webbfam...(a)DIESPAMDIEoptusnet.com.au> wrote: > >> OK, here is a mathematical statement: 2+2 = 5 > are you dumbnumbfik is the logical use of > numbers. > > MG
From: James Burns on 20 Apr 2010 20:21 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". 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. Jim Burns
From: James Burns on 20 Apr 2010 20:36 John Jones wrote: > James Burns wrote: >> Nam Nguyen wrote: >>> Peter Webb wrote: >>>> "John Jones" <jonescardiff(a)btinternet.com> wrote in message >>>> news:hqdmlj$uag$4(a)news.eternal-september.org... >>>>> Peter Webb wrote: >>>>>> >>>>>> So unless you can explain this counter-example, >>>>>> you are clearly wrong. >>>>> >>>>> See above. >>>> >>>> You are the person who introduced the concept of false >>>> mathematical statements, its up to you to define what >>>> that means in the context of your argument. >>>> >>>> According to you, is 2+2=5 : >>> >>> It's certainly up to JJ to answer this in his own way. >>> But here are mine. >>> >>>> a. A mathematical statement? >>> >>> In L(PA) yes, it's a mathematical statement. >>> I's exact formulation in that language is: >>> >>> SS0 + SS0 = SSSSS0 >>> >>>> b. False? >>> >>> It a meaningless question, without a context of >>> what model of what formal system which is the >>> underlying interpreting structure where its truth or >>> falsehood is asserted. In arithmetic modulo-1 system, >>> it's true but in other kind of arithmetic it might >>> be false. >> >> It is not meaningless if "2+2=5" is interpreted >> in the usual way. >> >> Is the problem you see that "the usual way" is not >> formalizable? Nearly everything we say or write is not >> formalizable. >> >> You seemed to have no problem understanding >> "The neighbor's dog barked all night." >> But you could be wrong! What if there is a planet >> on the opposite side of the Sun, matching Earth >> in every way, up to and including a language >> /almost/ the same as English, except that "dog" >> means "irridescent green"? Then >> "The neighbor's dog barked all night." >> makes no sense! >> >> However, if the sentence is understood *in the usual way*. >> then there is no problem. >> >> In fact, there is very rarely a problem between >> people understanding one another which is caused >> by different assumptions about things as fundamental as >> what language they are speaking. *AND* when there are such >> problems they are among the easiest to discover >> and correct. > That looked a bit like changing the goalposts. > You can't make an assessment of a statement based > on other statements. You have to limit yourself > to the statement that is at hand. Why am I limited to the statement at hand? I mean, you can make up that rule, if you want to. You can make up any rule, no matter how senseless, if you want to. However, *the usual way* sentences are understood is against a background of other sentences along with where, when and how they are used. Do you have any idea how to make sense of "My neighbor's dog barked all night." if you are limited to just that sentence? Jim Burns
From: John Jones on 20 Apr 2010 21:51 Jim Burns wrote: > Nam Nguyen wrote: >> Nam Nguyen wrote: >>> Jim Burns wrote: >>>> Nam Nguyen wrote: > >>>>> The point being is without a clear reference to >>>>> a context for being true, or being false, both >>>>> your (1) and his (2) would equally make no sense. >>>> >>>> Why do you say there is no context? Statements >>>> (1) and (2) have the context of other things that >>>> get referred to as "mathematical statements". >>>> >>>> Would you claim that "My neighbor's dog barked all >>>> night." makes no sense because you do not have >>>> a mathematical definition of "dog"? >>> >>> It's truth - not semantic - that's the issue here. > > When exactly did truth become the issue here? > > Does it *make sense* to speak of a mathematical > statement being true or false? Then we can speak > so. (I argued above that it does make sense.) Of course you can speak so. And we would all know what you meant. But then we would all, by claiming that, endorse a set of mathematical statements that aren't true. It's not because such statements represent the largest infinity, as the saying might go. Rather, it is that there is no criterion of a mathematical truth that doesn't circuitously rely on a mathematical falsehood. > Do we need to have specific mathematical statements > in mind, with their specific contexts, in order to be > able to speak so? I can't imagine why that might be > true. Certainly I can make mathematical statements > like "x = 1" without enough context to decide whether > they are true or false. You are appealing to contingencies. Mathematics has nothing to say about contingencies. A mathematical statement is complete.
From: John Jones on 20 Apr 2010 21:56
James Burns wrote: > John Jones wrote: >> James Burns wrote: >>> Nam Nguyen wrote: >>>> Peter Webb wrote: >>>>> "John Jones" <jonescardiff(a)btinternet.com> wrote in message >>>>> news:hqdmlj$uag$4(a)news.eternal-september.org... >>>>>> Peter Webb wrote: >>>>>>> >>>>>>> So unless you can explain this counter-example, >>>>>>> you are clearly wrong. >>>>>> >>>>>> See above. >>>>> >>>>> You are the person who introduced the concept of false >>>>> mathematical statements, its up to you to define what >>>>> that means in the context of your argument. >>>>> >>>>> According to you, is 2+2=5 : >>>> >>>> It's certainly up to JJ to answer this in his own way. >>>> But here are mine. >>>> >>>>> a. A mathematical statement? >>>> >>>> In L(PA) yes, it's a mathematical statement. >>>> I's exact formulation in that language is: >>>> >>>> SS0 + SS0 = SSSSS0 >>>> >>>>> b. False? >>>> >>>> It a meaningless question, without a context of >>>> what model of what formal system which is the >>>> underlying interpreting structure where its truth or >>>> falsehood is asserted. In arithmetic modulo-1 system, >>>> it's true but in other kind of arithmetic it might >>>> be false. >>> >>> It is not meaningless if "2+2=5" is interpreted >>> in the usual way. >>> >>> Is the problem you see that "the usual way" is not >>> formalizable? Nearly everything we say or write is not >>> formalizable. >>> >>> You seemed to have no problem understanding >>> "The neighbor's dog barked all night." >>> But you could be wrong! What if there is a planet >>> on the opposite side of the Sun, matching Earth >>> in every way, up to and including a language >>> /almost/ the same as English, except that "dog" >>> means "irridescent green"? Then >>> "The neighbor's dog barked all night." >>> makes no sense! >>> >>> However, if the sentence is understood *in the usual way*. >>> then there is no problem. >>> >>> In fact, there is very rarely a problem between >>> people understanding one another which is caused >>> by different assumptions about things as fundamental as >>> what language they are speaking. *AND* when there are such >>> problems they are among the easiest to discover >>> and correct. > >> That looked a bit like changing the goalposts. >> You can't make an assessment of a statement based >> on other statements. You have to limit yourself >> to the statement that is at hand. > > Why am I limited to the statement at hand? You are limited to the statement if you want to make an assessment of that statement. "limited" isn't limited in this sense. The limit arises when we suppose to consider other statements. A limit is introduced. > I mean, you can make up that rule, if you want to. > You can make up any rule, no matter how senseless, > if you want to. > > However, *the usual way* sentences are understood > is against a background of other sentences No. Not in logic or mathematics. > along > with where, when and how they are used. > Do you have any idea how to make sense of > "My neighbor's dog barked all night." > if you are limited to just that sentence? > > Jim Burns > > |