True, but not provable
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From: John Jones on 21 Apr 2010 00:00 Nam Nguyen wrote: > 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."? It doesn't matter what model is being used. Look. If an element of a model doesn't fulfil the criteria of being in that model, then, it isn't an element of the model. So 2+2=5, as a mathematical statement, is a statement that is not made within the mathematical model. Therefore, it isn't a mathematical statement. So the truth or falsity of "2+2=5" never arises. 2+2=5 is not a statement in the mathematical model: but that doesn't make "it" a statement in ANOTHER model!!
From: Nam Nguyen on 21 Apr 2010 00:24 John Jones wrote: > Nam Nguyen wrote: >> 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."? > > It doesn't matter what model is being used. Look. > > If an element of a model doesn't fulfil the criteria of being in that > model, then, it isn't an element of the model. What do you mean by "element" here? can you give an example of an "element" of a model? > So 2+2=5, as a mathematical statement, is a statement that is not made > within the mathematical model. What is "the" mathematical that you were referring to? > Therefore, it isn't a mathematical > statement. Can't a mathematical statement be defined as a wff? > > So the truth or falsity of "2+2=5" never arises. Of course it can: it's a wff (well-formed formula). > > 2+2=5 is not a statement in the mathematical model: but that doesn't > make "it" a statement in ANOTHER model!! What on earth is "the" mathematical model?
From: James Burns on 22 Apr 2010 12:36 Nam Nguyen wrote: > Jim Burns wrote: > >> It seems to me that knowing what is meant is >> all that can reasonably be required of statements, >> mathematical or otherwise. > > Really? Given the mathematical language [similar but > not identical to L(PA)] L(0,S,+,*,o) where o is a binary > relation symbol, what would the formula "2+2 o 5" _mean_ > to you? What does it *usually* mean? If I have no indication otherwise, I will assume that "2+2 o 5" means what it *usually* means. This is not a perfect solution. Whoever wrote "2+2 o 5" may have, for obscure reasons, meant it in some way /other than/ the *usual* way /and/ not mentioned that. Perhaps there is no *usual* way to understand "2+2 o 5". Then I would need more information from whoever wrote it in order to understand it. In practice, a writer nearly always foresees the need for more information and provides it (if they want to be understood), erring on the side of extra information, if they have any doubt (*usually*). But, wait! There is no *usual* way to understand "2+2 o 5", /plus/ you have provided no information about what /you/ mean by "2+2 o 5". This is an excellent example of the kind of thing I was talking about: a writer whose goal is /not/ to be understood, rather the goal is to be obscure. Thanks, Nam! All right, this is how it works: So, Nam: What /does/ "2+2 o 5" mean? It may be that you had nothing in mind for "2+2 o 5", or that you did but you don't feel like sharing. Then I will be left not understanding what /you/ meant by it. As I said, this is not perfect. *However*, I don't think it is possible to do better. If the purpose of a writer is to be obscure (/your/ purpose here), then I think it is asking too much of the reader to defeat the writer. > (It's a mathematical formula isn't it?) So? Did I claim that I can understand all mathematical formulas? >> Everything else changes, >> depending upon circumstances, up to and including >> whether a statement "should" be true. > > Per the example above, the meaning of a formula > changes too! Just so. /Depending upon circumstances/, the meaning of a formula changes. I'm glad we agree here. >> For example, >> Peter Webb used "2+2=5" as an example of a >> "mathematical statement" (call it something else, >> if you feel you must) that was false. > > Why can't it be true, when there's context that it is true? The context(s) where "2+2=5" is true is not the context of Peter Webb's use of "2+2=5". > You didn't seem to be coherent in what you said here. > First you said a statement's truth or falsehood could > be changed, Yes. "Depending upon circumstances", if you will recall. It seems like nit-picking, but I would like to clarify that I said a statement's meaning (and thus its truth and falsehood) could /change/, *not* that it could /be changed/. Circumstances are not necessarily under anyone's control. > but now you seemed to say "2+2=5" could _only_ be false! Yes. Given the *usual* way of understanding "2+2=5", then "2+2=5" can only be false. There /is/ a *usual* way of understanding it, and Peter Webb did not specify any other way of understanding it. Okay, I will admit that it is conceivable that PW actually had a secret meaning of "2+2=5" that he chose not to share with us. In that case, I would be wrong -- I would have missed PW's secret meaning. Did you have some other way of doing things, where I would have been able to read the secrets in Peter Webb's heart? >> *In the usual way*, whether something is a mathematical >> statement is determined by very simple syntactic rules, >> such as "If A is a mathematical statement >> then ~(A) is,too." > > Right. This is essentially the only point that I want to make to John Jones in this thread. I believe you have never given anyone cause to think you disagree with it. >> One can then argue that a >> particular statement is true or false, but, either way, >> (or any other way) it remains a statement. > > But if one can argue for a statement to be true, one can > also argue for it to be false as well. There's no intrinsic > truth value for a statement: that has to be argued for, by > citing a context! I mostly agree with you: There is no intrinsic truth value for a statement. A statement draws its meaning (and, thus, its truth value) from its context. A different context quite possibly brings a different meaning. However, although there is no /intrinsic/ truth value (or intrinsic meaning or intrinsic context) for a statement, there is very often a *usual* truth value (meaning, context). If the *usual* context is understood by all participants in an exchange of views, then it is not necessary to cite it. It is not necessary to cite the *usual* context, if it is clear that it is being used. This is a very important point. This is not just a question of the convenience of the writer. If it were always necessary to cite the context in order to understand a mathematical statement, then the citation itself (composed of mathematical statements) would need citations to be understood, and for those citations, more citations, ad infinitum. The only way to stop the infinite regress is to stop citing the context, at some point. The only feasible point at which to stop citing the context is one at which the reader can guess what the context is, without a citation. The only reasonable guess that /I/ can come up with (without citation) is: the *usual* context. What other guess would you suggest, an *unusual* context? If we must have a citation of the context in order to be understood, then we are fated not to be understood. Jim Burns
From: Nam Nguyen on 22 Apr 2010 01:09 Jim Burns wrote: > It seems to me that knowing what is meant is > all that can reasonably be required of statements, > mathematical or otherwise. Really? Given the mathematical language [similar but not identical to L(PA)] L(0,S,+,*,o) where o is a binary relation symbol, what would the formula "2+2 o 5" _mean_ to you? (It's a mathematical formula isn't it?) > Everything else changes, > depending upon circumstances, up to and including > whether a statement "should" be true. Per the example above, the meaning of a formula changes too! > For example, > Peter Webb used "2+2=5" as an example of a > "mathematical statement" (call it something else, > if you feel you must) that was false. Why can't it be true, when there's context that it is true? You didn't seem to be coherent in what you said here. First you said a statement's truth or falsehood could be changed, but now you seemed to say "2+2=5" could _only_ be false! > *In the usual way*, whether something is a mathematical > statement is determined by very simple syntactic rules, > such as "If A is a mathematical statement > then ~(A) is,too." Right. > One can then argue that a > particular statement is true or false, but, either way, > (or any other way) it remains a statement. But if one can argue for a statement to be true, one can also argue for it to be false as well. There's no intrinsic truth value for a statement: that has to be argued for, by citing a context!
From: Akira Bergman on 22 Apr 2010 20:20
"A false mathematical statement isn't a mathematical statement." False. This refers to its meaning, not to the construction of the statement. People have already pointed this out you many times but you keep insisting and creating more confusion. This is probably your purpose. You may also be nuts. For a statement to function as a binary switch, it has to be constructed according to a grammar. If the grammar fails then the meaning can not be considered, since it has no meaning. Grammar of language is like the axioms of mathematics. If there is no foundation, there is no building. If there is no assumption, there is no conversation. You made another statement before in another post (copied below). It was also false, while being grammatically correct. If you believed the truth of this statement then you should seek help. If you are doing these things to confuse people you should seek another kind of help, since this is all you do. "Thus the mathematical statement 2<4 means that there are fewer 2's than there are 4's." This statement is so bad that it makes me cringe on your behalf. |