True, but not provable
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From: Nam Nguyen on 17 Apr 2010 13:54 Peter Webb wrote: > > "John Jones" <jonescardiff(a)btinternet.com> wrote in message > news:hqapoj$lag$1(a)news.eternal-september.org... >> "Some mathematical statements are true, but not provable". Does that >> make sense? Let's make a grammatical analysis. >> >> 1) To begin, there are no mathematical statements that are false. > OK, here is a mathematical statement: 2+2 = 5 > > It is a mathematical statement and it is false. > > So unless you can explain this counter-example, you are clearly wrong. I've never been a fan of JJ's style of reasoning and I'm not defending his op here. But what you've implied above is: (1) There's a mathematical statement that is false. while what he said is: (2) There are no mathematical statements that are false. Assuming here by a "mathematical statement" we just mean a FOL wff, why do you think observation (1) is correct while (2) wrong?
From: Nam Nguyen on 17 Apr 2010 14:05 Nam Nguyen wrote: > Peter Webb wrote: >> >> "John Jones" <jonescardiff(a)btinternet.com> wrote in message >> news:hqapoj$lag$1(a)news.eternal-september.org... >>> "Some mathematical statements are true, but not provable". Does that >>> make sense? Let's make a grammatical analysis. >>> >>> 1) To begin, there are no mathematical statements that are false. > >> OK, here is a mathematical statement: 2+2 = 5 >> >> It is a mathematical statement and it is false. >> >> So unless you can explain this counter-example, you are clearly wrong. > > I've never been a fan of JJ's style of reasoning and I'm not defending his > op here. But what you've implied above is: > > (1) There's a mathematical statement that is false. > > while what he said is: > > (2) There are no mathematical statements that are false. > > Assuming here by a "mathematical statement" we just mean a FOL wff, > why do you think observation (1) is correct while (2) wrong? The point being is without a clear reference to a context for being true, or being false, both your (1) and his (2) would equally make no sense.
From: John Jones on 17 Apr 2010 21:19 Peter Webb wrote: > > "John Jones" <jonescardiff(a)btinternet.com> wrote in message > news:hqapoj$lag$1(a)news.eternal-september.org... >> "Some mathematical statements are true, but not provable". Does that >> make sense? Let's make a grammatical analysis. >> >> 1) To begin, there are no mathematical statements that are false. A >> false mathematical statement isn't a mathematical statement. It's a >> set of signs that merely look like a mathematical statement. >> > > OK, here is a mathematical statement: 2+2 = 5 > > It is a mathematical statement and it is false. What is a "false" mathematical statement? Is it a mathematical statement? does it adhere to the Peano axioms? > > So unless you can explain this counter-example, you are clearly wrong. See above.
From: John Jones on 17 Apr 2010 21:22 Jim Burns wrote: > Peter Webb wrote: >> "John Jones" <jonescardiff(a)btinternet.com> wrote in message >> news:hqapoj$lag$1(a)news.eternal-september.org... >> >>> "Some mathematical statements are true, but not provable". >>> Does that make sense? Let's make a grammatical analysis. >>> >>> 1) To begin, there are no mathematical statements that >>> are false. A false mathematical statement isn't a >>> mathematical statement. It's a set of signs that merely >>> look like a mathematical statement. >> >> OK, here is a mathematical statement: 2+2 = 5 >> >> It is a mathematical statement and it is false. >> >> So unless you can explain this counter-example, >> you are clearly wrong. > > JJ needs to re-define "mathematical statement" > in order to make it appear that he has drawn some > sort of useful conclusion. Compare to the explanation > of why all Scotsmen like haggis: because anyone not > liking haggis is no true Scotsman. > > One problem with JJ's re-definition -- > the motivating notion, about something > true but unprovable, remains just as true as > it ever was. The only effect of JJ's tactic is > that what we had called a "mathematical statement" > (and which could be either true or false) we now > need to call something else -- perhaps "woof" > would be a good choice. Then, instead of JJ's > sentence, we have "Some woofs are true, > but not provable." Not much of an improvement > that I can see. > > Jim Burns > A mathematical statement is one where general mathematical axioms are retained in the statement. There is no such retainment for a mathematical statement that is false. Hence, a mathematical statement that is false is not a mathematical statement.
From: John Jones on 17 Apr 2010 21:23
John Stafford wrote: > "John Jones" <jonescardiff(a)btinternet.com> wrote in message > news:hqapoj$lag$1(a)news.eternal-september.org... >> "Some mathematical statements are true, but not provable". > > What you described is a conjecture, not a proof. > >> Does that make sense? Let's make a grammatical analysis. > > Grammatical analysis is irrelevant except to clarify a statement that > has clear ambiguity. ...ye.s... |