True, but not provable
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From: John Jones on 16 Apr 2010 18:53 "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. Therefore, a true mathematical statement isn't a possibility. We can say "it is true that that is a mathematical statement", but then the fact that that statement is true does not make the mathematical statement true. There are no criteria of truth that a mathematical statement need satisfy. Thus, mathematical statements are neither true nor false. 2) It follows for reasons given above, that a mathematical statement that has not been proved isn't, therefore, necessarily a mathematical statement. There is really no reason to offer up such a beast as "mathematical" . "not proven2 isn't mathematically significant. It is, rather, a way of saying "work in progress". 3) Regarding a mathematical statement that is necessarily unprovable, and not merely unproven, the grammar of proof is undermined. Proof deals with objects that have something in common and that bear relationships to one another. Something that is "necessarily unprovable" has nothing in common with other objects of its kind. It follows that "necessarily unprovable" is a simple grammatical contradiction.
From: Peter Webb on 17 Apr 2010 03:07 "John Jones" <jonescardiff(a)btinternet.com> wrote in message news:hqapoj$lag$1(a)news.eternal-september.org... > "Some mathematical statements are true, but not provable". Does that make > sense? Let's make a grammatical analysis. > > 1) To begin, there are no mathematical statements that are false. A false > mathematical statement isn't a mathematical statement. It's a set of signs > that merely look like a mathematical statement. > OK, here is a mathematical statement: 2+2 = 5 It is a mathematical statement and it is false. So unless you can explain this counter-example, you are clearly wrong.
From: Zerkon on 17 Apr 2010 07:57 On Fri, 16 Apr 2010 23:53:33 +0100, John Jones wrote: > 1) To begin, there are no mathematical statements that are false. A > false mathematical statement isn't a mathematical statement. It's a set > of signs that merely look like a mathematical statement. I Don Getit. A falsehood can only be a statement which is then proved or known as false?
From: Jim Burns on 17 Apr 2010 09:49 Peter Webb wrote: > "John Jones" <jonescardiff(a)btinternet.com> wrote in message > news:hqapoj$lag$1(a)news.eternal-september.org... > >> "Some mathematical statements are true, but not provable". >> Does that make sense? Let's make a grammatical analysis. >> >> 1) To begin, there are no mathematical statements that >> are false. A false mathematical statement isn't a >> mathematical statement. It's a set of signs that merely >> look like a mathematical statement. > > OK, here is a mathematical statement: 2+2 = 5 > > It is a mathematical statement and it is false. > > So unless you can explain this counter-example, > you are clearly wrong. JJ needs to re-define "mathematical statement" in order to make it appear that he has drawn some sort of useful conclusion. Compare to the explanation of why all Scotsmen like haggis: because anyone not liking haggis is no true Scotsman. One problem with JJ's re-definition -- the motivating notion, about something true but unprovable, remains just as true as it ever was. The only effect of JJ's tactic is that what we had called a "mathematical statement" (and which could be either true or false) we now need to call something else -- perhaps "woof" would be a good choice. Then, instead of JJ's sentence, we have "Some woofs are true, but not provable." Not much of an improvement that I can see. Jim Burns
From: John Stafford on 17 Apr 2010 11:50
"John Jones" <jonescardiff(a)btinternet.com> wrote in message news:hqapoj$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. |