Re: Help in answering news story on refutation of fermat's last theorem

Jesse F. Hughes wrote:

> > Jesse F. Hughes wrote:

> >> That is very non-standard terminology. Indeed, it is so non-standard
> >> that many logicians would call it either confused or needlessly
> >> confusing.

Excuse me, Jesse, but wasn't calling my terminology "non-standard" and
possibly "confused" a rather strong and somewhat deragotary and
condescending statement?

Have you noticed where our disscussion is taking place? In sci.math.
It's not even cross-posted to sci.logic.

> Maybe that is common terminology among mathematicians. I guess it's
> been a long time since I've been around many mathematicians.

So, you call my terminology "non-standard" and possibly "confused" by
sci.math standards and then suddenly admit that you don't even know
what is standard terminology among the readers of sci.math and other
mathematicians.

Imagine that I, who hasn't been around many logicians, barged in onto
sci.logic and started calling your and other logicians' posts
"confused" and "non-standard". How would you take this?

> But it's
> not a particularly good terminology, as it conflates two distinct
> concepts and leads to confusion.

In the last few centuries, mathematicians have been able to develop
zillions of new theories - from differential topology to p-adic numbers
- without ever getting confused or asking help from amateur
philosophers. Never had any problems understanding each other. Why
would we start geting confused now?

Tell me. Imagine that two great mathematicians are in the middle of
talking about some abelian group G. And one of them asks:

- Is it true, J-P, that a + 0 = a for all a in G?
- Yes, Serge, it's true.

What is confusing about that? Who is confused? I am not. Are you?

Should J-P have instead answered:

- Is it true, J-P, that a + 0 = a for all a in G?
- Truth is a semantic concept, Serge. Whether a sentence is true has
to do with the meanings of the terms in the sentence. Instead of trying
to derive new algebraic theorems, let's spend the next 10 years
discussing the meanings of the terms "a", "+", "0", "=", "for", "all",
"in" and "G" in your sentence.

In any case, the original statement of mine which caused so much
opposition and condescention from you and a couple of other people was:

>>>>>> You can pick any axiomatic system you want. In some the
>>>>>> statement 0=1 will be true. In others - false.
>>>>>> As the previous poster told you, take the usual axioms
>>>>>> of integers, including inductive ordering, and let the
>>>>>> symbol "=" denote what we usually denote as "<".
>>>>>> Then "0=1" is a correct statement.

Wasn't this saying what you now say:

> Whether a sentence is true has to do
> with the meanings of the terms in the sentence.

----------------------------------------------------------------

Jesse F. Hughes wrote:

> anzaurres1@xxxxxxxxxxx writes:
>
> > Jesse F. Hughes wrote:
> >> anzaurres1@xxxxxxxxxxx writes:
> >>
> >> > Torkel Franzen wrote:
> >> >> anzaurres1@xxxxxxxxxxx writes:
> >> >>
> >> >> > You can pick any axiomatic system you want. In some the statement
> >> > 0=1
> >> >> > will be true. In others - false.
> >> >>
> >> >> There is no concept of a statement being true or false "in an
> >> >> axiomatic system" in logic.
> >> >
> >> > Torkel,
> >> >
> >> > When we, mathematicians, say that a statement is true in a given
> >> > axiomatic system, we mean that one can logically derive this statement
> >> > from the axioms.
> >>
> >> That is very non-standard terminology. Indeed, it is so non-standard
> >> that many logicians would call it either confused or needlessly
> >> confusing. Derivability and truth are two different concepts.
> >
> > I have no idea what you mean here. I don't even uderstand what you mean
> > by a "truth". Maybe specialists in logic do?
>
> Truth is a semantic concept. Whether a sentence is true has to do
> with the meanings of the terms in the sentence.
>
> Derivability is not a semantic concept. Whether a sentence is
> derivable in a theory does not depend on the meaning of the sentence.
>
> > What I know is what mathematicians, whom I know, in fileds other than
> > logic mean when they say that a certain statement S is true in a given
> > axiomatic system A. S is true in system A if one can derive (prove) S
> > from the axioms in A.
>
> Maybe that is common terminology among mathematicians. I guess it's
> been a long time since I've been around many mathematicians. But it's
> not a particularly good terminology, as it conflates two distinct
> concepts and leads to confusion.

.

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