Re: Torkel Franzen on truth

tchow@xxxxxxxxxxxxx wrote:
In article <vBD9j.29$Tx.18@pd7urf3no>,
Nam D. Nguyen <namducnguyen@xxxxxxx> wrote:
tchow@xxxxxxxxxxxxx wrote:
Are you convinced, for example, that sqrt(2) is irrational? On what basis?
On the basis of model that "sqrt(2) is irrational" is true, of course.

You didn't answer my first question directly. Are you convinced that sqrt(2)
is irrational?

But your first question is unanswerable, *without* a context/basis!
(Why did you ask "On what basis?" *immediately* after your first question?)

If you asked me whether or not the sentence "President Kennedy is dead" is
true/false, I'd react in the same way: no context no possible answer.
If this sentence is answered in a play tomorrow about an event in 1960,
the sentence could be false, in that context. If the play happens to be
actually in 1961, but about an imagined event in 2010 the sentence could
still be true or false, depending on the context of the plot the play-writer
intended to write. If this sentence is uttered in the "normal" (i.e. historical)
context, there are still other contexts to be content with: in some religion
"beliefs" there would be no dead, just one life after another; and accordingly,
President Kennedy would be still "alive", years after ... well, his "assassination"!

Philosophical "crab" right? Not really! Especially when talking about something
that looks like a FOL truth question, like is "sqrt(2) is irrational". Let's even
deal with a much simpler question: is "1+1=0" true? The way DMC, PS and you seem
to say is that there is certain *absolute* truth (value) about "1+1=0" we must
necessarily "believe" in, in much the same way some "religiously believe" Jesus
of Nazareth is only son of God. What I counter is that there's no such kind of
unchangeable belief in mathematical reasoning.

What would be a distinction between these 2 kinds of belief: for one thing, model-truth
belief (which you seemed to allude below) is changeable/relative/subjective; given the
same event, structure, sets of ... (or whatever we may want to call), we are at the
liberty to change that belief 180 degree and still are correct as far as mathematical
"belief" viz-a-viz reasoning is concerned.

That's not the same kind of religion beliefs: there its truth values are absolute, immutable,
independent of any human perception, or even ... well, belief!

Or are you convinced only of the statement, "in the standard
model of the integers, there are no integers m and n such that m^2 = 2 n^2"?

There's a misconception here that seems to have escaped your attention. A model
*always already* includes a *chosen* interpretation: hence a belief has been
"believed" already. What's important is this interpretation could always be
reversed to the other way - at will - and a opposite "belief" would occur.
Consequently, a mathematically *stated* belief could change back and forth,
as in the following "The Lady's Yes" poem:

"Yes," I answered you last night;
"No," this morning, Sir, I say.
Colours seen by candlelight,
Will not look the same by day.
[...]

In summary, for "there are no [nonzero] integers m and n such that m^2 = 2 n^2",
its truth, or its believed truth is quite subjective and relative, like the
"Colours seen by candlelight", but unlike religion truth and belief.

Which is my whole point here.


Let me assume that the latter formulation is the only one that you assent to.
Then let me ask this: Do you believe (note the word "believe" here) the
following statement?

(*) In the standard model of the integers, there are no integers m and n
such that m^2 = 2 n^2.

If so, on what basis do you believe (*)? Not on the basis of proof, according
to what you say later. So what other basis do you have?

.

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