trybulec at math.uwb.edu.pl
Thu Dec 24 09:22:49 EST 1998
On Mon, 21 Dec 1998, Michael Thayer wrote:
> > I don't either. But "2+2=4" seems to be absolutely true.
> >Andrzej Trybulec
> Yes, but WHY does it seem absolutely true??
> Is it any better grounded in our knowledge than either:
> 1."The Sun will rise tomorrow"
> 2."Winston Churchill was a Prime minister of England"
It is not the point. At least, my point was that even if we cannot define
what it means "true" in mathematics, there are sentences that are true
and we have no doubts about it. And in this sense they are absolutely true.
There are some other sentences (Continuum Hypothesis?) that sometimes are
true, sometimes not (and sometimes, or rather for some people, are
meaningless). The truth depends on some additional factors (the
interpretation, the model chosen as the standard model, philosophical views)
and in this sense they are relatively true (if or when they are true).
Of course, what I wrote may be meaningless for some members of f.o.m.,
sorry. I am a platonist (maybe not so extreme as Randall Holmes, but close)
so it is easier for me.
> I know it SEEMS absolutely true in a way that 1 or 2 do not; but it is
> clearly no more certain (and on similar grounds) than 1 or 2.
I agree with you. I feel that "2+2=4" is more true than 1 or 2. But I
think that nominalists believe that it is LESS true.
You have chosen extremely difficult sentences (purposefully?).
Both refer to the current moment.
"Winston Chrchill was the prime minister of England"
was false in the time of Elisabeth I.
I do not believe that the solar system will last to the eternity, so the
first sentence sooner or later will become false.
Moreover, the first sentence refers to the particular place in the space.
I am not certain what "tomorow" means when I flew from Warsaw to Edmonton
(the Sun did not rise, when it was supposed to rise), and going to the East
might be even more difficult (tomorrow happens before tomorrow).
The first sentence describes not the real physical fact, but (rather naive)
view of it. What is the meaning of it for astronauts? Once you are on the
These are technicalities, the real problem is with the second sentence.
What is the meaning of "the prime minister"?. To reduce it to physics
one have to do a lot of work (I do not know the British procedure, but
I guess one have define what MP means). The problem is not that eventually
you get a mess, not a definition. The problem is that it is not a definition,
the concept of prime minister is rather clear, and it does not matter
how he was chosen or nominated, the important thing is that the process
was legal, and how to define "legal" in physical terms?.
We deal with the first world (physical reality), some of us with the second
world (mathematics), what about the third world (as Karl Popper called it,
if I recall).
To wit, the problem that somebody does not believe in natural numbers is
not so serious, at least not so dangerous. The problem is with the people
that do not believe in "the president of USA" (I mean, they do not believe
in the concept, not that they trust him).
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