FOM: The meaning of truth
Kanovei
kanovei at wmwap1.math.uni-wuppertal.de
Fri Nov 3 15:03:05 EST 2000
> Date: Fri, 03 Nov 2000 11:41:53 -0500
> From: Joe Shipman <shipman at savera.com>
> there are no real unicorns
How do you know ? I would like to know what is your criteria
to deside ontological truth, then I apply those to the "sentences".
> I think we can agree that "X exists" implies "All the properties of X are
> determined".
I understand it that all properties of an existent X are
determined independently of "our" ability to ever have a chance
to have a knowledge on some of properties.
Note: this applies only to X which are physically existent,
as for those whose existence is only philosophical their
properties are exactly those which responsible philosophers
"enthink" into them (plus logical consequences).
By Goedel, the latter can never provide a full description of
a rather complicated X.
> for every pair of arithmetical sentences {S,~S} exactly one of them is
> true
Let S=Con ZFC. Which one of S, not-S is true ?
No, the question is, can you present any minimally thinkable procedure
(that may include travel to galaxies, precise counting stars in the
metagalaxy and electrons within the Solar system, just anything physically
thinkable, but not a reference to an oracle)
which will give us an answer ?
And IN WHICH SENSE (pls explain) you expect
one of them to be true (true in which sense, that is -- and I hope that
on this you will not answer: in the sense of the "truth predicate of ZFC").
> Since you call this a misinterpretation, you must think that only sentences which
> are provable mathematically are true "ontologically".
Please any example of the opposite. As you reject the existence of unicorns
on the base, presumably, that there is no evidence of them, be kind to let
me be sceptical in this case by the same reason.
> I would like to know is why you think that "X has been scientifically established"
> entails "The existence of a mathematical proof of X has been scientifically
> established".
Exactly by the same reason, a mathematical statement cannot have
truth value other that in the case there is a mathematical proof
of it. The specifics that separate mathematics from natural science
is that a mathematical statement scientifically found to be "0.9999999999 true"
is that far true not more than 0=1 is true.
> CT ...(The one I stated) ... says that any
> sequence we can generate by well-defined physical experiments is recursive.
Any such a sequence is finite first of all, because I
hardly see any experiment taking infinitely many steps as
either physical or well defined. Otherwise it is PHILOSOPHICAL
experiment, even if it involves physically valid procedures.
Note: physicists expect a full barion destruction in some not
fully known monent in future, after which any "experiments" will
be impossible together with any bodies of atoms.
V.Kanovei
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