FOM: The meaning of truth

[Joe Shipman]

Kanovei wrote:

> > 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".
>

Well, maybe I'm only 99.99999% sure there are no real unicorns....


> > 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.

Yes, that's what I mean.

> 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.

Well, your insistence on "physically" is maybe a little strong if we live in a finite
universe.  Whether the number of sign changes of pi(x)-li(x) for x < 10^(10^(10^34))) is
a multiple of 3 is a finitely decidable question in theory, and I don't think
philosophers have any choice in the matter, however the question doesn't seem to be
determined by properties of anything that physically exists.  Can you explain what you
mean by "physically existent"?


> > 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 ?
>

In my opinion, S is true.  Do you deny that exactly one of them 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)

If I could I would be guaranteed a Nobel Prize in physics; but as I have argued in
earlier postings, it is quite possible that the ultimate physical theory will involve
experimentally measurable sequences which are mathematically definable but not
recursive.

> > 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.
>

Is it the case that if one can not specify a particular example of a class, then the
class must be empty?  Do you think that any proof of "A or B" should in principle be
replacable by a proof of A or a proof of B?

> > 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.

But you only need finitely many elements of the sequence to get scientifically
established but unprovable statements.  If there is a definable nonrecursive
experimentally derivable sequence X=x1,x2,x3,..., then there is already a finite i such
that the statement asserting the value of x_i is a mathematically unprovable but
scientifically attainable truth.

-- JS