[Georges Quenot]>>Some people do argue that there is no arithmetical property
independent of us because there is no thing on which they would apply independentkly
of us. What we would call their arithmetical properties is simply a set of tautologies
that do come with them when they are considered but exist no more than them when they
are not considered.
[Bruno Marchal]>But then what would be an undecidable proposition?
>You know, about arithmetic, and about machines btw, a lot of people defends idea
>which are just no more plausible since Godel has proved its incompleteness theorems.
>Arithmetical proposition are just not tautologies. This is how Russell's and
>Whitehead logicism has break down. There is a ladder of arithmetical propositions
>which ask for more and more ingenuity to be proved. Actually arithmetical truth
>extend far beyond the reach of any consistent machine (and consistent human with
>comp). There is an infinity of surprise in there.
>I guess you know that there is no natural number p and q such that (p/q)(p/q) is
>equal to 2. If mathematical truth were conventionnal, why did the pythagoreans *hide*
>this fact for so long? So those propositions are neither tautologies, nor
>conventions.David Deutsch, following Johnson's criteria of reality, would say that
>such propositions kick back.
Since Georges Quenot's objection claims that nothing exists when unconsidered, be it a
mathematical structure or concrete singular objects to which it applies, isn't the
objection too broad to be singling out any particular physics-based cosmology as
objectionable? The objection seems too powerful & broad, & seems to apply with equal
force to all subject matters of mathematics & empirical research, from pointset
topology to Egyptology. I wouldn't demand that a philosophical objection, in order to
be valid at all, offer a direction for specific research, but I'd ask how it would at
least help research keep from going wrong, & I don't see how the present objection
would help keep any kind of research, mathematical or empirical, from getting onto
excessively thin ice, except perhaps by inspiring a general atmosphere of skepticism
in response to which people pay more attention to proofs, confirmations,
corroborations, etc. -- not that any such thing could actually overcome such a !
And the objection is stated with such generality, that I don't see how it escapes
being applied to itself, since, after all, it is about things & relations. If there's
nobody to consider concrete things or mathematicals, then there's nobody to consider
the objection to considering any unconsidered things to exist. The objection seems to
undercut itself in the scenario in which it is meant to have force. Unless, of course,
I've misunderstood the argument, which is certainly possible.