I agree with you Ben, you make a point. My objection admits indeed your wonderful generalization. Thanks.
At 11:07 13/01/04 -0500, Benjamin Udell wrote:
[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.
Best, Ben Udell