[FOM] Richard Epstein's view
Arnon Avron
aa at tau.ac.il
Fri Mar 30 02:36:10 EDT 2012
"With normal vision" - so blind people cannot understand claims of the
form "The formal sentence A is/isn't a theorem of the formal system T"?
"suitably programmed electronic computer" what is this? "suitable"
for what? And what is the criterion for being "suitably programmed"?
Can this be given any sensible (or at least non-circular) meaning
without understanding first the absolute nature of the truth of
propositions of the form we are discussing?
"concrete instantiations of its theoremhood" - Is the property of being
"concrete instantiation" of A absolute? Is at least the proposition "alpha
and beta are both concrete instantiations of A"
meaningful and absolute, or is it "only true or false in application"?
The truth it that I do not see a point in continuing this debate.
I do not believe that you personally hold the views you are trying
to defend, and I think that people who do believe that they have
such views will go on pretending that they do not recognize the existence
of absolutely true abstract propositions. They will continue to
suggest more and more complicated (and in my opinion - less
and less coherent) ways how to interprete what they are saying,
and this can go on for ever. So I'll stop here.
Arnon
On Tue, Mar 27, 2012 at 11:32:32AM -0400, Timothy Y. Chow wrote:
> Arnon Avron wrote:
>
> >Even people like Epstein should accept as meaningful and absolute
> >propositions of the sort: "The formal sentence A is/isn't a theorem of
> >the formal system T". I do not see how a view of mathematics (or science
> >in general) that denies this can be coherent, and in what possible sense
> >can the truth of such a proposition be "only true or false in
> >application".
>
> Here is a possible sense in which the truth of such a proposition might be
> regarded as "only true or false in application." One might maintain that
> the concept of a "formal sentence" is an abstraction of physically
> concrete marks, and that syntactic rules are an abstraction of physical
> processes for manipulating physically concrete marks. What is
> straightforwardly true is that (for example) a suitably trained human
> being with normal vision and motor skills will generate certain chalk
> marks on a chalkboard under certain conditions, or that (for example) a
> suitably programmed electronic computer with properly functioning hardware
> will generate certain patterns of pixels on an electronic display under
> certain conditions. The theoremhood of A is true only insofar as these
> concrete instantiations of its theoremhood are true.
>
> Tim
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