>I would say ontology is about the most exhaustive possible
>list of objective truths, and any entity referred to in this exhaustive
>list
>of objectively true statements "exists" by definition. With something like
>a
>unicorn, once you have all true statements about peoples' *concepts* of
>unicorns, you won't have any additional statements about what unicorns are
>"really" like; but with mathematics I think there can be statements that
>would be true even if no human had thought about them, or if they had
>thought about them but concluded they were false due to some mental error.
By the way, I just came across this website which supports my notion that
philosophers tend to define "ontology" in terms of the entities you'd need
to refer to in an exhaustive list of objectively true statements:
http://artsci.wustl.edu/~philos/MindDict/ontology.html
"The most familiar theory of ontological commitment is that offered by Quine
in his "On what there is" (1948). It may fairly be called the received view
of ontological commitment. In effect, it is a combination of a criterion of
ontological commitment and an account of that to which the criterion
applies.
The criterion itself is quite simple. A sentence S is committed to the
existence of an entity just in case either (i) there is a name for that
entity in the sentence or (ii) the sentence contains, or implies, an
existential generalization where that entity is needed to be the value of
the bound variable. In other words, one is committed to an entity if one
refers to it directly or implies that there is some individual which is that
entity.
Quine’s account of that to which the criterion applies provides the theory
some bite. On his account, a sentence is not, in fact, committed to an
entity if there is some acceptable paraphrase of it which avoids commitment
to it as per the criterion.
The appeal to paraphrase allows us to avoid the problem of Plato’s Beard, or
the problem of nonexistent entities to which we nonetheless apparently
refer. The names are to be eliminated in such a way that the remaining set
of true claims contains none committed to any such entity after the manner
of the theory. For example, the name ‘Pegasus’ is eliminated in favor of a
verb ‘Pegasize,’ which is understood as the thing one does when one is
Pegasus. We can then say that nothing Pegasizes."
[end quote]
Would there by any way to "paraphrase" statements about mathematical truths
purely in terms of statements about physical entities? I don't see how,
because again, there is always the possibility that all attempts to compute
some mathematical truth (say, whether a given axiomatic system can produce a
given proposition) using physical computers or brains could go wrong, but
that wouldn't change the mind-independent mathematical truth itself.
Jesse
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Received on Tue Jul 11 2006 - 22:20:37 PDT