>I would say ontology is about the most exhaustive possible
>list of objective truths, and any entity referred to in this exhaustive 
>of objectively true statements "exists" by definition. With something like 
>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:


"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 

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 

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.


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