>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. Quines 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 Platos 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 --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [email protected] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~----------~----~----~----~------~----~------~--~---
