My second example of why I don’t like ontology, is a TEDx talk by Kit Fine (h/t Brian Leiter). In that talk, Fine discusses what is the fundamental nature of the being of numbers.

It’s a puzzle to me that anyone would suppose that numbers have any fundamental being. It seems obvious that they do not.

Fine gives three possible versions of the nature of numbers. The first is due to Frege and Russell, the second to von Neumann, the third to Cantor. The only one of those that I find useful is von Neumann’s. But I do not take it as being about the nature of numbers. Rather, I take it as a useful way to model arithmetic within set theory. I have always assumed (perhaps wrongly) that was why von Neumann proposed that definition.

Kit Fine seems to think that there are puzzles about numbers and mathematics, that can be resolved by understanding the nature of numbers. He suggests that there is a puzzle as to why mathematics is so useful in science. Others apparently also see that as a puzzle. Fine asks (about numbers):

How can they be so far removed from the familiar world, yet so intimately connected to it?

Presumably, he thinks that understanding the fundamental nature of numbers will answer that question.

Numbers have no fundamental nature. Perhaps knowing that will help Fine.

The usefulness of numbers and of mathematics is explained by how we use them, not by what they are. The usefulness of numbers in science is explained by how scientists use them.

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Posted on January 21, 2015 at 21:37 (UTC) in mathematics, philosophy | RSS feed