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Home » Kit Fine: What are Numbers? at TEDxNewYork (Full Transcript)

Kit Fine: What are Numbers? at TEDxNewYork (Full Transcript)

Kit Fine

Kit Fine – Philosopher

Numbers are strange. They are not physical objects. No one has bumped into the number two or tripped over the number three; not even your crazy math professor. They are not mental objects either. The thought of your beloved isn’t your beloved no matter how much you might want it to be. And no more is the thought of the number three, the number three. Nor do numbers exist in space or time. You don’t expect to find the number three in the kitchen cupboard, and you don’t need to worry that numbers once didn’t exist or might one day cease to exist.

But even though numbers are far removed from the familiar world of thoughts and things, they’re intimately connected to that world because we do things with numbers. We count with them, we measure with them, we formulate our scientific theories with them. So this makes it all the stranger what they are.

How can they be so far removed from the familiar world and yet so intimately connected to it? In this talk I want to consider three views about the nature of number that were developed by mathematicians and philosophers around the end of the 19th century and the beginning of the 20th century. All of these views presuppose that strictly speaking what we count are not things, but sets of things.

A set is just many things, any things you like, considered as one. So for example, we have the set of beer bottles that you drank last night. The bottles are put in these braces to indicate that the six bottles are being considered as one object. Then we have the set consisting of your two favorite pets, Fido and Felix. Or we have a set consisting of all the natural numbers, so they’re put together in this very big set: 0, 1, 2, 3, 4 and so on. And so what we do when we count is associate a number with a set.

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