What Are Numbers?

The first man who noticed the analogy between a group of seven fishes and a group of seven days made a notable advance in the history of thought.

- Alfred North Whitehead, Science and the Modern World, II

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Plato claimed that numbers exist in some mind-independent abstract heaven. Nominalists claim that there is no such heaven. Clearly, we can't see, hear, taste or feel numbers. But if there are no numbers what is mathematics all about? John and Ken count on a great discussion with Gideon Rosen from Princeton University

Listen to the Philosophy Talk episode: What Are Numbers?

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Numbers do not exist in all cultures. There are numberless hunter-gatherers embedded deep in Amazonia, living along branches of the world’s largest river tree. Instead of using words for precise quantities, these people rely exclusively on terms analogous to “a few” or “some.”

In contrast, our own lives are governed by numbers. As you read this, you are likely aware of what time it is, how old you are, your checking account balance, your weight and so on. The exact (and exacting) numbers we think with impact everything from our schedules to our self-esteem.

But, in a historical sense, numerically fixated people like us are the unusual ones. For the bulk of our species’ approximately 200,000-year lifespan, we had no means of precisely representing quantities. What’s more, the 7,000 or so languages that exist today vary dramatically in how they utilize numbers.

Speakers of anumeric, or numberless, languages offer a window into how the invention of numbers reshaped the human experience...

Continue reading Caleb Everett's article: 'Anumeric' people: What happens when a language has no word for numbers?

Further Reading

Platonism about mathematics (or mathematical platonism) is the metaphysical view that there are abstract mathematical objects whose existence is independent of us and our language, thought, and practices. Just as electrons and planets exist independently of us, so do numbers and sets. And just as statements about electrons and planets are made true or false by the objects with which they are concerned and these objects’ perfectly objective properties, so are statements about numbers and sets. Mathematical truths are therefore discovered, not invented...

Continue reading the Stanford Encyclopedia of Philosophy article on Platonism in the Philosophy of Mathematics by Øystein Linnebo

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Related Topics

 ExistenceMathematics | Metaphysics

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