Are Numbers “Real”?

This Aeon Essay about whether numbers are cultural or innate is a rerun from 2017. But I read it again and it strikes me that the claims attributed to cognitive scientist Rafael Núñez are wrong on at least two counts.

Yet whether numbers really exist independently of humans ‘is not a scientific debate, but a philosophical, theological or ideological one’, said Núñez. ‘The claim that, say, five is a prime number independently of humans is not scientifically testable. Such facts are matters of beliefs or faith, and we can have conversations and debates about them but we cannot do science with them.’

This is doubly wrong.

First, I would argue that whether numbers “really exist” independently of humans is indeed a scientific question with little to learn from philosophical, theological or ideological perspectives.

And secondly I would say that, if numbers “really exist”, then the fact that five is a prime number independently of humans is indeed scientifically testable.

But first things first. The question of whether numbers “really exist” is really a question about whether or not our propensity to identify parts of our experience as separate countable things, and the binary logic that we use to relate propositions about them, are in fact capable of providing an optimal means for making predictions about what we will experience – or whether some modified “quantum” logic about not-exactly-countable objects with fuzzy boundaries may eventually do a better job. (Yes, some Philosopher may tell me that’s just one “Ontological Perspective”, but I would just ask them to come back when they have a better one.)

And with respect to the primality of five, I would say that (so long as our conventional rules of logic survive the test of experiment) one kind of scientific test of a proposition is provided by showing its logical relationship to others that have already been established. And the primality of five is indeed a logical consequence of the basic properties of numbers that we already consider well tested. (And, yes, some Philosopher may tell me that’s just one “Epistemological Perspective”, but I would just ask them to come back when they have a better one.)

But the article does raise some interesting questions about how our capacity for inventing and/or understanding numbers evolved – which I think are worthy of a subsequent posting.

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