A number is not a word, it is a set

What is it about?

In this article I argue that the concept of number, such as the concept of the number "five", does not depend on the number word, "five". Instead, a number can be defined as a set of elements that is intentionally placed in one-to-one correspondence with another set of elements. On this idea, the former set is the number, the latter set is the numbered. I argue that humans can engage in exact arithmetic on numerical magnitudes beyond their subitization span without having number words because of their ability to place sets in one to one correspondence with each other.

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Photo by Mick Haupt on Unsplash

Photo by Mick Haupt on Unsplash

Why is it important?

One should not assume that a prehistoric culture for which evidence of counting exists, such as the Neolithic Middle East, which used geometric tokens for counting, must have had number words. Likewise, one should not assume that a culture which has no number words cannot engage in exact arithmetic on sets of sizes exceeding the subitization span. Experiments concluding that indigenous groups with few or no number words cannot engage in exact arithmetic are flawed; these experiments did not control for participants' visual acuity, motivation, or IQ.

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