I think there's a sense in which moderns feel that the reals (or at least the rationals) are a natural category: that 5 and 0.3 are the same "kind of thing". Mathematicians talk about the distinction between different classes of numbers, but to most people they're all numbers.
Do you think that sense was shared by the ancients, or do you think that the linguistic distinction mirrored a stronger mental separation between the two? It sounds like it might have done if they had to do the work of duplicating proofs from one to the other. Did they have a single word to describe the shared concept?
Do you think that sense was shared by the ancients, or do you think that the linguistic distinction mirrored a stronger mental separation between the two? It sounds like it might have done if they had to do the work of duplicating proofs from one to the other. Did they have a single word to describe the shared concept?