3 ms·

I have a hard time believing this though. If there are no sheep, then would it really not be "obvious" to them that there are no sheep, i.e. zero sheep, or none

I have a hard time believing this though. If there are no sheep, then would it really not be "obvious" to them that there are no sheep, i.e. zero sheep, or none to be found? What would have been their answer if not something akin to this?

thfuran 2y ago
It's not that there's no concept of the absence of sheep, it's that there's no concept that that can be represented as some number of sheep.
- adrian_b 2y ago
  This may sound clever, but it fails the experimental tests. In most modern grammar theories and already in some of the works of the Ancient Greeks and Romans, a group of words is recognized as having the same nature if any of those words can be substituted for another of them in a given sentence. Given the sentences (which have one-to-one correspondences in the ancient languages): I see zero sheep. (In Latin, "null-" is the word stem for zero.) I see one sheep. I see two sheep. I see three sheep. ... both a modern grammarian and also some of the ancient ones will conclude that zero, one, two, three ... have the same nature. So zero was a concept that represented a certain quantity of sheep. The Romans might have not used the word "number" in reference to zero, but there is no doubt that they understood the concept of a set whose members are 0, 1, 2, 3 and so on. The proof is that the normal way of saying "some" in Latin, i.e. an unknown number that is at least 1, was to say "not zero", i.e. by identifying the subset 1, 2, 3, ... with the complement of the subset that contains 0 in the set of what now are called natural numbers. While they did not have standardized words for concepts like set, subset, complement, membership or quantifiers, these concepts of the modern set theory were nevertheless well understood by the educated people in the Ancient World as they were studied within Logic a.k.a. Dialectic.

thfuran 2y ago

It's not that there's no concept of the absence of sheep, it's that there's no concept that that can be represented as some number of sheep.

adrian_b 2y ago
This may sound clever, but it fails the experimental tests. In most modern grammar theories and already in some of the works of the Ancient Greeks and Romans, a group of words is recognized as having the same nature if any of those words can be substituted for another of them in a given sentence. Given the sentences (which have one-to-one correspondences in the ancient languages): I see zero sheep. (In Latin, "null-" is the word stem for zero.) I see one sheep. I see two sheep. I see three sheep. ... both a modern grammarian and also some of the ancient ones will conclude that zero, one, two, three ... have the same nature. So zero was a concept that represented a certain quantity of sheep. The Romans might have not used the word "number" in reference to zero, but there is no doubt that they understood the concept of a set whose members are 0, 1, 2, 3 and so on. The proof is that the normal way of saying "some" in Latin, i.e. an unknown number that is at least 1, was to say "not zero", i.e. by identifying the subset 1, 2, 3, ... with the complement of the subset that contains 0 in the set of what now are called natural numbers. While they did not have standardized words for concepts like set, subset, complement, membership or quantifiers, these concepts of the modern set theory were nevertheless well understood by the educated people in the Ancient World as they were studied within Logic a.k.a. Dialectic.