this post was submitted on 22 Jul 2023
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English usage and grammar
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It seems that 'less than' from math is referring to less value, which is uncountable. That one checks out.
Integers are countable too. I think in math one just pronounces
<as 'less than'it's not integers though, it's value. 3 < 5: the value of three is less than the value of five. it mirrors 8 > 5 (the value of eight is greater than the value of five). less/greater, fewer/more.
Not sure I follow: isn't the value of three just "three", and therefore, "the value of three is less than the value of five" reduces to "three is less than five"? My point was that even though integers represent countable objects -- and therefore would have fitted fewer/more better according to the "rule" -- no one in a math context would say "three is fewer than five". The relationship represented by "<" is simply pronounced as "less than" without much concern to the "rule".
yes, but my point is grammatically it refers to the value. 7 is countable (three 7s is 21) but values are uncountable (sort of)
it's not without concern for the rule, it's actually following the rule; just the rule gets a bit hard to follow around fungible things like numbers
Thanks for the clarification, I see you are making a distinction between the symbol 7 and the value 7. Then yes I was talking about the value.
At the risk of drifting off topic, I would still argue that integer values are closer to "countable" than "uncountable" -- in fact the mathematical notion of "countable" is defined as having one to one correspondence to integers, and is based on the intuition of integers representing the counting of objects. I do concede though that people have different intuitions and intuition is a tricky thing (I myself would consider the value of 2/3 or 3.14 to be closer to being "uncountable", but mathematically the set of rational numbers is considered countable, intuitively you just need to count in unit of 1/3 or 0.01, respectively)
okay yeah, i don't really know how to explain my position as i've always seen this as axiomatic
i would say linguistics are probably different to mathematics then, as countability is unrelated to integer correspondence. three and a half apples is obviously countable, but doesn't correspond to any integer.
linguistic countability is more related to whether an item can be treated as plural (some apples) or not (some milk)
you could say "six apples are on the table", whereas "six are divisible by three" sounds just as stupid as "milk are made by cows". so in this case 6 (the value) is uncountable.
also is this not contradictory? or do you mean correspond as in each number can be assigned to an integer?
hey, all good points. I was just trying to say that if one had to pursue logical consistency (which is my perception of the theme of the entire thread), then countability becomes a math problem.
no, and yes
meh, i'd say in general language isn't logically consistent with maths. the english language doubly so. maths has to have prescriptive rules that are internally consistent, english has descriptive rules that are more often broken than followed
i guess that makes sense, i suppose