Except

[rzach]

The truth conditions of "except" are given as the same as for "other than". But "except" is not a case of perfection, "Exeryone except Pavel" should be symbolized as Ax(~x = p <-> ...) not as Ax(x=p -> ...)`

[rzach]

See https://www.google.ca/books/edition/Quantifiers_in_Language_and_Logic/PrYUDAAAQBAJ?hl=en&gbpv=1&pg=PA297&printsec=frontcover

[rzach]

From @gfrost-arnold:

My class just went over Ch.25 (“Identity”), and I wanted to share part of our discussion with you, in case you might be interested or find it useful for any future re-writes. There are two related points; I feel more sure about the first than the second.

1: On pages 228-229, the book symbolizes the English sentence

'4. Pavel owes money to everyone except himself'

as

∀x(¬x=p → O(p,x)).

I think this does not accurately capture the original English sentence. For imagine a situation where Pavel owes money to literally everyone, INCLUDING himself. Then the above English sentence would be false in that scenario (right? or are my semantic intuitions incorrect?). But the FOL sentence would be true. So in that scenario, we have a truth-value mismatch between FOL sentence (T) and English sentence (F).

The following seems like a better symbolization of the English sentence to me: ∀x(¬(x=p) → O(p,x)) ∧ ¬O(p,p)

2: the textbook says that '4. Pavel owes money to everyone except himself' means the same thing as '2. Pavel owes money to everyone else.' I’m not sure that's right. Using the Gricean cancellation test (to distinguish literal semantic content from pragmatic implicatures), I think

‘Pavel owes money to everyone except himself—and to himself’

sounds contradictory, whereas

‘Pavel owes money to everyone else—and to himself’

does not sound contradictory to my ears (though it does sound inefficient and unnatural/ atypical). So the original English sentence in my first point above (your 2 on p.228) would be correctly symbolized by the symbolization in Forallx. And to be honest I’m not sure whether your sentence 3 (“Pavel owes money to everyone other than Pavel”) is more like 2 or 4 in this regard. (I’m slightly inclined toward 2? Not sure…)