That is, indeed, the idiomatic form. But it should properly be “Not all that glitters is gold”, because gold does, in fact, glitter, and therefore some things which glitter are indeed gold. And, of course, some are diamond.
Usually, sentences of the form “all that glitters is not gold” mean “not (all that glitters is gold)”. “All is not lost” does not mean that nothing got any worse. While it may seem weird for “not” to semantically modify the entire sentence while it syntactically modifies only “gold”, we do this all the time using other words: “we ate nothing” does not mean “we ate X” for X equal to “nothing”; it means “for all X, not (we ate X)”. For fun, see Wikipedia.
To imitate a friend of mine, how dare you try to make English make more sense.
“we ate nothing” does not mean “we ate X” for X equal to “nothing”; it means “for all X, not (we ate X)”
But surely “we ate X” can mean “X = {Y: We ate Y}”, as in “we ate a set of fried chicken legs”—and this would allow one to analyze “we ate nothing” to mean “we ate X” for X = emptyset.
Let “nothing” be the empty set, and say that “we ate X” means that X is the set of all things that we ate? How would that handle the sentence “No robot took off its hat”? My semantics say that that’s equivalent to “for no robot X, (X took off X’s hat)”; yours would say something like “(the set of no robots) took off (some value that isn’t a set of hats)”.
That is, indeed, the idiomatic form. But it should properly be “Not all that glitters is gold”, because gold does, in fact, glitter, and therefore some things which glitter are indeed gold. And, of course, some are diamond.
Usually, sentences of the form “all that glitters is not gold” mean “not (all that glitters is gold)”. “All is not lost” does not mean that nothing got any worse. While it may seem weird for “not” to semantically modify the entire sentence while it syntactically modifies only “gold”, we do this all the time using other words: “we ate nothing” does not mean “we ate X” for X equal to “nothing”; it means “for all X, not (we ate X)”. For fun, see Wikipedia.
To imitate a friend of mine, how dare you try to make English make more sense.
But surely “we ate X” can mean “X = {Y: We ate Y}”, as in “we ate a set of fried chicken legs”—and this would allow one to analyze “we ate nothing” to mean “we ate X” for X = emptyset.
Let “nothing” be the empty set, and say that “we ate X” means that X is the set of all things that we ate? How would that handle the sentence “No robot took off its hat”? My semantics say that that’s equivalent to “for no robot X, (X took off X’s hat)”; yours would say something like “(the set of no robots) took off (some value that isn’t a set of hats)”.