Are you not familiar with the term “vacuously true”? I find this very surprising. People who study math tend to make jokes with it.
The idea is that, if we were to render a statement like “Colorless green ideas sleep furiously” into formal logic, we’d probably take it to mean the universal statement “For all X such that X is a colorless green idea, X sleeps furiously”. A universal statement is logically equivalent to “There don’t exist any counterexamples”, i.e. “There does not exist X such that X is a colorless green idea and X does not sleep furiously”. Which is clearly true, and therefore the universal is equally true.
There is, of course, some ambiguity when rendering English into formal logic. It’s not rare for English speakers to say “if” when they mean “if and only if”, or “or” when they mean “exclusive or”. (And sometimes “Tell me which one”, as in “Did you do A, or B?” “Yes.” “Goddammit.”) Often this doesn’t cause problems, but sometimes it does. (In which case, as I’ve said, the solution is not to give their statement an ambiguous truth value, but rather to ask them to restate it less ambiguously.)
“Dragons are attacking Paris” seems most naturally interpreted as the definite statement “There’s some unspecified number—but since I used the plural, it’s at least 2—of dragons that are attacking Paris”, which would be false. One could also imagine interpreting it as a universal statement “All dragons are currently attacking Paris”, which, as you say, would be vacuously true since there are no dragons. However, in English, the preferred way to say that would be “Dragons attack Paris”, as CBiddulph says. “Dragons are attacking Paris” uses the present progressive tense, while “Dragons attack Paris” uses what is called the “simple present”/”present indefinite” tense. Wiki says:
The simple present is used to refer to an action or event that takes place habitually, to remark habits, facts and general realities, repeated actions or unchanging situations, emotions, and wishes.[3] Such uses are often accompanied by frequency adverbs and adverbial phrases such as always, sometimes, often, usually, from time to time, rarely, and never.
Examples:
I always take a shower.
I never go to the cinema.
I walk to the pool.
He writes for a living.
She understands English.
This contrasts with the present progressive (present continuous), which is used to refer to something taking place at the present moment: I am walking now; He is writing a letter at the moment.
English grammar rules aren’t necessarily universal and unchanging, but they do give at least medium-strength priors on how to interpret a sentence.
This sounds like it’s using Russell’s theory of descriptions, in that you’re replacing “Colorless green ideas do Y” with “For all X such that X is a colorless green idea, X does Y.” Not everyone agrees that this is a correct interpretation, in part because it seems that statements like “Dragons are attacking Paris” should be false.
I think it would be reasonable to say that “colorless green ideas” is not just a set of objects in which there are no existing members, but meaningless (for two reasons: “colorless” and “green” conflict, and ideas can’t be colored, anyway). I think that was Chomsky’s intention—not to write a false sentence, but a meaningless one.
The idea is that, if we were to render a statement like “Colorless green ideas sleep furiously” into formal logic, we’d probably take it to mean the universal statement “For all X such that X is a colorless green idea, X sleeps furiously”.
I don’t think so. “Smoking causes cancer” doesn’t express a universal (or existential) quantification either. Or “Canadians are polite”, “Men are taller than women” etc.
Grammatically, the most obvious interpretation is a universal quantification (i.e. “All men are taller than all women”), which I think is a major reason why such statements so often lead to objections of “But here’s an exception!” Maybe you can tell the audience that they should figure out when to mentally insert ”… on average” or “tend to be”. Though there are also circumstances where one might validly believe that the speaker really means all. I think it’s best to put such qualified language into your statements from the start.
Grammatically, the most obvious interpretation is a universal quantification
Here I mostly agree
I think it’s best to put such qualified language into your statements from the start.
Here I don’t, for the same reason that I don’t ask about “water in the refrigerator outside eggplant cells”. Because pragmatics are for better or worse part of the language.
Are you not familiar with the term “vacuously true”? I find this very surprising. People who study math tend to make jokes with it.
The idea is that, if we were to render a statement like “Colorless green ideas sleep furiously” into formal logic, we’d probably take it to mean the universal statement “For all X such that X is a colorless green idea, X sleeps furiously”. A universal statement is logically equivalent to “There don’t exist any counterexamples”, i.e. “There does not exist X such that X is a colorless green idea and X does not sleep furiously”. Which is clearly true, and therefore the universal is equally true.
There is, of course, some ambiguity when rendering English into formal logic. It’s not rare for English speakers to say “if” when they mean “if and only if”, or “or” when they mean “exclusive or”. (And sometimes “Tell me which one”, as in “Did you do A, or B?” “Yes.” “Goddammit.”) Often this doesn’t cause problems, but sometimes it does. (In which case, as I’ve said, the solution is not to give their statement an ambiguous truth value, but rather to ask them to restate it less ambiguously.)
“Dragons are attacking Paris” seems most naturally interpreted as the definite statement “There’s some unspecified number—but since I used the plural, it’s at least 2—of dragons that are attacking Paris”, which would be false. One could also imagine interpreting it as a universal statement “All dragons are currently attacking Paris”, which, as you say, would be vacuously true since there are no dragons. However, in English, the preferred way to say that would be “Dragons attack Paris”, as CBiddulph says. “Dragons are attacking Paris” uses the present progressive tense, while “Dragons attack Paris” uses what is called the “simple present”/”present indefinite” tense. Wiki says:
English grammar rules aren’t necessarily universal and unchanging, but they do give at least medium-strength priors on how to interpret a sentence.
This sounds like it’s using Russell’s theory of descriptions, in that you’re replacing “Colorless green ideas do Y” with “For all X such that X is a colorless green idea, X does Y.” Not everyone agrees that this is a correct interpretation, in part because it seems that statements like “Dragons are attacking Paris” should be false.
I think it would be reasonable to say that “colorless green ideas” is not just a set of objects in which there are no existing members, but meaningless (for two reasons: “colorless” and “green” conflict, and ideas can’t be colored, anyway). I think that was Chomsky’s intention—not to write a false sentence, but a meaningless one.
I don’t think so. “Smoking causes cancer” doesn’t express a universal (or existential) quantification either. Or “Canadians are polite”, “Men are taller than women” etc.
Grammatically, the most obvious interpretation is a universal quantification (i.e. “All men are taller than all women”), which I think is a major reason why such statements so often lead to objections of “But here’s an exception!” Maybe you can tell the audience that they should figure out when to mentally insert ”… on average” or “tend to be”. Though there are also circumstances where one might validly believe that the speaker really means all. I think it’s best to put such qualified language into your statements from the start.
Here I mostly agree
Here I don’t, for the same reason that I don’t ask about “water in the refrigerator outside eggplant cells”. Because pragmatics are for better or worse part of the language.