4 ms·

I would say that in every case there is a set of things (maybe with a single member) and a set of predicates (maybe with a single member), a mapping from the th

I would say that in every case there is a set of things (maybe with a single member) and a set of predicates (maybe with a single member), a mapping from the things to the predicates, and every mapping produces a true proposition. "Women and children were present" isn't saying the intersection of the women and children were present but that the things were women and children and they all were present. The rest of the variety of "meanings" of "and" are just inferences on top of this basic meaning. If things occur in sequence, for instance, we can infer causality from what we know about the things conjoined apart from the conjunction. Crucially, there is more here than just "joining multiple clauses together" (and many of the things conjoined aren't clauses), because "or" can be described this way too, but "and" does not mean the same thing as "or". With "or" you are only asserting that some of the propositions are true.

edflsafoiewq 6y ago
"(Women were present) and (children were present)"
- chalst 6y ago
  How would you distribute "Jack and Jill play together."? If you start introducing prepositions, then your theory of "and"-expansion is going to get quite complex as it covers more and more cases.
  - XorNot 6y ago
    Isn't this basically proper nouns implicitly creating a set of size 1?
powersnail 6y ago
The meaning of “and” in natural language predates the meaning of “and” used in logics and set theories. I’m not convinced that all semantics of “and” can be derived from set operations. 1) not every clause is a predicate and applying logical operators to a non-predicate makes very little sense to me. 2) I don’t see how ordering, time, and causation can be inferred, if you treat each clause as a predicate. “I punched Bob and apologized” has a different meaning than “I apologized, and punched Bob.” The AND as used in logics simply doesn’t embody this usage. —- It was a sloppy wording of mine to say that AND just join clauses together. I meant to say that it joins clauses together, and the relations between the clauses are not necessarily set union. Of course it can’t embody all relations, but more than set unions.
- DFHippie 6y ago
  I'm being a little sloppy in my language as well. Since words and phrases necessarily occur in sequence, if you are speaking of things can be and typically are in sequence, it is natural to infer that the speaker is presenting them in the sequence of their occurrence. The speaker can do this, the speaker and the hearer both know that the speaker can do this, and it is a common understanding between the speaker and the hearer that the speaker intends the hearer to receive a particular representation of events: this is the purpose of communication. This being so, the speaker presenting events out of their temporal sequence would be perverse. If the speaker knows the hearer will assume she is presenting events in their temporal sequence, she must present them in this sequence or explain that they are not so presented. To do otherwise would be understood by the speaker and hearer as deliberate deception. So the sequence comes not from the semantics of "and" but the pragmatics of speaking itself. In fact, you don't need "and" at all. If you leave "and" out -- asyndeton -- and list things, they will be understood to be in temporal sequence if they are the sort of thing that occur that way. "I opened the door. I went out." All of these "meanings of and" can be explained via pragmatics and a very simple meaning of "and". The meaning I provided was intended as a hand-wavy gesture in the direction of a more formal theory.
- mhink 6y ago
  > I’m not convinced that all semantics of “and” can be derived from set operations. Totally agree. I think part of the issue is that "natural-language and" behaves differently when you apply it to different parts of speech, and everyone in this thread is thinking of a different part! That being said, in the example sentences you gave ("I punched Bob and apologized" vs. "I apologized and punched Bob"), it's actually ambiguous whether they have equivalent meaning or not, when we ONLY consider grammar. Using ONLY the words in the sentence, the relationship between "apologized" and "punched" rests on our interpretation of "and"'s grammatical role. Taken in its usual sense as a conjunction, the two verbs are only related in the sense that the same subject performed them. But I think you're arguing that "and" places the two verbs in sequence (which prevents the sentence from being flipped without changing meaning.) The more I think about this, the more I don't think it follows. To read the verb phrase this way, the reader has to infer a missing conjunctive adverb: ("punched Bob and [then] apologized")... and in order to make that inference, you need context from the sentence. To make matters more complicated, we _could_ interpret the sentence in a way that doesn't imply the verbs are related: suppose the speaker is apologizing to some third party, and punches Bob for some unrelated reason. If we interpret it this way, the two sentences can be switched without changing the meaning too much. But all this just goes to show: your core point is correct: natural languages aren't formal languages, and trying to treat them as such is an exercise in frustration.

edflsafoiewq 6y ago

"(Women were present) and (children were present)"

chalst 6y ago
How would you distribute "Jack and Jill play together."? If you start introducing prepositions, then your theory of "and"-expansion is going to get quite complex as it covers more and more cases.
- XorNot 6y ago
  Isn't this basically proper nouns implicitly creating a set of size 1?

powersnail 6y ago

The meaning of “and” in natural language predates the meaning of “and” used in logics and set theories. I’m not convinced that all semantics of “and” can be derived from set operations. 1) not every clause is a predicate and applying logical operators to a non-predicate makes very little sense to me. 2) I don’t see how ordering, time, and causation can be inferred, if you treat each clause as a predicate. “I punched Bob and apologized” has a different meaning than “I apologized, and punched Bob.” The AND as used in logics simply doesn’t embody this usage. —- It was a sloppy wording of mine to say that AND just join clauses together. I meant to say that it joins clauses together, and the relations between the clauses are not necessarily set union. Of course it can’t embody all relations, but more than set unions.

DFHippie 6y ago
I'm being a little sloppy in my language as well. Since words and phrases necessarily occur in sequence, if you are speaking of things can be and typically are in sequence, it is natural to infer that the speaker is presenting them in the sequence of their occurrence. The speaker can do this, the speaker and the hearer both know that the speaker can do this, and it is a common understanding between the speaker and the hearer that the speaker intends the hearer to receive a particular representation of events: this is the purpose of communication. This being so, the speaker presenting events out of their temporal sequence would be perverse. If the speaker knows the hearer will assume she is presenting events in their temporal sequence, she must present them in this sequence or explain that they are not so presented. To do otherwise would be understood by the speaker and hearer as deliberate deception. So the sequence comes not from the semantics of "and" but the pragmatics of speaking itself. In fact, you don't need "and" at all. If you leave "and" out -- asyndeton -- and list things, they will be understood to be in temporal sequence if they are the sort of thing that occur that way. "I opened the door. I went out." All of these "meanings of and" can be explained via pragmatics and a very simple meaning of "and". The meaning I provided was intended as a hand-wavy gesture in the direction of a more formal theory.
mhink 6y ago
> I’m not convinced that all semantics of “and” can be derived from set operations. Totally agree. I think part of the issue is that "natural-language and" behaves differently when you apply it to different parts of speech, and everyone in this thread is thinking of a different part! That being said, in the example sentences you gave ("I punched Bob and apologized" vs. "I apologized and punched Bob"), it's actually ambiguous whether they have equivalent meaning or not, when we ONLY consider grammar. Using ONLY the words in the sentence, the relationship between "apologized" and "punched" rests on our interpretation of "and"'s grammatical role. Taken in its usual sense as a conjunction, the two verbs are only related in the sense that the same subject performed them. But I think you're arguing that "and" places the two verbs in sequence (which prevents the sentence from being flipped without changing meaning.) The more I think about this, the more I don't think it follows. To read the verb phrase this way, the reader has to infer a missing conjunctive adverb: ("punched Bob and [then] apologized")... and in order to make that inference, you need context from the sentence. To make matters more complicated, we _could_ interpret the sentence in a way that doesn't imply the verbs are related: suppose the speaker is apologizing to some third party, and punches Bob for some unrelated reason. If we interpret it this way, the two sentences can be switched without changing the meaning too much. But all this just goes to show: your core point is correct: natural languages aren't formal languages, and trying to treat them as such is an exercise in frustration.