6 ms·

The word “and” in English is simply there to join multiple clauses together. Whether it is a set union or set intersection, (or some other relations) depends on

The word “and” in English is simply there to join multiple clauses together. Whether it is a set union or set intersection, (or some other relations) depends on the sentence. Set union: they can read and write’ Set intersection: my jeans were creased and dirty Sequential: he turned round and walked out Causal: there was a flash flood and by the next morning the town was under water’ And, there are many more usages.

tel 6y ago
How is your set union example not another intersection (your quantification could go in one of two places though, they = (set of readers) cap (set of writers) versus they = { p in people such that (p writes) cap (p reads) }.
- remram 6y ago
  It depends if you consider the implied set to be the people (of which there are readers and writers) or the capabilities (reading and writing).
- powersnail 6y ago
  > they can read and write Note that I’m not joining people with AND. I joined abilities. For instance, to expand on the example. I have three Pokémons. They can read and write. I’m not saying that my three Pokémon are the intersection of reading Pokémon and writing Pokémon. There might be other Pokémon who can do just the same. I’m saying that what they can do is a union of writing and reading. EDIT: spelling
  - drdeca 6y ago
    But they are in the intersection of "entities that can read" with "entities that can write".
    - dragonwriter 6y ago
      Yes having attributes containing the union of the sets of attributes {“can read”} and {“can write”} means being in the intersection of the set of things having the attribute “can read” and that having the attribute “can write”. Set union, intersection, and membership are related that way. (Which means saying that “and” is about intersection and not union is nonsense, everything statement about set union can be rephrased to an equivalent statement about intersection, and vice versa.)
      - drdeca 6y ago
        Yeah, there's some duality there. If each predicate is identified with the set of things that satisfy that predicate, then the "and" of two predicates is identified with the intersection of the sets that satisfy the two predicated. On the other hand, if you instead use predicates by talking about the set of predicates that objects satisfy, then saying that something satisfies one set of predicates, and satisfies some other set of predicates, then that says that the thing satisfies all the predicates in the union of those two sets. For some relation R between elements of the set X and elements of the set Y (we can think of X as being the set of individuals, and Y as being a set of elementary unary predicates), for each x in X, we can refer to A(x) := {y in Y : x R y} , and for each y in Y we can talk about B(y) := {x in X : x R y} . When we say (x_1 R y_1) && (x_1 R y_2), this is equivalent to both (x_1 in B(y_1)) && (x_1 in B(y_2)) i.e. (x_1 in (B(Y_1) intersect(B(y_2)))) , and also to (y_1 in A(x_1)) && (y_2 in A(x_1)) , i.e. ({y_1} \subset A(x_1)) && ({y_2} \subset A(x_1)) i.e. (({y_1} union {y_2}) \subset A(x_1)) . Personally, if we are talking about a single x_1, and we are saying "and" about a number of different y_1 , y_2 , etc. , or if we are talking about each x in some collection but are saying the same thing about each of them, namely that for each x in the collection, that x R y_1 and that x R y_2 and that x R y_3 , I think it seems more natural to take the first of the two framings described above. That is, I think it seems more natural to say that for each x in the collection, that x \in (B(y_1) intersect B(y_2) intersect B(y_3)), rather than saying that ({y_1} union {y_2} union {y_3}) subset A(x) . Or, if we give the name W to the collection we are talking about, we could say that "W subset (B(y_1) intersect B(y_2) intersect B(y_3))". This seems to me a fairly natural way to say "all the W , y_1 , y_2, and y_3" ("each of my 3 pokemon can do reading, writing, and arithmetic") . The other way would end up more like, "({y_1} union {y_2} union {y_3}) subset (the intersection over all x in W, of A(x))". This works, but seems less natural to me. Also, especially in the case where you expect X to be substantially larger than Y.
  - gerdesj 6y ago
    "I have three Pokémons. They can read and write." cf: I have three Pokémons that can read and write. Now, thanks to what I can only describe as the implicit vagaries of English, the bounding (three) might now imply that I have three ... or more Pokémons! To make that sentence precise: I have three Pokémons and they can read and write. Here I am substituting and for a full stop (period.) When I deployed "that" I managed to muddy the waters. Mapping logical and Boolean operators to grammatical constructs is tricky and should not be taken lightly. Best to consider them separately. AND is not and (except when it is!) Be careful out there kids.
Toenex 6y ago
It's surprising how often you can replace 'but' with 'and' in a sentence.
- deleted 6y ago
  [deleted]
- jfoutz 6y ago
  coordinating conjunctions are wierd. and, or, for, but, yet, so, nor. Nor is sort of an oddball there, since it continues negated clauses, well I use it to. - my jeans were neither creased nor dirty. Yet fits in a ton of places as well.
- thaumasiotes 6y ago
  Why is that surprising? They have exactly the same meaning; the difference is that 'but' additionally carries information about the subjective point of view of the speaker. (Where 'and' indicates that two things are true, 'but' indicates that (1) two things are true; and (2) the speaker considers this surprising or anticipates that the listener might find it surprising.)
DFHippie 6y ago
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.
chalst 6y ago
This is correct. The technical word linguists use for the role words like "and" play is coordination. https://en.wikipedia.org/wiki/Coordination_(linguistics) https://en.wikipedia.org/wiki/Coordination_(linguistics)
linuxrebe1 6y ago
Short would be, 'and' implies, coincidence, not causality. 'Or' implies choice. If-then implies causality ("If my pants are dirty, then they need to be cleaned") The big difference I see is with 'OR' in programing the options are exclusive. Ex: "Are you tired or hungry" The answer is yes if you are tired. Yes if you are hungry, Yes if you are both. No if you are neither. This is natural English. In programming if you are both. The answer is No.(False)
- patmorgan23 6y ago
  Isn't OR in most languages non exclusive? If you want exclusive OR you use XOR.
_emacsomancer_ 6y ago
To join like constituents, not just clauses, as per your examples.
phkahler 6y ago
>> Set union: they can read and write’ >> Set intersection: my jeans were creased and dirty IMHO those are both unions. One describes two capabilities people have while the other describes two conditions some clothing has. They both become intersection when using the pair of conditions as selection or decision criteria. It's the difference between an assertion and a question.

tel 6y ago

How is your set union example not another intersection (your quantification could go in one of two places though, they = (set of readers) cap (set of writers) versus they = { p in people such that (p writes) cap (p reads) }.

remram 6y ago
It depends if you consider the implied set to be the people (of which there are readers and writers) or the capabilities (reading and writing).
powersnail 6y ago
> they can read and write Note that I’m not joining people with AND. I joined abilities. For instance, to expand on the example. I have three Pokémons. They can read and write. I’m not saying that my three Pokémon are the intersection of reading Pokémon and writing Pokémon. There might be other Pokémon who can do just the same. I’m saying that what they can do is a union of writing and reading. EDIT: spelling
- drdeca 6y ago
  But they are in the intersection of "entities that can read" with "entities that can write".
  - dragonwriter 6y ago
    Yes having attributes containing the union of the sets of attributes {“can read”} and {“can write”} means being in the intersection of the set of things having the attribute “can read” and that having the attribute “can write”. Set union, intersection, and membership are related that way. (Which means saying that “and” is about intersection and not union is nonsense, everything statement about set union can be rephrased to an equivalent statement about intersection, and vice versa.)
    - drdeca 6y ago
      Yeah, there's some duality there. If each predicate is identified with the set of things that satisfy that predicate, then the "and" of two predicates is identified with the intersection of the sets that satisfy the two predicated. On the other hand, if you instead use predicates by talking about the set of predicates that objects satisfy, then saying that something satisfies one set of predicates, and satisfies some other set of predicates, then that says that the thing satisfies all the predicates in the union of those two sets. For some relation R between elements of the set X and elements of the set Y (we can think of X as being the set of individuals, and Y as being a set of elementary unary predicates), for each x in X, we can refer to A(x) := {y in Y : x R y} , and for each y in Y we can talk about B(y) := {x in X : x R y} . When we say (x_1 R y_1) && (x_1 R y_2), this is equivalent to both (x_1 in B(y_1)) && (x_1 in B(y_2)) i.e. (x_1 in (B(Y_1) intersect(B(y_2)))) , and also to (y_1 in A(x_1)) && (y_2 in A(x_1)) , i.e. ({y_1} \subset A(x_1)) && ({y_2} \subset A(x_1)) i.e. (({y_1} union {y_2}) \subset A(x_1)) . Personally, if we are talking about a single x_1, and we are saying "and" about a number of different y_1 , y_2 , etc. , or if we are talking about each x in some collection but are saying the same thing about each of them, namely that for each x in the collection, that x R y_1 and that x R y_2 and that x R y_3 , I think it seems more natural to take the first of the two framings described above. That is, I think it seems more natural to say that for each x in the collection, that x \in (B(y_1) intersect B(y_2) intersect B(y_3)), rather than saying that ({y_1} union {y_2} union {y_3}) subset A(x) . Or, if we give the name W to the collection we are talking about, we could say that "W subset (B(y_1) intersect B(y_2) intersect B(y_3))". This seems to me a fairly natural way to say "all the W , y_1 , y_2, and y_3" ("each of my 3 pokemon can do reading, writing, and arithmetic") . The other way would end up more like, "({y_1} union {y_2} union {y_3}) subset (the intersection over all x in W, of A(x))". This works, but seems less natural to me. Also, especially in the case where you expect X to be substantially larger than Y.
- gerdesj 6y ago
  "I have three Pokémons. They can read and write." cf: I have three Pokémons that can read and write. Now, thanks to what I can only describe as the implicit vagaries of English, the bounding (three) might now imply that I have three ... or more Pokémons! To make that sentence precise: I have three Pokémons and they can read and write. Here I am substituting and for a full stop (period.) When I deployed "that" I managed to muddy the waters. Mapping logical and Boolean operators to grammatical constructs is tricky and should not be taken lightly. Best to consider them separately. AND is not and (except when it is!) Be careful out there kids.

Toenex 6y ago

It's surprising how often you can replace 'but' with 'and' in a sentence.

deleted 6y ago
[deleted]
jfoutz 6y ago
coordinating conjunctions are wierd. and, or, for, but, yet, so, nor. Nor is sort of an oddball there, since it continues negated clauses, well I use it to. - my jeans were neither creased nor dirty. Yet fits in a ton of places as well.
thaumasiotes 6y ago
Why is that surprising? They have exactly the same meaning; the difference is that 'but' additionally carries information about the subjective point of view of the speaker. (Where 'and' indicates that two things are true, 'but' indicates that (1) two things are true; and (2) the speaker considers this surprising or anticipates that the listener might find it surprising.)

DFHippie 6y ago

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.

chalst 6y ago

This is correct. The technical word linguists use for the role words like "and" play is coordination. https://en.wikipedia.org/wiki/Coordination_(linguistics) https://en.wikipedia.org/wiki/Coordination_(linguistics)

linuxrebe1 6y ago

Short would be, 'and' implies, coincidence, not causality. 'Or' implies choice. If-then implies causality ("If my pants are dirty, then they need to be cleaned") The big difference I see is with 'OR' in programing the options are exclusive. Ex: "Are you tired or hungry" The answer is yes if you are tired. Yes if you are hungry, Yes if you are both. No if you are neither. This is natural English. In programming if you are both. The answer is No.(False)

patmorgan23 6y ago
Isn't OR in most languages non exclusive? If you want exclusive OR you use XOR.

_emacsomancer_ 6y ago

To join like constituents, not just clauses, as per your examples.

phkahler 6y ago

>> Set union: they can read and write’ >> Set intersection: my jeans were creased and dirty IMHO those are both unions. One describes two capabilities people have while the other describes two conditions some clothing has. They both become intersection when using the pair of conditions as selection or decision criteria. It's the difference between an assertion and a question.