Illogical conjunctions

[Chuma]

When you think about it, conjunctions in (for example) English are not quite logical.

If you say "I like cats and dogs", this is in terms of set theory a union of sets. The set of things being liked is the combination of the set of cats and the set of dogs.

But if you say "I like cats which are big and fluffy", then it's an intersection of sets. The set of liked cats are only those that are in both the set of big cats and the set of fluffy cats.

Switch to "or", and you get the opposite. So basically, conjunctions of adjectives and verbs follow the same convention as formal logic ("and" is for unions), but conjunctions of nouns are the other way around.

Is this a universal thing? How weird would it be in a conlang to make them logically the same? So "I like cats or dogs" means "I like things that are cats or dogs".

[KathTheDragon]

This seems to be a general contrast between modifiers and non-modifiers. Compare:

• verbs: "they ran and walked their way around the course" (union)
• adverbs: "they moved swiftly and silently" (intersection)
• pronouns: "you and I are going to have fun" (union)
• ad-modifiers: "the intolerably and interminably loud party went til 2am" (intersection).

I'm not sure what you're getting at with "or" though. It can be both a union or an exclusive or:

• nouns: "I like cats or dogs" (xor, ?union)
• adjectives: "I like cats which are big or fluffy" (union or xor)
• verbs: "they ran or walked their way around the course" (xor, *union)
• adverbs: "do it swiftly or silently, I don't care" (union or xor)
• pronouns: "you or I are going to have fun" (xor, ?union)

From this it looks like unions are less acceptable only on non-modifiers, exactly those where "and" fulfills that role.

[bradrn]

Strange… although I agree with your judgments for ‘and’, I don’t agree with some of those for ‘or’:

[*]nouns: "I like cats or dogs" (xor, ?union)

This one is extremely hard to interpret for me, if not outright contradictory in most situations.

[*]verbs: "they ran or walked their way around the course" (xor, *union)

This one could easily be interpreted as a union: from the perspective of each individual person, it’s clearly xor, but when thinking about ‘they’ as a whole, it becomes clearer that ‘they’ are doing a combination of running or walking, i.e. a union.

[*]adjectives: "I like cats which are big or fluffy" (union or xor)
[*]adverbs: "do it swiftly or silently, I don't care" (union or xor)
[*]pronouns: "you or I are going to have fun" (xor, ?union)

I agree with these ones. (Though note that ‘union or xor’ is of course just a plain logical ‘or’.)

[KathTheDragon]

Ah, no, when I say "union or xor" I mean both readings are separately possible.

from the perspective of each individual person, it’s clearly xor, but when thinking about ‘they’ as a whole, it becomes clearer that ‘they’ are doing a combination of running or walking, i.e. a union.

This is clearly a property of "they" being plural, though, allowing a distributive reading. It has nothing to do with the sematics of "or".

[zompist]

If you say "I like cats and dogs", this is in terms of set theory a union of sets. The set of things being liked is the combination of the set of cats and the set of dogs.

But if you say "I like cats which are big and fluffy", then it's an intersection of sets. The set of liked cats are only those that are in both the set of big cats and the set of fluffy cats.

I'm not sure about this, but I think "and" has the same meaning, it's a matter of what exactly we're conjoining.

"I like cats and dogs" = "I like cats" ^ "I like dogs"
"I like cats that are big and fluffy" = "I like x : CAT(x) ^ BIG(x) ^ FLUFFY(x)"

Also, adjectives aren't always intersections: "Put the red and yellow balls in this box" means the union, not the intersection.

I think "I like sweet and salty snacks" is ambiguous. It could mean I like two types, or it could mean I want both flavors at once. In the first case it's "I like sweet snacks ^ I like salty snacks"; in the second it's "I like x : snacks(x) ^ sweet(x) ^ salty(x)".

[zompist]

Oh, and if you're wondering if any conlang has separated unions vs. intersections...

http://www.zompist.com/kebreni.htm#Conjunctions

[Pabappa]

I don't know if this is a conjunction, but the phrase all but.... bothered me when I was young since it means the opposite of what it looks like. I had only just become familiar with but meaning "except" at the time .

I saw it explained once but if it needs an explanation I'd say it qualifies as illogical.

[priscianic]

When you think about it, conjunctions in (for example) English are not quite logical.

If you say "I like cats and dogs", this is in terms of set theory a union of sets. The set of things being liked is the combination of the set of cats and the set of dogs.

But if you say "I like cats which are big and fluffy", then it's an intersection of sets. The set of liked cats are only those that are in both the set of big cats and the set of fluffy cats.

This question of whether and is always Boolean/intersective, or whether there's also a non-Boolean/non-intersective and, is actually a really deep and interesting, and there's not clear consensus yet about what's the right answer.

As you correctly point out, there is strong motivation to believe that certain uses of and are not intersective. Zompist suggests that it's possible to paraphrase the meaning of your sentence I like cats and dogs in terms of Boolean AND:

I'm not sure about this, but I think "and" has the same meaning, it's a matter of what exactly we're conjoining.

"I like cats and dogs" = "I like cats" ^ "I like dogs"

This is true for this particular case, but it fails for other cases, especially those where you quantify over cats and dogs. For example, consider the following sentence: I saw five [cats and dogs]. In that sentence, there's a reading where you saw 5 animals total, and each of the animals was either a cat or a dog. This reading cannot be (straightforwardly) captured by means of Boolean AND; for instance, giving it a meaning like I like 5 cats ∧ I like 5 dogs is clearly inaccurate, and giving it a meaning like I like five x : CAT(x) ∧ DOG(x) is also inaccurate (that would mean that each of the five animals your saw is simultaneously a cat and a dog, like in the Nickolodeon cartoon). Instead, the meaning is more like this: there's a set of five animals, each of which is either a cat or a dog, and I like each member of that set.

Another reason to believe in the existence of a non-Boolean and is in cases of collective predicates (predicates that can only be true of a plurality). For instance, consider the following example: Cosmo and Wanda met yesterday. Note that it's impossible to say #Cosmo met or #Wanda met (the # marks semantic/pragmatic infelicity). Intuitively, this is because one person cannot "meet": meeting requires at least two individuals. So the obvious Boolean AND analysis of this sentence, Cosmo met yesterday ∧ Wanda met yesterday, faces some challenges. Instead, the interpretation seems to be like this: there's a set of individuals composed of Cosmo and Wanda, and each member of that set met the other yesterday.

For a formal discussion of the relevant issues and the broader debate, you can see Viola Schmitt's (2018) overview article on Boolean and non-Boolean conjunction (though beware that it's extremely technical).

Switch to "or", and you get the opposite. So basically, conjunctions of adjectives and verbs follow the same convention as formal logic ("and" is for unions), but conjunctions of nouns are the other way around.

Is this a universal thing? How weird would it be in a conlang to make them logically the same? So "I like cats or dogs" means "I like things that are cats or dogs".

I'm less familiar with the literature on disjunction, but there are a lot of very interesting and unsolved problems here, and I don't think the relevant split is between noun phrase and non-noun phrase disjunction. For instance, you get conjunctive readings in other contexts, like under the scope of possibility modals, as in: you can stay or leave. These are known as "free choice" effects, and the intuition is that this sentence means the same thing as a conjunction of two possibility modals: you can stay ∧ you can leave. In other words, you have a "free choice" between the two options. And it's hard to see how to get this reading from the combination of a possibility modal and Boolean OR.

It's also hard to commit to a Boolean OR analysis of or in alternative questions, like Did Timmy stay home or go out? (though there are analyses of alternative questions are disjunctions of polar questions, e.g. Did Timmy stay home, or did Timmy go out?; see Uegaki 2014 and citations therein). Naively applying Boolean OR to this sentence would give you a meaning something like this: is it true that: Timmy stayed home ∨ Timmy went out. Assuming that Timmy staying home and Timmy going out completely exhausts all possibilities (i.e. there is no possibility of Timmy simultaneously not staying home and not going out, and instead existing in some mysterious liminal space between the two), then this question is completely trivial: the answer should always be "yes"! Indeed, there is a way of reading this question that way (i.e. as a polar question, whose answer is "yes" or "no"), though it's quite facetious. The more natural reading is the "alternative question" reading, which is something like this: tell me which of these propositions is true: {Timmy stayed home, Timmy went out}. Note that the alternative question reading can't be conjunctive either. However, note that some argue that alternative questions are actually disjoined polar questions:

Interestingly, many languages do actually distinguish between Boolean OR and the or that appears in alternative questions, and this disambiguates between the polar question reading and the alternative question reading. Mandarin is one such language: háishi gives you alternative questions, and huò(zhe) is Boolean OR, and this can disambiguate between an alternative question and a polar question (at least for some speakers; huò(zhe) apparently is unacceptable in polar questions for some speakers):

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1)  Zhāngsān xǐhuān Lǐsì háishi Wángwǔ (ne)?
    Zhangsan like   Lisi HAISHI Wangwu (NE)
    ‘Does Zhangsan like Lisi or Wangwu?’    (alternative question)
	Possible answers: {Lisi, Wangwu}

2)  Zhāngsān xǐhuān Lǐsì huò(zhe) Wángwǔ ma?
    Zhangsan like   Lisi HUO(ZHE) Wangwu Q
    ‘Does Zhangsan like Lisi or Wangwu?’    (polar question)
	Possible answers: {yes, no}

However, the contrast between háishi and huò(zhe) is not that simple: háishi isn't just found in alternative questions. There are some contexts where you can get both: for instance, with dōu, you can get either, with a conjunctive reading in both cases ("both X and Y"):

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3)  Zhāngsān {háishi, huò(zhe)} Lǐsì dōu jìn   lái  le.
    Zhangsan {HAISHI, HUO(ZHE)} Lisi DOU enter come LE
    ‘Both Zhangsan and Lisi came in.’

See Erlewine (2017) for some discussion and an analysis.

There's also a (more recent) tradition of analyzing natural langauge disjunction not as Boolean OR, but rather as a means of creating sets of propositions. So a disjunction like p or q is given a meaning as the set of the propositions p and q, {p, q}, rather than the proposition p ∧ q . The idea is that this kind of meaning, when combined compositionally with other kinds of operators, is more adequate for accounting for the various kinds of disjunctive/conjunctive readings you get of natural language disjunction. See Alonso-Ovalle (2006) for an analysis in this vein (again, extremely technical).

Some less technical (but correspondingly less informative about the nitty-gritty of the semantics) work that might be relevant for you is Haspelmath's (2007) chapter on the typology of coordination. Another interesting case is Warlpiri, which only has one coordinator manu, which sometimes seems to get a conjunctive interpretation, sometimes a disjunctive interpretations, and sometimes is ambiguous (Bowler 2014).

Suffice it to say that conjunction and disjunction is surprisingly complicated in natural language, and the more people poke at it the more puzzles arise.

[zompist]

I'm not sure about this, but I think "and" has the same meaning, it's a matter of what exactly we're conjoining.

"I like cats and dogs" = "I like cats" ^ "I like dogs"

This is true for this particular case, but it fails for other cases, especially those where you quantify over cats and dogs. For example, consider the following sentence: I saw five [cats and dogs]. [...]

I'm not going to deeply defend my informal analysis, but I'd just point out that, in general, the fact that some sentences are complicated does not mean that all sentences are complicated. I didn't say or mean that all conjoined arguments equate to conjoined propositions— I agree that in some cases, they absolutely don't.

But I did purposely avoid using sets, because I'm not convinced that sets are needed to explain the semantics of that example.

[priscianic]

I'm not sure about this, but I think "and" has the same meaning, it's a matter of what exactly we're conjoining.

"I like cats and dogs" = "I like cats" ^ "I like dogs"

This is true for this particular case, but it fails for other cases, especially those where you quantify over cats and dogs. For example, consider the following sentence: I saw five [cats and dogs]. [...]

I'm not going to deeply defend my informal analysis, but I'd just point out that, in general, the fact that some sentences are complicated does not mean that all sentences are complicated. I didn't say or mean that all conjoined arguments equate to conjoined propositions— I agree that in some cases, they absolutely don't.

But I did purposely avoid using sets, because I'm not convinced that sets are needed to explain the semantics of that example.

Thanks for the clarification. It did sound like, when you said "I think 'and' has the same meaning, it's a matter of what exactly we're conjoining", you wanted to defend an analysis that commits to and always being some kind of Boolean/intersective conjunction. For what it's worth, there are people who argue for that kind of view: among others, Winter (2001), Champollion (2016), and for a particularly extreme version of this, Schein (2017).