What does "or" mean?

[Observer]

Consider the following English sentences.
"Do you want brocolli or asparagus with dinner?"
"Do you want cake or ice cream for dessert?"

I understand the first sentence to mean, "You must choose brocolli or asparagus. You can have both, but not neither."

I understand the second sentence to mean, "You may have cake or ice cream for dessert. You can have neither, but not both."

I form this understanding from external information (not many people like brocolli or asparagus; many people like cake and ice cream); I cannot derive it from the word "or."

If my understanding of the sentences is correct, then according to the Wikipedia article on truth tables, the former sentence uses the true meaning of "or." The second sentence uses the meaning of "nand."

I tend to think of "or" in the second sentence's meaning. To me, "or" the English word actually means "nand."

What does "or" mean to you?

(Also, do you know of any natlangs which would use two different words in place of "or" if the English sentences were translated into them?)

[Jipí]

FWIW, both your example sentences offer the same choices IMO, expectations about tastes aside:

- have broccoli / have cake; disregard aspargus / ice-cream
- have aspargus / ice-cream; disregard broccoli / cake

The way the questions are posed would suggest to me that the speaker expects you to choose from one of the two items and go with that, but not with none or both, thus I'd read both statements as XOR. However, maybe I can't decide and make a choice outside of that expectation:

- have neither (both are meh)
- have both (hell, why not!?)

Human brains fortunately don't break when being fed with unexpected information.

[cromulant]

There are two usages of "or." What they have in common is that they both conjoin members of a set that is not obligatorily all-inclusive. In one usage of "or," the members of the set are mutually exclusive. In the other usage, they are not. I'd say the mutually exclusive usage is the 'canonical' definition'--most people probably think of "or" as conjoining mutually exclusive elements. But it does not always.

I'd normally interpret your (written) example "Do you want brocolli or asparagus with dinner?" to mean that the two choices are mutually exclsuive; you can't have them both. That's the default reading, at least in written language. But in spoken language, by changing the intonation the same sentence, it can mean that asparagus is also available if you don't want broccoli, and you can (perhaps) have them both.

I'll try to demonstrate the intonational difference. Acute accent = high intonation, grave = low. Note the punctuation as well--I'm using it improperly on purpose, to show intonation.

"Do you want bróccoli?, or aspáragus with dinner?" Not mutually exclsuive.

"Do you want bróccoli or aspàragus with dinner." Mutually exclusive.

Also, Guitarplayer is right that the choice of foods offered doesn't affect the semantics of "or." Like I said, that's encoded more in intonation. Also, I happen to prefer asparagus and broccoli to ice cream and cake.

[Izambri]

"gold"

[Ziz]

There are two usages of "or." What they have in common is that they both conjoin members of a set that is not obligatorily all-inclusive. In one usage of "or," the members of the set are mutually exclusive. In the other usage, they are not. I'd say the mutually exclusive usage is the 'canonical' definition'--most people probably think of "or" as conjoining mutually exclusive elements. But it does not always.

I'd normally interpret your (written) example "Do you want brocolli or asparagus with dinner?" to mean that the two choices are mutually exclsuive; you can't have them both. That's the default reading, at least in written language. But in spoken language, by changing the intonation the same sentence, it can mean that asparagus is also available if you don't want broccoli, and you can (perhaps) have them both.

I'll try to demonstrate the intonational difference. Acute accent = high intonation, grave = low. Note the punctuation as well--I'm using it improperly on purpose, to show intonation.

"Do you want bróccoli?, or aspáragus with dinner?" Not mutually exclsuive.

"Do you want bróccoli or aspàragus with dinner." Mutually exclusive.

Also, Guitarplayer is right that the choice of foods offered doesn't affect the semantics of "or." Like I said, that's encoded more in intonation. Also, I happen to prefer asparagus and broccoli to ice cream and cake.

I dunno. At least for me, I think I'd only get that they're not supposed to be mutually exclusive if I knew beforehand that both is an option. As in, like, I live with the person and I know we have both broccoli and asparagus in the fridge and that (s)he wouldn't mind preparing both. Otherwise, I'd usually say something geeky and artificial like "and/or" if I wanted to convey that both may be had, or I'd simply append "or both" to the end.

"Do you want bróccoli or aspáragus or bòth?"

Actually, that's the only one that would work for me. The contrived "and/or" thing sounds odd in questions.

EDIT: I agree with the intonation thing for your second example, it's just that the intent behind the first one isn't obvious to me at all.

[spats]

"gold"

This reminds me of something random.

I was with a community chorus which sang a setting of Emma Lazarus' "The New Colossus". Great setting, great poem, always brings a bit of a tear to my eye.

Anyway...

The funny thing was the last line: "I lift my lamp beside the golden door."
Which for some reason (probably the close proximity of "golden") always parsed as "d'or".

[cromulant]

@Antirri: the example sentence Observer provided might not be the best for illustrating inclusive or, but the usage exists.

[zompist]

In ordinary language "or" has the meaning of inclusive or and the implicature of exclusive or.

That is, it's not a contradiction if both conjoints are true, but it's pragmatically marked. If you meant both you should say "and", and if choosing both is a likely possibility it's usually stated as such ("do you want chocolate or vanilla or both?").

Particular situations may have different pragmatics. Food choices always add the possibility of choosing none; that's just a fact about situations involving food-- you don't have to eat. If you're filling out a tax form ("if you are a 89c corporation or a farm worker..."), it's a good guess that the or's are inclusive.

[faiuwle]

My father has an incredibly irritating habit of answering questions of the form "do you want X or Y?" (meaning, make a choice between X and Y) with "yes". He doesn't do it because he misunderstands, but because he thinks it's cute or funny, like the xkcd strip that interpreted "will you marry me?" as some kind of experimental question.

[Observer]

I would like to see a survey conducted.

According to the Wikipedia page on "and/or," if one asked, "Do you want cake, pie or brownies?" that would imply the possibilities of having one, two or three of the desserts. To my ears, it sounds exclusive.

The article suggests "He will eat either cake, pie, or brownies." to impart exclusivity. That sounds unnatural to me.

Perhaps it's the way I mentally parse logical connectives. To my ears, "and" means "both or neither, but not one or the other." For instance, "Can you drive your brother and sister to school? They missed the bus." Either you can drive them both, or you can't. You wouldn't take one of them and not the other. If I were asked, "Do you want cake and ice cream?" I would not assume having only one is an option. I would ask for clarification.

Mentally, I parse that as "do you want" and "cake-and-ice-cream." I unitize whatever is connected by "and." Similarly, I suppose I read "or" as "nand" because I unitize whatever is connected by "or."

[Bob Johnson]

What, seriously? People who aren't logic or programming geeks take English or as inclusive?

[Radius Solis]

I would like to see a survey conducted.

According to the Wikipedia page on "and/or," if one asked, "Do you want cake, pie or brownies?" that would imply the possibilities of having one, two or three of the desserts. To my ears, it sounds exclusive.

The article suggests "He will eat either cake, pie, or brownies." to impart exclusivity. That sounds unnatural to me.

What's unnatural is not the exclusivity but the use of "either X or Y" with three possibilities. That template is normally used when there are exactly two possibilities. To indicate a XOR for three, you repeat the conjunction: "either X or Y or Z".

But surely you will agree that "He will eat either cake or pie" and "He will eat either cake or pie or brownies" are XOR operations. The word or when used by itself has an inclusive meaning with a possible exclusive implicature depending on external knowledge, while the pair either - or offers an explicitly exclusive alternative, and and/or offers an explicitly inclusive one.

[Qwynegold]

(Also, do you know of any natlangs which would use two different words in place of "or" if the English sentences were translated into them?)

Yes, Finnish.

Do you want broccoli or asparagus with dinner?
Halu-at-ko parsakaali-a vai parsa-a illalli-sen kanssa?
want-2SG-Q broccoli-PTV or asparagus-PTV dinner-GEN with

Do you want cake or ice cream for dessert?
Halu-at-ko kakku-a tai jäätelö-ä jälkiruo-aksi?
want-2SG-Q cake-PTV or ice.cream-PTV dessert-TRANSL

[tatapyranga]

(Also, do you know of any natlangs which would use two different words in place of "or" if the English sentences were translated into them?)

Yes, Finnish.

Do you want broccoli or asparagus with dinner?
Halu-at-ko parsakaali-a vai parsa-a illalli-sen kanssa?
want-2SG-Q broccoli-PTV or asparagus-PTV dinner-GEN with

Do you want cake or ice cream for dessert?
Halu-at-ko kakku-a tai jäätelö-ä jälkiruo-aksi?
want-2SG-Q cake-PTV or ice.cream-PTV dessert-TRANSL

Cool.

[zompist]

Again, I think context is highly important. Thinking about menus is misleading, because that's a domain where the possibility of ordering two things, or none, can't be dismissed. But think about things like—

Give me liberty or give me death!
Is she hot or not?
With the entree you get soup or salad.
Is he dead or alive?
I'm going to Harvard or Yale.

There are all clearly XOR, largely because the pragmatics of these domains imply an exclusive choice. (Yes, you can order both soup and salad, but it'll cost you extra.)

Then there's contexts where the usual case is to choose one, but it wouldn't be a contradiction to choose both:

Do you like blondes or brunettes?
Do you want soup or salad?
I'd like to study Chinese or Japanese.
You should talk to your therapist or your rabbi.
Elderly people benefit from keeping a dog or cat.
You can play it on Xbox or Playstation.

There's also what we might call "bureaucratic or", which is always inclusive:

File this form if you are a 587c corporation or a farm worker.
Republicans would never vote for a Mormon or a woman!

[Observer]

Radius Solis, the "either ... or" sentences do explicitly indicate exclusivity to me. The use of "and/or" does implicitly indiciate inclusivity. I still think of a stand-alone "or" as "nand," unless the choices are binary ("Is it dead or alive?").

Qwynegold, that's interesting. I might expect multiple ors in a conlang, but it's a pleasant surprise to find such in a natlang. Do vai and tai mean "and/or" and "xor" respectively?

[CaesarVincens]

Latin also distinguishes between two basic 'or's
"aut" is the 'xor' or - one or the other, but not both
"vel" is the 'or' or - one or the other or both

A 'not(and)' or could be interesting as well (one or the other, or both, but not neither.) likewise with a 'not(xor)'

[Bob Johnson]

A 'not(and)' or could be interesting as well (one or the other, or both, but not neither.) likewise with a 'not(xor)'

You could even derive all the other conjunctions from nand, though it might get long-winded.

[faiuwle]

Republicans would never vote for a Mormon or a woman!

Is there ever a case where "[negative verb] X or Y" wouldn't work out to "not X and not Y"? I'm not sure that's some kind of special context so much as just a property of negation. Besides, not(xor) means "either both or neither" which is not really a job for a negative morpheme in English, anyway.

[zompist]

Republicans would never vote for a Mormon or a woman!

Is there ever a case where "[negative verb] X or Y" wouldn't work out to "not X and not Y"? I'm not sure that's some kind of special context so much as just a property of negation.

I think you're right; the ambiguity of the positive disappears with the negative.

Besides, not(xor) means "either both or neither" which is not really a job for a negative morpheme in English, anyway.

It could be useful: "You have to hire Fred not-xor Mary!" "Give the treats to Billy not-xor Bobby." "Put in a left not-xor right paren."

(Surely there must be conlangs with all 14 reasonable logical connectors. Lojban, sadly, has just five!)

[Ouagadougou]

Actually, I think 6 is the maximum needed, if you cut out Q and ~P AND Q:

P AND ~P
P
P AND Q
P OR Q
P AND ~Q
P XOR Q

The rest could be made via regular derivation: if P AND Q is P Q chuni, for instance, then P NAND Q might be P Q anachuni.
Something similar could be done with conditionals, &c.

[Trailsend]

My father has an incredibly irritating habit of answering questions of the form "do you want X or Y?" (meaning, make a choice between X and Y) with "yes". He doesn't do it because he misunderstands, but because he thinks it's cute or funny, like the xkcd strip that interpreted "will you marry me?" as some kind of experimental question.

IMD that's grammatical, and pretty common--answering "yes" to an "or" question indicates "both/all," typically (but not always) in a situation where inclusion is unanticipated.

A: So are you taking that class for interest, or to satisfy a major requirement?
B: Yes.
A: Ha, lucky you! My major core is all boring.

[MisterBernie]

My father has an incredibly irritating habit of answering questions of the form "do you want X or Y?" (meaning, make a choice between X and Y) with "yes". He doesn't do it because he misunderstands, but because he thinks it's cute or funny, like the xkcd strip that interpreted "will you marry me?" as some kind of experimental question.

IMD that's grammatical, and pretty common--answering "yes" to an "or" question indicates "both/all," typically (but not always) in a situation where inclusion is unanticipated.

But I don't think that's what the example is about; it's about giving the mathematician's answer.

A: "Is the light green or red?"
B: "Yes."

[Skomakar'n]

"gold"

I just went back to this thread to check whether someone had posted this. It never fails.

(Also, do you know of any natlangs which would use two different words in place of "or" if the English sentences were translated into them?)

Yes, Finnish.

Do you want broccoli or asparagus with dinner?
Halu-at-ko parsakaali-a vai parsa-a illalli-sen kanssa?
want-2SG-Q broccoli-PTV or asparagus-PTV dinner-GEN with

Do you want cake or ice cream for dessert?
Halu-at-ko kakku-a tai jäätelö-ä jälkiruo-aksi?
want-2SG-Q cake-PTV or ice.cream-PTV dessert-TRANSL

Would parsaa in this case be pronounced with /a:/ or /a.a/?

[faiuwle]

My father has an incredibly irritating habit of answering questions of the form "do you want X or Y?" (meaning, make a choice between X and Y) with "yes". He doesn't do it because he misunderstands, but because he thinks it's cute or funny, like the xkcd strip that interpreted "will you marry me?" as some kind of experimental question.

IMD that's grammatical, and pretty common--answering "yes" to an "or" question indicates "both/all," typically (but not always) in a situation where inclusion is unanticipated.

But I don't think that's what the example is about; it's about giving the mathematician's answer.

A: "Is the light green or red?"
B: "Yes."

Yes, what he always means by it is "yes, one of those". Then he chuckles at his cleverness.