What does "or" mean?

[zompist]

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.

All you need is two, nand and nor. But that's cheating. A certain amount of kudos will accrue to anyone who has non-derived roots for all 14.

(The other two-- a 'connector' whose output is always true and one that's always false-- are just dumb, though I suppose it would have jocular uses.)

[Observer]

Trailsend, your "yes" to an "or" question example sounds strange to me. Do people talk like that where you live?

zompist, can you give examples in English of all fourteen logical connectors? Looking at the Wikipedia article on logical connectives, I'm unsure how something like material nonimplication would be used if English had a morphemic word for such.

[zompist]

zompist, can you give examples in English of all fourteen logical connectors? Looking at the Wikipedia article on logical connectives, I'm unsure how something like material nonimplication would be used if English had a morphemic word for such.

You can work them all out yourself from that table.

E.g. the one you highlight is P ∧ ¬Q. You could read that as "p but not q", or "p except for q".

[Izambri]

"gold"

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

My doctor's prescription.

[Izambri]

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."

Oh, yes, at least!!! I was expecting that answer.

And who says "yes", says "sugar", "tomorrow" or whatever.

[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.

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.

Ah! Right. That is quite irritating.

Trailsend, your "yes" to an "or" question example sounds strange to me. Do people talk like that where you live?

Yep.

[Observer]

zompist, I can work them out that way, however, I can't necessarily see how such a concept would work as a non-derived root. P & Q is easy. "Cake and ice cream." How would "P but not Q" work as a word like "and?" Let's invent the word "zog" to mean "P but not Q." "You can have cake zog ice cream." I can't imagine someone actually saying that. One would simply say, "Do you want cake?" Why offer a choice that's not available? When would a morphemic word for such constructions as "P but not Q" ever be used in everyday speech? Perhaps the reason all fourteen logical connectors don't appear as non-derived roots in any language is because they aren't useful in colloquial speech. I can't see their potential use. Can you?

Trailsend, where do you live?

[cromulant]

zompist, I can work them out that way, however, I can't necessarily see how such a concept would work as a non-derived root. P & Q is easy. "Cake and ice cream." How would "P but not Q" work as a word like "and?" Let's invent the word "zog" to mean "P but not Q." "You can have cake zog ice cream." I can't imagine someone actually saying that. One would simply say, "Do you want cake?" Why offer a choice that's not available? When would a morphemic word for such constructions as "P but not Q" ever be used in everyday speech? Perhaps the reason all fourteen logical connectors don't appear as non-derived roots in any language is because they aren't useful in colloquial speech. I can't see their potential use. Can you?

You can't imagine anyone actually saying "but not"?

That phrase is used all the time. Part of your trouble imagining it being used may be that you seem to be restricting your examples to situations in which someone is offering someone else a choice. (That said, I don't even think "you can have cake but not ice cream" sounds strange at all). Googling the phrase gave me hits like "in the world but not of the world," "down but not out," "why Kosovo but not Palestine," "abandoned but not forgotten," and many more. The common thread being that the conjoints would normally seem to belong together (the second being an implication of the first), but against expectations, do not.

I would not be at all surprised if one or more natlang out there has a non-derived word for "but not." I can also imagine a contraction of "but not" arising, and eventually replacing the two words.

[faiuwle]

We also do already have single (though not all underived) words for "but not" - "sans"/"without" and "less". Normally Q is either a part of P, or assumed to come with P unless otherwise specified, but that's to be expected.

[Trailsend]

Trailsend, where do you live?

Western US, currently

[Qwynegold]

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?

Sorry I can't answer that. I don't understand logical notation at all, and trying to explain the difference between these two words breaks my head because it's not as simple as that. I discussed these two words in, was it "help your fluency"?, some time ago.

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

With /a:/. A double vowel always stand for a long vowel in Finnish, except for when there's a dash between. (The dash in that sentence was just for showing morpheme boundaries. )

[jal]

If we cut it up in two phrases, a nand-meaning becomes more clear:

Do you want asperagus? Or broccoli?

But I'd figure that would usually only be said that way when it's clear the one asked doesn't agree with the first choice.


JAL

[Observer]

cromulant, I see. For some reason, I was blocking out such common examples as "down but not out" because I was focused on imagining a morphemic "P but not Q."

The material conditional may not work as a morphemic word. "If P then Q." It would seem to require two separate words.

"If the speed of light in a vacuum is constant, then nothing can travel faster than light."

Inventing the morphemic word "blit" to mean "if P then Q," how would that sentence be reconstructed?

"The speed of light in a vacuum is constant, blit nothing can travel faster than light."

Does that work?

Qwynegold, I'll check out that topic.

[zompist]

Read the article you just linked to-- it contains a one-word equivalent in the first sentence.

[CaesarVincens]

Or change the position of "blit"
"Nothing can travel faster than light, blit the speed of light in a vacuum is constant."
This is of course equivalent to several actual English phrases:
"Nothing can travel faster than light, if the speed of light in a vacuum is constant."
"Nothing can travel faster than light, given (that) the speed of light in a vacuum is constant."
"Nothing can travel faster than light, provided (that) the speed of light in a vacuum is constant."
Etc.
"That" may be optional with certain participles (for me provided works alright, but given is highly questionable).

In English, the "then" is optional most times; in Latin, it's never expressed; in Classical Greek, it's more complicated, but it (or something like "then") is generally only expressed with Irrealis conditions.

[Qwynegold]

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?

Sorry I can't answer that. I don't understand logical notation at all, and trying to explain the difference between these two words breaks my head because it's not as simple as that. I discussed these two words in, was it "help your fluency"?, some time ago.

On second thought, I think the thing is that vai can only be used in interrogative sentences, while tai can be used in both interrogative and declarative sentences. When it's used in questions, it expects either alternative or "none" as an answer, while vai only expects either of the alternatives as an answer. "Both" would be an unexpected answer for both vai and tai questions.

[Observer]

Zompist, I'm not versed in linguistics. Is "implies" classified as the same sort of word as "but," "and" and "or?"

CaesarVincens, "if" alone seems adequate when you rearrange the sentence that way. Perhaps "if/then" is an artifact of word order.

Qwynegold, that's interesting; a conjunction only usable in questions. Does anyone know any other languages that have such a thing?

Wiktionary says tai is inclusive and vai is exclusive, in addition to the question-asking limitation.

[Qwynegold]

Wiktionary says tai is inclusive and vai is exclusive, in addition to the question-asking limitation.

Oh, I see. It says: While it is often said that tai is to be used in affirmative clauses and vai is to be used in question clauses, a more precise difference is that tai is an inclusive or, while vai is an exclusive or. For instance, while Söitkö sinä leivän tai hedelmät? and Söitkö sinä leivän vai hedelmät? are both correct. The former asks in a yes or no question if you ate either bread or fruit or no, while the latter asks which you ate, the bread, or the fruit.

[CaesarVincens]

Also, Observer,

"The speed of light in a vacuum is constant, blit nothing can travel faster than light."
"The speed of light in a vacuum is constant, thus nothing can travel faster than light."
"The speed of light in a vacuum is constant, therefore nothing can travel faster than light."

Notice the difference between those and the following:

"Nothing can travel faster than light, if the speed of light in a vacuum is constant."

With a 'thus' or 'therefore', we have a statement and a consequence of that statement. With 'if', we have a statement and a condition for that statement. While the two sentences are in some sense semantically equivalent, the syntax and the implications differ.

Also, 'implies' is a good, old-fashioned verb, while 'but', 'and', and 'or' are conjunctions. However, in logic, "implies" is often used in the sense of "if-then".
For example, "if X, then Y." is logically the same as "X implies Y."

[blank stare II]

Caesar you are a wealth of information, and have a knack at explaining things.

I can also imagine a contraction of "but not" arising, and eventually replacing the two words.

IMD, that is, the one found in my region of southern Appalachia, we say b'not all the time. It's cold, b'not too cold.

[IMD means "in my dialect"]

[CaesarVincens]

Thank you, blank stare.

I think I probably say something like [bənɑt] for "but not" in casual speech.

[Fëorpáþ]

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

Where I come from this question is often answered with Yes or No. "Yes" would be taken as choosing the latter option and "No" the former option, as well as "both" being a third option, of course.