This is of course related to why the famous joke "Is it a boy or a girl? Yes." is so hilarious.
You have to be very careful in reasoning about natural language based solely on the written record, since spoken language regularly includes features, such as the suprasegmentals (stress and intonation) in the above examples, that aren't recorded in the orthography.
I used to drive my friend crazy when he would ask if I wanted a peanut butter and jelly sandwich or a ham and cheese sandwich and I would answer yes.
Do you want to eat pizza or garlic bread? - exclusive
In natural language "and" works like a inclusive or. If there is pizza and garlic bread I can choose to eat one or both. Or is always exclusive in this sentence.
Do you want to eat some pizza or some garlic bread? - probably inclusive or
Also, I would interpret the first question as "addition" (pizza with garlic bread, on the model of mac and cheese), not as an inclusive or.
Somewhat related: the Ada language uses and, or, xor for its logical operators, but uses and then and or else for the short-circuit forms. [0] Not a very natural solution in my opinion.
[0] https://en.wikibooks.org/wiki/Ada_Programming/Operators#Shor...
On second thought I was mistaken about the example I gave. If someone says You can have tea OR coffee they're really expressing a NAND. You can have at most one out of the two options. Unlike with XOR, you're permitted to have neither.
To express XOR, you'd need to say You must have tea or coffee.
Only to IT people though. Common folks will just look at you in a weird way...
But in this case there is actually a slight chance that nobody recognizes this as a joke at all...
But I figured most mathematicians are IT people, too. But there is at least also a third group: philisophers. They have formal logic, too (in university), but seldom math.
So in the spirit of the joke:
"Only to IT people though. "
Would have to be:
"Only to IT people and/or math people and/or philosophers, though. "
Desire for formal correctness satisfied?
"Do you like pizza, or?"
Depending on the exact statement, you might catch more or less flak.
English is way too ambiguous for this example and often relies heavily on context. Wanting to eat pizza does not preclude also wanting to eat pasta. If it was exclusive or, and you wanted to eat both pizza and pasta, the honest answer to this question would be "no," but what you should say is "yes."
Even sentences that on their face are strictly propositional will, in actual situated language use, have implied meanings (a pragmatic level). The canonical example is where one person says "It's cold" (at it's core a statement of fact), after which another person closes a window, or hands them a jacket, or follows with "Let's go home, then". If you want to give an account of natural language meaning that's even remotely complete, you cannot stop at what's in the sentence at the surface, you absolutely have to look at why it's being said.
Indeed, if you think of an actual situation where someone would say "do you want to eat pizza or pasta?", I think you'd find that it does, in fact, imply that the two are exclusive in that context - say if you're at a restaurant where they only expect you to order one main course. But this is not a problem at all, it's just how language works.
(And personally, on the subject of logic and language, I'd even go as far as to say that logic is based on natural language rather than the other way around, but I think that might be tough sell to the mathematically minded.)
It was actually this specific question that made it clear to me that this is not the case.
In order to narrow down our takeout options, the girlfriend and I regularly ask questions like, "Do you want pizza or pasta?" meaning "Are any or all of these meal options acceptable to you?" (at which point the conversation continues with maybe us listing a few restaurants which offering one or both options.) This is the same exact phrase, but from context it is inclusive or.
>> - say if you're at a restaurant where they only expect you to order one main course.
Indeed, if the question was something like "Would you like soup or salad?" where, from context, the choice is binary and exclusive.
It doesn't answer the question. The questioner is asking for your help in making a decision. If you are completely neutral about the two, then most people answer with the phrase, "Either one is fine". Saying just "yes" sounds like you misunderstood the question --- unless you say it with a wry smile, showing that you mean to be funny in your answer.
(I suppose occasionally someone could ask the question with a different inflection, with the last word at a higher pitch, meaning, "Are either of these fine with you?" rather than, "Please pick one.")
> Similarly with the boy or girl question, "no" may be stillborn.
The sex is set at conception.
> > Similarly with the boy or girl question, "no" may be stillborn.
> The sex is set at conception.
Not necessarily - at conception, the cells could be XX, XY, but also XXY (not to mention, they could be X- or -Y). After conception, chymerism could occur, where XX and XY twins become conjoined and a single fetus develops having both XX and XY chromosomes in different parts of the body - the sex will mostly be determined by which DNA is used when forming the gonads. It could also end up developing both kinds of gonads. But even if the fetus develops testicles, there is a chance that it has some kind of testosterone resistance and ends up with a completely female phenotype. Of course, there is also a possibility that no gonads are developed. This is all staying well in the realm of biological sex, and disregarding other hormonal complications that could happen based on what the mother is doing and her health, and disregarding any morphological abnormalities that could cause surface-level confusion between biologically male and female sexual organs.