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I am learning logic now and I realized that the word 'or' in my language actually means XOR, not or.

Is this true also in English?

When someone says for example : "my car is red or a Mercedes" I believe that the listener actually perceives that if the car is red then it is not a Mercedes and vice versa.

Is there a word in English language that actually represents correctly the mathematical 'or' concept?

Bram28
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yoyo_fun
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2 Answers2

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Short answer: no.

Sometimes English speakers will say something like 'either P or Q' to try an express an exclusive or, but even that expression cannot be assumed to express an exclusive or. For example, if I say: 'when I am old, I want to be either rich or happy', don't think that I would mind being both rich and happy!

Bram28
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  • You are correct in the last sentence but this is not true for all cases. For example if someone says that he wants to have a car that is blue or yellow he actually means exclusive or. Or if he says that he wants a house in New York or California. In the first example it is easy to realize that he thinks about XOR because it is not possible for a car to be both blue or yellow but in the last sentence he could actually have two houses... I guess the actual meaning of OR when said in natural language depends on the context. – yoyo_fun Nov 25 '16 at 20:17
  • Yes, exactly: In English it depends on the context. If a waiter in a restaurant says 'do you want soup or salad?', it is clearly meant exclusive. Same for a mathematician saying 'every number is even or odd'. So in English, you can't determine whether it is meant inclusively or exclusively given the word itself: the context will (hopefully!) make clear whether it was meant inclusively or exclusively. But apparently, in your language, the words do make it clear without the context, right? So do you have a different word for the inclusive or? What language is this? – Bram28 Nov 25 '16 at 20:36
  • No, my language is the same as English from this point of view. I would be very curious to find a language that actually has a word to distinguish between these two concepts. I think it would be a good idea to actually introduce a word for this. it would make mathematics and logic learning easier for everybody. – yoyo_fun Nov 25 '16 at 20:41
  • Yes, I wonder there is such a natural language that does that ... and if speakers of that language would be better logicians! – Bram28 Nov 25 '16 at 21:02
  • @yoyo_fun The sentence "I'd like to have a house in New York or California" means just one house (which of course can't be in both states) because the phrase "a house" is singular, regardless of the meaning of the word "or". "I'd like to own real estate in New York or California" doesn't rule out the possibility of owning property in both states. In general, though, the meaning of "or" in English depends on the context. – Mitchell Spector Nov 25 '16 at 22:24
  • @yoyo_fun: German entweder X oder Y corresponds roughly to English either X or Y but unlike the English is pretty reliably exclusive or. – Brian M. Scott Nov 26 '16 at 00:25
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It is not true that in spoken language, "or" always means XOR. It ultimately depends on context as well as intonation. For example, if I ask, "Do you have a pen or pencil that I could borrow?" do you really perceive this as XOR?

In spoken language, and for that matter, even in formal written mathematics, we often make the logic more precise through careful phrasing. Compare:

Would you like cake or ice cream? Or both?

You can have either cake or ice cream. Which would you prefer?

Finally, it would represent a kind of communication breakdown to interpret such questions too literally. If I ask whether you want cake or ice cream, and your answer is "yes", then you're being cheeky. This is also good for cheap humour in science fiction where robots learn to talk.

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