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BradenSeptember 30, 2023
Inclusive vs Exclusive “Or”
In English, there is the inclusive “or” and the exclusive “or” but, in symbolic logic, there is only the inclusive “or”. However, still knowing which “or” is being referred to is essential for a sound translation into symbolic logic. Sometimes, in speaking English, we refer to the exclusive “or” when we use an “either… or…” statement. The “either” is used to specify that the “or” being used is the exclusive one. So, when told something like “you can have either a hamburger or a pizza”, this means you can have one or the other but not both. In logic however, there’s no way to translate an exclusive “or” so you *either* just make it inclusive or you translate it into one of two conditionals (viz., if hamburger, then no pizza, if no hamburger then pizza, if pizza, then no hamburger, or if no pizza then no hamburger). Each of these conditions allow you only “one or the other but not both” since having one entails not having the other.
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In general I think you should refer to context. While an or devoid of context is basically impossible to tell, an or that is attached to an either is almost always an exclusive or. In this question for example we can say pretty confidently that this is an exclusive or, since it's really an either or.
The lsat will usually try to clarify, either by giving us an either or, an x or y but not both, or an X or Y or both. These cases are pretty clear, they more or less tell us exactly what we need to know. There may be some less common cases where it isn't clear from the context or the statements, in those cases I think I would presume the or to be exclusive unless you can make a good argument for it to be inclusive.
I would like to add that I've never seen a question that actually hinges on your understanding of the word or without useful context clues.
In terms of symbols I like to use just "or" for an exclusive or, although I also like Or BNB to make clear to myself that it's an exclusive or but not both. I also like ORb/orB to denote an inclusive or.
