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‘Or’, vel, and cancellation

In this article, we see how the apparent exclusivity of 'or' is open to cancellation.
Two hands, one adult, one child, index fingers pointing towards each other
© University of York

What we’ve just seen is that we can reconcile the idea that ‘or’ has the same truth-table as vel with the sorts of judgements we make about it being wrong to say an ‘or’ sentence. The question is whether we should say that ‘or’ always has the same truth-table as vel. So far it looks like we have something of a standoff here.

One further point in favour of the constant vel interpretation of ‘or’ is that the suggestion of exclusivity is cancellable. For example, it seems to be coherent to say ‘Alex is meeting with Mattie or Alex is meeting with Sarah, and in fact Alex might be meeting with both’. Try this with the other examples. (Examples (5) and (6) aren’t cancellable, but that’s because of the meaning of the plugged-in sentences.)

© University of York
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Logic: The Language of Truth

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