10 Jan 2025 update: added list item (12)

Modality is possibility/necessity, presumably called that because one can think of possibility and necessity as modes of truth. Something is necessary if it must be that way. The possible can be understood in terms of the necessary (and vice versa), so one might say that something is possible if it’s not necessarily not that way. Forgive the double negative, but that’s how it is. For example, it’s possible that I will be late for work tomorrow: the statement is not necessarily false.

It will be helpful to describe metaphysical modality in the context of two other kinds of modality: physical and logical. It’s incumbent on me to describe only necessity since, as I mentioned, possibility and necessity are definable in terms of each other. First, what is physical necessity? Something is physically necessary if it must be the case given the laws and boundary conditions of nature. For example, it’s physically necessary that a stone will fall if dropped. Something is logically necessary if it must be that way given the rules of logic. For example, it’s logically necessary that God either exists or he doesn’t.

What, then, is metaphysical necessity? Something is metaphysically necessary if it must be that way given our intuitions about what could have been real. Metaphysics is that branch of philosophy concerned with the nature of reality, whether physical or not. It’s best to look at examples. Here are twelve statements that, though logically possible, are necessarily false in the metaphysical sense:

1. 7 + 5 = 13
2. Jim is taller than himself
3. Prime Minister Thatcher is a prime number
4. The ball is both red and green all over at once
5. The chair created itself
6. Mary danced with the square circle
7. God committed adultery
8. There is something with a shape but no size
9. Joe traveled to a time before he was born and killed his grandfather
10. The desk on which I’m now typing is made of ice
11. Alex’s thirty-first birthday party preceded itself in time
12. It’s good to torture and rape a little girl for fun

None of these statements is contradictory, but all of them are absolutely incapable of corresponding to reality.

An argument is a set of premises leading to a conclusion. The strength of this “leading” can vary. Sometimes, that all the premises should be true but the conclusion false is logically absurd, and sometimes it’s only unlikely. We’ve all encountered arguments such that its premises are lovely, the connection between its premises and conclusion is very strong, and its conclusion is incompatible with other propositions we believe. When this happens, we’re forced to give up either some of the premises or these other beliefs. We should give up whatever we are less sure of. In my experience, arguments with the most unpleasant conclusions have premises such that one is far less sure of them than he is of the beliefs he would have to give up to accept the conclusion.