Language

I would like to ask you if we can define "possibility" (and "impossibility", "necessity" and "contingency") in the following way: If something is true, then it is possible. On the contrary, from something being possible, it does not follow that it is true. If something is necessary, then it is true. On the contrary, from something being true, it does not follow that it is necessary. I am assuming, of course, that we can easily define the four first terms from each other (for example, if something is necessary, then it is not possible that it is not true). Isn't this a good way to define possibility, at least taking "possibility" in its ordinary more or less vague meaning?

Comments

Consider the schema: "For every p, given Op, it follows that p: but it is not the case that for every p, given p, it follows that Op". For what fillings for O does this come out true?

Certainly if we put Op = it is necessary that p, we get a truth. But equally Op = Jack knows that p works too. And if we put Op = p and q (for some fixed contingent q), the result will again be true.

So just requiring the schema to hold isn't enough to fix it that Op = it is necessary that p as opposed to the alternatives. Hence requiring the schema to hold is certainly not enough to define the notion of necessity.

[A little wrinkle. The scope of the negation in the schema is important here. For take the variant schema "For every p, given Op, it follows that p, but given p, it doesn't follow that Op". This variant isn't satisfied by Op = it is necessary that p. For suppose p is a proposition of the form Necessarily q. Since (at least for many kinds of necessity, by a standard argument) Necessarily q entails Necessarily necessarily q, then, in this sort of instance, given p, it does follow that Op where O is it is necessary that.]

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