When speaking about modality what we mean is the broad study of possibility, and the ways in which we can make use of labels and concepts such as necessity, randomness, contingency, etc.
It seems to me that some of the statements we make about contingency, or, in Leibniz’ language, logically possible ways the world might be, assume that we are saying something intelligible. For instance, if I propose that there may be some logically possible world in which I was not born, I would want to say that this is an intellectually live suggestion of a logically possible world. However, it becomes more difficult, if we are determinists, to say any such thing is ‘logically possible’ since it becomes ambiguous what that really means; It is apparently ‘not’ logically possible, on determinism, that something which did happen could have failed to happen. This is one of the arguments I gave recently to a friend, in support of belief in Free Will, because it’s denial if replaced with determinism collapses modal distinctions.
However, what of some of the less clear cut cases. For instance, what about saying that it is logically possible that God doesn’t exist? Well, that means that we think that Atheism is logically possible. However, a theist who takes the (Anselmian) definition of God seriously will have to, it seems to me, be a non-cognitivist with regard to atheism – the theist will not be able to imagine any way the world might be such that God does not exist or fails to exist. In other words, atheism is not an intellectually live option for the ardent theist. This is significant I think, because a theist must recognize that she is only provisionally entertaining atheism when entertaining atheists, but so long as she has a clear and distinct idea of that-than-which-nothing-greater-can-be-conceived it isn’t really possible for her to take the suggestion seriously that ‘God’ does not exist. Some philosophers, including Alexander Pruss, have used the language ‘broadly logically possible’ in just such a provisional way.
There may be harder questions though. For instance, “is it logically possible for something to travel faster than the speed of light?” This question is odd because of course for any speed we can simply add more and ‘imagine’ that something travels faster, a bit like we can imagine a taller building for any building of a finite size. However, if Einstein is right about his formula, then it is physically impossible to travel faster than the speed of light. Usually there is a distinction between what is physically possible and what is logically possible, but if our statement is supposed to be ‘logically possible’ about the universe, then it becomes difficult to see the distinction between logical and physical possibility. It is not logically possible that it is physically possible for an object in our universe to travel faster than the speed of light (assuming E=MC2). Doesn’t that mean that we need to say that it is only broadly logically possible that something physically travel faster than the speed of light (on the same assumption)? Of course, given how tenuous science is, I wonder how we could ever even know that. More curious still, to my mind, is the question of Leibniz’s reasoning from the divisibility of bodies to the existence of monads. He argues that the ‘atom’ cannot exist (the indivisible smallest possible unit of matter or ‘bodies’). This is because he seems to think that the definition of body simply logically entails its divisibility, if it is extended in space then it must be compound. However, isn’t this question begging? Suppose I am able to think of a unit of matter than-which nothing smaller can be imagined (or ‘none’ smaller). If this is even possible then Leibniz is definitely question-begging. If it is always in principle possible to imagine something smaller by dividing a body (which isn’t clear if bodies are all constituted by material atoms in the true sense) then maybe it is at least possible that material atoms exist.
On this note, one might wonder about the more fundamental question, which is whether science can ever in principle inform modal logic? For instance, if science finds that light really is the speed than which nothing greater could travel, or if science finds that atoms exist (which science has not yet found) then would it inform our modality? I’m not sure it would, seeing as science is so tenuous, and indeed it is always logically possible for some theory in science to be overturned by the very nature of the case. What then can referee between two modal logicians who have contrary intuitions, such as Leibniz and anyone who thinks that material atoms are not offensive to reason? It is hard to see what can. The same can be said for those who see the Principle of Sufficient Reason as Self-evident, and others who see it as self-evidently false. Rational intuition is the only thing that can inform modality.
At the risk of sounding continental, I wonder at this point if anyone foresees, as a logical next-step in the conversation, Bonaventure’s suggestion that knowledge and wisdom are not differentiated in kind but by degrees according to the traditionally Augustinian ‘construal’ of knowledge (see especially Andreas Speer for Bonaventure’s epistemology). Perhaps one’s basic values play a fundamental role in understanding rational intuition clearly. Perhaps this provides a theological account for the variance of rational intuitions when it comes to such matters as the PSR. For, if one agrees that the end of philosophy is the ultimate happiness of man, then it seems plausible if not inevitable that philosophy is necessarily oriented towards God, and therefore towards theology. If somebody does philosophy, therefore, without a desire to find the Summum Bonum then perhaps they aren’t doing philosophy properly at all, and thus their intuitions are set according to their values. In fact, perhaps (and this sounds rather harsh, but seems to be a corollary point) they aren’t “being human” right, or not realizing the ends towards which man is by nature oriented. Of course, this objection is a double edged sword, for even if true the philosopher who has, let us say ‘Humean’ intuitions for the sake of argument, they can easily simply accuse a theist of having different values inform their intuitions here. The question must then be pushed back to the level of what values man ought to adopt, or more personally, what questions (or kinds of questions) the philosopher ought to be most concerned about answering.
From a Theological perspective, perhaps the closer one comes to God mystically, the more clearly they can discern even modal intuitions. Thus the beatific vision has noetic qualities or a noetic effect which serve(s) to inform one’s modal intuitions.