[Here's a draft of my thesis introduction, minus footnotes. Other chapters will follow in due course. Feedback welcome - especially on minor points - the damn thing's due in a couple of weeks!]
How can we know what is possible or necessary? Empirical investigation might inform us of how the world is. But how can we learn about what isn’t, yet could have been, the case? How are we to distinguish such contingent falsehoods from genuine impossibilities, which are not only false but necessarily so, such that there is no way that they could have been true? What, we may ask, is the scope of possibility? We may clarify these problems by recasting them in the idiom of “possible worlds”. The actual world corresponds to the universe, or all that actually exists. It is the way things actually happen to be. But things could have turned out differently: there are other possible worlds, or ways a world could be. It happens that there are not any unicorns. But presumably there could have been. That is, there are possible (non-actual) worlds where unicorns exist. More generally, we can identify possibility with truth in some possible world, and necessity with truth in all possible worlds. A statement is contingent if it is true in some possible worlds but not others. In this framework, modal space – the range of possible worlds – provides the scope of possibility.
Often we are interested only in a restricted subset of modal space. For instance, when thinking about what’s nomologically possible - possible given the actual laws of nature - we should only consider those possible worlds that have the same laws of nature as our own. But perhaps these laws could have been different, so that there are possible worlds where this is the case. Such worlds would not be “nomologically possible”, of course, but they would still be possible in a more fundamental sense, which we can call “metaphysical possibility”. They are ways the world could have been. It is this broad notion that the present work is concerned with.
Sometimes we use talk of possibility in a subjective epistemic sense, merely to highlight what might be true for all we know. To a novice mathematician, it might seem “possible” in this sense that there is a greatest prime number. But though he might not yet know it, others have proven that this is not really possible. There is no way the world could turn out that would make his claim true. Rather, it is false in all possible worlds that there is a greatest prime number. As this example demonstrates, metaphysical possibility is an objective notion, concerned with how the world could have turned out in fact, rather than how it might be for all we know. We should similarly distinguish metaphysical necessity from epistemic certainty. For instance: I certainly know that, as it happens, I exist. But although my existence is (epistemically) certain, I presume it is not necessary. Things could have been different – there are possible worlds where I don’t exist. It’s just that those worlds are incompatible with the contingent evidence that is available to me through introspection, so that I can know them to be non-actual. That doesn’t make them any less possible in the metaphysical sense.
A more promising epistemic distinction holds between a priori and a posteriori statements. This concerns the mode or basis of justification, rather than strength of credence. Let us say that a statement is knowable a priori iff it can be conclusively justified by reason alone, without appeal to experience. (Experience may be required in order to acquire the concepts one is reasoning about, but that need not cast doubt on the possibility of a priori justification. Experience may be a necessary precondition for thought without thereby playing a justificatory role.) Truths of mathematics and logic are paradigm examples of the a priori. These may be contrasted with empirical or a posteriori statements, which require experiential justification. Our familiar everyday beliefs about the world tend to be of this latter sort, as are the claims of empirical science.
It is natural to expect a close connection between this epistemic distinction and the metaphysical distinction between necessity and contingency. After all, contingent claims are true in some worlds but not others, so how could one know them to true without first looking to see which world one is in? This line of thought suggests that in order to know something a priori, without appeal to experience, it must be true in all possible worlds, i.e. necessarily true. Conversely, if a claim will turn out true no matter how the world is, then looking at the world might seem superfluous. If it is necessary, then it should be knowable a priori. Combining these claims yields the Coincidence Thesis:
(CT): For any statement S: S is a priori iff S is necessary.
CT offers one way to establish Modal Rationalism: the thesis that we have a priori access to the space of possible worlds. On this view, we can discover what’s possible by determining what is consistent and cannot be ruled out a priori. Empirical investigation comes later, when we wish to see which possibility is actual. Experience may then inform us of how the world is, but we do not need it in order to learn how the world could have been. This prior task may be conducted by reason alone.
Remarkably, Kripke established that CT is in fact false. We can provide counterexamples both in the form of contingent a priori statements, and others that are necessary yet a posteriori. This disconnects modal theorizing from a priori reflection in a way that clearly threatens modal rationalism. Chapter One of this sub-thesis explores Kripke’s arguments, and shows how the semantic framework of Epistemic Two-Dimensionalism promises to restore the link between reason and modality that found naïve expression in CT. Chapter Two introduces the idea of “strong necessities” that elude even the 2-D framework. Finally, the third chapter explores a conception of ‘primitive modality’ that can help motivate the radical challenge of strong necessities, though I suggest a way to reconcile modal primitivism with modal rationalism.
It’s worth noting that this dispute has broader implications for philosophical methodology, by influencing the kinds of arguments that metaphysicians may employ. Several important arguments depend on the inference from conceivability (or a priori coherence) to possibility legitimated by modal rationalism. For example, Chalmers argues from the conceivability of “zombies” – creatures physically identical to us but lacking phenomenally conscious experiences – to their metaphysical possibility, and hence the falsity of physicalism. That is, if modal rationalism is correct, then conceivability arguments of this sort can establish that the physical alone does not suffice to guarantee consciousness. Or consider the following variation of Moore’s ‘Open Question Argument’ against meta-ethical naturalism: assuming that the coincidence of goodness with any natural property (say happiness) is an ‘open question’, modal rationalists may infer that the two could therefore come apart, and so are distinct properties. More generally, given the necessity of identity, modal rationalism enables the powerful argumentative strategy of inferring actual non-identity from merely conceivable non-identity. Without it, such inferences would become suspect; and the philosopher’s toolkit would be that much more limited. So let us turn now to this fundamental question of whether modal rationalism is defensible...