8. See Kenny 1973, Kripke 1982, Malcolm 1989, Boghossian 1989, and Canfield 1996.
Part V
Modality
14
Possibility, Necessity, and Actuality: Concretism
14.1 Introduction
In the next three chapters, we consider a subject that has been central to philosophy from the time of Parmenides on, namely, modality. The study of modality is the study of possibility, necessity, contingency, and actuality. Ordinary English contains a variety of modal vocabulary. Consider, for example, the following:
(1) THP had oatmeal for breakfast this morning but could have had Cheerios instead.
(2) Had THP's spouse made pancakes and eggs this morning, he would have eaten them instead of oatmeal.
(3) It's not possible to travel from the Earth to Mars in 15 minutes.
(4) Texas's offense will probably improve in the upcoming football season, but it might not.
Each of these truths makes a claim about a way the world could, would, can't or might (and hopefully will!) be. Words like ‘could’, ‘would’, ‘possible’, ‘might’, ‘must’, ‘will’, ‘necessary’, and so on are modal. They concern not just what is, but what could or will or must be.
When we study modality, we are studying the nature of truths about what could or will or must be, especially as that nature contrasts with the nature of truths about what simply is. When we study the metaphysics of truths like ‘The cat is on the mat’, we are concerned with the metaphysics of the cat and the mat and the relation between them. But things aren't so straightforward with truths like ‘The cat might be on the mat.’ The actual nature of the cat and the mat, and the actual relations between them don't seem to be the only things that matter. The cat needn't be on the mat for it to be true that the cat might be on the mat. But then, how must the cat and the mat be for this to be true?
Do these facts fall within the scope of metaphysics? One might argue that they are really epistemological in nature (concerned merely with what we know or don't know). Without a doubt, there are uses of ‘might’, ‘must’, ‘possibly’, and ‘necessarily’ that are epistemic in character. For example, if one observes that one's lawn is wet in the morning, one might utter the following:
(5) It might have rained last night or the sprinklers might have gone on.
If one's spouse assures one that she turned the sprinklers off last evening, one might then conclude:
(6) It must have rained last night.
The ‘might’ of (5) seems to express something like ‘for all I know’. One doesn't know that it didn't rain last night, so it might have. Conversely the ‘must’ of (6) expresses knowledge: one now knows that it rained last night, so it ‘must’ have rained.
However, there are other uses of these words that seem to have nothing to do with knowledge. For example, one might conclude, after years of study, that Lee could have won the battle at Gettysburg if he had avoided certain strategic errors, like ordering Pickett's charge. By saying that Lee ‘could’ have won the battle, one is not expressing any doubt or ignorance as to whether he did in fact lose the battle. We all know that is true. The metaphysical sense of ‘could’ concerns whether there exists an alternative scenario of the right sort according to which Lee did win the battle, even if we know that all such scenarios are counterfactual.
This in turn leads to the problem of what exactly is a mere possibility. Philosophers of modality since the time of Leibniz have found it convenient to think in terms of possible worlds. But what is a possible world? Roughly, a possibility is a maximal way the world might be. A way the world might be is a situation or scenario that could occur or could have occurred (in that metaphysical sense of ‘could’). THP could have had oatmeal for breakfast, RCK might have worn a green shirt yesterday, Lyle could have colored with crayons rather than markers; these are ways the world might be. But two plus two's being five, substance S's being both human and non-human, and that ball's being both red and blue all over at the same time, these are ways the world could not be. They are ways, but not ways the world might be. They are not possible ways. A way the world might be is maximal if and only if every proposition is either true or false according to it. Consider a possibility like THP's having oatmeal for breakfast. This possibility represents THP's having oatmeal, but represents nothing about the color of RCK's shirt. But a possibility like THP's having oatmeal for breakfast and RCK's wearing a green shirt yesterday represents THP's having oatmeal and RCK's shirt. It is, we might say, more representationally rich. A maximal possibility is maximally representationally rich. One cannot pick a proposition that a maximal proposition represents nothing about. Maximal possibilities represent THP's breakfast choice, RCK's shirt color, the facts of math, the existence of God, and so on. We can thus think of a possible world in the following way:
Def D14.1 Possible World. A possible world is a possibility that is maximal in that every proposition is either true or false according to it.
As we move forward, we will consider various views about the precise nature of possible worlds, but each view is compatible with this initial characterization.
The vast majority of maximal possibilities somehow misrepresents the world. Indeed, all but one must do so. One maximal possibility represents THP's having oatmeal for breakfast, one that he had yogurt, one that he had an egg sandwich, and so on. Only one of these possibilities matches the actual state of the world. This special maximal possible way the world might be, this special possible world, is the actual world.
We can use possible worlds to explain certain modal notions. Here are a few examples. The sentence ‘The cat might be on the mat’ is true if and only if there is a possible world of a certain sort according to which the cat is on the mat. ‘It's not possible to travel from Earth to Mars in 14 minutes’ is true if and only if there is no possible world of a certain sort according to which someone travels from Earth to Mars in 15 minutes. And ‘You must help old ladies cross the street’ is true if and only if every world of a certain sort is such that you help old ladies cross the street. Patterns emerge here. ‘Necessarily p’ is true if and only if p is true according to all worlds of a certain sort; ‘Possibly p’ is true if and only if p is true according to (at least) one world of a certain sort; and ‘Impossibly p’ (that is, ‘Necessarily not p’) is true if and only if p is true according to no worlds of a certain sort. Further, we can say that p is contingent if and only if p is true according to (at least) one world of a certain sort and is false according to (at least) one world of that sort.
The reader would be right to wonder why the phrase ‘of a certain sort’ shows up in the previous paragraph. The reason is simple: there are different types of possibility, necessity, and impossibility. For example, consider (3) again, that it is not possible to travel from Earth to Mars in 25 minutes. This is true in one sense, in that given the state of existing technology, such a fast trip cannot happen. But there is another sense in which it is false, since it's possible for technology to improve quite dramatically. We might say that travelling from Earth to Mars in 25 minutes is technologically impossible but metaphysically possible, possible in the broadest sense. There are other varieties of possibility as well. For example, things that are possible given the actual laws of nature are nomologically possible. And, as we have already seen, there are epistemological possibilities. This list could be extended further. We use ‘of a certain sort’ to accommodate these distinctions. Just as there are nomological possibilities, there are nomologically possible worlds. Just as there are technological possibilities, there are technologically possible worlds.
A corollary of this is that modal vocabulary in natural languages like English are flexible. The same modal terms can be used to designate different species of modality. It's important to mark, in particular cases, what species is in view. Our discussion of modality will focus on metaphysical possibility, necessity, and impossibility, that broadest kind of modality.
Before we move on, it mi
ght be worth offering an example of why one might care about this issue, an example of why the study of modality matters to philosophy more generally. It is plausible that modality is importantly connected to understanding. Understanding a contingent claim, a claim that might be true and might be false, seems to require the capacity to conceive of possibilities according to which the claim is true and possibilities according to which the claim is false. Additionally, if one embraces Possible Worlds, then there is a question about just how many there are. One answer is quite simple and principled: one, and it just is the actual world. This is Necessitarianism:
Necessitarianism. The only possible world is the actual one.
If Necessitarianism were true, then there would be nothing that is true only contingently.1 Anything that is actually true would be necessarily true. That is, all truths would be incapable of being false. Clearly, Necessitarianism entails metaphysical fatalism, the view that there are no contingent truths about the future. If there are any future truths, they are also necessarily true.
If fatalism were true, then all deliberation about future actions would be in some sense illusory or ill-founded. All of our deliberations presuppose that certain matters are up to us and so not yet fully decided or fated. As Aristotle noted, it is impossible to deliberate about the past, given that past facts are now necessary and fixed. Anything that follows of necessity from such fixed past facts is also beyond the scope of rational deliberation. No one, for example, would deliberate about whether the law of gravity should continue to hold or whether the sun should rise (assuming that the rotation of the earth is already fully determined by the condition of the solar system). We deliberate only about matters that we take to be ones over which we hold some power of deciding between real alternatives. The Rational Practices Presumption (PEpist 2.1) gives us a reason to reject Necessitarianism.
It might be argued that rational deliberation requires only the epistemic possibility of alternative futures. All we must assume is that we do not know with certainty how the future is fated to unfold. However, this is simply false. Whenever we find out, after the fact, that we were wrong in thinking that the future was really open with respect to certain alternatives, we conclude that our deliberation about which alternative to bring about was empty and pointless. For example, suppose that one believes that one has two alternatives open to one: to leave or to stay in one's living room. If it turns out that one is locked in one's living room in such a way that one cannot possibly leave, then one's deliberation about whether or not to leave is, objectively speaking, pointless. This is so even if it is, subjectively speaking, a reasonable thing for one to deliberate. A metaphysical fatalist must believe that there are never real alternatives open to anyone. Thus, she must believe that all deliberation is objectively pointless. Believing this, she cannot rationally engage in deliberation at all.
Clearly, there is an immediate decision that must be made regarding possible worlds. Just one of the following must be true:
14.1T Possible Worlds. There are possible worlds.
14.1A No Possible Worlds. There are no possible worlds.
If we plump for Possible Worlds, there are two broad issues to examine. The first issue concerns what sorts of things possible worlds are. There are two primary questions in this area. First, what exactly are possible worlds? Some philosophers think possible worlds are something like a parallel universe “out there” somewhere, while others think they are more like propositions or mathematical structures or other abstract objects. Second, how are things true or false according to possible worlds? That is, how is that possible worlds represent things?
The second issue is whether modal facts are reducible to facts about possible worlds. This breaks into two sub-issues as well. The first is whether facts about possibility and necessity are reducible to facts about possible worlds, and the second is whether facts about actuality are so reducible. And if modal facts are not reducible to facts about possible worlds, what other options are there for explicating modal truth, and how then do possible worlds fit into the mix?
We begin with two contrasting views about the nature of possible worlds, Concretism and Abstractionism:
14.1T.1T Concretism. Possible worlds are maximal concrete objects.
14.1T.1A Abstractionism. Possible worlds are maximal possible abstract objects.
The fundamental difference between Concretism and Abstractionism is whether possible worlds are concrete or abstract. The distinction between abstract and concrete objects isn't easy to characterize, but there are at least two features that helpfully distinguish them. First, concrete objects, but not abstract objects, typically have a definite location in space and time. Concrete objects, at least in typical cases, are not wholly located at more than one spatiotemporal location. Abstract objects, on the other hand, tend to have no spatiotemporal location at all, or are at least capable of being wholly in many spatiotemporal locations. Second, concrete objects, but not abstract objects, have active and passive powers. Concrete objects can change other concrete objects, and are able to undergo change themselves. Abstract objects do neither. Concretism, then, is roughly the view that possible worlds are like parallel universes, universes like our own, populated with donkeys and buildings and people and stars and so on (more on this below). Abstractionism is roughly the view that possible worlds are maximal possible propositions. As will emerge, these differences manifest in still further, possibly more fundamental disagreements between Concretists and Abstractionists, both with respect to how possible worlds represent and with respect to whether modal facts are reducible to facts about possible worlds.
14.2 Concretism: Worlds as Universes
Concretism is the view that possible worlds are like parallel universes. The thought behind Concretism is, therefore, deceptively simple. But one important motivation for it is deceptively simple as well. Consider (7):
(7) Grass is green.
No doubt (7) is true. We can further note that (7) describes the way the world is: grass's being green is a way the world is. As we have seen, though, the world might have been a different way. Grass might have been purple. Grass's being purple is a way the world might have been. Notice that in both cases, we have spoken of ways. In the first case, we spoke of a way the world is; in the second, a way the world might be. But what are these ways? In the case of grass's being green, it's tempting to think that that way consists in there being certain things with certain features in certain relations. The fact that grass is green is a way the universe is. So it is also tempting to think that the actual world, the maximal way the world in fact is, is just the universe (where that is taken as including even non-physical things, if such there be). But if ways are just facts, then there must exist the fact that grass is purple. Grass's being purple is a way, and ways consist in there being certain things with certain features, in certain relations. Thus it follows that there are certain things with certain features, in certain relations, such that grass is purple. Counterintuitively, then, we have arrived at a commitment to the claim that there is, in some sense, purple grass. Indeed, there are humans that can fly without mechanical aid, there are objects unaffected by gravity, and so on. Possible worlds are, in this sense, just parallel universes. And these other ways, the possible but non-actual ones, are merely possible, rather than actual, because the relevant facts are not part of our world. David Lewis, the most prominent defender of Concretism (see especially Lewis (1986a)), offers this Concretist slogan: every way the world might be is a way some world is.
It is important to forestall a common confusion at this point. Concretists do not say that there is actually existing purple grass. They simply say that there is purple grass, purple grass that really does exist. But this grass is non-actual. It is merely possible. The difference between actual and merely possible objects, however, does not consist in a special way that merely possible objects exist. Rather, it is a matter of proximity. In particular, it is a matter of proximity to you and us. What it is to be actu
al, according to Concretism, is to be part of our world. We fill out these points about possible and actual truth in what follows.
There are two crucial parts of Concretism that allow it to make sense of modal truths. First, recall the connection we noted above between possible worlds and modal vocabulary. ‘Possibly p’ is true if and only if there is at least one world (of a certain sort) according to which p is true; ‘Necessarily p’ is true if and only if p is true according to every world (of a certain sort); ‘Impossibly p’ is true if and only if p is false according to every world (of a certain sort); and so on. Concretists embrace these connections. Indeed, Concretism is a simple-minded extension of these connections. To see why this is so, we need to consider the second part of Concretism.
Second, then, Concretists say that non-modal propositions are true according to possible worlds in just the way that they are true according to our world, the actual world. Whatever it takes for a non-modal proposition to be true in the actual world, that's what it takes for a non-modal proposition to be true in any other possible world. For example, consider (8):
(8) There are talking donkeys.
What would it take for (8) to be true? That is, what would it take for (8) to be true in, or true according to, the actual world? The answer seems pretty obvious: Talking donkeys would have to be part of our world. Concretists say that other possible worlds are just like ours, so the account of the according to relation goes in just the same way. In particular, it's true according to some world w that there are talking donkeys if and only if there are some talking donkeys that are a part of w. On this view, what it is for something to be true according to a merely possible world is just what it is for something to be true according to the actual world. The Concretist account of the according to relation is not, therefore, a modal account (at least insofar as one's story about truth in our world is non-modal).
The Atlas of Reality Page 52
