Putting these two items together, we can see how Concretists account for the truth of modal claims. Consider (8) again. The proposition that there are talking donkeys is actually false but possibly true. It is actually false because the proposition that there are talking donkeys is false according to our world, which is to say, no part of our world is a talking donkey. Actual truth is truth in our world. Actual falsity is falsity in our world. On the other hand, (8) is possibly true because there is a possible world according to which there are talking donkeys, which is to say, there are talking donkeys that are part of some world or other. We can generalize these accounts. With respect to possibility, necessity, and so on, we can say that a proposition p is possibly true if and only if there is a world w according to which p is true, where for Concretists that means that the parts of w have the right properties and stand in the right relations so that p is true. The account for necessity and so on works similarly. It's possible that grass is purple if and only if there is a world with purple grass as a part; it's necessary that the God of Christianity exists if and only if the God of Christianity is a part of every world, and so on. With respect to actuality, a proposition p is actually true if and only if my world is such that p. So, it's actually the case that grass is purple if and only if our world has purple grass in it, and it's actually the case that the God of Christianity exists if and only if the God of Christianity is a part of our world.
More technically, to say that something is possible is simply to say that it is true, when its quantificational phrases and terms are interpreted in the widest possible way, taking into account the whole of reality (i.e., taking into account all of the parallel universes). Consider (9):
(9) Possibly, there are talking donkeys.
Both (8) and (9) contain the quantificational phrase ‘there are’. Other quantificational phrases include ‘something is’, ‘nothing is’, ‘everything is’, ‘no one is’, ‘some dogs are’, ‘all trees are’, and so on. Quantificational phrases have a domain, which is the class of objects relevant to determining the truth of the claim involving that quantifier. For example (and simplifying somewhat), the domain of ‘all trees are’ is just the class of trees. If one said ‘All trees are F’, the way to check the truth of that claim is to see whether everything in the class of trees is F. If so, then ‘All trees are F’ is true. If not, then that sentence is false. Ordinarily, the largest domain that is relevant to claims containing a quantificational phrase is the class of all actually existing things. For example, the way to check whether (8) is true is to look around in the class of all actually existing things to see whether that class includes any talking donkeys. If so, then (8) is true; if not, then (8) is false.
Concretists, though, think that modal vocabulary expands the domain of quantification even further, out to the class of all existing things, rather than just the class of all actually existing things. Concretists, of course, take these to be different classes, since the actually existing things are just the things that exist in our world. Things in other worlds do not actually exist. Back to (9): Concretists say (9) is true just in case there are talking donkeys in the largest domain, that is, just in case they exist in some possible world or other. In fact, (9) is equivalent to one reading of (8). (8) is false, we have seen, if the domain of ‘there are…’ is the class of actually existing things. If we interpret ‘there are’ as speaking of anything, without restriction, then (8) is true, so long as there is at least one possible world in which some donkey talks.
Having sketched the nature of Concretism, and seen how Concretists might supply as many worlds as there are possibilities, we now face an obvious question: Why in the world would one ever embrace this crazy view?!? It's just so implausible that there are loads of other concrete universes that aren't parts of our world, and even if there were, how could we ever know that there are such things at all? We'll return to the second half of this question in a little while. Right now, we will focus on the first half.
At the beginning of this chapter, we noted something odd about modal truths, namely, that they seem to have little if anything to do with the way the world actually is. What, then, one might wonder, could ground the truth of modal claims? One way to deal with this oddity is to find some existent things in which one can ground modal truths, and then find a way to reduce modal locutions to locutions having to do with those existent things. In other words, if we can find a way to reduce modal truths to truths of some other, more easily understood sort, then we can minimize the oddity that is modal truth.
Concretism offers such a reduction of possibility, impossibility, necessity, and related matters. David Lewis (1986a) argues that Concretism allows one to claim that no modal truth is fundamental, whether about possibility, contingency, necessity, or impossibility. Further, Lewis claims this reduction as a reason to believe that Concretism is true. In fact, Lewis claims that Concretism offers a way to reduce a number of challenging philosophical items, from possibility and necessity to counterfactuals, properties, propositions, mental content, supervenience, and more. We focus on the reduction of modality here. (But we encourage the reader to think about, for example, how Concretism helps Reductive Nominalists (7.1A.1T/8.1T) deal with the extensionality problems we considered in Chapter 8.) Suppose presently that Concretism can successfully reduce modal facts to facts about possible worlds. (This supposition is challenged by the problem of isolation, considered below.) Then Concretism enjoys an advantage in terms of qualitative economy over any view of modality that requires fundamental modal truths, and still more so over any view that requires fundamental truths and that can't also offer reductive accounts of those other things (PMeth 1.4).
This advantage in qualitative simplicity, however, exacts a steep quantitative cost. On top of all the green grass that exists in our world, Concretists must commit to the existence of all the possible purple, pink, and magenta grass inhabiting other worlds. Concretism includes not just actual humans, but all the merely possible ones as well; not just any actual extraterrestrial persons, but all possible extraterrestrial persons; not just the actual coffee beans, but all the possible ones as well. This is not to mention the objects whose kinds we have never even conceived, the true aliens. If something is even possible, the according to Concretism, it exists. Abstractionists don't have to commit to all this grass and coffee or humans and aliens. It is true that Ockham's Razor implores us to prioritize qualitative economy over quantitative economy (PMeth 1.4.1), but quantitative economy counts for something. It's vital, then, that one consider whether Concretism's reductive accounts of these various notions are successful.
At any rate, in Chapter 15, we will see that Abstractionism cannot supply a reductive account of modal truths, and this gives some reason to prefer Concretism. For now, we focus on Concretism's reduction strategy.
Concretism offers a reductionistic account of possibility and actuality because there are no modal notions deployed in the final analysis. We have seen that Concretism's account of the way possible worlds represent is non-modal. Parthood is not a modal notion. And what makes something a part of our world is not modal either. Concretists reduce modal notions like possibility, necessity, and so on to facts about the intrinsic makeup of the very many existing concrete worlds. To exploit the more technical bits about quantification above, we can see that Concretist accounts are reductionistic because quantification is not modal, and Concretists say that modal vocabulary simply specifies a domain of quantification. Further, Concretism reduces facts about actuality to facts about the intrinsic makeup of our world. Thus, Concretism requires Modal Indexicalism and denies Modal Anti-Indexicalism:
14.2T Modal Indexicalism. All attributions of actuality are indexical in character.
14.2A Modal Anti-Indexicalism. Some attributions of actuality are not indexical in character.
Concretism is Indexicalist in that it specifically deploys the notion of something's being related in some way to us. This is one way, but not the only way, for an at
tribution to be indexical.
Def D14.2 Indexicality. An attribution is indexical in character if the content of a thought making the attribution depends essentially on some extrinsic feature of that thought or its thinker (such as location in space, time, or “logical space”).
Consider the following thoughts:
(10) Austin is here.
(11) I am hungry.
(12) It is now noon, EDT on 17 July 2016.
(13) A human being has actually walked on the moon.
It is fairly uncontroversial that thoughts (10) and (11) are indexical in character. What is thought by means of (10) and (11) depends upon who is thinking them and where he or she is located while thinking them.
There is some controversy about whether (12) is indexical, a controversy we will explore in detail in Chapters 20 and 21. But here is a foretaste: so-called “B-Theorists” or “Anti-Tensers” (20.2A) hold that (12) is indexical in character. On these views, (12) expresses a different thought, depending on when it is (tenselessly) being thought. “A-Theorists” or “Tensers” (20.2T), in contrast, believe that (12) is non-indexical. Its content is to ascribe a metaphysically primitive property of present-ness to a moment of time.
Modal Indexicalism's reduction of actuality parallels the reduction of time in Anti-Tensism. Modal Indexicalists think that (13) is indexical in character. It is either true or false, depending on “where” (or “in which world”) it is being thought. In the world that we call the actual world, our world here, (13) is true, since a successful moonwalk is part of our world. However, there are other possible worlds, worlds without moonwalks, and when (13) is thought in those worlds, it is false. Which world is actual for one is relative, on this view, to the perspective that one occupies.
Modal Anti-Indexicalists, by contrast, think that all this is confused. The proposition expressed by (13) attributes a special, metaphysically primitive property of actuality to some world containing a moonwalk. In our case, (13) attributes the property of actuality to the actual world. Since a human being did indeed walk on the moon, (13) is true simpliciter (that is, true absolutely and without qualification), and not merely true here in our possible world.
The distinction between Modal Indexicalism and Anti-Indexicalism seems to be a consequence of a metaphysical disagreement about the nature of possible worlds themselves. Indexicalists must be Concretists. Otherwise, the indexicality does no work. In contrast, Anti-Indexicalism situates much more nicely with Abstractionism. At any rate, whether or not our universe is part of a multiverse of parallel universes is, for Anti-Indexicalists, completely irrelevant to evaluating propositions about actuality. If dragons existed in some parallel universe, then the Anti-Indexicalists would conclude that (14) is true:
(14) Dragons actually exist.
Parallel universes would, for Anti-Indexicalists, be every bit as actual as our own, local universe. A possible world is something altogether different. A non-actual possible world is a way for all of reality to be, other than the way it actually is.
Now consider Possible Actuality:
Possible Actuality. If there is more than one possible world, then which world is actual is a contingent matter. That is, a possible world is a world that could have been actual.
Concretists, if they reject Necessitarianism, must not claim, given Possible Actuality, that the actuality of the actual world is due to some essential feature of that world. Each world has its essential features as a matter of necessity, not contingently. And all of the facts about what would be true if the world were actual—the content of a possible world—are essential to that world.
Def D14.3 Content of Worlds. The content of a possible world is the class of propositions that would be true if that world were actual.
Essentiality of World-Content. The content of each possible world is essential to it.
However, possible worlds have intrinsic properties of only two kinds. First, there are properties determined by a world's content, and second, there is (possibly) the primitive property of actuality. Hence, Concretists must deny that which world is actual is determined by the intrinsic properties of that world. Thus, the actuality of the actual world must consist in its extrinsic relation to something. The only plausible “somethings” that might be relevant are us. Hence, Concretists must embrace Modal Indexicalism.
14.3 Problems for Concretism
So far, we have canvassed the nature of Concretism and described the ways that it carries out its reduction of possibility and actuality. It is time to turn to problems for the view. (Another problem, having to do with the way Concretism handles de re modality, is explored in Chapter 16.)
1. The problem of irrelevance. Concretism seems to give an obviously incorrect account of the truth of modal claims (Plantinga 1974: 116; van Inwagen 2001: 222, 226). Whether there are parallel universes is relevant to what is actually the case, not to what is possibly or necessarily the case. Any universes running in parallel to ours are just as much part of actual reality as our own universe is. The distinction between local and remote universes has nothing to do with the distinction between actual and non-actual possibilities. Appealing to facts about parallel universes to ground modal truths is like appealing to facts about a thing's shape in order to ground truths about its color.
Concretists would insist that what goes on in parallel universes has everything to do with what is possibly and necessarily the case. What it is for a proposition to be possibly true is for there to be a world according to which that proposition is true. And what it is for a proposition to be necessarily true is for it be true according to every world. And Concretism's parallel universes just are possible worlds. What possible worlds are like has everything to do with modality, and so what Concretism's universes are like has everything to do with modality as well. Importantly, though, Concretists would also claim that here in the actual world, these proposition really do have the property of being possibly or necessarily true.
This dispute raises an important methodological point. Concretists defend their theory on the grounds of its simplicity, theoretical power, and consistency with linguistic data. The modal sentences that we believe to be true can be supplied simple, straightforward truthmakers by Concretists, in the form of concrete universes of the right kind. However, their opponents will point out that there is one important bit of data that contradicts Concretism, namely, our naive, intuitive sense that the sort of truthmakers supplied by Concretists are of the wrong sort. Facts in other universes just couldn't make our ordinary assertions about possibility true, given our understanding of what those assertions mean.
Concretists could reply in one of two ways. First, they could simply dispute the supposed semantic data. They could claim that, for all we could know as competent speakers of English, these assertions of possibility might be made true by facts about isolated, concrete universes. Alternatively, they might concede that their opponents have access to some genuinely recalcitrant data, while insisting that the other virtues of Concretism are so great that we should dismiss these wayward intuitions as mistaken. If our semantic intuitions are fallible, then they may fall as “spoils to the victor”.
2. The problem of ethical fatalism. There are a variety of ethical absurdities that seem to follow from Concretism. In particular, Concretism seems to entail a kind of moral fatalism. Every possible choice is made by someone in some world. For example, if THP actually chooses to wear a green shirt rather than an orange shirt, then in some other world THP (or someone very like him, one of his counterparts, see below) chooses an orange shirt rather than a green one. The same goes for our moral choices. For every bad choice made by someone in our world, the corresponding good choice is made by someone like us in another world, and vice versa. Further, nothing any of us can do can possibly change the total quantity of happiness and unhappiness in reality, since that is inexorably fixed by the collection of possible worlds. At most, we can affect the amount of happiness contained by the actual world, that is, by o
ur own local world (see Adams 1974: 215–216).
Bizarrely, if there are no duplicate possible worlds (if each possible world is qualitatively and internally unique in some way), then acts of masochism and self-denial would be morally heroic. By harming myself, I am sparing one of my counterparts that same harm, by making the harm happen in my world instead of his (see Pruss 2011: 105–106 for this and other ethical absurdities).
Concretists reply that ethics must be agent-centered. We have no obligation to reduce the total amount of evil and suffering and increase the amount of good and pleasure in existence overall. We only have an obligation to reduce the total amount of evil and suffering and increase the amount of good and pleasure near us, in our own possible world.
3. The problem of scientific induction. David Lewis (1986a) couples Concretism to Neo-Humeism (4.4T). Given that the main argument for Concretism is its theoretical usefulness for supplying reductive accounts of various notions (see above), it is no surprise that Lewis would hope to reduce facts about conditionals, laws, and powers in a Neo-Humeist way, exploiting the resources of Concretism. But as we discussed in Chapter 5, if Neo-Humeism is true, then there are far more worlds (by any reasonable measure of ‘more’) that agree with all of our past observations but which fail to obey any simple generalizations and laws hereafter (and anywhere beyond our actual, past observations). We would seem then to have no reason for believing that the actual world is one of the few regular, well-behaved worlds, and so any confidence in scientific induction would be unwarranted.
As we saw, Neo-Humeists must respond by asserting that a preference for simplicity and inductive uniformity is simply a primitive, underivable postulate of reason, unaffected by considerations of what is true in the majority of worlds empirically similar to ours. We have already discussed the main objection to this reply, namely, that this additional postulate of reason is ad hoc, and so counts against the simplicity of the Concretists' account.
The Atlas of Reality Page 53
