The Atlas of Reality

by Robert C. Koons,Timothy Pickavance

  Worlds, then, according to Pictorial Abstractionism, represent by being “built up” out of parts which have certain features and which are arranged in a certain way, where those parts and their features and arrangements match the features and arrangements of the things represented. That is how worlds represent according to Pictorial Abstractionism:

  15.1T.1A.2 Pictorial Abstractionism. Structural Abstractionism is true, and worlds represent in the way pictures do, namely, by having components that literally share features with what they represent.

  15.2.2.1 The problem of representational detail.

  The problem of alien possibilities plagues Pictorial Abstractionism no less than Linguistic Abstractionism, and for the same reasons. Pictorial Abstractionists build up propositions, in a picture-like way, from actually existing items. That these items are combined in a picture-like way, rather than a language-like way, is inessential to developing the problem of alien possibilities.

  But there is a further problem for Pictorial Abstractinoism: the problem of representational detail. The problem is that, in order for the Pictorial Abstractionists to have their pictures represent every feature of a world in maximal detail, worlds must turn out to just be Concretist worlds. Recall the picture of Tim, Jamie, Lyle, and Gretchen, and the impish-smile part in the head part of the Gretchen-part of the picture, which represents Gretchen's impish smile. What is it for a picture to have an impish-smile part? In the case of representing the color of a thing, it's not hard to see how the relevant part of two-dimensional picture can literally just have the property it represents. Likewise with relations among the sizes of things. A picture can represent that Jamie is twice the height of Lyle by having the Jamie-part be twice the size of the Lyle-part. But it's odd to think of a part of a picture as literally just impish. It is, anyway, unless we're talking about four-dimensional pictures or models that involve mental properties as well. Pictorial Abstractionists must therefore think of their worlds as four-dimensional, in some sense. And this will be required more generally, though, to represent temporal relations. And now we're getting ourselves into trouble. Worlds, on this view, are four-dimensional objects literally exemplifying all of the properties of the objects they represent. How could these worlds be abstract? They are colored, shaped, spatially and temporally extended objects. That's just a Concretist world!

  Pictorial Abstractionists might respond by trying to identify a feature that Concretist worlds have that their worlds don't, or vice versa. The feature is going to have to simply be the property of being abstract, but it's not clear what content we can give to that property at this point. Abstract things like numbers and sets aren't colored or shaped in any meaningful sense. Only concrete things like people and rocks have those sorts of properties! Once we give worlds all of the representational detail they need, they morph into Concretist worlds. We think this is a serious, potentially lethal worry for Pictorial Abstractionism.

  15.3 Aristotelian Theories of Possibility

  If we reject the theories we've encountered to this point, what are we left with? There is one other reductive account to consider, an account which grounds possibility in the actual possession of causal powers. Alexander Pruss (2002, 2011) has recently defended such a view, Aristotelian Modality. The basic idea is that a proposition is possible if there is some actually existing thing that has the power to bring about the truth of that proposition. More precisely:

  15.2T.7 Aristotelian Modality.

  It (tenselessly) is possible for p to be the case if and only if there is, was or will be a time at which it is, was or will be possible for p to be the case;

  it is now simply possible for something to exist or to fail to exist if and only if something now has the power to cause or to prevent its coming into existence;

  it is now simply possible for some things to stand in some natural relation if and only if something now has the power to make those things to stand in that relation;

  it is now possible for p to be the case iff either it is now simply possible for p to be the case or it is simply possible for it to be simply possible for p to be the case or it is simply possible that it is simply possible that it is simply possible that p, and so on.

  On the Aristotelian account, the fundamental modal notion is that of being possible at a time. Tenseless possibility is derivative. Thus, what is possible changes as time passes. In fact, fewer things are possible over time, as the opportunities for things to exercise their powers pass. If we want Aristotelian Modality to line up with the standard practice in contemporary modal logic, according to which everything that is or was actually the case is possible, then we will have to modify clause (i) of Aristotelian Modality to include present and past actuality as cases of tenseless possibility:

  (i) It (tenselessly) is possible for p to be the case if and only if there is, was or will be a time at which it is, was or will be possible for p to be the case, or it is now or once was the case that p.

  Possibility for the Aristotelian is an iterative or recursive concept, as clause (iv) of Aristotelian Modality makes clear. That is, we define first a base case of possibility, simple possibility, and then permit something to be possible simpliciter if it can be reached by repeated applications of clause (iv). This is a standard way of defining operations in mathematics (for example, addition and multiplication can be defined this way).

  One way for something to be possible is for actual things to have the power to make it so. Another way would be for actual things to have the power to give something the power to make it so. A still further way would be for actual things to have the power to give something the power to give something the power to make it so, and so on. Ultimately, all possibilities are grounded in the actual powers of actual things at some point in history. Aristotelian Modality, therefore, validates the Branch principle that Shoemaker used to defend Causal Structuralism (a variety of Strong Powerism 4.4A.3):

  Branch. For every possible world w, there is a time t such that w and the actual world are exactly alike up until time t.

  Since the notion of power is central to Aristotelian Modality, we get sub-varieties of the view depending on one's metaphysical account of powers. It is possible to combine Aristotelian Modality with Strong Nomism (4.4A.2), Strong Powerism, and Neo-Humeism (4.4T). You can't be an Aristotelian and a Strong Hypotheticalist (4.4A.1), since Strong Hypotheticalism entails that possibility is a fundamental notion. Strong Hypotheticalists are committed to fundamental modal truths, since conditionals are modal. The most natural combination would be to join an Aristotelian Modality with Strong Powerism, especially with a Dual-Aspect Theory (Section 6.2.2). This would seem to have been Aristotle's own position. It is natural because there is a connection between conditionals and laws, and modality more generally. Strong Powerism reduces conditionals and laws to powers, and Aristotelian Modality reduces modality to powers. The two views, therefore, couple nicely. Further, by combining the two, one makes gains in the realm of simplicity (PMeth 1), especially with respect to qualitative economy (PMeth 1.4.1), since one can use the fundamental notion of a power to account for conditionals, laws, and modality.

  ARISTOTELIAN POSSIBILITY AND NEO-HUMEISM We should consider, however, the option of combining Aristotelian Modality with Neo-Humeism. Neo-Humeists, unlike Hume himself, believe in causal powers; they just believe that truths about causal powers are grounded in more fundamental truths about the patterns and regularities in the spatiotemporal distribution of qualities. There is one serious point of tension between Neo-Humeism and Aristotelian Modality, a point that concerns the Branch principle. Suppose the past is finite, with a very first moment of time. Then the Branch principle entails that all modality is ultimately grounded in the powers of the things that existed in the first moment of time. However, there were, as yet, no interesting diachronic patterns of qualities in place at that first instant. The simplest scientific account of the world at that moment would have included no dynamic laws at all. Consequently, Neo-Humeists must
deny that anything had any power in the first instant, which means that no possible world could branch off from the actual world then. It would only be after enough time has passed to bring about scientifically relevant regularities that anything could be said to have any power.

  This result is quite bizarre. If we take the finitude of the past to be a real possibility, then Neo-Humeists must confront the small worlds objection that we considered (Section 5.2.2). At the very beginning of history, the universe would have been exactly the sort of small world that puts such pressure on Neo-Humeism. It seems that there should be a fact of the matter about what would or would not have been possible from the very beginning, but Neo-Humeists can give no account of this.

  Neo-Humeists could respond by embracing Eternalism (to be discussed in Chapters 20 and 21 as 20.2A.1T), according to which all of the world's future history exists (tenselessly) at all times, including the very beginning. However, this would mean that bodies existing at the beginning of time would have different and contrary sets of powers, depending on which future history we take as actual. In addition, trying to combine Neo-Humeism, Eternalism, and Aristotelian Modality would lead to a kind of vicious circularity: what is possible in the future could not be grounded without first determining what happens in the future, but what happens in the future must be at least possible from the point of view of the past.

  15.4 Conclusion

  In this chapter, we have canvassed a number of Abstractionist views of modality. As we have seen, there are plausible Abstractionist reductions of actuality, but Abstractionist entails that there are fundamental truths about possibility and necessity. Different Abstractionist views are usefully categorized on the basis of whether and how possible worlds represent. But each type of Abstractionism faces serious hurdles. In the next chapter, we turn to questions of de re modality, which concerns what is possible and necessary for objects.

  Note

  1. Even if we thought, for reasons considered in Section 12.2.2, that there could be more than one actual world (due to ontological vagueness), there would have to be some severe limits on how varied the actual worlds could be, and this would again have to be a brute necessity for Simple Anti-Indexicalism.

  16

  De Re Modality and Modal Knowledge

  16.1 Modality De Re: Transworld Identity and Counterpart Theory

  To this point, we have focused mainly on how possible worlds relate to the truth and falsity of modal claims (or propositions), and therefore to whether claims are necessarily true, necessarily false, possibly true, possibly false, and so on. This issue is that of modality de dicto, modality concerning propositions. But there is another type of modality, one toward which we gestured above, namely modality de re. This has to do with the modal status of relations between things and their properties, with whether things possess properties necessarily, contingently or not even possibly. Consider the following:

  (1) If there is a largest solar planet, then, necessarily, it revolves around the sun.

  Read in one way, this sentence expresses a truth. On this reading, (1) expresses the idea that the proposition expressed by the sentence, ‘If there is a largest solar planet, then whatever is the largest solar planet revolves around the sun’, is necessarily true. This seems to be the case, since it is part of the definition of ‘solar planet’ that any solar planet revolves around the sun. If a possible world contains no largest planet, then this proposition is vacuously true, and if it does contain a largest solar planet, then that planet must (in that world) revolve around the sun. Hence, the proposition cannot be false, and so (1) is true. This is the de dicto reading of (1), on which (1) attributes necessity to something that is said (‘dicto’ in Latin).

  However, there is another way of reading (1), on which (1) says about the thing that is in fact the largest planet, namely, Jupiter, that it necessarily revolves around the sun. This is the de re (‘about a thing’) reading, a reading which attributes the necessary possession of a property (that of revolving around the sun) to a thing (Jupiter). Read this way, (1) is false. If the sun were to have a close encounter with another star, Jupiter could be flung out of our solar system. Or, we could build a big enough rocket to shoot Jupiter into deep space. There's nothing about Jupiter the thing that necessitates its revolving around the sun.

  Quine (1953/1980) argued that attributions of de re necessity are just nonsensical. According to Quine, the only sort of necessity is de dicto. For example, suppose that every brilliant mathematician in Austin is also an Olympic cyclist and vice versa. It is necessarily the case that every Olympic cyclist in Austin has two legs (let's assume that the kind of cycling involved in the Olympics requires the use of two legs), but it is not necessarily the case that every Olympic cyclist in Austin can prove theorems, even though the very same things belong to the two classes.

  However, many contemporary metaphysicians, and most metaphysicians of the past, would disagree with Quine. There seem to be some properties that are necessarily possessed by certain things, independently of how they are described or designated. For example, Jupiter has the property of being identical to Jupiter, and it seems that it has that property in any possible world, no matter how it is described or what other properties it has or doesn't have. Some philosophers, such as Saul Kripke, have argued that the origin of a thing is an essential property of that thing, where an essential property of a thing is a property whose possession by it is a de re necessity. If RCK's actual parents are Bruce and Margaret, it seems plausible to think that he would have Bruce and Margaret as his parents in any possible world. Anything in any world with different parents wouldn't be RCK himself. For similar reasons, it seems plausible to think that it is de re necessary that if THP exists, then THP is human. Nothing could have been THP without belonging to his actual species. The question thus arises as to how it is that worlds represent things as having properties, since that question will be connected to questions about the essences of things.

  The question that has dominated discussions of modality de re in recent philosophical work is whether one and the same object can exist in many possible worlds. Those who think that objects can exist in many possible worlds believe in Transworld Identity. Those who deny Transworld Identity believe in Worldbound Individuals, which is the idea that everything is worldbound, existing in only one possible world.

  16.1T Transworld Identity. Some things exist in more than one possible world.

  16.1A Worldbound Individuals. Each possible individual exists, as a matter of necessity, in one and only one possible world.

  The most common version of Worldbound Individuals is Counterpart Theory (16.1A.1), which says that although individuals are worldbound, they nonetheless have counterparts in other worlds that represent them in those alternative possibilities. We discuss this view in Section 16.1.2 below. At any rate, there are disputes even about what it is for a single object to exist in more than one possible world. The differences to do with de re modality are driven in large measure by differences about the nature of possible worlds more generally, which drive differences about what it is for something to be in a world, or alternatively, differences in what it is for a world to involve some thing. In particular, Abstractionists tend to go for Transworld Identity, while Concretists tend to go forCounterpart Theory. We examine these views in turn, and display how a commitment to Abstractionism naturally drives one toward Transworld Identity, while a commitment to Concretism naturally drives one toward Counterpart Theory.

  16.1.1 From Abstractionism to Transworld Identity

  Abstractionism naturally drives one toward Transworld Identity. To see that this is so, let's consider a natural Abstractionist characterization of modality de re. Consider the claim that Lyle is essentially human. This claim is true if and only if Lyle has the property of being essentially human. Being a modal claim, there is a connection between its truth and facts about possible worlds, even if the connection is not a reductive one. So, despite being anti-reductionist about modali
ty, Abstractionists can agree that Lyle has the property of being essentially human if and only if every possible world that represents Lyle at all represents him as having the property of being human. But what is it for a possible world to represent Lyle as being a certain way? We considered three Abstractionist views of representation above, but there is something that they have in common in this area: almost every Abstractionist view agrees that, however Lyle gets represented, a world does not represent him by having him as a part.1 Lyle is a part of no possible world (not even the actual one), in a strict sense. The only sense in which Lyle is part of a world is that he is represented by it. Lyle is literally part of the actual world if Concretism is true, but he is not literally a part of any world if Abstractionism is true. He is simply represented. The actual world represents him as he is; the others as he could have been.

  There are differences, though, in how the Abstractionist views represent Lyle as being some way or other. If Magical Abstractionism is true, we can't say anything meaningful at all about how this happens. However, it will be the case that the worlds that represent Lyle have certain representational features in common. For example, every world that represents Lyle have the property of representing Lyle. (Uninformative, but that's to be expected!) Consider (2) and (3):

  (2) Elsie is necessarily a dog.

  (3) Joe Biden might have been a plumber.

  Linguistic Abstractionists will say that (2) comes out true if and only if every world containing a “name” for Elsie contains a “sentence” which contains a “name” for Elsie “grammatically” associated in the right way with a “predicate” designating the property of being a dog. Similarly, (3) is true if and only if there is a world containing a sentence containing a name of Joe Biden grammatically associated in the right way with a predicate designating the property of being a plumber. Worlds represent Lyle by having a “name” of him as a constituent. Maybe, for example, a world represents Lyle, Elsie, and Joe Biden by having their respective haecceities as parts. If Pictorial Abstractionism is true, then (2) is true if and only if every world-picture has no part that is both an Elsie-part and a non-dog-part, and (3) is true if and only of some world-picture has a part that is both a Joe-Biden-part and a plumber-part. Worlds represent Lyle by having a highly detailed, four-dimensional, abstract simulacrum of Lyle as a part.