The upshot is that we cannot simply identify necessity with what can be known a priori. There are powerful counterexamples to the claim that everything knowable a priori is necessary and to the claim that everything necessary is knowable a priori.
There is, however, a plausible move that could be made in defense of the necessity-apriority connection. We could distinguish between sentences or statements, on the one hand, and propositions, on the other (as we did in Chapter 2). It is clear that we cannot know a priori that the sentences (9) through (11) are true: that is, we cannot know a priori that they express true propositions. However, it might be that the propositions that these sentences express all have the same logical form, namely, x = x. If so, those propositions can all be known a priori, since they are all instances of a law of logic, namely, the reflexivity of identity.
There is, however, a counter-move that also has some plausibility. We could suppose that each of the sentences necessarily expresses the proposition that it does. For example, it is plausible to suppose that the names ‘Mark Twain’ and ‘Samuel Clemens’ (as used in our actual context) are essentially names of the very person (the famous American author) that they are in fact names of. Now, of course, it is not necessarily true that any name spelled ‘M-a-r-k (space) T-w-a-i-n’ is a name for that same author. That string of letters and spaces could be the name of anyone or anything. I could give my pet rock the name ‘Mark Twain’ if I wanted to. However, we should think twice about identifying names with strings of letters and spaces. A name is a peculiar kind of word, with its own history and use. When we use the string of letters to name both the author and my pet rock, we have introduced two different names, each with the same spelling as the other. Such names are merely homonyms, not strictly identical. With this picture of naming in mind, it now seems plausible that (9), if it and its constituent words and names exist, must be true. It must express a true proposition of the form ‘x = x’, and yet this necessity cannot be known a priori.
This last point is a special case of another claim about necessity made by Saul Kripke (1972), namely, the necessity of origins. It seems plausible to suppose that each concrete thing, whether a person, an artifact or a name, has its origin essentially. It is impossible that this very person, say, Elizabeth II of England, could have existed with entirely different parents, that is, with parents other than George VI and Queen Elizabeth. In particular, Elizabeth II couldn't have been created, Frankenstein-style, in a laboratory from spare parts. However, we do not know Elizabeth II's actual origins a priori. So, here again we find necessities that can only be known a posteriori.
16.2.3 Knowledge of possibility: patchwork principles
We never perceive non-actual possibilities directly. How could we? They aren't actual! How, then, do we know anything about them at all? One plausible route to our knowledge of merely possible worlds is to think of them in terms of rearranging the contents of the actual world. We take things of a kind that have really happened in the actual world and construct a non-actual scenario by arranging them in a novel spatial and temporal order. If we do this according to certain rules, the thought goes, we can be confident that our rearranged scenarios represent real possibilities. Thus, our knowledge of at least some possibilities can be secured.
This process of construction is something like the way we make patchwork quilts: we cut up pieces of fabric from an already-existing cloth, and then we stitch the pieces together in new ways. Because there is something intuitively attractive about supposing that rearrangements of the contents of the actual world represent real possibilities, David Lewis formulated what he called ‘patchwork principles’ (see especially Lewis (1986a)). These principles are Lewis's attempt to codify the rules that govern our rearrangements of actual things to represent possible scenarios. Here are two versions of Lewis's patchwork principles, one involving finitely complex recombinations, and the other extending the principle to the infinite.
PMeta 5.1 Finite Spatiotemporal Patchwork. If it is possible for an event or process of (intrinsic) type A to occur, and if it is possible for an event or process of type B (distinct from A) to occur, and if there is enough room in the history of the world to locate in it instances of both events or processes without overlap in time and space, then it is possible for an event or process of type A to be realized together with an event or process of type B.
PMeta 5.2 Infinite Spatiotemporal Patchwork. If T is a class of types of events or processes, and for each member of T, it is possible for an event or process of type T to occur, and if there is enough room in the spacetime expanse of the world of the world to locate within it instances of each of the types in T without overlap in space and time between the instances, then it is possible for all the types in T to be realized together.
For example, clearly football matches are possible, since some of them are actual. For example, in 2011 Tottenham and Real Madrid clashed in the UEFA Champions League. Let football matches be events of the type FOOTBALL. But it also seems that quidditch matches are possible, though none actually occur. Surely it's at least possible that something occur which is intrinsically exactly like the match between Ireland and Bulgaria which Harry Potter and friends witness at the 1994 Quidditch World Cup (in Harry Potter and Goblet of Fire). Let quidditch matches, or anyway things intrinsically identical to quidditch matches, be events of the type QUIDDITCH. If you think that events of the types FOOTBALL and QUIDDITCH are possible separately, then Finite Spatiotemporal Patchwork demands that one also think that there is a world in which a FOOTBALL event and a QUIDDITCH event both occur, which is just to say that it is possible that there be both a football match and a quidditch match. This is just what we would expect, since it is intuitively plausible to suppose that a single world could contain both types of events. Indeed, if the world were as the Harry Potter series depicts it, we would be in just such a world! Similarly, suppose you think that Light Cycle matches (of Tron fame) are possible, or anyway that events intrinsically like Light Cycle matches are possible. Let's say these matches are of the type LIGHTCYCLE. Finite Spatiotemporal Patchwork then demands that there be a single world in which events of the types FOOTBALL, QUIDDITCH, and LIGHTCYCLE all occur. (Iterations of this recipe for four types, five types, and so on are easy to construct.)
Infinite Spatiotemporal Patchwork simply extends this idea to arbitrarily large classes of types of events or processes. Again, this is intuitively plausible antecedently, and so our patchwork principles are tracking our intuitions about what is possible.
Patchwork principles ensure that there are enough worlds to match the number of possibilities, and also give us some insight into how we are able to know what other possible worlds are like. We know what they are like, in at least some cases, because they are just rearrangements of things like the ones in the actual world. We'll return to a different epistemological question shortly.
16.2.4 Aristotelian/Powerist conceptions of modal knowledge
As we discussed in Chapter 15, Powerists (4.4A.3) and defenders of Aristotelian Modality (15.2T.7) have a more empirical approach to our knowledge of modality. We discover what can happen by investigating the natures or essences of things, where the nature or essence of a thing consists of the most fundamental powers and potentialities of that thing. On this view, modal facts (facts about what is possible) are grounded in facts about the essences of actual things, and not vice versa (Fine 1994a, 1994c). Powers and essences are discovered experimentally, as we described in Section 6.1.2, on the epistemological consequences of Powerism.
Aristotelian Modality provides support for Kripke's thesis of the essentiality of origins. If something X comes into existence, there must have been something Y there beforehand with the power of generating X. Suppose it were possible for X to have had a completely different origin, with a different source or originator. Then there must have been some other possible thing Z, not identical to Y, with the power of generating X. If two distinct things had the power of generating X, then each coul
d have exercised its power independently of whether the other did. Thus, it would have been possible for both Y and Z to generate X in the same world. But then X would have come into existence twice, which is surely impossible. Thus, if X has an origin in time, it is essential to X that it have the source it actually has. For similar reasons, it must be essential to X that its originator's power to create X could only be exercised in unique and unrepeatable circumstances. Thus, the entire origin of X must be essential to it.
16.3 Conclusion
We introduced the distinction between de dicto and de re necessity, and then we explored different ways of making sense of de re necessity—necessities involving particular individuals. For Concretists, de re possibilities for one thing involve the states of concrete counterparts of that thing in other worlds. Concretists are Counterpart Theorists. For Abstractionists, in contrast, one and the same thing can participate in both actual and merely possible situations. Abstractionists go for Transworld Identity. This gives rise to an especially vivid version of the irrelevance objection to Concretism that we first discussed in Chapter 15, namely, the Humphrey Objection.
We then turned to questions involving our knowledge of the merely possible. Much of that discussion concerned the issue of the relationship between possibility and conceivability. Most philosophers accept Imagination as Guide to Possibility (PEpist 1), which suggests that conceivability is a good guide to metaphysical possibility (although perhaps not an infallible one). However, some metaphysicians go farther and identify what is possible with what is conceivable by us, or perhaps with what we are justified (all things considered) in believing to be possible. Saul Kripke has argued that this identification of the possible with the conceivable fails in both directions. Most importantly, there seem to be metaphysical necessities that can only be known a posteriori, and whose contradictories are fully conceivable.
On the positive side, we have not ruled out the use of conceivability as a fallible guide to possibility. In addition, there are plausible patchwork principles that enable us to extend our knowledge from simple scenarios to much larger ones. Finally, if we adopt Aristotelian Modality, there is room for empirical and scientific investigation of the essences of things.
Notes
1. The exception is Lagadonian Linguistic Abstractionism, according to which things serve as their own “names”. It will turn out that this nicety won't matter for what we're about below, and anyway, the contrast here is between how things are parts of Concretist worlds versus how they are represented by Abstractionist worlds. Such a contrast exists even on the Lagadonian Linguistic Abstractionist view.
2. But see McDaniel (2004) for a defense of Overlapping Concrete Worlds.
3. ‘Ludovicus’ is Latin for ‘Lewis’.
4. Sider (2002) develops an explicitly counterpart-theoretic variety of Abstractionism.
5. This terminology has been used in the literature in a few interrelated senses. The differences would not substantively affect the discussion to follow.
6. This is a bit of a simplification. For example, if one thought that bare particulars merely individuate without grounding identity, one cannot use bare particulars to solve the present problem. But one could nonetheless deploy a transworld analogue of, for example, Primitive Identity (9.2T).
7. Here is the proof that they are equivalent (using parentheses to mark scope). (If q is negative epistemic conceivable, then q is possible) entails (if not-(q is possible), then not-(q is negative epistemic conceivable)), by contraposition. Distributing the negations in the antecedent and consequent, and using Def D16.6.1, it follows that (if q is impossible, then NOT(we cannot know a priori that q is false)). Distributing the negation in the consequent and assuming that q is false entails not-q is true, we get (if not-q is necessary, then we can know a priori that not-q is true). This is just the thesis that Necessity Entails A Priori Knowability, where p = not-q.
Part VI
Space and Time
17
Is Space Merely Relational?
In Part VI (Chapters 17–21), we will examine the nature of space and time, the framework that somehow contains all of the world's physical and living things, along with their associated events, actions, and processes. These questions have constituted a large part of metaphysics and the philosophy of nature from the time of the ancient Greeks.
In Chapter 17, we focus on a question that both metaphysicians and theoretical physicists share: is space a thing or world of things in its own right or does it consist merely in relations among bodies or physical events? Substantivalists take space to be composed of places, real entities that exist in themselves, whether occupied or unoccupied. Relationists, in contrast, take the talk of spatial locations to be merely a way of keeping track of the spatial relations among physical things.
In Section 17.1, we give an overview of the various theories that we will consider here. There are three Substantivalist theories, namely, the Theory of Spatial Qualities, Spatial Monism, and Body-Space Dualism, and two Relationist theories, namely, Aristotelian Relationism and Modern Relationism. We examine the three Substantivalist theories in Section 17.2 and the two Relationist theories in Section 17.3. In the final section, Section 17.4, we turn to a serious metaphysical problem for all of the theories of space, that of accounting adequately for vacuums, holes, and other forms of absence.
17.1 The Nature of Location
It should be uncontroversial that at least some things are located in space and that different things occupy different locations. Further, as we discussed in connection with Solipsism in Chapter 13, we seem to perceive things in space and to remember thingsas located in space. These perceptual seemings have a right to be taken seriously, in the absence of strong arguments to the contrary.
But what does it mean for something to be located somewhere? Are places things and location a relation between a place and something else? If places are things, what kinds of things are they? For example, are places individuals or a kind of property? We first must choose between Spatial Substantivalism and Spatial Relationism:
17.1T Spatial Substantivalism. Places exist and are G-fundamental.
17.1A Spatial Relationism. Places are not G-fundamental.
The concept of G-fundamentality was introduced in Chapter 3 (D3.5): an entity is G-fundamental if and only if its existence is ungrounded. We also introduced there the narrower category of O-fundamentality: an entity is O-fundamental if and only if its essence does not involve any other entity. We will focus exclusively here on the broader issue of G-fundamentality. When we use the term ‘fundamental’ throughout this chapter, we will always mean ‘G-fundamental’.
One might think, given the more or less uncontroversial points about things having location, that Spatial Substantivalism will win the day. However, Substantivalism involves more than the mere reality of space and locations. It involves the existence of places. Substantivalists reify space itself, as a thing in which other things are located. According to Substantivalists, places really exist, and things are located by being in a place. In contrast, Spatial Relationists deny that places really exist. There are located things, but being located is not a matter of being in some place. Rather, having location is simply a matter of bearing various other relations, like contiguity, distance, direction, to other things.1 Spatial Relationists favor the conceptual grounding of truths about locations in terms of the facts about spatial relations, leaving no room for real, much less fundamentally real, places.
One terminological complication: ‘Substantivalism’ is the traditional name for the view expressed in 17.1T, but this thesis does not assert that places or parts of space are substances in the sense discussed in Chapter 9. In particular, Substantivalism does not by itself entail that spatial locations persist through time. Substantivalists could suppose that every location exists for only a moment.
Spatial Substantivalism comes in two forms, depending on whether places are properties or not. Assuming that places are properties amounts
to the Theory of Spatial Qualities; the alternative version of Substantivalism is Spatial Particularism. Spatial Particularism in turn comes in two forms, Body-Space Dualism and Spatial Monism. According to Body-Space Dualism, both places and located bodies are fundamental particular things. Spatial Monists maintain that only places are fundamental particulars. For Spatial Monists, “bodies” are simply places that have a peculiar kind of body-ish or en-mattered quality.
Spatial Relationists also come in two forms, Aristotelian and Modern. Modern Relationists believe that the fundamental spatial relation is the distance between dimensionless point-masses, while Aristotelian Relationists take the fundamental spatial properties to be volume and shape, and the only fundamental spatial relation to be contiguity (or contact).
We consider these views in turn.
17.2 Spatial Substantivalism
Consider Spatial Substantivalism. The first question that arises for Substantivalists concerns the nature of places themselves. There are two plausible answers to this question:
17.1T.1T Theory of Spatial Qualities. Places are fundamental properties or qualities, and location is predication: a place is predicated of the things located there.
The Atlas of Reality Page 60
