Actuality, Possibility, and Worlds

Alexander R. Pruss

• Publisher: Continuum
• Year: 2011
• ISBN:
  9781441142719
• Edition: 1
• Topic: Theology & Religion
• Subtopic: Philosophy of Religion

Actuality, Possibility and Worlds is an exploration of the Aristotelian account that sees possibilities as grounded in causal powers. On his way to that account, Pruss surveys a number of historical approaches and argues that logicist approaches to possibility are implausible. The notion of possible worlds appears to be useful for many purposes, such as the analysis of counterfactuals or elucidating the nature of propositions and properties. This usefulness of possible worlds makes for a second general question: Are there any possible worlds and, if so, what are they? Are they concrete universes as David Lewis thinks, Platonic abstracta as per Robert M. Adams and Alvin Plantinga, or maybe linguistic or mathematical constructs such as Heller thinks? Or is perhaps Leibniz right in thinking that possibilia are not on par with actualities and that abstracta can only exist in a mind, so that possible worlds are ideas in the mind of God?

Part I

Introduction

Section 1 Generic definitions and basic modal realism

Modal assertions involving possibility and necessity are not only a part of our ordinary languages, but also a part of our philosophical patrimony. There are many things we could not say if we confined ourselves to non-modal language. We could not mark the difference between a unicorn,¹ which could exist, and a square circle, which could not. Modality is a natural way of marking the difference between, on the one hand, the relation of Smith being a bachelor to Smith being unmarried, and, on the other hand, the relation of Smith being 50 feet tall to Smith not being a mammal. Someone could not fail to be unmarried if he is a bachelor, but he could be a mammal even if he were 50 feet tall — though in fact no mammal is that tall.

It is important for ethical purposes to say what could have been done but was left undone, and what would have happened had it been done. It is plausible that a human being can only be held responsible for an act if it was at least logically possible that he avoid it. When we say that moral worth supervenes on actions and non-moral circumstances, we are saying that it could not be the case that someone’s moral worth was different though his actions and the non-moral circumstances were the same.

When we discuss the problem of evil, we sometimes wonder whether it is possible for God and evil to co-exist, a different problem from the de facto question of whether the evils of this world make the existence of God probable or not.

When we talk of natural objects, we often cannot specify the kind that the object falls into without talking of dispositional properties. Something might in fact live all its life just like a horse, but if it is true that were it poked in the underbelly, where in fact it never was poked, it would suddenly and naturally sprout wings and fly away, then it is not a horse.

Our expressive capabilities would be greatly impoverished without “can be,” “might be,” “must be,” “is possible,” “is necessary,” “would be,” and their ilk. We need these terms to talk of the reality around us. Yet, paradoxically, talk involving possibility often does not appear to be about anything real. The unicorn that is possible does not exist, I have not done otherwise than I have, and the actions and non-moral circumstances are only as they are.

A popular and vivid way to organize one’s modal notions is to think of a “possible world,” a way (with “way” understood so broadly as not to prejudice the ontological question of what possible worlds are) that a cosmos could have been. Different possible worlds are different ways that our world could have been.

The main alternative to thinking of modality in this global sense is thinking of it in a local sense, of thinking of alternative ways that portions of this world could have been. It does appear that such piecemeal modality is what ordinary language users are often interested in. When we say that Hitler might never have been born, we do not seem to mean that there is some possible world in which he doesn’t exist — e.g. a world at which the universe has always had an unchanging constant energy density. We mean that that portion of this world which consist of the birth of Hitler might not have been, even though much of the rest of the world, especially at least the distant past prior to Hitler’s birth, was almost the same, and the laws of nature were those that we have. However, what exactly is to be kept fixed in this “might never have been born” claim depends on the context. Thus, while apparently speaking only of portions of worlds, the context determines what whole worlds we are speaking of, namely what portions of the actual world are supposed to be imagined as remaining in that possible scenario in which Hitler had never been born. Hence, to disambiguate our ordinary piecemeal talk of possibility, we bring in whole possible worlds.

The need to talk of whole worlds is shown particularly clearly when we make counterfactual utterances. For we can ask questions like: “How might or would have the course of history gone had Hitler never been born?” And on a plausible account of how to think about such questions, we should think of whole worlds in which Hitler was not born, and to say what holds in such worlds. Given what our context fixes, namely most events prior to Hitler’s birth and the laws of nature, we can easily say certain things about what happens in those worlds at present (in our reference frame). For instance, the course of events in other galaxies up to the present would be the same as in the actual world whether the awful events of the twentieth century occurred on earth or not, if only because the information about these events, traveling at the speed of light, has not yet arrived there. But the arrangement of matter would be slightly to significantly different within 120 light-years of earth. On earth, the arrangement of matter would be significantly different, while on Pluto there would only be minor differences, for instance due to the tiny variations in gravitational force (even an infant Hitler exerts a gravitational force, and the tanks of the Third Reich exert a greater one, so that had Hitler not been born, Pluto would have been slightly differently located). Our comfort in saying in the same breath that events in other galaxies would have been the same, but events on earth here would have been different, does indicate that it is appropriate to analyze counterfactual situations holistically.

Moreover, what is possible in a portion of the world may well depend on global features of the world, such as laws of nature. It is impossible for there to be a world with exceptionless laws of nature like ours but where things do not fall when dropped under appropriate conditions; however, apart from such laws, it is certainly possible. And it is arguably impossible that there be unjustified evil, i.e. evil the permitting of which serves no moral purpose in any portion of the universe if there is an all-powerful, all-knowing and all-good being anywhere in space (if this is possible for such a being) or outside of space. Moreover, in worlds where there is such a deity, what evils can exist in a portion of the world may well depend on what happens elsewhere in the world, since the justification of some evil in one portion of the world can depend on events elsewhere. Our ordinary modal claims need to be contextually disambiguated, and when thus disambiguated are seen to involve whole possible worlds. Because of all this, possibility and necessity prima facie require reference to be made to whole possible worlds, and so one should try to make sense of possible worlds.

Given a basic notion of possible worlds, whatever their ontology, we need some correlative notions. By “the (or our) cosmos” I shall mean the aggregate of all actually existing things. If one is fine with arbitrary mereological sums, one can take that aggregate to be a mereological sum. By “the (or our) universe” I shall mean the aggregate of all actually existing spatio-temporal things. If one is worried about the existence of this mereological sum, one should be able to paraphrase talk of the cosmos, universe, and other aggregates, into plurally quantified talk.

Each world corresponds to or represents a way the cosmos could have been. In what way this representation works is one of the central questions for our investigation. One of the worlds shall be distinguished as “the actual world,” i.e. the world that represents the way our cosmos in fact, or actually, is. An individual “exists in” a world w if, were that world actual, that individual would exist, or, equivalently, if w represents the cosmos as containing that individual. A proposition is “true at” a world w if, were that world actual, that proposition would be true, or, equivalently, if w represents the cosmos as described by that proposition.

What the notions of “represents,” “actual,” “exists in,” and “true at” really signify will depend on what our ontology of possible worlds is. There are many possible such ontologies. In particular, there is the crazy one, which nonetheless will be conceptually useful at times to keep in mind, that there necessarily is an infinite Platonic library somewhere that contains physical books, each of which gives a maximal consistent description of a cosmos in some fixed language. On this view, a world is one of these books. A world represents a given way of being a cosmos if the book that the world is correctly describes the way that that cosmos would be. A world is actual if everything written in it is true. A proposition is true at a world if it is expressed by some sentence in the book. An individual exists in a world if the world describes the individual as existing.

Other theories will have other renderings of the basic notions. For instance, David Lewis (1986a) thinks that each possible way that the universe could be is a way that some concretely existing universe really is. Moreover, cosmoi and universes are the same for him. Thus, worlds are concrete universes. A world represents some cosmos if it is that cosmos. The actual world is the world we inhabit. A proposition is true at a world if it truly describes a state of affairs obtaining in that world. An individual exists in a world if it inhabits that world.

A Propositional Ersatzist may take a world to be a maximal collection of compossible propositions. The actual world is that particular collection all of whose propositions are true. A world corresponds to a cosmos by having as its members propositions true of that cosmos. A proposition is true at a world if it is a member of it. An individual exists in a world if some proposition in that world says that the individual exists.

Leibniz, on the other hand, thinks that worlds are maximally consistent ideas in the mind of God. The actual world is the idea that God has chosen to actualize. An idea corresponds to a universe by being a mental representation of it. A proposition is true at a world if it is a part of, or maybe represented by, that world. An individual exists in a world if the idea represents him as existing.

We can now give a possible worlds semantics for possibility and necessity claims. It is (metaphysically) possible that p providing there is a world w at which p is true. It is (metaphysically) necessary that p providing p is true at every world. This yields the standard duality between possibility and necessity: p is possible if and only if ∼p is not necessary. Possible worlds now let us consider “local” and “global” modalities in a uniform way. When I say “Hitler might not have existed” in an ordinary way, and not by way of stating a merely metaphysical possibility, I am saying that the proposition, that Hitler does not exist is true at some world that matches ours in various relevant respects. When I say “It is logically possible that unicorns exist,” I may just be making the claim that the proposition that unicorns exist is true at some world, without putting any restriction on which worlds are relevant here.

Some further terms are useful. A proposition is contingent providing it is true at some but not all worlds, i.e. providing that neither the proposition nor its negation is a necessary truth. An individual x is a necessary being if it exists in all worlds. An individual is a contingent being if it exists at some but not all worlds. Occasionally, I shall use □ and ◊ to indicate necessity and possibility, respectively.

But of course all of this raises two basic ontological questions. The first is the grounding problem. What ontological features of reality make the right modal assertion be true? The second is the worlds problem. Possible worlds are very useful, but what are they? This book is devoted to these two problems.

I will begin with a clarification of the kind of modality that we are after: metaphysical modality rather than strictly logical modality. For we are interested in the kind of modality that is objective and independent of the vicissitudes of our language, and as shall be argued, this kind of modality is metaphysical modality. Next, I will sketch several different approaches to the grounding and/or worlds problems. Doing this should help clarify what exactly is at issue in the two problems.

Since the main argument for possible worlds is from their theoretical utility, in Part II we will examine a number of uses that are made of possible worlds. Some applications fail and others succeed. Overall, we will see that there is some reason to accept possible worlds. Starting with Part III, we will examine in detail four proposals for dealing with the grounding problem. Of these proposals, all but the Spinozistic–Tractarian one will offer solutions to the worlds problem. First I examine the two most promising contemporary approaches, the Lewisian approach that claims all possible worlds to exist as concrete, physical universes (Part III) and the various “ersatzist” approaches on which possible worlds are “ersatz” linguistic or Platonic entities rather than concrete universes (Part IV). The Lewisian account will be seen to fail, both because it does not actually provide the reductive analysis of modality it promises and because it gives rise to multiple paradoxes. Of the ersatzist approaches, some, such as the Platonic, will be seen as at least offering a useful account of possible worlds, but ...

Table of contents

• Cover
• Title
• Copyright Page
• Dedication
• Contents
• Preface
• Chapter 1: Introduction
• Chapter 2: Applications and pseudo-applications
• Chapter 3: The Lewisian ontology of extreme modal realism
• Chapter 4: Platonic ersatz ontologies
• Chapter 5: Sketches towards a Spinozistic-Tractarian account of modality
• Chapter 6: Aristotelian-Leibnizian ontology
• Chapter 7: Final conclusions
• Chapter 8: Appendix
• Bibliography and Further Reading