We generalize ordinary register machines on natural numbers to machines whose registers contain arbitrary ordinals. Ordinal register machines are able to compute a recursive bounded truth predicate on the ordinals. The class of sets of ordinals which can be read off the truth predicate satisfies a natural theory SO. SO is the theory of the sets of ordinals in a model of the Zermelo-Fraenkel axioms ZFC. This allows the following characterization of computable sets: a set of ordinals is ordinal register (...) computable if and only if it is an element of Gödel’s constructible universe L. (shrink)

Our world is a world of change. Children are born and grow into adults. Material possessions rust and decay with age and ultimately perish. Yet scepticism about change is as old as philosophy itself. Heraclitus, for example, argued that nothing could survive the replacement of parts, so that it is impossible to step into the same river twice. Zeno argued that motion is paradoxical, so that nothing can alter its location. Parmenides and his followers went even further, arguing that the (...) very concept of qualitative change is inconsistent. Change in any respect is impossible, they argued, as change requires difference and nothing differs from itself. Few today would accept the Eleatic conclusion that change is impossible. But the topic of change continues to be a source of much debate, as it brings together various issues that are central to metaphysics, language, and logic – including identity, persistence, time, tense, and temporal logic. Author Recommends Wasserman, Ryan. 'The Problem of Change.' Philosophy Compass 1 (2006): 1–10. This article presents the problem of change and provides a brief survey of potential solutions. Haslanger, Sally. 'Persistence Through Time.' The Oxford Handbook of Metaphysics . Eds. M. Loux and D. Zimmerman. Oxford: Oxford University Press, 2003. This article presents the problem of change and provides a detailed survey of potential solutions. Heller, Mark. 'Things Change.' Philosophy and Phenomenological Research 52 (1992): 695–704. This article presents, explains, and defends the temporal parts solution to the problem of change. Hinchliff, Mark. 'The Puzzle of Change.' Philosophical Perspectives 10 (1996): 119–36. This article presents, explains, and defends the presentist solution to the problem of change. Wasserman, Ryan. 'The Argument from Temporary Intrinsics.' Australasian Journal of Philosophy 81 (2003): 413–19. This article presents, explains, and defends the relationist solution to the problem of change. Sider, Theodore. Four-Dimensionalism . Oxford: Oxford University Press, 2001. This book provides an introduction to various issues related to the problem of change, including the nature of time, tense, and persistence. Chapter 5 presents, explains, and defends the stage-view solution to the problem of change. Online Materials Change. URL: http://plato.stanford.edu/entries/change/ The Stanford Encyclopedia of Philosophy entry on change, by Chris Mortensen. Time. URL: http://plato.stanford.edu/entries/time/ The Stanford Encyclopedia of Philosophy entry on time, by Ned Markosian. Temporal Parts. URL: http://plato.stanford.edu/entries/temporal-parts/ The Stanford Encyclopedia of Philosophy entry on temporal parts, by Katherine Hawley. Material Constitution. URL: http://plato.stanford.edu/entries/material-constitution/ The Stanford Encyclopedia of Philosophy entry on material constitution, by Ryan Wasserman. Persistence Bibliography. URL: http://tedsider.org/teaching/pp_bibliography.pdf A bibliography on change and related issues, by Theodore Sider. Sample Syllabus Books on Syllabus Rea, Michael. Material Constitution: A Reader . Lanham: Rowman & Littlefield, 1997. Sider, Theodore. Four-Dimensionalism . Oxford: Oxford University Press, 2001. van Inwagen, P. and Zimmerman, D. 2008. Metaphysics: The Big Questions . 2nd ed. Oxford: Blackwell, 2008. Week 1: Time and Tense Four-Dimensionalism , chapters 1 and 2. Markosian, Ned. 'A Defence of Presentism.' Oxford Studies in Metaphysics, Volume 1. Ed. D. Zimmerman. Oxford: Oxford University Press, 2004: 47–82. In van Inwagen, P. and Zimmerman, D. Metaphysics: The Big Questions. 2nd ed. Oxford: Blackwell, 2008: 116-123. In van Inwagen, P. and Zimmerman, D. Metaphysics: The Big Questions. 2nd ed. Oxford: Blackwell, 2008: 124-129. Week 2: Time and Persistence Four-Dimensionalism , chapter 3. McGrath, Matthew. 'Temporal Parts.' Philosophy Compass 2 (2007): 730–48. In van Inwagen, P. and Zimmerman, D. Metaphysics: The Big Questions. 2nd ed. Oxford: Blackwell, 2008: 265-267. Hawthorne, J, Scala, M., and Wasserman, R. 'Recombination, Humean Supervenience, and Causal Constraints: An Argument for Temporal Parts?' Oxford Studies in Metaphysics , Volume 1. Ed. D. Zimmerman, Oxford: Oxford University Press, 2004: 301-318. Week 3: Change and Presentism In van Inwagen, P. and Zimmerman, D. Metaphysics: The Big Questions. 2nd ed. Oxford: Blackwell, 2008: 141-149. In van Inwagen, P. and Zimmerman, D. Metaphysics: The Big Questions. 2nd ed. Oxford: Blackwell, 2008: 267-269. In van Inwagen, P. and Zimmerman, D. Metaphysics: The Big Questions. 2nd ed. Oxford: Blackwell, 2008: 269-281. Week 4: Change and Temporal Parts Four-Dimensionalism , pp. 92–8. Heller, Mark. 'Things Change.' Philosophy and Phenomenological Research 52 (1992): 695–704. Lombard, Lawrence. 'The Doctrine of Temporal Parts and the "No Change" Objection.' Philosophy and Phenomenological Research 54 (1994): 365–72. Week 5: Change, Relationism, and Adverbialism Hawley, Katherine. 'Why Temporary Properties are not Relations between Physical Objects and Times.' Proceedings of the Aristotelian Society 98 (1998): 211–16. Wasserman, Ryan. 'The Argument from Temporary Intrinsics.' Australasian Journal of Philosophy 81 (2003): 413–19. Lewis, David. 'Tensing the Copula.' Mind 111 (2002): 1–13. Caplan, Ben. 'Why so Tense about the Copula?' Mind 114 (2007): 703–8. Week 6: Change and Tropes Ehring, Douglas. 'Lewis, Temporary Intrinsics and Momentary Tropes.' Analysis 57 (1997): 254–8. MacBride, Fraser. 'Four New Ways to Change Your Shape.' Australasian Journal of Philosophy 79 (2001): 81–9. Simons, Peter. 'On Being Spread Out in Time: Temporal Parts and the Problem of Change.' Existence and Explanation . Eds. W. Spohn, B.C. van Fraassen, and B. Skyrms. Dordrecht: Kluwer, 1991: 131-147. Weeks 7 and 8: Special Topic – Material Change Four-Dimensionalism , chapter 5. Selections from Material Constitution: A Reader. Week 9: Special Topic – Change of Position In van Inwagen, P. and Zimmerman, D. Metaphysics: The Big Questions. 2nd ed. Oxford: Blackwell, 2008: 186-195. In van Inwagen, P. and Zimmerman, D. Metaphysics: The Big Questions. 2nd ed. Oxford: Blackwell, 2008: 195-215. Week 10: Special topic – Changing the Past In van Inwagen, P. and Zimmerman, D. Metaphysics: The Big Questions. 2nd ed. Oxford: Blackwell, 2008: 224-235. van Iwagen, Peter. 'Changing the Past.' Oxford Studies in Metaphysics , Volume 5 . Ed. D. Zimmerman. Oxford: Oxford University Press, 2009: 1-22. Hudson, H. and Wasserman, R. 'Van Inwagen on Time Travel and Changing the Past.' Oxford Studies in Metaphysics , Volume 5. Ed. D. Zimmerman. Oxford: Oxford University Press, 2009: 41-49. (shrink)

Metaphysics is sensitive to the conceptual tools we choose to articulate metaphysical problems. Those tools are a lens through which we view metaphysical problems; the same problems look different when we change the lens. There has recently been a shift to "postmodal" conceptual tools: concepts of ground, essence, and fundamentality. This shift transforms the debate over structuralism in the metaphysics of science and philosophy of mathematics. Structuralist theses say that patterns are "prior" to the nodes in the patterns. In modal (...) terms this would mean that the nodes cannot vary independently of the pattern. But its postmodal meaning is unclear. Does it mean, e.g., that a fundamental account of reality somehow speaks only of patterns? What would that mean? Three structuralist positions are examined through a postmodal lens: nomic/causal/dispositional essentialism, structuralism about individuals (e.g., structural realism, e.g., ante rem mathematical structuralism), comparativism about quantities. The question of when theories are equivalent, and how that impacts the debate over structuralism, is also discussed. (shrink)

In order to perfectly describe the world, it is not enough to speak truly. One must also use the right concepts - including the right logical concepts. One must use concepts that "carve at the joints", that give the world's "structure". There is an objectively correct way to "write the book of the world". Much of metaphysics, as traditionally conceived, is about the fundamental nature of reality; in the present terms, this is about the world's structure. Metametaphysics - inquiry into (...) the status of metaphysical questions - turns on structure. The question of whether ontological, causal, or modal questions are "substantive" is in large part a question of whether the world has ontological, causal, and modal structure - whether quantifiers, causal relations, and modal operators carve at the joints. (shrink)

Precis of my book by this title, for a symposium.

Most facts of grounding involve nonfundamental concepts, and thus must themselves be grounded. But how? The leading approaches—due to Bennett, deRosset, and Dagupta—are subject to objections. The way forward is to deny a presupposition common to the leading approaches, that there must be some simple formula governing how grounding facts are grounded. Everyone agrees that facts about cities might be grounded in some complex way about which we know little; we should say the same about the facts of grounding themselves. (...) The kinds of facts that might enter into the grounds of the facts of grounding are explored at length. (shrink)

Shamik Dasgupta has argued that realists about natural properties (and laws, grounding, etc.) cannot account for their epistemic value. For "properties are cheap": in addition to natural properties and any value the realist might attach to them, there are also "shmatural" properties (standing to natural properties like charge and mass as Goodman's grue and bleen stand to green and blue) and a corresponding "shmvalue" of theorizing in terms of them. Dasgupta's challenge is one of objectivity: the existence of the "shmamiked" (...) network of concepts threatens the objectivity of facts stated using the unshmamiked network. But the challenge can be repelled given a proper understanding of objectivity itself. (shrink)

Mereological nihilism says that there do not exist (in the fundamental sense) any objects with proper parts. A reason to accept it is that we can thereby eliminate 'part' from fundamental ideology. Many purported reasons to reject it - based on common sense, perception, and the possibility of gunk, for example - are weak. A more powerful reason is that composite objects seem needed for spacetime physics; but sets suffice instead.

Elizabeth Barnes and Mari Mikkola raise the important question of whether certain recent approaches to metaphysics exclude feminist metaphysics. My own approach does not, or so I argue. I do define “substantive” questions in terms of fundamentality; and the concepts of feminist metaphysics are nonfundamental. But my definition does not count a question as being nonsubstantive simply because it involves nonfundamental concepts. Questions about the causal structure of the world, including the causal structure of the social world, are generally substantive (...) because their answers are not sensitive to any alternate, equally good conceptual choices we could have made. I also argue that such questions are substantive regardless of the ontology of social kinds. (shrink)

Persistence through time is like extension through space. A road has spatial parts in the subregions of the region of space it occupies; likewise, an object that exists in time has temporal parts in the various subregions of the total region of time it occupies. This view — known variously as four dimensionalism, the doctrine of temporal parts, and the theory that objects “perdure” — is opposed to “three dimensionalism”, the doctrine that things “endure”, or are “wholly present”.1 I will (...) attempt to resolve this dispute in favor of four dimensionalism by means of a novel argument based on considerations of vagueness. But before argument in this area can be productive, I believe we must become much clearer than is customary about exactly what the dispute is, for the usual ways of formulating the dispute are flawed, especially where three dimensionalism is concerned. (shrink)

In , Peter van Inwagen asked a good question. (Asking the right question is often the hardest part.) He asked: what do you have to do to some objects to get them to compose something---to bring into existence some further thing made up of those objects? Glue them together or what?1 Some said that you don’t have to do anything.2 No matter what you do to the objects, they’ll always compose something further, no matter how they are arranged. Thus we (...) learned of the fusion of the coins in our pockets and the Eiffel tower. (shrink)

According to the high-dimensional approach to quantum mechanics (a.k.a. wavefunction realism), the fundamental space of our world has an unfathomably large number of dimensions. This account is empirically adequate only if the three-dimensional manifest image can somehow be recovered from high-dimensional reality. A proper understanding of inter-level metaphysics (a.k.a. metaphysical explanation, grounding, etc.) shows that the manifest image can indeed be recovered, and answers the most concerning objections to high-dimensionalism. But it also shows that high-dimensionalism has disturbing consequences about the (...) objectivity of the manifest image. (shrink)

According to Timothy Williamson, we should accept the simplest and most powerful second-order modal logic, and as a result accept an ontology of "bare possibilia". This general method for extracting ontology from logic is salutary, but its application in this case depends on a questionable assumption: that modality is a fundamental feature of the world.

This anthology introduces advanced undergraduates and beginning graduate students to today's debates in metaphysics. The book consists of essays by contemporary metaphysicians, and all but one appear here for the first time. For each of nine topics, there are two essays, one "pro-" and one "con-".

This is a symposium on my book, Writing the Book of the World, containing a precis from me, criticisms from Dorr, Fine, and Hirsch, and replies by me.

Personal identity is not always symmetric: even if I will not be a later person, the later person may have been me. What makes this possible is that the relations that are criterial of personal identity---such as memory and anticipation---are asymmetric and "count in favor of personal identity from one side only". Asymmetric personal identity can be accommodated by temporal counterpart theory but not by Lewisian overlapping aggregates of person stages. The question of uncertainty in cases of personal fission (and (...) in Everettian quantum mechanics) is also discussed. (shrink)

There will be a few themes. One to get us going: expansion versus contraction. About an object, o, and the region, R, of space(time) in which o is exactly located,1 we may ask: i) must there exist expansions of o: objects in filled superregions2 of R? ii) must there exist contractions of o: objects in filled subregions of..

We often speak of an object being composed of various other objects. We say that the deck is composed of the cards, that a road is the sum total of its sections, that a house is composed of its walls, ceilings, floors, doors, etc. Suppose we have some material objects. Here is a philosophical question: what conditions must obtain for those objects to compose something? In his recent book Material Beings, Peter van Inwagen addresses this question, which he calls the (...) ‘special composition question’; his answer is:1 (1) For any material objects X , the X s compose something iff the activity of the X s constitutes a life, or there is only one of the Xs. Additionally, he accepts a simpler thesis that follows from (1):2 (2) Every material object is either a mereological atom or a living thing, where a mereological atom is an object lacking proper parts. (2) may seem radical. If it is true then there are no tables, chairs, planets, protons, galaxies, gas stations, etc. But van Inwagen does not hold it lightly— there are serious difficulties with alternate views. Moreover, he claims that.. (shrink)

Logic for Philosophy is an introduction to logic for students of contemporary philosophy. It is suitable both for advanced undergraduates and for beginning graduate students in philosophy. It covers (i) basic approaches to logic, including proof theory and especially model theory, (ii) extensions of standard logic that are important in philosophy, and (iii) some elementary philosophy of logic. It emphasizes breadth rather than depth. For example, it discusses modal logic and counterfactuals, but does not prove the central metalogical results for (...) predicate logic (completeness, undecidability, etc.) Its goal is to introduce students to the logic they need to know in order to read contemporary philosophical work. It is very user-friendly for students without an extensive background in mathematics. In short, this book gives you the understanding of logic that you need to do philosophy. (shrink)

Kripke's objections to descriptivism may be modified to apply to Scott Soames's pragmatic account from his book Beyond Rigidity. Further, intuitions about argument-validity threaten any theory in the vicinity of Soames's.

If one's political engagement is to be shaped fundamentally by the Scriptures, it means developing a biblical understanding on a given issue by means of a process vastly more complex than selecting a few isolated proof-texts related to it.

"Composition as identity" is the radical claim that the whole is identical to the parts - radical because it implies that a single object can be identical to many objects. Composition as identity, together with auxiliary assumptions, implies the principle of "collapse": an object is one of some things if and only it is part of the fusion of those things. Collapse has important implications: the comprehension principle of plural logic must be restricted, plural definite descriptions such as "the Cheerios (...) in the bowl" are empty, Composition as identity does not preclude emergent properties (contrary to what McDaniel has argued), and drastic simplifications of mereological and logical ideology are extensionally available. (shrink)

Logic begins but does not end with the study of truth and falsity. Within truth there are the modes of truth, ways of being true: necessary truth and contingent truth. When a proposition is true, we may ask whether it could have been false. If so, then it is contingently true. If not, then it is necessarily true; it must be true; it could not have been false. Falsity has modes as well: a false proposition that could not have been (...) true is impossible or necessarily false; one that could have been true is merely contingently false. The proposition that some humans are over seven feet tall is contingently true; the proposition that all humans over seven feet tall are over six feet tall is necessarily true; the proposition that some humans are over seven feet tall and under six feet tall is impossible, and the proposition that some humans are over nine feet tall is contingently false. Of these four modes of truth, let us focus on necessity, plus a fifth: possibility. A proposition is possible if it is or could have been true; hence propositions that are either necessarily true, contingently true, or contingently false are possible. Notions that are similar to the modes of truth in being concerned with what might have been are called modal. Dispositions are modal notions, for example the disposition of fragility. Relatedly, there are counterfactual conditionals, for example “if this glass were dropped, it would break.” And the notion of supervenience is modal.1 But let us focus here on necessity and possibility. Modal words are notoriously ambiguous (or at least context-sensitive2). I may reply to an invitation to give a talk in England by saying “I can’t come; I have to give a talk in California the day before”. This use of “can’t” is perfectly appropriate. But it would be equally appropriate for me to say that I could cancel my talk in California (although that would be rude) and give the talk in England instead. What I cannot do is give both talks.. (shrink)

In "Sider on Existence" (Noužs, 2007), David Liebesman and Matti Eklund argue that my "indeterminacy argument", according to which quantifiers are never vague, clashes with my "naturalness argument", according to which quantifiers "carve at the joints". There is, I argue, no outright inconsistency. But Liebesman and Eklund have shown that my arguments are not as independent as it may have appeared. The best defense of the indeterminacy argument is via the naturalness argument.

Quantifier variantists accept multiple alternative ontological languages in which quantifiers obey the usual inference rules despite having different meanings. But collapse arguments seem to show that these quantifiers would be provably equivalent to one another. Cian Dorr has pushed this discussion forward by formulating the collapse argument in terms of an algebra of meanings that are common amongst the languages. I attempt to show that quantifier variantists can respond. But an important distinction between types of quantifier variance emerges, between those (...) in which quantifier meanings draw on a single objective backbone of “portions of reality,” and those (such as the type that is arguably associated with neo-Fregeanism) in which they do not. (shrink)

Some philosophers believe that everyday objects are 4-dimensional spacetime worms, that a person (for example) persists through time by having temporal parts, or stages, at each moment of her existence. None of these stages is identical to the person herself; rather, she is the aggregate of all her temporal parts.1 Others accept “three dimensionalism”, rejecting stages in favor of the notion that persons “endure”, or are “wholly present” throughout their lives.2 I aim to defend an apparently radical third view: not (...) only do I accept person stages; I claim that we are stages.3 Likewise for other objects of our everyday ontology: statues are statue-stages, coins are coin-stages, etc. At one level, I accept the ontology of the worm view. I believe in spacetime worms, since I believe in temporal parts and aggregates of things I believe in. I.. (shrink)

This volume concerns the status and ambitions of metaphysics as a discipline.

According to Ross Cameron's version of the moving spotlight theory of time, (1) Past and future entities exist; (2) the properties and relations they have are those they have now; but nevertheless (3) there are no fundamental past- or future-tensed facts; instead, tensed facts are made true by fundamental facts about the possession of temporal distributional properties and facts about how old things are. I argue that the account isn't sufficiently distinct from the B-theory to fit the usual A-theorist's tastes (...) and arguments, since i) like the traditional spotlight it consists of a B-theoretic metaphysics with one small A-theoretic element tacked on, and since ii) in a sense it does not admit fundamental change. I also argue that the proposed grounding of tensed facts in tenseless facts does not work in certain cases. (shrink)

An introduction to temporal parts theory. Most of us believe in spatial parts: hands are spatial parts of people, an electron is a spatial part of a hydrogen atom, the earth is a spatial part of the solar system. Why are these parts "spatial" parts? Because they are spatially smaller: the hand is spatially smaller than the person, the electron is spatially smaller than the atom, the earth is spatially smaller than the solar system. Temporal parts, then, are parts that (...) are temporally smaller. My current temporal part, "me-today", we might call it, is temporally smaller than me, since it exists today and only today. Temporal parts theory says that objects are made up of temporal as well as spatial parts. (shrink)

Sometimes we give truth-conditions for sentences of a discourse in other terms. According to Agustín Rayo, when doing so it is sometimes legitimate to use the terms of that very discourse, so long as the terms do not occur in the truth-conditions themselves. I argue that giving truth-conditions in this "outscoping" way prevents one from answering "discourse threat" (for example, the threat of indeterminacy).

Most accounts of cognitive scaffolding focus on ways that external structure can support or augment an agent’s cognitive capacities. We call cases where the interests of the user are served benign scaffolding and argue for the possibility and reality of hostile scaffolding. This is scaffolding which depends on the same capacities of an agent to make cognitive use of external structure as in benign cases, but that undermines or exploits the user while serving the interests of another agent. We develop (...) criteria for scaffolding being hostile and show by reference to examples including the design features of electronic gambling machines and casino management systems that hostile scaffolding exists and can be highly effective. In cases where the scaffolding is deep and permits the offloading of significant cognitive work, hostile scaffolding exploitatively manipulates cognitive processing itself. Given the extent of human reliance on scaffolding this is an important and neglected vulnerability. [This is an updated version of the paper, added in February 2023.]. (shrink)

In this chapter the author examines the idea of time's motion, or flow, more carefully, by comparing it to the motion of ordinary objects. Ordinary objects move with respect to time. So if time itself moves, it must move with respect to some other sort of time. But what would that other time be? Most motion takes place with respect to the familiar timeline, but time itself moves with respect to another timeline, hypertime. Hypertime is supposed to be a sort (...) of time. Hypertime must move with respect to yet another sort of time, hyper‐hyper time. Space‐time diagrams can be used to represent all of history; everything that has ever happened or ever will happen can be fit into a space‐ time diagram somewhere. According to the space‐time theory, time and space are analogous in many ways. Finally the author argues against the space‐time theory. (shrink)

One often hears a complaint about “bare particulars”. This complaint has bugged me for years. I know it bugs others too, but no one seems to have vented in print, so that is what I propose to do. (I hope also to say a few constructive things along the way.) The complaint is aimed at the substratum theory, which says that particulars are, in a certain sense, separate from their universals. If universals and particulars are separate, connected to each other (...) only by a relation of instantiation, then, it is said, the nature of these particulars becomes mysterious. In themselves, they do not have any properties at all. They are nothing but a pincushion into which universals may be poked. They are Locke’s “I know not what” (1689, II, xxiii, §2); they are Plato’s receptacles (Timaeus 48c–53c); they are “bare particulars”.1 Against substratum theory there is the bundle theory, according to which particulars are just bundles of universals. The substratum and bundle theories agree on much. They agree that both universals and particulars exist. And they agree that a particular in some sense has universals. (I use phrases like ‘particular P has universal U ’ and ‘particular P ’s universals’ neutrally as between the substratum and bundle theories.) But the bundle theory says that a particular is exhaustively composed of (i.e., is a mereological fusion of) its universals. The substratum theory, on the other hand, denies this. Take a particular, and mereologically subtract away its universals. Is anything left? According to the bundle theory, no. But according to the substratum theory, something is indeed left. Call this remaining something a thin particular. The thin particular does not contain the universals as parts; it instantiates them. (shrink)

This is a symposium on my book, Writing the Book of the World, containing a precis from me, criticisms from Contessa, Merricks, and Schaffer, and replies by me.

Presentism is the doctrine that only the present is real. Since ordinary talk and thought are full of quantification over non-present objects, presentists are in a familiar predicament: in their unreflective moments they apparently commit themselves to far more than their ontological scruples allow. A familiar response is to begin a project of paraphrase. Truths appearing to quantify over problematic entities are shown, on analysis, to not involve quantification over those entities after all. But I think that we might be (...) better off abandoning paraphrase altogether. I suggest a project of discovering “underlying truths” rather than paraphrases. I will explore this strategy as applied to defending presentism, but my hope is that lovers of desert landscapes everywhere will herein find words of comfort. (shrink)

The slogan “the whole is nothing over and above the parts” and related vague thoughts animate many theories of parthood and arguably are central to our ordinary conception. I examine some issues connected with this slogan.

While many are impressed with the utility of possible worlds in linguistics and philosophy, few can accept the modal realism of David Lewis, who regards possible worlds as sui generis entities of a kind with the concrete world we inhabit.1 Not all uses of possible worlds require exotic ontology. Consider, for instance, the use of Kripke models to establish formal results in modal logic. These models contain sets often regarded for heuristic reasons as sets of “possible worlds”. But the “worlds” (...) in these sets can be anything at all; they can be numbers, or people, or sh. The set of worlds, together with the accessibility relation and the rest of the model, is used as a purely formal structure.2 One can even go beyond establishing results about formal systems and apply Kripke models to English, as Charles Chihara has recently argued.3 Chihara shows, for instance, how to use Kripke models (plus primitive modal notions) to give an account of validity for English modal sentences. In other cases worlds are not really needed at all. It is often vivid to give a counterexample thus: “There is a possible world in which P. Since your theory implies that in all worlds, not-P, your theory is wrong.” But the counterexample could just as easily be given using modal operators: “Possibly, P. Since your theory implies that it is necessary that not-P, your theory is wrong.”. (shrink)

Some say that presentism precludes time travel into the past since it implies that the past does not exist, but this is a bad argument. Presentism says that only currently existing entities exist, and that the only properties and relations those entities instantiate are those that they currently instantiate. This does in a sense imply that the past does not exist. But if that precluded time travel into the past, it would also preclude the one-second-per-second “time travel” into the future (...) that is ordinary persistence, for presentism accords the future the same ontological status as the past. Instead of quantifying over past and future objects and events, presentists speak a tensed language, regimented with primitive sentential tense operators. For a presentist, a persisting person is one who did exist, and who will exist. Regimented, these claims become: it was the case that she exists, and it will be the case that she exists. The presentist may then apply the same strategy to time travel proper. Suppose Katy travels back to the time of the dinosaurs. The presentist can say that it was the case two hundred million years ago that Katy exists. This claim, which consists of a present-tense statement “Katy exists” embedded within the past tense operator it was the case two hundred million years ago that, is exactly the sort of statement about time that a presentist is free to accept. This has all been made clear by Simon Keller and Michael Nelson ( ). In addition to rebutting the bad argument against the consistency of presentism and time travel, Keller and Nelson argue positively in favor of consistency by showing how to translate David Lewis’s ( ) account of time travel into the presentist’s tensed language. The appearance of con ict between presentism and time travel, they argue, is due only to the fact that most defenders of time travel (for example Lewis) have tended to phrase their defenses in nonpresentist terms. As much as I applaud their rebuttal of the bad argument, I wish to sound a note of caution.. (shrink)

When is there no fact of the matter about a metaphysical question? When multiple candidate meanings are equally eligible, in David Lewis's sense, and fit equally well with ordinary usage. Thus given certain ontological schemes, there is no fact of the matter whether the criterion of personal identity over time is physical or psychological. But given other ontological schemes there is a fact of the matter; and there is a fact of the matter about which ontological scheme is correct.

A property, F, is maximal iff, roughly, large parts of an F are not themselves Fs.' Maximality makes trouble for a recent analysis of intrinsicality by Rae Langton and David Lewis.

Eternalists say that non-present entities (for instance dinosaurs) exist; presentists say that they do not. But some sceptics deny that this debate is genuine, claiming that presentists simply represent eternalists' quantifiers over non-present entities in different notation. This scepticism may be refuted on purely logical grounds: one of the leading candidate ‘presentist quantifiers’ over non-present things has the inferential role of a quantifier. The dispute over whether non-present objects exist is as genuine and non-verbal as the dispute over whether there (...) is life on other planets. (shrink)