# LOGIC AND METAPHYSICS

Last Updated 15/08/05

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1. The Paper
3. Topics

# 1. The Paper

The Logic and Metaphysics paper covers many of the central problems of philosophy. Do not be misled by the occurrence of the word ‘logic' in the title of the paper: it is not primarily about formal logic (the sort of thing you will have learned in your first year) but about what is sometimes called ‘Philosophical Logic'. Philosophical Logic is about philosophical problems that arise in reflecting on logic, and in applying logic to the following areas: the analysis of reasoning (e.g. validity, conditionals); the study of aspects of natural language (e.g. names, descriptions); the treatment of certain traditional metaphysical problems (e.g. truth, existence, necessity).

You are expected, of course, to know the basics of elementary logic: the propositional calculus and predicate calculus. You should understand the truth-functional account of the sentential connectives (‘and', ‘or', ‘not', ‘if...then...' and ‘if and only if') and how to use truth-tables to test for validity. You should have an understanding of the existential and universal quantifiers, and the notion of a variable, and you should also know how the propositional and predicate calculi can be supplemented by the modal operators ‘necessarily' and ‘possibly'. In short, the course assumes as much logic as is contained in an elementary logic textbook such as Hodges's Logic, (Harmondsworth: Penguin, 1977), or Guttenplan's Languages of Logic, (2 nd ed. Oxford: Basil Blackwell, 1997). (A useful handbook that summarises the main elements of predicate logic and set theory is John Pollock, Technical Methods in Philosophy, (Boulder, Colo.: Westview Press, 1990).)

What about metaphysics? Like many terms in philosophy, the term ‘metaphysics' does not have one clear and uncontroversial definition. The term originally derives from the name of Aristotle's Metaphysics which was so-called because it came straight after his Physics in the ordering of his works. These days, metaphysics is normally taken to cover very general questions about what there is and how the world works: questions about substance, identity, universals, time and causation, for instance. Many of the problems addressed will be familiar from the study of the history of philosophy, particularly from those philosophers found in the Modern Philosophy paper. The way in which many of these subjects are treated in contemporary philosophy means that there is considerable overlap of issues in the philosophy of logic and metaphysics as conceived by the philosophers of the Modern period. (This is particularly obvious in the issues concerning necessity, truth, realism, essence, identity and existence.) Given this, it is not really possible to draw a sharp line between what is ‘logic' and what is ‘metaphysics', and the paper is not divided into sections.

## Anthologies

• Beebee, Helen, and J. Dodd, eds., forthcoming. Reading Metaphysics. Oxford: Blackwell. Aimed at undergraduates, due to be published in 2006.

• Crane, T., and K. Farkas. eds. 2004. Metaphysics: A Guide and Anthology. Oxford: Oxford University Press. A large collection of classic and contemporary readings, with substantial editorial introductions.

• Frege, G. 1997. The Frege Reader. Trans., and ed., M. Beaney. Oxford: Blackwell.

• Gale, Richard, ed., Blackwell Guide to Metaphysics. Oxford: Blackwell.

• Grayling, A. C. ed. 1995. Philosophy: a Guide Through the Subject. Oxford: Oxford University Press. The chapter on Metaphysics gives introductions to the problems of causation, time, universals and substance; the chapter on Philosophical Logic introduces many of the issues mentioned under ‘Language and Logic' below.

• Hughes, R. I. G. ed. 1993. A Philosophical Companion to First-Order Logic. Indianapolis: Hackett. Contains many important papers on the philosophy of logic.

• Kim, J., and E. Sosa. eds. 1999. Metaphysics: An Anthology. Oxford: Blackwell.

• LePoidevin, R., and M. MacBeath. eds. 1993. The Philosophy of Time. Oxford: Oxford University Press. Very useful collection of papers on the philosophy of time.

• Loux, Michael. 2001. Metaphysics: Contemporary Readings. London: Routledge. A companion volume to Loux's textbook (see below) containing an excellent selection of readings, though the number of topics covered is not as extensive as some other anthologies.

• Loux, Michael and D. Zimmerman, 2003, The Oxford Handbook of Metaphysics. Oxford: Oxford University Press. A collection of newly written essays and survey articles; useful for exploring the current state of the debate.

• Martinich, A. P. ed. 1990. The Philosophy of Language, 3 rd ed. Oxford: Oxford University Press. All the essays in §3 and §4 are central to the philosophy of language aspects of the course.

• Mellor, D. H., and Alex Oliver. eds. 1997. Properties. Oxford: Oxford University Press. A collection of many essential papers on universals and properties.

• Moore, A. W. ed. 1993. Meaning and Reference. Oxford: Oxford University Press. Useful collection of classic papers and more up-to-date works on the philosophy of language.

• Quine, W.V. 1953. From a Logical Point of View. Cambridge, Mass.: Harvard University Press. A very useful collection of papers by one of the most influential philosophers and logicians of the twentieth century.

• Strawson, P. F. ed. 1967. Philosophical Logic. Oxford: Oxford University Press. Contains many classic papers on the philosophy of logic and language.

• Sosa, E., and M. Tooley. eds. 1993. Causation. Oxford: Oxford University Press. Contains many of the classic papers on causation, some of which are also relevant to the Epistemology and Methodology paper.

• van Inwagen P., and D. W. Zimmerman, eds. 1998. Metaphysics: the Big Questions. Oxford: Blackwell.

## Books

• Blackburn, S. 1984. Spreading the Word: Groundings in the Philosophy of Language. Oxford: Clarendon Press. Quite advanced introduction to the philosophy of language, containing many of the author's own views.

• Haack, Susan. 1978. Philosophy of Logics. Cambridge: Cambridge University Press. Some good surveys; worth looking at.

• Kripke, Saul. 1980. Naming & Necessity. Oxford: Blackwell. One of the classics of 20 th century philosophy; essential reading.

• Loux, Michael. 1998. Metaphysics: A Contemporary Introduction. London: Routledge. A companion volume to Loux's Contemporary Readings. Very clear and useful discussions of a limited number of topics in metaphysics, including substance, universals and time.

• Lowe, E.J. A Survey of Metaphysics. 2002. Oxford: Oxford University Press. An excellent introduction to metaphysics, with a wide coverage of issues, from a leading metaphysician.

• McCulloch, G. 1989. The Game of the Name: Introducing Logic, Language and Mind. Oxford: Clarendon Press. Chapters 1-4. Especially good introduction to the ideas of Frege and Russell.

• Read, Stephen. 1995. Thinking about Logic: an Introduction to the Philosophy of Logic. Oxford: Oxford University Press.

• Sainsbury, Mark. 1991. Logical Forms: an Introduction to Philosophical Logic. Oxford: Blackwell. Good introduction to the main areas of the philosophy of logic, with useful exercises.

• van Inwagen, P. 1993. Metaphysics. Oxford: Oxford University Press. (Second edition Boulder: Westview 2002.) An excellent introduction to metaphysics, difficult in parts.

# 3. Topics

## Language and Logic

### Sense and reference

How does language relate to reality? How is it that words can be about things or refer to things? Referring expressions or singular terms, expressions which pick out a particular object, are normally divided into three categories: proper names (‘Julius Caesar', ‘Rome'), descriptions (‘the conqueror of Gaul') and demonstratives (‘this', ‘that', ‘that city', ‘this emperor'). Names and descriptions need to be treated separately. (Demonstratives are treated in the philosophy of language section of this Guide.) The standard reading for this topic is contained in the anthologies edited by Martinich and Moore mentioned above; there is an excellent introductory essay in sections 1 & 2 of Mark Sainsbury, ‘Philosophical Logic', in A. C. Grayling, ed., Philosophy. There are short versions of writings by Mill and Frege, with commentary, in Chapter One of Reading Philosophy of Language, eds. J. Hornsby and G. Longworth (Oxford: Blackwell forthcoming). Frege's classic theory of sense and reference is an essential theme. Frege thought that there are two aspects to the meaning of any term: its reference (what it applies to in the world) and its sense (the way in which the term presents its reference). So the two terms ‘Julius Caesar' and ‘the Roman conqueror of Gaul' have the same reference but different senses. See Frege, ‘On Sense and Reference', in the Frege Reader, reprinted in Moore and in Martinich. See also Michael Dummett, ‘Frege's Distinction Between Sense and Reference', in Moore and in Dummett's Truth and Other Enigmas, (London: Duckworth, 1978). For discussion, see Gareth Evans, The Varieties of Reference, (Oxford: Clarendon Press, 1982), chapter 1; Gregory McCulloch, The Game of the Name, chapters 1&5; David Bell, ‘Reference and Sense: an Epitome', in C. Wright, ed., Frege: Tradition and Influence, (Oxford: Blackwell, 1984) and ‘How “Russellian” was Frege?', Mind 99 (1990): 267-277; and Dummett, Frege: Philosophy of Language, (London: Duckworth, 1981) chapters 1, 5 & 6. For more on Frege see the section Philosophies of Frege, Russell and Wittgenstein in this guide.

### Descriptions

Descriptions can be divided into two kinds: definite (‘the emperor') and indefinite (‘an emperor'). Most philosophical debate has centred upon definite descriptions. Russell argued that the logical form of sentences containing definite descriptions is that of existentially quantified sentences. The logical form of ‘The F is G' is: there is exactly one F which is G.

For an introduction to the theory, see the essays by Russell in Martinich and Moore, and L. Linsky, Referring, (London: Routledge & Kegan Paul, 1967). Section 2 of Mark Sainsbury, ‘Philosophical Logic' in A. C. Grayling, ed., Philosophy, and McCulloch (chapters 2-3) also give good introductions to the area. An excellent collection of essays on this subject (including classics by Russell, Strawson and Donnellan and more recent work) is Gary Ostertag, ed., Definite Descriptions (Cambridge, Mass.: MIT Press 1998).

For criticism of Russell's theory see P. F. Strawson, ‘On Referring', (in Martinich and in Moore) and Keith Donnellan, ‘Reference and Definite Descriptions', (in Martinich). Kripke attacks Donnellan's criticism of Russell in ‘Speaker's Reference and Semantic Reference', (in Martinich).

For a defence of Russell, see Gareth Evans, The Varieties of Reference, (Oxford: Clarendon Press, 1982) chs. 2 and 9.3 and Stephen Neale, Descriptions, (Cambridge, Mass.: MIT Press, 1990) chapters 1-3.

For some recent developments, see Peter Ludlow, http://plato.stanford.edu/entries/descriptions/ ; Peter Ludlow and Gabriel Segal, ‘On a Unitary Semantical Analysis for Definite and Indefinite Descriptions' in A. Bezuidenhout and M. Reimer, eds., Descriptions and Beyond: An Interdisciplinary Collection of Essays on Definite and Indefinite Descriptions. (Oxford: Oxford University Press 2003), Stanley, J. and Z. Szabó, ‘On Quantifier Domain Restriction', Mind and Language 15, (2000) 219-61; Szabó, Z., ‘Descriptions and Uniqueness', Philosophical Studies 101, (2001) 29-57. Graff, D., ‘Descriptions as Predicates', Philosophical Studies 102, (2001) 1-42.

For a historical discussion of what Russell's original paper was attempting to do, see Peter Hylton, ‘Russell on Denoting' in N.Griffin, ed., The Cambridge Companion to Russell (Cambridge: Cambridge University Press, forthcoming). For a general account of Russell, see A.D. Irvine, ‘Bertrand Russell' http://plato.stanford.edu/entries/russell/. The publication of ‘On Denoting' in 1905 is commemorated with a special issue of Mind in 2005: see http://mind.oxfordjournals.org/.

### Names

Both Frege and Russell are often attributed the view that names have, in some sense, descriptive meaning: e.g. the meaning of the name ‘Julius Caesar' may be given by the description, ‘the Roman conqueror of Gaul'. This thesis was brilliantly criticised by Saul Kripke in Naming and Necessity, (Oxford: Blackwell, 1980). Despite the apparently narrow range of the topic, Kripke's work has had a deep effect on many areas of philosophy. The whole book is essential reading. (Bear in mind that one could consistently hold Kripke's views on names together with Russell's view on descriptions ; Kripke for example gives a defence of Russell on descriptions in the paper cited in section ii above.)

For an introduction to this issue, see section 1 of Mark Sainsbury, ‘Philosophical Logic', in A. C. Grayling, ed., Philosophy ; McCulloch, ch. 4; and Evans, ‘The Causal Theory of Names', in Moore and in Martinich. See also, Marga Reimer's article on ‘Reference' at http://plato.stanford.edu/entries/reference/, much of which is about names. John Searle defends a descriptive theory of proper names in ‘Proper Names' (in Martinich, originally in Mind 67 (1958)166-173).

More advanced discussion can be found in Gareth Evans, The Varieties of Reference, (Oxford: Clarendon Press, 1982), ch. 11; and in M. Dummett, Frege: Philosophy of Language, (London: Duckworth, 1981), appendix to ch.5; T. B urge, ‘Reference and Proper Names', Journal of Philosophy 70 (1973) 425-439; Jason Stanley, ‘Names and Rigid Designation' in B. Hale and C. Wright, eds., A Companion to the Philosophy of Language (Oxford: Blackwell 1997); Scott Soames, Beyond Rigidity: The Unfinished Semantic Agenda of Naming and Necessity. Oxford: Oxford University Press 2002; Christopher Hughes, Names, Necessity and Identity (Oxford: Oxford University Press 2004).

### Conditionals

Conditional statements, those involving ‘if...then...' constructions, are central to logic and to reasoning in general. But there are many kinds of conditional statement, and there is no clear consensus about how to understand, or even to classify, these different kinds.

Two excellent introductions to the whole area are Dorothy Edgington, ‘Conditionals' http://plato.stanford.edu/entries/conditionals/, and Jonathan Bennett, A Philosophical Guide to Conditionals (Oxford: Oxford University Press 2003). Dorothy Edgington's ‘On Conditionals', Mind 104 (1995: 235-329), gives a more detailed (and difficult) introduction to the main issues.

In propositional logic we learn to translate ‘if...then...' as the material conditional (symbolised as ‘ ® '). But this does not seem to capture the meaning of ‘if...then...' in natural language. For one thing, there are the so-called ‘paradoxes of material implication': according to the truth-tables for ‘ ® ', any conditional with a false antecedent is true; and any conditional with a true consequent is true. (The antecedent is the statement before the ‘then'; the consequent is the statement after the ‘then'.) So ‘If the Pope is not Catholic, then Paris is in Italy' and ‘If Paris is in Italy, then the Pope is Catholic' both come out true on this interpretation. See Sainsbury, Logical Forms, chapter 3, for a useful introduction. The essays by Grice, Jackson, Stalnaker (essay VII) and Edgington, in F. Jackson, ed., Conditionals, (Oxford: Oxford University Press, 1991) are essential further reading.

Philosophers tend to draw a distinction between two types of conditionals. Compare ‘If Booth didn't kill Lincoln, someone else did' with ‘If Booth hadn't killed Lincoln, someone else would have'. The former is assertible on the basis simply of knowing that Lincoln was indeed assassinated, while one will only assert the latter if one believes in conspiracy theories. The distinction described as that between ‘indicative' versus ‘subjunctive' conditionals, or between ‘indicative' and ‘counterfactual' conditionals, but these labels are controversial as is the criterion and place to make the division.

Modern discussion of ‘counterfactual/subjunctive' conditionals begin with N. Goodman, Fact, Fiction and Forecast, (4 th ed. Cambridge, Mass.: Harvard University Press, 1983). David Lewis ( Counterfactuals, (Oxford: Basil Blackwell, 1973)) and Stalnaker (Essay II in Jackson) give an account of counterfactuals in terms of possible worlds: ‘if it were the case that A, then it would be the case that B' is analysed as, ‘in the closest possible worlds in which A is true, B is true.' This analysis has been very influential in other areas (for instance in Nozick's theory of knowledge: see Epistemology & Methodology).

### Existence

What is the logical form of sentences like ‘God exists'? Debate on this question has often focused on the question whether ‘exists' functions as a logical predicate, like ‘walks', true of individuals, or should be interpreted as the existential quantifier; the denial that ‘exists' is a predicate is associated with Kant's critique of the ontological argument for the existence of God (see his Critique of Pure Reason, translated by Paul Guyer and Allen W. Wood, (Cambridge: Cambridge University Press, 1998) A592/B620-A603/B631), and with Frege (see The Foundations of Arithmetic: a Logico-mathematical Enquiry into the Concept of Number, translated by J. L. Austin (2 nd ed. Oxford: Basil Blackwell, 1953), p.65); it has recently become popular to question this interpretation. One of the background issues here is the need to make sense of singular negative existential statements, such as ‘Lao Tzu does not exist'.

For introduction to these issues see section 3 of Mark Sainsbury, ‘Philosophical Logic', in A. C. Grayling, ed., Philosophy, and Stephen Williams's essay ‘Existence', in J. Kim and E. Sosa, eds., A Companion to Metaphysics (Oxford: Blackwell, 1995). For some historical background, see Barry Miller, ‘Existence' http://plato.stanford.edu/entries/existence/.

For the idea that there is simply a univocal notion of existence associated with the existential quantifier, see Quine, ‘On What There Is', in From a Logical Point of View; for a contrasting view see Nathan Salmon, ‘Existence', in James E. Tomberlin, ed., Metaphysics, Philosophical Perspectives 1, (Atascadero, Cal.: Ridgeview, 1987). Gareth Evans, The Varieties of Reference, (Oxford: Oxford University Press, 1982), ch.10, contains an invaluable survey of earlier discussions and an important proposal about how to interpret negative singular existential statements (a brief gloss on this is provided in Sainsbury's essay). For a contrasting view of empty names see Keith Donnellan, ‘Speaking of Nothing', Philosophical Review 83 (1974): 3-31. Michael Dummett, ‘Existence', in his The Seas of Language, (Oxford: Oxford University Press, 1993), criticises Evans's account and defends a Fregean approach to empty names; David Wiggins, in ‘The Kant-Frege-Russell View of Existence', in W Sinnot-Armstrong, ed., Modality, Morality, and Belief: Essays in Honor of Ruth Barcan Marcus (Cambridge: Cambridge University Press, 1994), defends the Kant-Frege account of ‘exists' and combines this with a modification of Evans's account (an excellent primer for this is Mark Sainsbury's ‘Names, Fictional Names, And “Really”': Supplement to the Proceedings of The Aristotelian Society 73, (1999): 243-269.) For a useful recent collection of essays, see A. Everett and T. Hofweber, eds., Empty Names, Fiction and the Puzzles of Non-Existence (Stanford: CSLI 2000).

For a survey of the various forms of ontological argument see Graham Oppy, Ontological Arguments & Belief in God, (Cambridge: Cambridge University Press, 1995).

### Validity, Logical Consequence and Entailment

The central concept of logic is the concept of a valid argument: an argument in which the truth of the premises in some way guarantees the truth of the conclusion. An argument can be valid without its premises being true; validity demands only that if the premises are true, then the conclusion must be. (A sound argument is a valid argument with true premises.) How should we understand validity? For one traditional account see Quine, Philosophy of Logic, (Englewood Cliffs: Prentice-Hall, 1970), chapters 1, 2, and 4. A good general introduction to the issue is Sainsbury, Logical Forms, chapter 1. Also central is Alfred Tarski's ‘Truth & Proof', in Hughes, ed., A Companion to First-Order Logic.

A very clear introduction to the concept of logical consequence is J.C. Beall and Greg Restall, ‘Logical Consequence' http://plato.stanford.edu/entries/logical-consequence/. This also has a useful bibliography. For a more advanced, controversial and partly historical (but nonetheless very clear) treatment, see John Etchemendy, The Concept of Logical Consequence (Cambridge, Mass.: Harvard University Press, 1990), which challenges Tarski's account; for one response (of many) see William Hanson, ‘The Concept of Logical Consequence', Philosophical Review, 106, (1997): 365-409.

A related question is the question of what it is for something to entail something else. On the standard interpretations of entailment, anything follows from a contradiction. Some philosophers have taken this as reason to revise our notion of entailment. For a classic statement of these issues see Peter Geach, ‘Entailment', in his Logic Matters, (Oxford: Blackwell, 1972) and D. H. Rice, ‘Entailment', Mind 95 (1986): 345-360. One revision is relevance logic: see Stephen Read, Thinking about Logic: an Introduction to the Philosophy of Logic, (Oxford: Oxford University Press, 1994) ch. 6; and Edwin Mares ‘Relevance Logic' http://plato.stanford.edu/entries/logic-relevance/.

### Alternative Logics

For various reasons, philosophers have proposed alternative logics to the standard or ‘classical' logic that one is taught in elementary logic classes. For an introduction to these difficult issues start with Susan Haack, Philosophy of Logics, chs. 9-11, and her Deviant Logic, Fuzzy Logic: Beyond the Formalism, (Rev. ed. Chicago: University of Chicago Press, 1996). Alternative logics may add elements to classical logic or they may subtract them. Stewart Shapiro's, ‘Classical Logic' http://plato.stanford.edu/entries/logic-classical/ is an account of the basic assumptions of classical logic, but requires some technical ability.

We can distinguish between the basic elements of classical logic being supplemented and its basic assumptions being revised.

Three notable ways in which logic may be supplemented include (i) modal logic, which is used to formalise talk of possibility: see further the entry below on modal logic, and the Symbolic Logic section of this Guide; (ii) tense logic, to handle means we have in natural language of talking of the past or present: see the entry below on time and tense for more on the philosophical significance of this; (iii) and second-order logic which includes quantification into predicate position as well as subject position in sentences—for more on this see the Set Theory and Further Logic and Mathematical Logic sections of this Guide, and the entry on Set Theory in the Philosophy of Mathematics section of this Guide.

One other way in which classical logic may be revised is by removing some of its assumptions about what can exist: ‘free' logics allow for the occurrence of empty terms within well-formed formulae, requiring consequent modifications of the rules for the existential and universal quantifiers. For outlines of various forms of free logic, and their philosophical significance (i.e. to issues of reference, descriptions and existence) see Karel Lambert, ed., Philosophical Applications of Free Logic (Oxford: Oxford University Press, 1991). See in particular, the editor's introduction and the papers by van Fraasen and Burge.

Other modifications to classical logic: intuitionists refuse to endorse the law of bivalence, that every sentence is determinately true or false—for an introduction to these issues see Michael Dummett, ‘The Philosophical Basis of Intuitionistic Logic', in his Truth & Other Enigmas (London: Duckworth, 1978) and also the reading later in this section under Realism, Idealism, and Anti-Realism; quantum logicians deny the distributive law for disjunction, for an introduction to this see Hilary Putnam's ‘Is Logic Empirical?', in his Mathematics, Matter & Method, Philosophical Papers, Vol. 1, (2 nd ed. Cambridge: Cambridge University Press, 1979); and paraconsistent logics even allow for the truth of contradictions: for this see T. Smiley and G. Priest, ‘Can contradictions be true?', Proceedings of the Aristotelian Society Supplementary Volume 67 (1993: 17-33, 35-54) and Graham Priest and Koji Tanaka, ‘Paraconsistent Logic' http://plato.stanford.edu/entries/logic-paraconsistent/. For scepticism about alternative logics, see Quine, Philosophy of Logic (Englewood Cliffs: Prentice-Hall, 1970) chapter 6.

One of the main motivations philosophers have found for endorsing non-classical logic has been the problems posed by vagueness in natural language; for reading on these matters see the next section below.

### Vagueness

Many people think that logic should be able to accommodate vague predicates (like ‘bald' and ‘heap') and that this gives us a reason for departing from classical logic. See Roy Sorensen, ‘Vagueness' http://plato.stanford.edu/entries/vagueness/, and Mark Sainsbury, Paradoxes, (2nd ed. Cambridge: Cambridge University Press, 1995) chapter 2, for an introduction. See T. Williamson, ‘Vagueness and Ignorance', Proceedings of the Aristotelian Society Supplementary Volume 66 (1992): 145-162, for the view that vagueness need not require giving up classical logic. See also Williamson's book Vagueness, (London: Routledge, 1994) for an exhaustive survey of approaches to the problem since ancient times and Williamson's own solution to it. A good critique of Williamson is Mark Sainsbury's ‘Vagueness, Ignorance, and Margin for Error', British Journal of Philosophy of Science 46 (1995): 589-601. The Southern Journal of Philosophy, Supp. Vol. 33 (1995), contains a number of important essays on vagueness including essays by Sainsbury, Tye, Wright, and Williamson. One important sub-debate in this area is whether there can be vague objects: for an argument that there cannot be see Gareth Evans's short (one page) paper in Analysis 38 (1978): 208, reprinted in his Collected Papers, (Oxford: Clarendon Press, 1985) and in Crane and Farkas (eds.) Metaphysics: A Guide and Anthology ; this issue is discussed by Williamson in his book, and by Sainsbury in the above mentioned article; see also Terence Parsons and Peter Woodruff, ‘Wordly Indeterminacy of Identity', Proceedings of the Aristotelian Society 95 (1995): 171-191. An indispensable collection is R. Keefe and P. Smith, eds., Vagueness: a Reader (Cambridge, Mass.: MIT, 1997).

## Truth and Objectivity

### Theories of truth

What is truth? That is, what is it for something to be true (or false)? A preliminary question is: what sorts of things are true or false? What, for instance, should we understand the p s and q s in our truth-tables to be standing in for? Some candidates for ‘truth-bearers' are sentences, statements, propositions, assertions, beliefs or judgements. A useful discussion is E. J. Lemmon, ‘Sentences, Statements and Propositions', in B. Williams, ed., British Analytic Philosophy, (Routledge & K. Paul, 1966). See also Strawson, ‘On Referring', in Moore, ed., Meaning and Reference, and Richard Cartwright, ‘Propositions', in his Philosophical Essays, (Cambridge, Mass.: MIT Press, 1987). For the bearing of these questions on logic, Richard E. Grandy, ‘What do “Q” and “R” stand for Anyway?', in Hughes, ed., A Philosophical Companion to First-Order Logic, is a very useful introduction.

The next question is: what is it about a true statement, proposition (or whatever) that makes it true? There are various traditional answers: truth consists in a relation between the proposition and a fact (the correspondence theory: see Marian David, ‘The Correspondence Theory of Truth' http://plato.stanford.edu/entries/truth-correspondence/ ); the truth of a proposition consists in its membership of some specified coherent set of propositions or beliefs (the coherence theory: see james O. Young, ‘The Coherence Theory of Truth' http://plato.stanford.edu/entries/truth-coherence/ ); truth just is the property of propositions or beliefs which enables us to succeed in our endeavours (the pragmatic theory: see Jerome Dokic and Pascal Engel, Truth and Success London: Routledge 2002); the whole nature of truth can be explained in terms of the principle ‘“ P ” is true if and only if P ' (the redundancy, deflationary or minimalist theory: see Daniel Stoljar, ‘The Deflationary Theory of Truth' http://plato.stanford.edu/entries/truth-deflationary/).

General reading on these issues should include: Ralph Walker, ‘Theories of Truth' in Bob Hale and Crispin Wright, eds., A Companion to the Philosophy of Language (Oxford: Blackwell 1997); Simon Blackburn, Spreading the Word, chapters 7-8; Haack, Philosophy of Logics, chapter 7; Paul Horwich, ‘Theories of Truth', in Hughes, ed., A Philosophical Companion to First-Order Logic ; Paul Horwich, Truth (Oxford: Basil Blackwell, 1990; 2 nd edition Oxford University Press 1998; see especially the postscript); M. Dummett, ‘Truth', in Strawson, ed., Philosophical Logic, also reprinted in Dummett's Truth & Other Enigmas, (London: Duckworth, 1978); Donald Davidson, ‘True to the Facts' in his Inquiries into Truth and Interpretation (Oxford: Oxford University Press 1984); the anthology, edited by Simon Blackburn and Keith Simmons, Truth, (Oxford: Oxford University Press, 1999), contains classic papers by Austin and Strawson, and some useful contemporary material on minimalism/deflationism. A huge and useful collection is Michael Lynch, ed., The Nature of Truth (Cambridge, Mass.: MIT Press 2001).

More advanced reading would include: F. P. Ramsey, ‘Facts and Propositions,' Proceedings of the Aristotelian Society 27 (1927); reprinted in his collected papers, D. H. Mellor, ed., Philosophical Papers, (Cambridge: Cambridge University Press, 1990) and in Blackburn and Simmons; Anil Gupta, ‘A Critique of Deflationism' Philosophical Topics 21 (1993): 57-81, reprinted in Blackburn and Simmons; D. Grover, J. Camp, and N. Belnap, ‘A Prosentential Theory of Truth', Philosophical Studies 27 (1975): 73-125, reprinted in Grover's The Prosentential Theory of Truth, (Princeton, N. J.: Princeton University Press, 1992); Donald Davidson, ‘The Structure and Content of Truth' Journal of Philosophy, 87 (1990): 279-328; and his ‘The Folly of Trying to Define Truth' Journal of Philosophy 93 (1996): 263-278 (reprinted in Blackburn and Simmons); Scott Soames, Understanding Truth (Oxford and New York: Oxford University Press 1997); David Wiggins, ‘What Would be a Substantial Theory of Truth?' in Z. Van Straaten, ed., Philosophical Subjects (Oxford: Oxford University Press 1980) and his ‘Truth, and Truth as Predicated of Moral Judgements' in his Needs, Values, Truth (3 rd edition Oxford: Oxford University Press 1998); Crispin Wright, Truth & Objectivity (Cambridge, Mass.: Harvard University Press, 1992) chapters 1-2.

In addition to these issues there is the ancient puzzle of the liar sentence, ‘This sentence is false'. For an introduction to the paradox, see Sainsbury, Paradoxes, (2 nd edition Cambridge: Cambridge University Press, 1995) chapter 5; for more advanced discussion see the introduction to R. Martin, ed., Recent Essays on Truth & the Liar (Oxford: Clarendon Press, 1984)) and among the difficult but important papers collected there, look in particular at those by Kripke, Burge and Parsons.

One impact of the liar puzzle was the problem of providing a definition of truth for formal languages. See Tarski, ‘The Semantic Conception of Truth', in Feigl and Sellars, eds., Readings in Philosophical Analysis, (New York: Appleton-Century-Crofts Inc.,1949)). For an elementary introduction, see section 6 of Mark Sainsbury, ‘Philosophical Logic', in A. C. Grayling, ed., Philosophy. See also Quine, Philosophy of Logic, (Englewood Cliffs: Prentice-Hall, 1970). Tarski's theory of truth has inspired a number of different accounts of truth in general, and there is a lively debate over the status and significance of Tarski's theory of truth for formal languages for an account of the nature of truth in general. For contrasting (rather difficult, but rewarding) treatments see Hartry Field's ‘Tarski's Theory Of Truth', Journal of Philosophy, 69, (1972): 347-375 and Richard Heck, ‘Tarski, Truth, and Semantics', Philosophical Review 106 (1997): 533-554.

### Realism, idealism and anti-realism

Is the world independent of our experience of it? Realists hold that it is; idealists and phenomenalists deny that this is so. What arguments can one give against them? Are there other forms of attack on realism? Can we really make sense of a world independent of how we conceive it to be?

Introductory reading: the Introduction to Part II of Crane and Farkas, ed., Metaphysics: a Guide and Anthology ; part II of this book also contains some classic readings by Locke, Berkeley and Kant. Realism in general is defended by Thomas Nagel, The View from Nowhere, (Oxford: Oxford University Press, 1986) ch. 6, and (under the name of ‘metaphysical realism') attacked by Hilary Putnam in Reason, Truth & History, (Cambridge: Cambridge University Press, 1981) chs. 1 & 2.

On the issue of idealism, see Howard Robinson, ‘Selection from Matter and Sense ' in Crane and Farkas, (eds.); J. Foster, ‘Berkeley on the Physical World', in J. Foster, and H. Robinson, eds., Essays on Berkeley: a Tercentennial Celebration, (Oxford: Clarendon Press, 1985). In its 20 th century form of phenomenalism, idealism is discussed by A. J. Ayer, ‘Phenomenalism', Proceedings of the Aristotelian Society 47 (1947): 163-196, reprinted in his Philosophical Essays, (London: Macmillan, 1954), W. V. Quine, ‘Two Dogmas of Empiricism', in his From a Logical Point of View, (Cambridge,Mass.: Harvard University Press,1953), and I. Berlin, ‘Empirical Propositions and Hypothetical Statements', in his Concepts & Categories: Philosophical Essays, (London: Hogarth, 1978).

Michael Dummett has been influential in framing the questions about realism in a new way: see his ‘Realism' in Crane and Farkas (ed.); and The Interpretation of Frege's Philosophy, (London: Duckworth, 1981) ch.20, and ‘Realism & Anti-Realism', in his The Seas of Language, (Oxford: Clarendon Press, 1993); John McDowell, ‘Anti-Realism and the Epistemology of Understanding', in H. Parret, and J. Bouveresse, eds., Meaning and Understanding, (Berlin: de Gruyter, 1981); and Crispin Wright, Truth & Objectivity, (Cambridge, Mass.: Harvard University Press, 1992) esp. chs.13; for a survey of different kinds of realism and anti-realism, see Alexander Miller's ‘Realism' http://plato.stanford.edu/entries/realism/#9.

### Subjective and objective

Related to the issue of realism is the question of subjective and objective conceptions of reality. What do the terms ‘subjective' and ‘objective' really mean? An objective conception of the world is sometimes described as one from a ‘God's eye point of view', or from no point of view at all. But is it possible to get a purely objective conception of the world? Are the only real things those which are purely objective? Or does it make sense to suppose that there are subjective ‘facts'?

For the general issue, see T. Nagel, ‘Subjective & Objective', in his Mortal Questions, (Cambridge: Cambridge University Press, 1979); see also his The View from Nowhere, (Oxford: Oxford University Press, 1986) ch. 4; B. Williams, Descartes: the Project of Pure Enquiry (London: Penguin, 1978), ch. 8, pp.23652, and ch. 10; and A. W. Moore, Points of View, (Oxford: Clarendon Press, 1997) especially chs. 1-4.

For the distinction between primary and secondary qualities, see the excerpt from Locke's Essay in Crane & Farkas, Metaphysics ; J.L. Mackie, Problems from Locke (Oxford: Oxford University Press 1976) ch. 1; Colin McGinn, The Subjective View: Secondary Qualities and Indexical Thoughts (Oxford: Clarendon, 1983) chs. 13, 6; and F. Jackson, Perception: a Representative Theory, (Cambridge: Cambridge University Press, 1977) ch. 5 on the subjectivity of colours, tastes and so on. An interesting (both philosophically and historically) paper on the distinction between primary and secondary qualities is A.D. Smith ‘Of Primary and Secondary Qualities', Philosophical Review 99: 221-54. John McDowell discusses the distinction, and the analogy between secondary qualities and values in ‘Values & Secondary Qualities', in T. Honderich, ed., Morality & Objectivity: a Tribute to J. L. Mackie, (London: Routledge and Kegan Paul, 1985).

For more on the specific case of colour, see Alex Byrne and David R. Hilbert, eds., Readings on Color, Vol. 1, (Cambridge, Mass.: MIT Press, 1997) in particular the papers by Johnston, Broackes, Boghossian & Velleman, and Campbell.

## Mind and Nature

(For further details on these topics, see the Philosophy of Mind)

### The place of the mind in nature

What are we? Are human beings and other creatures with minds simply part of the natural order? Dualists claim that our existence as conscious and rational creatures proves the existence of immaterial substances. Naturalists claim that our lives are as governed by the laws of nature, as are the physical objects with which we interact. Some naturalists are dualists, but chiefly naturalism has come to be associated with materialism or physicalism, and the rejection of dualism.

On physicalism and dualism: see (for dualism) S. Kripke, Naming & Necessity, (Oxford: Blackwell, 1980) lecture 3, and F. Jackson, ‘Epiphenomenal Qualia', Philosophical Quarterly 32 (1982): 127-136, reprinted in William G. Lycan, ed., Mind & Cognition: a Reader, (Oxford: Basil Blackwell, 1990); for materialism/physicalism see David Lewis, ‘An Argument for the Identity Theory', in Journal of Philosophy 63 (1966): 17-25, reprinted in his Philosophical Papers, Vol. 1, (New York: Oxford University Press, 1983); and D. Davidson, ‘Mental Events' & postscript, in his Essays on Actions & Events, (Oxford: Clarendon Press, 1980). P.F. Strawson argues against the coherence of dualism, ‘Self, Mind & Body', in his Freedom & Resentment: and Other Essays, (London: Methuen, 1974); dualism is defended by W. D. Hart, The Engines of the Soul, (Cambridge: Cambridge University Press, 1988) chs. 1-3, and John Foster, The Immaterial Self: a Defence of the Cartesian Dualist Conception of the Mind, (London: Routledge, 1996). See also S. Shoemaker, ‘On an Argument for Dualism', in his Identity, Cause & Mind: Philosophical Essays, (Cambridge: Cambridge University Press, 1984). Some physicalists have argued that we will never be able fully to explain consciousness, even though we have good reason to believe that physicalism is true. See Nagel, ‘What is it like to be a bat?', in his Mortal Questions, (Cambridge: Cambridge University Press, 1979) and The View from Nowhere, (Oxford: Oxford University Press, 1986) chs. 2 & 3; and Colin McGinn, ‘Can we Solve the Mind-Body Problem?' Mind 98 (1989): 349-366, reprinted in his The Problem of Consciousness: Essays Towards a Resolution, (Oxford: Basil Blackwell,1991).

### Reduction and supervenience

There are many different kinds of phenomena, biological, chemical, physical, social and psychological, recognised by the various sciences and by common sense. How are all these phenomena, and the different theories of these phenomena, related? A popular theory earlier in this century was Reductionism, the theory that all sciences reduce to physics (see Nagel, and for recent discussion, Smith). These days the weaker thesis is preferred, that all the non-physical supervenes upon the physical—where X supervenes upon Y if there can be no difference in X without a difference in Y (see Kim and Horgan for discussion). Kim's Mind in a Physical World: an Essay on the Mind-body Problem and Mental Causation, (Cambridge, Mass.: MIT Press, 1998) is a recent defence of reductionism.

• Nagel, E. 1961. The Structure of Science: Problems in the Logic of Scientific Explanation. London: Routledge and Kegan Paul.

• Smith, Peter. 1992. ‘Modest Reductions and the Unity of Science'. In D. Charles, and K. Lennon, eds., Reduction, Explanation and Realism. Oxford: Clarendon Press.

• Kim, J. 1984. ‘Concepts of Supervenience'. Philosophy and Phenomenological Research 45:153-176. Reprinted in Supervenience and Mind: Selected Philosophical Essays. Cambridge: Cambridge University Press, 1993.

• —. 1985. ‘Psychophysical Laws'. In E. Lepore, and B. McLaughlin, eds., Actions and Events: Perspectives on the Philosophy of Donald Davidson. Oxford: Basil Blackwell. Reprinted in Supervenience and Mind.

• —. 1998. Mind in a Physical World: an Essay on the Mind-body Problem and Mental Causation. Cambridge, Mass.: MIT Press.

• Charles, David. 1992. ‘Supervenience, Composition and Physicalism'. In D. Charles, and K. Lennon, eds., Reduction, Explanation and Realism. Oxford: Clarendon Press.

• Papineau, D. 2002. Thinking about Consciousness. Oxford: Oxford University Press. Ch.1.

• Horgan, Terence. 1993. ‘From Supervenience to Superdupervenience: Meeting the Demands of the Material World'. Mind 102: 555-586.

### Personal identity

As well as the question of how peoples' minds are related to their physical natures, there is the question of what makes any individual person the person that they are, and what makes someone the same person over time. These are the questions of personal identity. For the reading on this topic, see ‘Identity & Substance' below.

### Free will

Do we have free will? Is it up to us or within our control which actions we perform? There are two parts to the problem. The first is the problem of whether freedom is inconsistent with determinism, or whether, on the contrary, it actually requires determinism. The second is whether the free will problem is rightly so-called: does control over or freedom of action require that we possess a freedom specifically of our will or decision making capacity—a control over which action we decide to perform?

• Pink, T. 2004. Free Will: A Very Short Introduction. Oxford: Oxford University Press.

• O'Connor, T. ed., 1995. Agents, Causes and Events: Essays on Indeterminism and Free Will. Oxford: Oxford University Press. Contains various attempts to make sense of freedom in the absence of the pre-determination of actions by events.

• Watson, G. 1982. ed. Free Will. Oxford: Oxford University Press (new reprint 2003). Contains a selection of important papers, including key readings below.

### Freedom and Determinism

• Ayer, A. J. 1984. Freedom and Morality: and Other Essays. Oxford: Clarendon Press.

• van Inwagen. P. 1975. ‘The Incompatability of Free Will and Determinism'. Philosophical Studies 27: 185-199.

• Strawson, P. F. 1974. ‘Freedom and resentment'. In his Freedom and Resentment: and Other Essays. London: Methuen.

• Chisholm, R.M., 1964. ‘Human Freedom and the Self' in Crane & Farkas, ed., Metaphysics.

• Clarke, R. 2003. Libertarian Accounts of Free Will. Oxford: Oxford University Press.

• Fischer, J. M. 1994. The Metaphysics of Free Will: an Essay on Control. Oxford: Blackwell.

• Kane, R. 2002. The Oxford Handbook of Free Will. Oxford: Oxford University Press.

• Loewer, Barry 1998. ‘Freedom from Physics' in Crane & Farkas, ed., Metaphysics.

• Strawson, G. 1986. Freedom and Belief. Oxford: Clarendon Press.

• Wiggins, D. 1973. ‘Towards a reasonable libertarianism'. In Ted Honderich, ed., Essays on Freedom of Action. London: Routledge and Kegan Paul.

### Freedom and Free Will

• Frankfurt, H. 1971 Freedom of the Will and the Concept of a Person'. Journal of Philosophy 68: 5-20.

• Kane, R. 1996. The Significance of Free Will. Oxford: Oxford University Press.

• Pink. T. 1997. ‘Reason and Agency'. Proceedings of the Aristotelian Society 97: 263-280.

• —. 1996. The Psychology of Freedom. Cambridge: Cambridge University Press. Esp. chapters 1-4.

• Velleman, J. David.1989. Practical Reflection. Princeton: Princeton University Press.

## Necessity and analyticity

It is important to distinguish between the following three pairs of ideas: necessary—contingent; a priori—a posteriori; analytic—synthetic. Necessary truths are those which cannot be false, or could not have been otherwise; contingent truths are those which can be false, or might have been otherwise. A priori and a posteriori knowledge can be roughly distinguished as follows: something is known a priori when its justification does not depend on any further experience; a posteriori when its justification does depend on further experience. The third distinction is between analytic statements, which are supposed to be true solely because of the meaning of the terms involved; and synthetic statements, which are true because of what the terms involved mean, plus the way the world is. The notion of a priori knowledge is dealt with on the Epistemology and Methodology paper, but it will crop up on this paper too. For introductory material on this whole area, see the ‘Introduction' to Part V of Crane & Farkas, ed., Metaphysics, and Joseph Melia, Modality (London: Acumen 2003).

### The nature of necessity/necessary truth

What is the nature of necessity? A traditional idea is that necessary truths are true because they are analytic (and it is usually assumed that analytic statements are known a priori ). See, for example, A. J. Ayer, Language, Truth and Logic, (Harmondsworth: Penguin, 1971; first published 1936) chapter 4. This idea comes under attack from at least two sides. On the one hand, Quine has attacked the idea of a principled distinction between the analytic and the synthetic at all, see ‘Two Dogmas of Empiricism', in From a Logical Point of View; ‘Carnap on Logical Truth', and ‘Truth by Convention', in The Ways of Paradox, (Cambridge, Mass.: Harvard University Press, 1966). For a recent response, see Paul Boghossian, ‘Analyticity Reconsidered', Noûs 30 (1996): 360-39; and in B. Hale, and C. Wright, eds., A Companion to the Philosophy of Language, (Oxford: Blackwell, 1997). On the other hand, Kripke has argued that some necessary truths are known a posteriori and are not analytic, see ‘Identity and Necessity', in Moore, and also in T. Honderich, and M. Burnyeat, eds., Philosophy as it is, (Harmondsworth: Penguin, 1979); see also the selection from Naming and Necessity in Crane & Farkas, ed., Metaphysics.

The Epistemology and Methodology section of this Guide contains discussions of the question of our knowledge of necessity and possibility. But essential reading in this area must include T. Gendler and J. Hawthorne, eds., Conceivability and Possibility (Oxford: Oxford University Press 2002), with its indispensable introduction.

### Modal logic and possible worlds

The study of necessity was invigorated by the use of the idea of a possible world in the interpretation of modal logic (the logic of possibility and necessity). ‘Necessarily P' is true iff ‘P' is true in all possible worlds; ‘Possibly P' is true iff ‘P' is true at some possible world. But what are possible worlds? Lewis argues that they are entities just like this world: see On the Plurality of Worlds, (Oxford: Basil Blackwell, 1986) chapter 1; Stalnaker gives a different account, and a good survey of the issue in ‘Possible Worlds', in Honderich, and M. Burnyeat, eds., Philosophy as it is, (Harmondsworth: Penguin, 1979), also in Stalnaker's Inquiry, (Cambridge, Mass.: MIT Press, 1984). D.M. Armstrong defends the claim that facts about necessity and possibility depend on facts about this world alone: see the selection from A Combinatorial Theory of Possibility in Crane & Farkas, ed., Metaphysics. A good collection of readings on this topic (though now slightly out of date) is M. Loux, ed., The Possible and the Actual: Readings in the Metaphysics of Modality, (Ithaca, N. Y.: Cornell University Press, 1979). Quine is sceptical of possible worlds, as he is of modal logic in general: see ‘Reference and Modality', in From a Logical Point of View, and ‘Carnap and Logical Truth', and ‘Necessary Truth', in The Ways of Paradox (Cambridge, Mass.: Harvard University Press, 1966).

Good introductions to the use of possible worlds are: Sainsbury, Logical Forms, chapter 5, and section 5 of Mark Sainsbury, ‘Philosophical Logic', in A. C. Grayling, ed., Philosophy ; Joseph Melia, Modality (London: Acumen 2003). An excellent and thorough account of the debate about possible worlds with much original material is John Divers, Possible Worlds (London: Routledge 2002). Another advanced discussion is Graeme Forbes, The Metaphysics of Modality, (Oxford: Clarendon Press, 1985).

## Identity

When we say that A is identical with B, what are we saying? We are not saying that two things are the same thing, for no two things are the same thing! But if we are saying that one thing is itself, then we seem to be saying something completely trivial, since we know a priori that everything is itself. Yet surely we can learn something when we discover, for example, that Hesperus (the morning star) is Phosphorus (the evening star)? For a classic answer to this puzzle, see Frege, ‘On sense and reference', in Moore, and Martinich.

For a short introduction to the question of identity, see ‘Introduction' to Part VIII of Crane & Farkas, eds., Metaphysics. A longer introduction is Harold Noonan, ‘Identity' http://plato.stanford.edu/entries/identity/, especially sections 1, 2, 3, 4 and 5.

Three central issues here are: the relationship between identity and necessity; the relationship between identity and distinguishing things into kinds; and the special issue of personal identity. But divisions of issues here are somewhat arbitrary: the concept of identity also has a link to the question of universals (section g) and plays an important role in discussions of the problem of persistence of objects over time (which is often called the problem of ‘identity over time': see next section below).

### Identity and necessity

Kripke's essay ‘Identity and Necessity', in Moore, and in Honderich, and M. Burnyeat, eds., Philosophy as it is, (Harmondsworth: Penguin, 1979), revolutionised the study of identity. See also his Naming and Necessity (Oxford: Blackwell, 1980). Kripke argued that certain identity statements are necessarily true, even if they are known a posteriori (see above). See also Alan Gibbard, ‘Contingent Identity', Journal of Philosophical Logic 4 (1975): 187-221.

### Identity and individuation

Must objects fall under kinds, often called sortals? Can two objects be in the same place at the same time? Essential reading here includes:

• Ayers, M. R. 1991. Locke: Epistemology and Ontology. 2 Vols. London: Routledge. Vol. 2, pts. I & III.

• Fine, Kit. 2003. ‘The Non-identity of a Material Thing and Its Matter', Mind 112: 195-234.

• Gibbard, A. 1975. ‘Contingent Identity', Journal of Philosophical Logic 4: 187-221.

• Johnston, Mark. 1992. ‘Constitution Is Not Identity', Mind 101: 89-105.

• Lowe, E.J. 1989. Kinds of Being. Oxford: Blackwell, 1989.

• Strawson, P. F. 1959. Individuals: an Essay in Descriptive Metaphysics. London: Methuen, 1959. Ch.1.

• Wiggins, D. 1968. ‘On Being in the Same Place at the Same Time'. Philosophical Review 77: 90-95.

• —. 2001. Sameness and Substance Renewed. Cambridge: Cambridge University Press. Chs.1, 2.

(See also section on ‘the composition of objects' in the section below.)

### Personal identity

make a difference? Does persistence of personal identity turn on continuity of psychological properties, having the same memories, desires and intentions as some earlier individual? Or does it turn on being physically continuous with an earlier subject? Is personal identity what matters to us, wouldn't we be just as well off if a perfect physical and psychological replica was to survive into the future?

• Noonan, Harold 1989. Personal Identity. London: Routledge. (2 nd edition 2003.) This book is a general survey of the history of the problem of personal identity, and an account of the debate as it now stands.

• Parfit, D. 1971. ‘Personal Identity'. Philosophical Review 80: 3-27. Reprinted in J. Glover, ed., The Philosophy of Mind, Oxford: Oxford University Press, 1976; and in Honderich, and M. Burnyeat, eds., Philosophy as it is, Harmondsworth: Penguin, 1979.

• —. 1984. Reasons & Persons. Oxford: Oxford University Press. Pt.3.

• Williams, Bernard 1970. ‘The Self and the Future'. Philosophical Review 79: 161-180. Reprinted in Problems of the Self. Cambridge, Cambridge University Press, 1973.

• —. 1957. ‘Personal Identity & Individuation'. Proceedings of the Aristotelian-Society 57: 229-252. Reprinted in Problems of the Self. Cambridge, Cambridge University Press, 1973.

• Garrett, Brian 1998. Personal Identity and Self-Consciousness. London: Routledge. (A very readable account of the recent debate.)

• Wiggins, D. 2001. Sameness and Substance Renewed. Cambridge: Cambridge University Press Chapter 7.

• Lewis, D. 1983. ‘Survival & Identity'. In his Philosophical Papers. Vol.1. New York: Oxford University Press.

• Johnston, M. 1987. ‘Human Beings'. Journal of Philosophy 84: 59-83.

• Snowdon, P. F. 1990. ‘Persons, Animals and Ourselves'. In C. Gill, ed., The Person and the Human Mind: Issues in Ancient and Modern Philosophy. Oxford: Clarendon Press; reprinted in Crane & Farkas (eds.) Metaphysics: a Guide and Anthology.

• Olson, E. 1997. The Human Animal. New York: Oxford University Press.

• Cassam, Q. 1992. ‘Reductionism & First Person Thinking'. In D. Charles, and K. Lennon, eds., Reduction, Explanation and Realism. Oxford: Clarendon Press.

• Perry, J. 1975. ed. Personal Identity. Berkeley: University of California Press. Contains many useful articles in addition to those mentioned above.

## Objects, substances and events

The notion of a material object has played a central role in philosophical discussions of what there is (ontology). What are material objects, and how should they be distinguished from one another and from other concrete entities, such as events? A traditional view, deriving from Aristotle, places the notion of substance at the heart of an ontology; but some philosophers today deny any role for the notion of substance. But even those who reject substance have to give some account of what it is for an object to persist over time, given that objects change their properties (the problem of change, or identity over time; Lewis calls this the ‘problem of temporary intrinsics'). A live contemporary question is under what conditions the parts of an object combine to make up a complex object (the problem of material consitution or composition).

### Substance

In the tradition of thought which comes to us from Aristotle, substances (‘primary substances' in Aristotle's sense) are the fundamental entities which persist over time and are the bearers of properties. Is a substance something over and above its properties? Those who want to explain or analyse the notion of substance have often presented the choice as one between treating substances as ‘bundles' of properties, or as treating the substance as a combination of a ‘bare particular' and the properties. But are these the only options?

• Crane, Tim & K. Farkas, eds., 2004. ‘Introduction' to Part III of Metaphysics: A Guide and Anthology.

• Robinson, Howard, 2004. ‘Substance' http://plato.stanford.edu/entries/substance/.

• David Wiggins, 1995. ‘Substance' in the Metaphysics section of Grayling, ed., Philosophy ;

• Lowe, E.J., 1998. ‘Substance and Dependence'. Chapter 6 of his The Possibility of Metaphysics: Substance, Identity and Time. Oxford: Oxford University Press.

• Locke, John, 1690. Selection from Essay Concerning Human Understanding Book II: chapter xxiii. in Crane & Farkas, Metaphysics.

• Bennett, Jonathan, 1987. ‘Substratum' reprinted in V. Chappell, ed., Locke. Oxford: Oxford University Press

• Black, Max, 1952. 'The Identity of Indiscernibles'. Mind. 61, 153-164. Reprinted in Michael J. Loux (ed.) Metaphysics. London and New York: Routledge 2001.

• Robert Adams, 1979. ‘Primitive Thisness and Primitive Identity', in Crane & Farkas, Metaphysics and other anthologies.

• Van Cleve, James, 1985. ‘Three Versions of the Bundle Theory', Philosophical Studies, 47: 95-107; reprinted in Loux's Metaphysics: a Contemporary Reader.

### Persistence

How do things persist or continue to exist over time? A recent way of approaching this question, inspired by David Lewis (see below), distinguishes between those who think of objects as extended in the three dimensions of space but wholly present at each moment of their existence (‘3 dimensionalists') and those who think of objects as extended across space and time (‘4 dimensionalists'). In Lewis's/Johnston's terminology, 3 dimensionalists say that objects ‘endure' and 4 dimensionalists say that they ‘perdure'. 4 dimensionalists also distinguish their view by saying that objects have temporal parts or stages (hence that me yesterday is a part of me, for example). 3 dimensionalists deny this.

#### On the basic problem of identity over time or persistence

• Gallois, André, 2005. ‘Identity through time' http://plato.stanford.edu/entries/identity-time/

• Haslanger, Sally, 2003. ‘Persistence through time' in Loux & Zimmerman, eds., The Oxford Handbook to Metaphysics.

• Chisholm, R.M. 1976. ‘Identity through Time' in Crane & Farkas, eds., Metaphysics.

• David Lewis, 1986. Selection from On the Plurality of Worlds, in Crane & Farkas, eds., Metaphysics.

• Shoemaker, S. 1984. ‘Identity, Properties & Causality'. In his Identity, Cause & Mind: Philosophical Essays. Cambridge: Cambridge University Press.

• Armstrong, D. M. 1980. ‘Identity through Time'. In P. van Inwagen, ed., Time & Cause: Essays Presented to Richard Taylor. Dordrecht: D. Reidel.

• Butterfield, Jeremy, 1984. ‘Spatial and Temporal Parts', Philosophical Quarterly 35: 32-44.

• Hawley, Katherine, 2002. How Things Persist. Oxford: Oxford University Press.

• Heller, Mark. 1984. ‘Temporal Parts of Four Dimensional Objects', Philosophical Studies 46: 323-334.

• Hirsch, E. 1982. The Concept of Identity. New York: Oxford University Press.

• Johnston, M. 1987. ‘Is there a Problem about Persistence?'. Proceedings of the Aristotelian Society Supplementary Volume 61: 107-135.

• Lowe, E.J. 1987. ‘Lewis on Perdurance Versus Endurance'. Analysis 47: 152-54.

• Merricks, Trenton. 1994. ‘Endurance and Indiscernibility'. Journal of Philosophy 91 (1994): 165-184.

• Sider, Theodore, 2001. Four Dimensionalism: An Ontology of Persistence and Time. Oxford: Oxford University Press.

### The composition of objects

Under what circumstances do a collection of objects make up or compose another? Philosophers who adopt the mereological principle of unrestricted composition say that any and every combination of objects compose another (they are sometimes called ‘universalists'). Others say that no objects ever compose any others (they are sometimes called ‘nihilists'). Some try to find a middle path: van Inwagen, for example, holds that objects compose another object when their joint activity constitutes a life.

An excellent anthology of essential readings is Michael Rea, ed., Material Constitution, Lanham, Md.: Rowman & Littlefield, 1997. The question is obviously connected to the questions (mentioned above) of substance, identity and individuation, and persistence.

• Burke, Michael. 1994a. ‘Preserving the Principle of One Object to a Place: a Novel Account of the Relations Among Objects, Sorts, Sortals, and Persistence Conditions', Philosophy and Phenomenological Research 54: 591-624; reprinted in Rea 1997.

• Fine, Kit. 1999. ‘Things and Their Parts', Midwest Studies in Philosophy, 23: 61-74.

• Rea, Michael. 1995. ‘The Problem of Material Constitution', Philosophical Review 104: 525-552.

• Thomson, J.J. 1983. ‘Parthood and Identity Across Time'. Journal of Philosophy 80 (1983): 201-219. Reprinted in Jaegwon Kim and Ernest Sosa, eds., Metaphysics ; and in Rea 1997.

• van Inwagen, Peter, 1995. Material Beings. Ithaca: Cornell University Press. See also the selections from this book in Crane & Farkas, eds., Metaphysics.

• van Inwagen, Peter, 1981. ‘The Doctrine of Arbitrary Undetached Parts', Pacific Philosophical Quarterly 62: 123-37.

### Events

In addition to concrete objects there are also those things which happen to them: events. Should we treat events as themselves concrete particulars (Davidson), or as akin to facts (Kim)?

• Davidson, D. 1967. ‘Causal Relations'. Journal of Philosophy 64: 691-703. Reprinted in Essays on Actions and Events. Oxford: Clarendon Press, 1980; and in Sosa and Tooley eds., Causation.

• —. ‘The Individuation of Events'. Reprinted in Essays on Actions and Events. Oxford: Clarendon Press, 1980.

• —. ‘Events as Particulars'. Reprinted in Essays on Actions and Events. Oxford: Clarendon Press, 1980.

• —. ‘Eternal vs. Ephemeral Events'. Reprinted in Essays on Actions and Events. Oxford: Clarendon Press, 1980.

• Kim, J. 1976. ‘Events as Property-Exemplifications'. In M. Brand, and D. Walton, eds., Action Theory. Dordrecht: Reidel. Reprinted in Supervenience and Mind: Selected Philosophical Essays. Cambridge: Cambridge University Press, 1993.

• Lewis, D. 1986. ‘Events' and ‘Postscripts'. In Philosophical Papers, Vol. 2. New York: Oxford University Press.

• Quine, W. V. 1985. ‘Events & Reification'. In E. Lepore, and B. McLaughlin, eds., Actions & Events. Oxford: Basil Blackwell. Also see Davidson's reply.

• Mellor, D. H. 1981. Real Time. Cambridge: Cambridge University Press. Ch.8.

## Universals

### Particulars and their properties

Two chairs can be the same colour, or the same shape, or be made of the same material. When we say that this chair is the same as that one, we do not seem to be talking about strict numerical identity: no two chairs can be literally the same chair. So what do we mean when we say that two chairs have the same colour? Philosophers say that the chairs are of the same kind, or the same type. But what is this ‘sameness of type'? Many have thought that we can only answer this question by positing universals (like properties and relations) in the world as well as particulars (like substances, objects and events). The collection edited by D. H. Mellor and A. Oliver, eds., Properties, contains many of the key readings on this subject.

#### Introductory material

• Armstrong, D. M. 1989. Universals: An Opinionated Introduction. Boulder: Westview Press (selection reprinted in Crane & Farkas, ed., Metaphysics, Part IV).

• Crane, Tim & Katalin Farkas, 2004, ‘Introduction' to Part IV of Metaphysics: a Guide and Anthology

• Plato, selections from Parmenides and Republic in Crane & Farkas, ed., Metaphysics, Part IV.

• Russell, Bertrand. 1912. The Problems of Philosophy. 2 nd ed. Oxford: Oxford University Press, 1998. Chs. 9-10.

• Macbride, Fraser, 1998. ‘Where are Particulars and Universals?' Dialectica 52: 207-37.

• Oliver, A. 1997. ‘The Metaphysics of Properties.' Mind 105: 1-80. This ‘state of the art' article is a fairly exhaustive survey of the current state of debate.

• Swoyer, Chris. 2000. ‘Properties'. http://plato.stanford.edu/entries/properties/

### Nominalism and realism

Realists about universals claim that there is a fundamental distinction between particulars, like individual physical objects, and universals. Nominalists (e.g. Quine) claim that only particulars exist. Nominalists therefore have to account for facts about sameness of type. They typically do this in terms of notions like resemblance, or class-membership. An alternative is trope theory, which treats the fundamental entities of the world as property instances or tropes (see Williams).

• Armstrong, D. M. 1978. Universals and Scientific Realism. 2 Vols. Cambridge: Cambridge University Press. Vol. 1: Nominalism and Realism.

• Crane, Tim. 1995. ‘Universals'. In A. C. Grayling, ed., Philosophy.

• Devitt, M., D. M. Armstrong, and W. V. Quine 1980. Pacific Philosophical Quarterly 61. The first two are reprinted in Mellor and Oliver, eds. Properties.

• Lewis, D. 1983. ‘New Work for a Theory of Universals'. Australasian Journal of Philosophy 61: 343-377. The selections from this paper in Mellor and Oliver contain the material relevant to this issue.

• –. 1986. On the Plurality of Worlds. Oxford: Basil Blackwell. Ch.1.5.

• Teichmann, R. 1989. ‘Three Kinds of Realism about Universals'. Philosophical Quarterly 39: 143-165.

• Williams, D.C. 1955. ‘The Elements of Being' in Crane & Farkas, eds., Metaphysics, and in other anthologies.

### The nature of universals

If universals exist, then what is their nature? Should they be individuated in terms of the causal powers of the things which instantiate them (Shoemaker)? Or in terms of their place in laws of nature (Mellor)? Can a tenable distinction be made between natural properties and other properties?

• Armstrong, D. M. 1978. Universals and Scientific Realism. 2 Vols. Cambridge: Cambridge University Press. Vol. 2. A Theory of Universals. Chs.1-3.

• Shoemaker, S. 1980. ‘Causality and Properties'. Reprinted in Identity, Cause and Mind: Philosophical Essays. Cambridge: Cambridge University Press, 1984.

• Taylor, B. 1993. ‘On Natural Properties in Metaphysics'. Mind 102: 81-100.

• Mellor, D. H. 1991. ‘Properties & Predicates'. In Matters of Metaphysics. Cambridge: Cambridge University Press.

• Lewis, D. 1983. ‘New Work for a Theory of Universals'. Australasian Journal of Philosophy 61: 343-377. Abridged in Mellor & Oliver, and in Crane & Farkas, eds., Metaphysics Part IV.

## Causation and Laws

The notions of cause and effect are fundamental to our conception of the world. But what is causation? What is the connection between causation and regularities (Hume, Anscombe), and causation and causal explanation (Owens, Lewis)? Can we give an analysis of causation in terms of necessary and sufficient conditions (Mackie) or in terms of counterfactuals (Lewis)? Must all causation be backed by general laws, or are there purely singular facts about causation (Anscombe, Ducasse, Foster)? Should we think of causes and effects as events (Davidson) or as facts (Mellor)? Can there be probabilistic causation?

### The analysis of causation: regularity and counterfactuals

• Hume, D. Treatise, I.3, 14/15.

• —. An Enquiry concerning Human Understanding, sec.VII. (reprinted in Crane & Farkas, eds., Metaphysics )

• Crane, Tim. 1995. ‘Causation'. In A. C. Grayling, ed., Philosophy. Elementary introduction.

• Owens, D. 1992. Causes and Coincidences. Cambridge: Cambridge University Press. Chs. 3 & 4

• Jonathan Schaffer, 2003, ‘The Metaphysics of Causation' http://plato.stanford.edu/entries/causation-metaphysics/ An advanced introduction, but nonetheless extremely clear.

##### The regularity account
• Anscombe, G. E. M. 1971. ‘Causality & Determination'. Reprinted in Sosa, ed., Causation and Conditionals. Oxford: Oxford University Press, 1975; and in Sosa and Tooley, eds., Causation.

• Ducasse, C. J. 1923. ‘On the Nature and Observability of the Causal Relation'. Reprinted in Sosa, ed., Causation and Conditionals. Oxford: Oxford University Press, 1975; and in Sosa and Tooley, eds., Causation.

• Foster, J. 1985. Ayer. London: Routledge. Ch.3, sec.7.

• Mackie, J. L. 1965. ‘Causes and Conditions'. American Philosophical Quarterly 2: 245-264. Reprinted in Sosa, ed., Causation and Conditionals. Oxford: Oxford University Press, 1975; and in Sosa and Tooley, eds., Causation.

##### The counterfactual account
• Lewis, D. 1986. ‘Causation', and. In Philosophical Papers, Vol. 2. New York: Oxford University Press; reprinted in Sosa and Tooley, eds., Causation, and in Crane & Farkas, eds, Metaphysics. This was Lewis's original statement of his view. For a criticism, see the essays by Kim and Horwich in Sosa and Tooley, eds., Causation.

• For Lewis ‘s later statements of his view, see:

• ‘Postscripts' in Philosophical Papers Volume II ; for criticism see:

• Menzies, Peter, 1996. ‘Probabilistic Causation and the Pre-emption Problem'. Mind 105: 85-117.

• McDermott, Michael, 1995. ‘Redundant Causation', British Journal for the Philosophy of Science, 40: 523-544.

• Schaffer, Jonathan, 2000. ‘Trumping Preemption', Journal of Philosophy, 97: 165-81.

• For Lewis's last statements on the issue:

• Lewis, D. 2000. ‘Causation as Influence', Journal of Philosophy, 97: 182-97.

• Lewis, D. 2004. ‘Void and Object' in Hall, N., & L. Paul, eds., 2004. The Counterfactual Analysis of Causation Cambridge, Mass: MIT Press.

For a survey, see:

##### Other issues
• Tooley, M. 1990. ‘Causation: Reductionism versus Realism'. P hilosophy and Phenomenological Research 51: 215-236. Reprinted in Sosa and Tooley, eds., Causation. On the question of whether causation can be reductively explained at all.

• Gasking, D. 1955. ‘Causation and Recipes', Mind, 64: 479-487. An early and very clear statement of the ‘manipulability' approach to causation. For a contemporary survey of this issue, see Woodward, James, 2001. ‘Causation and Manipulability' http://plato.stanford.edu/entries/causation-mani/

• Price, Huw, ed., forthcoming, Russell's Republic. Oxford: Oxford University Press. A collection of essays on Russell's skeptical view that causation, like the monarchy, is an idea which has had its day.

### What are causes and effects?

• Davidson, D. 1967. ‘Causal Relations'. Journal of Philosophy 64: 691-703. Reprinted in Essays on Actions and Events. Oxford: Clarendon Press, 1980; and in Sosa and Tooley eds., Causation, and in Crane & Farkas, eds., Metaphysics. For a discussion of Davidson, see Simon Evnine, Donald Davidson, Cambridge: Polity, 1991, Ch.2.

• Mellor, D. H. 1991. ‘The Singularly Affecting Facts of Causation'. In Matters of Metaphysics. Cambridge: Cambridge University Press.

• —. 1995. The Facts of Causation. London: Routledge. More difficult material.

### Causation and causal explanation

• Lewis, D. 1986. ‘Causal Explanation'. Reprinted in Philosophical Papers, Vol.2. New York: Oxford University Press.

• Ruben, David-Hillel. 1993. ed. Explanation. Oxford: Oxford University Press. This collection contains many central papers on the concept of explanation.

• —. 1990. Explaining Explanation. London: Routledge. A useful introduction to the issue.

• Lipton, P. 1990. ‘Contrastive Explanations'. Philosophy 64: 247-266.

• Papineau, D. 1995. ‘Methodology'. In A. C. Grayling, ed., Philosophy.

### Laws of Nature

Philosophical accounts of explanation and causation often appeal to the idea of a law of nature (for instance, Hempel's account of explanation; Humean accounts of causation). But what is a law of nature? How are laws distinguished from merely accidental generalisations? One view, defended by Ramsey and Lewis, is that it is merely a form of regularity. Some recent accounts of laws have diverged from this in claiming that laws are metaphysical relations between universals.

• Hempel, C. 1966. Philosophy of Natural Science. Englewood Cliffs, N. J.: Prentice-Hall. Ch.5.3.

• Ayer, A. J. 1956. ‘What is a Law of Nature?'. Revue Internationale de Philosophie 10: 144-165. Reprinted in The Concept of a Person: and Other Essays. London: Macmillan, 1973.

• Nagel, E. 1961. The Structure of Science: Problems in the Logic of Scientific Explanation. London: Routledge and Kegan Paul. Ch.4.

• Papineau, D. 1986. ‘Laws and Accidents'. In C. Wright, and G. Macdonald, eds., Fact, Science and Morality: Essays on A.J. Ayer's Language, Truth and Logic. Oxford: Basil Blackwell.

• Ramsey, F. 1928. ‘Law and Causality'. In Philosophical Papers, edited by D. H. Mellor. Cambridge: Cambridge University Press, 1990.

• Lewis, D. 1973. Counterfactuals. Oxford: Basil Blackwell.

• Dretske, F. 1977. ‘Laws of Nature'. Philosophy of Science 44: 248-268.

• Armstrong, D. M. and Adrian Heathcote, 1991. ‘Causes and Laws'. Nous 25:63-73.

• —. 1983. What is a Law of Nature? Cambridge: Cambridge University Press.

• Mellor, D. H. 1991. ‘Necessities and Universals in Laws of Nature'. In Matters of Metaphysics. Cambridge: Cambridge University Press.

• van Fraassen, B. 1989. Laws and Symmetry. Oxford: Clarendon Press. Pt.I.

### Probabilistic causation

The view that determinism is false is becoming increasingly popular. Is the fact that an event is not fully determined to occur incompatible with its having been caused? Or can an analysis of causation be given which replaces the idea that a cause is sufficient for its effects with the idea that a cause raises the probability of its effects? Can a cause lower the probability of an effect? Can we use probability to analyse ‘population-level' causal facts, for example the fact that smoking causes cancer?

• Eells, E. 1991. Probabilistic Causality. Cambridge: Cambridge University Press. Introduction.

• Dupré, J. 1984. ‘Probabilistic Causality Emancipated'. In Peter A. French, Theodore E. Uehling, Jr., Howard K. Wettstein, eds., Causation and Causal Theories. Midwest Studies in Philosophy 9. Minneapolis: University of Minnesota Press.

• Eells, E. 1987. ‘Probabilistic Causality: reply to John Dupré's “Probabilistic Causality Emancipated”'. Philosophy of Science 54: 105-114.

• Mellor, D. H. 1995. The Facts of Causation. Selections in Crane & Farkas, eds., Metaphysics, Part VI.

• Sober, E. 1986. ‘Causal Factors, Causal Inference, Causal Explanation'. Aristotelian Society Supplementary Volume 60: 97-114.

• Papineau, D. 1986. ‘Causal Factors, Causal Inference, Causal Explanation'. Aristotelian Society Supplementary Volume 60: 115-136.

• Lewis, D. 1986. ‘Causation: Postscripts'. In Philosophical Papers, Vol. 2. New York: Oxford University Press.

• Salmon, W. C. 1984. Scientific Explanation and The Causal Structure of the World. Princeton, N. J.: Princeton University Press.

• Menzies, P. 1989. ‘Probabilistic Causation and Causal Processes: a critique of Lewis'. Philosophy of Science 56: 642-663.

• Cartwright, N. 1979. ‘Causal Laws and Effective Strategies'. Noûs 13: 419-437; reprinted in her How the Laws of Physics Lie. Oxford: Clarendon Press, 1983.

## Time and Space

### Time and 'tense' (the 'flow' of time)

There are two very different ways of thinking and talking about time: in terms of the concepts of past, present or future (what McTaggart called the ‘A' series), or in terms of the concepts of being earlier, later or simultaneous (what McTaggart called the ‘B' series). Is one of these ways of thinking more fundamental, that is, is one reducible to the other? The ‘tenseless' theory of time says that the latter is more fundamental; the ‘tensed' view says that the former is ineliminable and irreducible.

• Le Poidevin, Robin, 2003. Travels in Four Dimensions Oxford: Oxford University Press. Chapter 8.

• Dainton, Barry, 2001. Time and Space. Chesham: Acumen.
NB These two books provide very useful introductions to all the issues in this section.

• McTaggart, J. M E. 1927. ‘The Unreality of Time'. In LePoidevin & MacBeath, The Philosophy of Time and in Crane & Farkas, eds., Metaphysics.

• Prior, A. N. 1962. ‘Changes in Events and Changes in Things'. In LePoidevin & MacBeath.

• Mellor, D. H. 1981. Real Time. Cambridge: Cambridge University Press. Ch.6. Reprinted in LePoidevin & MacBeath.

• Mellor, D.H., 1998. Real Time II. London: Routledge. A heavily revised version of the 1981 book.

• Dummett, Michael, 1960. ‘A Defence of McTaggart's Proof of the Unreality of Time' Philosophical Review 69: 497-504. Reprinted in Dummett, Truth and Other Enigmas. London: Duckworth 1978.

### Time, change and reductionism about time and space

Is time simply the dimension of change? Some philosophers argue that time without change is impossible. Others argue that we could have no evidence for the passage of time if there were no change. See Shoemaker for an argument that time without change is conceivable. This is connected to the question about whether time is reducible to the temporal relations between events, and whether space is reducible to the spatial relations between objects. Relationists or Reductionists about time and space are those who think it is. Those who deny this are sometimes called ‘substantivalists'.

• Shoemaker, S. 1969. ‘Time without Change'. Journal of Philosophy 66: 363-381. Reprinted in his Identity, Cause & Mind: Philosophical Essays. Cambridge: Cambridge University Press, 1984; and in LePoidevin & MacBeath.

• Forbes, G. 1993. ‘Time, Events and Modality'. In LePoidevin and MacBeath.

• Sklar, L. 1974. Space, Time & Spacetime. Berkeley: University of California Press. Ch.IV.

• Newton-Smith, W. H. 1986. ‘Space, Time, and Space-Time: a Philosopher's View'. In Raymond Flood and Michael Lockwood, eds., The Nature of Time. Oxford: Basil Blackwell. A good introduction to reductionism about time.

• —. 1980. The Structure of Time. London: Routledge and Kegan Paul. A more detailed treatment of the question.

• Smart, J.J.C., 1963. ‘The Space-Time World', in Philosophy and Scientific Realism Routledge and Kegan Paul; reprinted in Crane & Farkas, eds., Metaphysics.

### The direction of time and the direction of causation

Time is one of the four dimensions of spacetime. Time can be distinguished from the three spatial dimensions in that it has a ‘direction'. It is possible to travel in all three dimensions of space in any direction. But in time it seems that we can only ‘travel' in one direction, from the past into the future. What accounts for the direction of time? How is it related to the direction of causation?

• Dummett, M. 1964. ‘Bringing about the Past'. Philosophical Review 73: 338-359. Reprinted in Truth & Other Enigmas, London: Duckworth, 1978; also in LePoidevin and MacBeath.

• —. 1986. ‘Causal Loops'. In Raymond Flood and Michael Lockwood, eds., The Nature of Time. Oxford: Basil Blackwell. Reprinted in The Seas of Language. Oxford: Clarendon Press, 1993.

• Lewis, D. 1976. ‘The Paradoxes of Time Travel'. American Philosophical Quarterly 13: 145-152. Reprinted in Philosophical Papers, Vol.2. Oxford: Oxford University Press, 1986, and in Crane & Farkas, eds., Metaphysics: a Guide and Anthology.

• —. 1979. ‘Counterfactual Dependence and Time's Arrow'. Nous 13: 455-476. Reprinted Philosophical Papers, Vol.2.

• Mellor, D. H. 1981. Real Time. Cambridge: Cambridge University Press. Chs.9 & 10.

• Sorabji, R. 1988. Matter, Space and Motion: Theories in Antiquity and their Sequel. London: Duckworth. Ch.10.

• Price, H. 1996. Time's Arrow & Archimedes' Point: New Directions for the Physics of Time. Oxford: Oxford University Press.