The Oxford Companion to Philosophy Part 71 docx

finding satisfies a criterion for finding it true; and so on, ad infinitum. Where other sentences get a permanent truth assignment, some self-referential sentences (the liar para- dox is one) oscillate indefinitely. Various interpretations may be placed on such data, including assigning ‘values’ other than the true–false pair. The patterns of ‘valuation’ produced by various rules may make an interesting object of mathematical study. It is rather like a psychiatrist classi- fying ‘paradoxical’ personality types, love–hate relation- ships, double or multiple binding personal interactions, manic-depressives, etc., from a detached perspective. Classical logical laws cannot be treated as applicable sequentially without ignoring the universality which is essential to their identity. If a claim is found true, then found false, then true, and so on indefinitely, then either half of these ‘findings’ are mistaken or else it was not the same claim from one ‘finding’ to the next. However, the anti-traditionalist may not be concerned with how classical laws need to be applied. He may have been led by his exposure to paradoxes and antinomies to have given up the belief that there is in matters of theory any mandatory received opinion or any fundamental prin- ciples to get into conflict of a privileged logical kind which it is essential to proper thinking to resolve. He can agree with the classicist that without the absolutely universal and necessary logical principles there is no fixed basis for determining the correct response to a paradox or anti- nomy, but draw a very different moral. His response to those troubled by paradox may be like that of the psych- iatrist easing a patient’s distress not by answering his ques- tions, but by changing his attitude towards them. This conflict over the very identity and nature of the conflict illustrates how, in a paradox case, we may encounter considerable difficulty in achieving agreement about the correct description of the problem. Whether an opinion has a status that would make its rejection signifi- cant, or a ‘law’ is really fundamental, may be unclear. And even the significance of rejection or conflict may be a mat- ter of disagreement. It is perfectly compatible with classical logic to regard difference of opinion as healthy or even desirable. But those who wish further not to be con- strained by the idea that one side in a contradiction must be wrong will not settle for that. Paradox cases raise general questions about method and principle, which is one reason the topic has been of such interest in philosophy. j.c. *Moore’s paradox; two-envelope paradox. J. C. Beall (ed.), Liars and Heaps: New Essays on Paradox (Oxford, 2003). John Buridan, Sophisms on Meaning and Truth, tr. Theodore Kermit Scott (New York, 1966). James Cargile, Paradoxes (Cambridge, 1979). Robert L. Martin (ed.), Recent Essays on Truth and the Liar Paradox (Oxford, 1984). W. V. Quine, ‘The Ways of Paradox’, in The Ways of Paradox (New York, 1966). Bertrand Russell, ‘Mathematical Logic as Based on the Theory of Types’, in Logic and Knowledge (London, 1956). R. Sorensen, A Brief History of the Paradox (Oxford, 2003). paradoxes, logical. F. P. Ramsey held that ‘the well known contradictions of the theory of aggregates . . . fall into two fundamentally distinct groups’. The first group ‘involve only logical and mathematical terms’ and have come to be called (by many) ‘logical paradoxes’. The sec- ond group ‘cannot be stated in logical terms alone’ and ‘contain some reference to thought, language, or symbol- ism, which are not formal, but empirical terms’. Ramsey held that the *paradoxes of the second group ‘may be due not to faulty logic or mathematics, but to faulty ideas con- cerning thought and language’, and in that case, ‘they would not be relevant to mathematics or logic, if by “logic” we mean a symbolic system, though of course they would be relevant to logic in the sense of the analysis of thought’. Those who follow Ramsey’s suggestion call the second group ‘semantic paradoxes’. All but one of Ramsey’s examples come from Principia Mathematica, where they are listed under the common heading of ‘Contradictions which have Beset Mathemat- ical Logic’. The ones he calls ‘logical’ are Russell’s paradox, Burali-Forti’s paradox, and the paradox of the relation which holds ‘between two relations when one does not have itself to the other’. The ones now called ‘semantic’ (by those who accept this distinction) are the liar paradox, Berry’s paradox, Konig’s paradox of the least indefinable ordinal, Richard’s paradox, and Grelling’s paradox. (The last is the one paradox not in the Principia list.) Ramsey’s distinction should be regarded as controver- sial. His two alternative meanings for ‘logic’—‘a symbolic system’ and ‘the analysis of thought’ do not rule out non- logical symbolic systems or psychology, and are, anyway, not mutually exclusive. The notions of reference, defin- ition, or truth have as much claim to belong to logic as does the notion of a class. This was clearly the intention of the authors of Principia since they attempted to allow these terms to occur in their ideal language while at the same time laying down rules which would prevent con- tradictions formulated in such terms from being derivable in their system. A pragmatic motive for Ramsey’s distinction arises from the fact that, in order to both allow the ‘semantic’ terms and avoid contradictions, Principia presents what is known as ‘the ramified’ (as opposed to ‘the simple’) theory of types. On the simple theory, both the propositional functions ‘x is a general’ and ‘x has all the qualities of a great general’ would be of type 1, one type above that of the things (individuals) to which they apply. But the latter function is built up by quantifying the function ‘x is a qual- ity of a great general’, which, in the simple theory, would be of type 2. And this fact about its derivation is important to the Principia treatment of ‘semantic’ paradoxes. Func- tions are not ordered simply by the order of their argu- ments but by the order of the arguments to the ‘matrices’ from which the functions are derived. (Matrices, roughly, are what is left when quantifiers are deleted from a for- mula.) The ramified hierarchy of orders is the basis for a rule requiring that a proposition of the nth order can only be allowed apparent variables of order n – 1. This is much 680 paradoxes more restrictive than the simple type rule that a propos- itional function of type n determines a class whose mem- bers are of type n –1. The simple rule would have ‘a property of individual a’ represent a property of type 2 whose instances would be type 1 properties of a. But the ramified rule would make that phrase illegitimate and give us instead an infinite hierarchy of properties: ‘a first-order property of a’, ‘a second-order property of a’, etc. This was so restrictive as to rule out the definition of the least upper bound of a class of real numbers. The Principia response was ‘the axiom of reducibility’, which guarantees that for every such function of a in the infinite hierarchy, there is an extensionally equivalent first-order function. Ramsey argued that the axiom of reducibility is implaus- ible, and unnecessary if Principia is restricted to terms of set theory, which would be all that is required for its pri- mary mission of being a foundation for mathematics. This has been a popular idea, and today it is the simple theory of types that would be most likely to be discussed by set theorists. There is nothing wrong in that, but it would be unfortunate if the success of a simplification of one theory of sets were mistaken for a conclusive basis for a distinc- tion between ‘logical’ and ‘semantic’. j.c. F. P. Ramsey, ‘The Foundations of Mathematics’, in The Founda- tions of Mathematics and Other Logical Essays, ed. R. B. Braith- waite (London, 1945). Bertrand Russell and Alfred North Whitehead, ‘Introduction to the Second Edition’, in Principia Mathematica (Cambridge, 1962). parallel distributed processing. A form of computation in which items are represented not by symbols but by pat- terns of activity distributed over a network of simple pro- cessing units. Particular patterns result from massively parallel computations of the levels of activation in individ- ual units. Connections between the units excite or inhibit the spread of activation. As a model of human *cognition it is proposed as a rival to the *language of thought hypothesis, one that offers a closer approximation to brain processing. b.c.s. *connectionism. P. Smolensky, ‘The Proper Treatment of Connectionism’, in Behavioural and Brain Sciences (1988). parallelism, psychophysical. The thesis that mind and body never influence one another, but nevertheless progress along parallel paths, as though they interacted. This response to the *mind–body problem is partially motivated by the view that two distinct kinds of being or substance exist, immaterial and material, and by the diffi- culty of understanding how substances of either kind can act upon substances of the other. Leibniz held that God arranged things in advance so that our minds and bodies would be in harmony with one another and with what happens to all other substances: the doctrine of *pre- established harmony. In the absence of some such explan- ation, parallelism would be a remarkable coincidence; but one suspects that a being capable of instituting pre- established harmony could also find a way to allow mind and body to interact. a.r.m. *occasionalism. G. W. Leibniz, Philosophical Papers and Letters, ed. L. E. Loemker (Chicago, 1956), chs. 35–6, 47, 52, 54–5, 58, 60–1, 63, 67, 71. paralogisms. In Kant’s critical philosophy, a fallacious argument. In the Critique of Pure Reason Kant identifies three paralogisms in the first edition and a fourth in the second edition. They are invalid inferences to conclusions expressing the simplicity of the soul, the personality of the soul, the immortality of the soul, and the existence of the external world. In each case, the mistake is to try to derive a tenet of transcendental realism from premisses express- ing only transcendental idealism—that is, conclusions about a putative non-spatio-temporal reality from pre- misses only about possible appearances. s.p. Kant, Critique of Pure Reason, tr. Norman Kemp Smith (London, 1978). paraphrasis: see Bentham; contextual definition. Pareto optimality. Pareto optimality, developed by Vilfredo Pareto, is the most widely accepted criterion of economic efficiency. A state of a given system (e.g. a distribution of a given quantity of goods) is Pareto opti- mal, and thus efficient, if and only if there is no feasible alternative state of that system (e.g. no feasible alternative distribution of those goods) in which at least one person is better off and no one is worse off. And, for purposes of this criterion, a person is ‘better off’ with some alternative A rather than B if and only if this person prefers A to B. An advantage of this criterion is that it provides a way of evalu- ating alternative social states that does not require inter- personal utility comparisons. d.w.has. Allen Buchanan, Ethics, Efficiency, and the Market (Totowa, NJ, 1985). Parfit, Derek (1942– ). Best known for his innovative ideas about the nature of *personal identity, where he contends that, in a significant sense, ‘identity’ is not what matters in the continuity and persistence of persons throughout their lives. This view was outlined in a num- ber of articles in the 1970s but was fully expounded in his Reasons and Persons (Oxford, 1984). In that book, he draws out some of the consequences of his views for moral the- ory, arguing that certain traditional conceptions of pru- dence and self-interest must be questioned once the conception of the nature of the self on which they depend is criticized. His theories have excited considerable com- ment. Since 1967 a Fellow of All Souls, Oxford, he is also a keen architectural photographer. n.j.h.d. Parmenides (fl. c.480 bc). Citizen of Elea and leading fig- ure of the *Eleatics. His philosophical work was expounded in his poem, of which more than a hundred lines survive. The poem begins with a first-person narra- tive of an allegorical journey, at the end of which the Parmenides 681 narrator meets a goddess. The goddess tells him: ‘you are to find out everything: both the steadfast heart of well- rounded Reality, and the opinions of mortals, which con- tain no genuine proof’. In the rest of the poem, in a long speech, the goddess fulfils the double promise. The section on ‘Reality’ (or ‘Truth’: the translation is controversial), of which much survives, expounded and claimed to prove the truths Parmenides took to be demonstrable. An indubitable foundation for knowledge is found, as by Descartes, in the mind and its relation to its objects. (1) One cannot coherently doubt that thinking is possible and actually occurs. (2) Thinking must have an object which exists. On these two principles all positive knowledge rests. It follows that (3) something exists; and (4) ‘what is not’ is not a possible object of speech or thought, so that any attempted theory must be incoherent if it involves apparent reference to anything as non-existent. The next step, since it must be that something exists, is to consider the aggregate of all that exists, ‘that which is’ or ‘whatever is’. Arguments relying heavily on (4) above are deployed to show that this must have certain properties. (1) It cannot come to be nor cease to be. (2) It has no gaps but is a coherent whole. (3) It is ‘not deficient’, hence com- plete and bounded, hence cannot be changed or moved, ‘but remaining the same in the same and on its own it lies, and so remains steadily there’. (4) It is ‘perfect from every direction, like the mass of a well-rounded ball, in equipoise every way from the middle’. Another thesis, announced but not explicitly proved, states: ‘nor was it ever nor will it be, since it all is now together, one, coherent’. There is continuing controversy about the meaning of these conclusions and about the arguments by which they are supported. The arguments are presented as com- pelling demonstrations of necessary truths, but they indis- putably contain gaps and ambiguities. They often seem to appeal to intuitions drawn from common experience of a spatially and temporally extended world; and the words used to express the conclusions are drawn from everyday vocabulary and have spatial and temporal connotations. The problems in the theory of Reality therefore raise the central question of Parmenides’ view of ordinary experience. This is perhaps to be found in the last part of the poem, the account of ‘the opinions of mortals’ (of which not much survives), and in occasional asides earlier. The ‘opinions’, as expounded by Parmenides, constitute a systematic cosmological theory (dualistic, showing inter- est in astronomy and biology, and traces of the ideas and interests of Pythagoras and his sect). This theory, how- ever, is said to be undemonstrable, ‘deceptive’, and based on a mistake. Yet it is also described as ‘likely’ and ‘reli- able’, and as the best of its kind. The ‘mistake’ or ‘decep- tion’ therefore is not that of taking the false for the true but of taking the unprovable for the true; and it is a purely the- oretical mistake, with no practical consequences. On this reading, Parmenides does not deny the reality of the ordinary world, but denies only the possibility of knowledge about it. It must therefore be identified, not with Reality, but with some non-essential aspect of it. The logical exploration of Reality reveals, then, its essential and ascertainable structure. This structure can hardly be spatio-temporal, if that implies some real connection with the spatial and temporal relationships of ordinary experi- ence. For Parmenides denies the applicability of the past and future tenses to Reality, so that temporal succession must be an illusion. Likewise, ordinary spatial perspec- tives, and therefore all ordinary spatial intuitions, are pre- sumably no certain guides. If Reality is ‘bounded’ and ‘spherically symmetrical’, the words must be understood in transferred senses, indicating that Reality is essentially complete, definite, and without differences of aspect. If Reality is known by human thought, it would seem that that thought too cannot be purely superficial but must find a place within the essential structure of Reality. Cryptically, Parmenides says that ‘you will not find think- ing apart from what is, in which it [thinking] is made mani- fest’. This may indicate an idealist conclusion: that Reality is itself a thinking thing, and the object of its own thought. e.l.h. A. H. Coxon, The Fragments of Parmenides (Assen, 1986). A. P. D. Mourelatos, The Route of Parmenides (New Haven, Conn., 1970). G. E. L. Owen, ‘Eleatic Questions’, Classical Quarterly (1960). parsimony, law of: see Ockham’s razor. partiality and impartiality. Moral philosophers with widely different outlooks, including Kantians and utilitar- ians, have argued that impartiality is an important, or even constitutive, element in moral thinking. Some dissidents, however, suggest that this ideal is defective, and that par- tiality, in some cases, is morally permissible, or even desir- able. But disagreement about what impartiality requires threatens this debate with collapse. Impartiality enjoins us, at the least, to give equal con- sideration to all persons in our moral thinking. Nepotism, which favours one’s relatives, violates the requirement. But does impartiality demand that we treat everyone equally? Partialists often insist that relational facts can sometimes justify different treatment: we invite friends rather than strangers to parties, and we take our own chil- dren, excluding others, on holiday. In response, impartial- ists claim that their requirement comes into play at a more fundamental level. Relational facts may be granted rele- vance, so long as the principles we adopt can themselves be impartially endorsed (I must allow, in caring especially for my children, that others may care for theirs). s.d.r. *equality; justice. Ethics, 101, no. 4 (July 1991), contains a symposium on Impartial- ity and Ethical Theory. particular proposition. In *traditional logic propositions construed as having the form ‘Some S areP’ or ‘Some S are not P’ were called particular and contrasted with the uni- versal forms ‘All S are P’ and ‘No S are P’. In *predicate cal- culus, propositions like ‘Some men are mortal’ are 682 Parmenides regarded as having existential import and represented as ‘There is an x such that x isS and xis P’, which may be sym- bolized as ‘∃x(Sx & Px)’. c.w. P. F. Strawson, Introduction to Logical Theory (London, 1952), chs. 6, 7. particulars and non-particulars. Particulars are normally contrasted with *universals, the former being instances of the latter—as a particular apple is an instance of the uni- versal, or kind, apple. Particulars (in this broad sense) may be concrete, existing in space and time—as does a particu- lar apple—or they may be abstract, as in the case of math- ematical particulars like sets. (Sometimes, however, the term ‘abstract particular’ is used to denote what is other- wise known as a particularized quality or individual prop- erty, such as the redness of this apple.) Some philosophers, notably P. F. Strawson, draw a dis- tinction between particulars and individuals. On this view, some but not all individuals are particulars, though all particulars are individuals—particulars being spatio- temporally existing individuals governed by determinate criteria of *identity. Amongst ‘non-particulars’ Strawson lists such items as properties, numbers, propositions, and facts. e.j.l. P. F. Strawson, Individuals: An Essay in Descriptive Metaphysics (London, 1959). Pascal, Blaise (1623–62). A near contemporary of *Descartes, Pascal played a considerable role in the scien- tific revolution of the early modern period, and his achievements included inventing the first mathematical calculator, and establishing the possibility of a vacuum. He is best known for his religious writings, which began after his nuit de feu (‘night of fire’) on 23 November 1654, when he had a powerful conversion experience. Pascal rejected conventional philosophical ‘proofs’ of God’s existence, maintaining that the nature and existence of God were beyond the power of human reason to estab- lish; instead, God was the ‘God of Abraham, Isaac and Jacob, not the God of the philosophers’, and had to be approached via a living tradition of faith. Pascal is famous for his ‘wager’ argument, which is not a demonstration of God’s existence, but a ‘pragmatic argu- ment’—an attempt to show it is rational to set about becoming a religious believer; for if there is a God, the believer can look forward to an ‘infinity of happy life’, while if there is no God, nothing of significant value will have been lost. In order to acquire belief, Pascal recom- mends that we embark on a course of praxis, such as regu- larly going to church, which ‘in the natural course of events will make you believe’. j.cot. Blaise Pascal, Pensées [c.1660], ed. L. Lafuma (Paris, 1962); English tr. A. J. Krailsheimer (Harmondsworth, 1966). A. J. Krailsheimer, Pascal (Oxford, 1980). Ward E. Jones, ‘Religious Conversion, Self-Deception and Pas- cal’s Wager’, Journal of the History of Philosophy, 36 no. 2 (April 1998). Pascal’s wager. An argument for the rationality of believ- ing in God, assuming that no satisfactory evidence is avail- able. Pascal argues that the expected value of theistic belief is vastly greater than that of unbelief, since if one believes, and commits oneself to a life of faith in God etc., and it turns out to be true, then one wins an enormous good (Heaven etc.). But if one believes, and it turns out to be false, then one has lost little, if anything. Therefore (unless the probability of God’s existence is infinitesimal), it is rational to adopt theistic belief and the corresponding mode of life. g.i.m. William James, The Will to Believe (New York, 1897). Blaise Pascal, Pensées, tr. H. F. Stewart (London, 1950). passion and emotion in the history of philosophy. The term ‘passion’ has a long and convoluted history, both in and out of philosophy. Aristotle used the term pathé (plural) to refer to such things as ‘anger, fear, pity, and the like’ which lead to ‘one’s condition becoming so trans- formed that his judgment is affected, accompanied by pleasure and pain’ (Rhetoric). Aristotle’s analysis of anger included a distinctive cognitive component, a specified social context, a behavioural tendency, and physical arousal. (He had little to say of ‘feeling’.) He insisted that having the right passions was essential to the virtuous life. The Stoics, too, took an interest in emotion on the way to forming their ethics. But whereas Aristotle took emo- tion to be essential to the good life, the Stoics analysed emotions as conceptual errors, conducive only to misery. Passions are mistaken judgements about the world and one‘s place in it. In the Middle Ages, passions remained central to concerns in religion and ethics, especially mat- ters of faith and sinfulness. Aquinas distinguished between the higher and the lower passions, faith and love among the former, greed, lust, anger, envy, and pride among the latter. So, too, in Buddhism, there were important distinc- tions between desirable aesthetic rasas (e.g. the erotic) and ordinary agitating klesas (e.g. lust). Descartes summarized a good deal of his philosophy in his treatise The Passions of the Soul, where he insisted that the passions involve the interaction of mind and body in an undeniable way. A passion is both physiology (the agi- tation of the ‘animal spirits’), a ‘perception which we relate to our soul’, and an attitude toward the world. Hatred, for example, ‘arises from the perception of an object’s potential harmfulness and involves a desire to avoid it’. But Descartes also uses the term ‘emotion’, as did Spinoza and Hume after him, to refer to the move unruly passions. That term, which has all but replaced ‘passion’ as the general term for the various phenomena grouped together by Aristotle, did not receive its current broad meaning until the mid-nineteenth century with the psy- chologizing of the field. Today, ‘emotion’ is the category term, and ‘passion’ is reserved for an overwhelming and all-absorbing emotion or desire. The psychological maturity of the concept of emotion is marked Charles Darwin’s 1872 treatise On the Expression of Emotion in Animals and Men, and William James’ seminal passion and emotion in the history of philosophy 683 essay ‘What is an Emotion?’, of 1884. Darwin pointed out the continuity between humans and their near kin in the mammalian world, and James urged a somewhat reduc- tive understanding of emotion as the sensations that accompany physiological disturbances caused by upset- ting perceptions. The recent history of interest in emotion has been largely framed by reactions to James and a renewed defence of physiology-based (or neurology- based) theories of emotion. Jean-Paul Sartre is one of those who reacted to James. In a ‘phenomenological’ analysis of emotion, he argued that emotions are ‘magical transformations of the world’—strategies for coping with a difficult world. r.c.sol. Thomas Dixon, From Passions to Emotions (Cambridge, 2003). Susan James, Passion and Action (Oxford, 1997). Robert C. Solomon, Not Passion’s Slave (Oxford, 2003). passions, reason as the slave of the: see reason as the slave of the passions. past: see time. paternalism. The power and authority one person or institution exercises over another to confer benefits or prevent harm for the latter regardless of the latter’s informed consent. Paternalism is thus a threat to auton- omy as well as to liberty and privacy. On any normative theory, however, paternalism is desirable toward young children, the mentally ill, and others similarly situated. Liberals invariably seek to limit paternalism to the mini- mum; their criterion is whether a fully rational person informed of all the relevant facts would consent to the intervention—as might be presumed of an unconscious accident victim whose life is at risk—on the ground that the current paternalism would protect or augment free- dom at later stages. Under such a criterion, legal paternal- ism in the form of legislation that creates ‘crimes without victims’ (e.g. gambling, homosexuality) would be unjusti- fied state interference with consensual private conduct among adults. h.a.b. *liberalism; liberty. Joel Feinberg, Harm to Self (New York, 1986). Rolf Sartorius (ed.), Paternalism (Minneapolis, Minn., 1983). patriotism. Patriotism, is, unlike nationalism, a senti- ment, not a doctrine. It involves love of and support for one’s country, which, while etymologically one’s ‘father- land’, i.e. native land, may be an adoptive homeland, though not, perhaps, as the Latin motto ubi bene ibi patria has it, simply the place where one is well off. Yet, in classic- al *republicanism, by contrast with most sorts of nation- alism, there is a connection between the fact that one’s country benefits one and one’s supposed special *obliga- tion to love and support it. Enemies of such special obliga- tions, like *cosmopolitans (e.g. Martha Nussbaum), thus tend to be suspicious of patriotism, while *communitar- ians (e.g. Alasdair MacIntyre) are more favourably dis- posed to it. Its bad press—‘the last refuge of a scoundrel’ (Samuel Johnson), ‘no patriot yet but was a fool’ (Dry- den)—is referable to the fact either that it may, as a senti- ment, be unreasonably immoderate, or that, as Hume argued, it involves pride in what relates to oneself, which, while natural, cannot be justified to those with other attachments. p.s. *nationalism. M. C. Nussbaum et al., For Love of Country (Boston, 1996). I. Primoratz (ed.), Patriotism (New York, 2002). M. Viroli, For Love of Country (Oxford, 1995). Peacocke, Christopher (1950– ). Professor at New York University, formerly at Oxford, Peacocke has worked in the philosophy of mind, language, and logic, and more recently at the intersection of metaphysics and epistemol- ogy, where he has argued for a new *rationalism. In Sense and Content (1983) he argued that experiences have ‘sensa- tional properties’: properties which are not simply a mat- ter of how the experience represents the world to be. Subsequently he developed an account in which experi- ences have non-conceptual contents: the representational content of the perceiver’s experience is not wholly deter- mined by the concepts the perceiver possesses. Whether this claim is defensible depends on what the concepts are—and this naturally became a focus of Peacocke’s work. He argues that there is no more to a concept than what is specified by an account of what it takes for a thinker to possess that concept. The theory of any given concept, then, is the theory of the possession conditions for that concept. t.c. C. Peacocke, A Study of Concepts (Cambridge, Mass., 1992). —— Being Known (Oxford, 1999). —— The Realm of Reason (Oxford, 2004). Peano, Giuseppe (1858–1932). Italian mathematician, now mainly remembered for what are called ‘Peano’s pos- tulates’, characterizing the natural numbers. They state that 0 is a number which is not the successor of any num- ber, that every number has just one successor which is a number, and that no two numbers have the same succes- sor. In addition, there is the crucial postulate of math- ematical induction, which ensures that the natural numbers are the least class containing 0 and closed under the successor function. In fact Peano took the postulates (with acknowledgement) from Dedekind, who should be counted as their author. Peano was an important influence on Russell, and gave him the idea of deriving mathematics from logic. Much of the notation of Principia Mathematica is in fact based on that of Peano and his school. d.b. *logic, history of. H. Wang, ‘The Axiomatisation of Arithmetic’, Journal of Symbolic Logic (1957). Pears, David (1921– ). British philosopher who has written extensively on topics in the philosophy of language and the philosophy of mind, on Wittgenstein, on Russell, and on 684 passion and emotion in the history of philosophy Hume. He was a Student of Christ Church, Oxford and has taught at the University of California, Los Angeles. Pears is the translator, with Brian McGuinness, of Wittgenstein’s Tractatus, and his major interest is, per- haps, in the work of Wittgenstein, both early and late. The culmination, to date, of this work, is his two-volume study of the development of Wittgenstein’s philosophy, The False Prison. In this study Pears stresses the continuity of Wittgenstein’s philosophy and emphasizes the import- ance of his post-Tractatus discussions of *solipsism and *phenomenalism to the philosophy of the Philosophical Investigations. The second volume also contains a lengthy discussion of the rule-following considerations and the *private language argument and an assessment of Kripke’s interpretation of Wittgenstein’s argument. h.w.n. D. Pears, The False Prison (Oxford, 1988). Peirce, Charles Sanders (1839–1914). American philoso- pher who is perhaps best known as the originator of *prag- matism. He was educated at Harvard, where his father was a mathematics professor. His greatest philosophical influence was Kant, and he saw himself as constructing the philosophical system that Kant might have developed had he not been so ignorant of logic. But the influence of Thomas Reid and other common-sense philosophers became increasingly important: in late writings, the two influences were combined in his ‘critical common- sensism’. Describing himself as a logician, Peirce made major contributions to formal logic (independently of Frege he and his students developed a logic of quantifiers and relations after 1880) and to the study of the logic of science. Indeed, he lectured on these topics at Harvard in the late 1860s and held a lectureship in logic at Johns Hopkins University from 1879 until 1884. But he also served as an experimental scientist, working at the Harvard laboratory after he had graduated in chemistry, and being employed for over twenty years by the United States Coastal Survey. Peirce was a difficult man, widely perceived as an immoral libertine, prone to paranoia and wild mood swings, and possessing an assessment of his own intellec- tual powers which may have been accurate but which was sometimes accompanied by contempt for the capacities of those of lesser talents. In 1884, when confident of obtain- ing tenure at Johns Hopkins, information about his irreg- ular life-style, together with suspicion of his unorthodox religious beliefs, led to his being removed from his post. From then until his death, it was understood that he could expect no orthodox academic employment: he lived pre- cariously with his second wife in north-eastern Pennsylva- nia, writing extensively and giving a few important series of lectures arranged by his friend William James. He never completed the canonical statement of his philosophical position that he sought, but he published extensively and left hundreds of thousands of manuscripts; his work is gradually becoming more readily available. Theory of Inquiry and Pragmatism. In a late paper, Peirce described himself as a ‘laboratory philosopher’, claiming that years of laboratory experience encouraged him, like any experimentalist, to approach all issues in the distinc- tive manner which comprises his pragmatism. This is clearest in the approach to epistemological matters which emerges in his earliest published work, from the 1860s and 1870s—most clearly in a series of papers in the Popular Science Monthly (1877–8). His epistemological work begins from a rejection of Cartesian strategies in philosophy. They do not, he pointed out, accord with our ordinary practice of carrying out investigations: the latter is a co-operative venture, while Descartes suggests that a responsible investigator should carry out a solitary investigation of his or her cog- nitive standing. Ordinary inquiry takes for granted all the propositions we find certain as we begin the inquiry, while Descartes’s sceptical arguments prompt philosophical doubt about what occasions no real doubt. And ordinary inquiry is impressed by the number and variety of the arguments supporting a conclusion, while the Cartesian requires a single indubitable train of reasoning to ground any belief. Peirce proposes to begin from our everyday and scientific experience of inquiry, and to investigate the norms which govern cognition on that basis. The first paper of the series suggests that inquiry begins only when one of our previously settled beliefs is dis- turbed, and it is ended as soon as we have a new answer to the question that concerns us: the aim of inquiry is to replace doubt by settled belief. What methods should we use if we are to carry out our inquiries well? He considers four, the first three being devised to bring to light the key features of the fourth. (1) The method of tenacity requires us to choose any answer, and to take all means necessary to maintain it; (2) the method of authority requires us to defer to an authority and accept whatever the authority requires (it may be no accident that Peirce wrote soon after the bull of papal infallibility had been promulgated); and (3) the a priori method requires us to go by what seems agreeable to reason. It will be no surprise that these methods fail: the second has the advantage over the first that our beliefs will escape the constant buffeting of dis- putes from those who have decided differently, but we are still likely to meet those who accept a different authority, and our own authority will not be able to settle matters about everything. So fixation of belief must be independ- ent of will or human choice. The third method secures that, but it is likely to make belief a matter of fashion: selec- tion of belief still has a subjective basis. Hence we should adopt (4) the ‘method of science’, which holds that ‘there are Real things, whose characters are entirely independ- ent of our opinions about them; those realities affect our senses according to regular laws, and, though our sensa- tions are as different as our relations to the objects, yet, by taking advantage of the laws of perception, we can ascer- tain by reasoning how things really are’. Peirce probably believed that this claim was a presup- position of inquiry and that we should adopt only such methods as were in accord with it. The remainder of the series of papers offers a more detailed account of what this Peirce, Charles Sanders 685 method involves: Peirce was one of the first philosophers to arrive at a satisfactory understanding of statistical rea- soning, and this is central to his account of science. He is a ‘contrite fallibilist’: any of our current certainties might turn out to be mistaken, but relying upon them will not prevent our making cognitive progress; any errors will emerge with time. The ‘pragmatist principle’ forms part of this theory of inquiry, and was elaborated in the second paper of the series, ‘How to Make Our Ideas Clear’. When William James won notoriety for pragmatism, crediting it to Peirce, the latter renamed his principle *‘pragmaticism’. It is a rule for clarifying the content of concepts and hypoth- eses, and is supposed to reveal all features of the meaning of concepts and hypotheses that are relevant to scientific investigations. Suppose I wish to test whether a sample before me is sodium. In the light of my knowledge of sodium, I can predict that if it is sodium then, if I were to drop it into hot water, it would ignite: I make predictions about the consequences of actions if the hypothesis is true. Peirce expresses his principle: ‘Consider what effects, which might conceivably have practical bearings, we con- ceive the object of our conception to have. Then our con- ception of those effects is the whole of our conception of the object.’ When I have listed all the predictions I would make about the consequences of my actions if the sub- stance were sodium, I have a complete clarification of my understanding of the hypothesis: nothing which could be relevant to testing it scientifically has been omitted. As well as showing its value in clarifying hypotheses, and arguing that it can be used to dismiss some metaphys- ical ‘hypotheses’ as empty, Peirce illustrates the value of his pragmatism by clarifying our conception of truth and real- ity. If a proposition is true, then anyone who investigated the matter long enough and well enough would eventually acknowledge its truth: truth is a matter of long-term con- vergence of opinion. ‘The opinion which is fated to be ultim- ately agreed upon by all who investigate, is what we mean by the truth, and the object represented in this opin- ion is the real.’ Although the principle bears a superficial resemblance to the *verification principle of the later Logical Positivists, there are important differences. First, there is no suggestion that, in clarifying our conception, we list only those conditional expectations that are analytic or true by definition: Peirce expects the content of a concep- tion or hypothesis to develop as our scientific knowledge advances. And, second, as he developed his philosophical position, he insisted that the principle could only be taken seriously by someone who shared his realism about natural necessity: the conceptual clarifications are expressed as subjunctive *conditionals (‘would-bes’); and such conditionals report real facts about the world. System. Peirce’s logic is a theory of cognitive norms: methods of inquiry, standards of inference, rules for identi- fying plausible hypotheses, principles for clarifying mean- ings, and so on. He was unsatisfied with the kind of grounding he provided for cognitive norms in the papers just discussed, and his attempts to correct the Kantian frame- work were directed at remedying this. His sophisticated *architectonic approach to philosophy rested upon a clas- sification of the sciences. Logic was the least fundamental of three normative sciences, being a special application a system of norms initially developed in ethics and aesthet- ics. All of these investigations made use of a system of *cat- egories, a correction of Kant’s system, which was defended through a kind of phenomenological investiga- tion. And these philosophical and phenomenological inquiries used mathematical methods to study experience and reality, mathematics being the only discipline which had, and needed, no foundations. So Peirce’s later work developed a highly sophisticated account of how we can have knowledge of cognitive or logical norms. His system of categories is most easily understood from the perspective of his logic of relations. Properties and relations can be classified according to the number of relata they have: ‘ . . . is blue’ is a one-place predicate, ‘ . . . respects . . . ’ is a dyadic, two-place relation, and ‘ . . . gives . . . to . . . ’ is a triadic, three-place relation. Peirce argued that a language adequate for scientific or descriptive pur- poses must contain terms of all these three kinds, but that there are no phenomena which can only be described in a language which contains expressions for four-place rela- tions. Thus he classified phenomena and elements of real- ity numerically: according to whether they are forms of firstness, secondness, or (like giving) thirdness. The irre- ducibility of thirdness is, he thinks, a distinctive part of his philosophical outlook, something which allies him with realist philosophers in opposition to nominalism. In early work, his defence of his categories was largely found in his work on formal logic, but later he turned to phenomen- ology: reflection on experience of all kinds was to con- vince us that triadicity was ineliminable but that no more complex phenomena were involved in experience. Thus we are aware that our experiences have raw quali- tative characters which do not directly involve relations with other things: they exhibit firstness. They also stand in relations to each other, interacting against one another and so on: this involves secondness, as when fire immedi- ately follows our dropping the sodium in hot water. But we are aware that this interaction is intelligible, it is ‘medi- ated’: we can bring it down into a continuous spread of small changes which go together to make up the big one; and we are aware that it conforms to a law. Finding it intel- ligible introduces thirdness: we understand the two elem- ents of the interaction by reference to a third mediating fact. The aim of inquiry, for Peirce, is to find the thirdness (law and pattern) in the manifold of sensory experiences that we undergo. The norms employed by the scientific method are to be vindicated by showing how they provide means for finding more and more pattern and mediation (more and more thirdness) in the world of our experience. Signs. According to Peirce, the most important forms of thirdness involve *meaning and representation, and all of his work is underpinned by a sophisticated theory of 686 Peirce, Charles Sanders meaning: his semiotics. He probably believed that every- thing was a sign, but the signs of most interest to him were thoughts and ‘the assertions of a scientific intelligence’. This theory of meaning (‘speculative grammar’) was to provide foundations for his writings in logic. The key to the thirdness involved in signs was Peirce’s notion of interpretation. A *sign denotes an object only by being understood or interpreted as standing for an object: and this interpretation will always be another sign with the same object. Semiotics is thus primarily a theory of understanding, an account of how we are guided and constrained in arriving at interpretations of signs. Interpretation often involves inference, developing our understanding of the object in question. Thus my under- standing of your assertion that you are tired may be manifested in my thinking that you want me to believe you are tired, in my believing you are tired, in my expect- ing you to fall asleep, in my offering you a cup of coffee, and so on. The interpreting thought mediates between the sign and its object. Peirce was famous for his classifications of signs, and some of his terminology has acquired wide currency. For example, signs can be distinguished according to the fea- tures of them exploited in arriving at an interpretation. A symbol denotes a particular object because there exists a practice of interpreting it as denoting that object; an index denotes an object to which it stands in a direct existential relation; the conventions governing the use of ordinary indexical expressions such as ‘this’ do not fix the reference unaided but rather guide us in interpreting it as an index. And iconic signs share some feature with their object which each could possess if the other did not exist: maps are straightforward examples, the conventions governing their use fixing how we are to interpret them as icons. Mathematical and logical symbolisms are iconic represen- tations, and it was important for Peirce that sentences of natural languages have iconic elements too: formal infer- ence exploits the fact that sentences exhibit a form which is shared with their subject-matter. Much of Peirce’s later work attempted to use this systematic theory of meaning to provide a proof of the pragmatist principle. Science itself is a process of sign interpretation. And Peirce’s account of scientific reasoning has some import- ant elements. As mentioned above, Peirce models all inductive reasoning on statistical sampling: quantitative induction involves attempting to estimate the chance of a member of a population having a particular property; and qualitative induction tests hypotheses by sampling their consequences. He denies that induction ever establishes that a conclusion is true or even probable. Rather, the practice of inductive testing is justified because continued use of it will eventually lead us to converge on the correct value for the chance of a member of the population having the property in question. The pragmatist principle teaches that *probability is a *propensity: if the chance of a coin coming up heads is 0.43, then, if we were to continue to toss it fairly, the proportion of times on which it comes up heads would converge on 0.43. The logic of *abduction is a logic of discovery: it studies how we are guided in constructing new hypotheses from the ruins of defeated ones; and it examines the norms guid- ing us in deciding which hypotheses are worth testing. All scientific activity is grounded in the hope that the universe is intelligible, and intelligible to us. And we are to take ser- iously no hypothesis that ‘blocks the road of inquiry’, forc- ing us to accept regularities as brute or inexplicable. It is connected to this that Peirce espouses ‘synechism’, the doctrine that we are to expect the universe to display con- tinuities rather than discontinuities. Peirce contributed to the mathematical analysis of continuity, exploiting his ideas about the logic of relations and trying to use it as the basis of his realism about natural necessity: continuity is ‘ultimate mediation’. The logic of abduction advises us to favour theories that posit continuities over those that allow for brute unmediated discontinuities. Metaphysics. Although Peirce envisaged that pragmatism would eliminate ‘ontological metaphyics’, he claimed that scientific progress demanded that we construct a ‘scien- tific metaphysics’. Supposedly this was an empirical discip- line, differing from the special sciences in using no sophisticated techniques of experiment and observation: it was ‘coenoscopic’, relying only on familiar everyday observations which are surprising only because their familiarity prevents our noticing them. In part, it was an attempt to describe how the world must be if science was to be possible—if there were to be no inexplicable phe- nomena, if ‘realism’ was to be true, if the three categories were to be as Peirce suggested. And in part it was an exer- cise in ‘descriptive metaphysics’: drawing out features of our everyday conception of mind or matter (for example) can be a valuable corrective to unthinking theoretical prejudices, especially in psychology. Two elements of this metaphysics are especially inter- esting. Peirce defended an evolutionary *cosmology, explaining how the world of existing things and law- governed behaviour evolved from pure possibility. Offer- ing an evolutionary explanation of law, he argued, was the only alternative to asserting that fundamental laws are simply true, with no explanation of why they obtain being available. If every regularity must have an explanation, we avoid a regress of ever more general and abstract laws by invoking a historical explanation. And Peirce’s account of how this evolutionary process works leads to a form of objective idealism according to which matter is ‘effete mind’, and physical phenomena are modelled on thought and sign interpretation rather than the mental being reduced to the physical. This is because a ‘realist’ account of law involves finding ‘mediation’ in the natural world, and sign interpretation is our best model of mediation. Secondly, it may accord with the importance he attached to statistical reasoning in science that he accepted tychism, the thesis that there is absolute chance, that the universe is not wholly governed by determinist laws. This partly reflects his understanding of the importance of statistical laws in science, and his understanding that Peirce, Charles Sanders 687 observation could never establish that laws were so exact as never to permit slight deviations. He also supposed it was required to explain the evolutionary process dis- cussed in his cosmology: without appeal to such ‘chance spontaneity’, he doubted that we could make sense of growth and increasing complexity. c.j.h. *fallibilism. J. Brent, Charles Sanders Peirce: A Life (Bloomington, Ind., 1993). M. Fisch, Peirce, Semeiotic and Pragmatism (Bloomington, Ind., 1986). N. Hauser and C. Kloesel (eds.), The Essential Peirce (Blooming- ton, Ind., 1992). C. J. Hookway, Peirce (London, 1985). C. Kloesel et al. (eds.), Writings of Charles S. Peirce: A Chronological Edition (Bloomington, Ind., 1982– ). C. Misak (ed.), The Cambridge Companion to Peirce (Cambridge, 2004). C. S. Peirce, Reasoning and the Logic of Things (Cambridge, Mass., 1992). Pelagius ( fl. 400). British theologian. Settled at Rome, he enjoyed a following of high-born Christian rigorists, to whom he taught that perfection is possible. When he fled to Palestine via Africa before the impending sack of Rome by the Visi-goths in 410, Augustine, apprised of his teach- ings, accused him of denying *original sin and the need for grace. Pelagianism is the doctrine that without God’s aid men are ‘able to fulfil the divine commands’, or at least (semi-Pelagianism) to ‘believe, will, desire, try’. Both ver- sions are ambiguous between denying that the powers of good acting or willing must be granted by God and denying that the exercise of those powers must be helped or caused by God. The doctrines were anathematized in the fifth and sixth centuries, and again by the Council of Trent (1545– 63), agreeing in this with Luther and Calvin. c.a.k. B. R. Rees, Pelagius: A Reluctant Heretic (Woodbridge, 1988). Penelope’s wooers. Aristippus said that those that studied particular sciences, and neglected philosophy, were like Penelope’s wooers, that made love to the waiting women. Francis Bacon, Apophthegmes New and Old (London, 1625). This aphorism could mean either that any study other than philosophy is only indulged in because of inability to succeed at philosophy, or that those frustrated in reaching satisfactory philosophical conclusions scientize the sub- ject. The tendency of Logical Positivists to do the latter led Wittgenstein to accuse them of not really doing philosophy, and he would probably say the same of today’s *cognitive-science philosophers. Despite his dogmatic-sounding strictures, however, he himself produced a new way of philosophizing. j.o’g. *Logical Positivism. people. The whole body of enfranchised or qualified citi- zens, generally linked by a common language and history, considered in democratic theory as the ultimate source of political *authority. The general slogan that political authority derives from the people is compatible with a large number of modes in which the will or consent of the people is made known to the political authority, and it is compatible with despotic as well as liberal forms of gov- ernment. For example, according to Hobbes, individuals covenant with each other to submit their wills to the will of one who is thereby authorized to act on their behalf. The authority of this Leviathan therefore derives from the people, but it is an absolute and potentially despotic authority. Locke, on the other hand, grants the people power to alter the legislature when it acts contrary to the trust they have placed in it. Burke recommends yet another form of representation of the people—one in which there is a communion of interests and a sympathy in feelings and desires. This ‘virtual representation’ of a *‘natural aristocracy’ does not attach importance to a universal fran- chise. In the nineteenth century the idea of ‘the people’ became identified in philosophers such as Hegel with ‘the nation’. The spirit of the people became a mystical entity, or Volkgeist, which identified and unified a nation. r.s.d. *democracy. G. H. Sabine, A History of Political Theory (London, 1937). perception. The extraction and use of information about one’s environment (exteroception) and one’s own body (proprioception). The external senses—sight, hearing, touch, smell, and taste—though overlapping to some extent, are distinguished primarily by the kind of informa- tion they convey (e.g. about light, pressure, sound, and temperature). Proprioception concerns stimuli arising within, and carrying information about, one’s own body: acceleration, position and orientation of limbs, and so on. Perception is of either things or facts. Seeing an object or an event (both count as things for this classification), a cat on the sofa, a man on the street, an eclipse, or a rob- bery, does not require that the object or event be identi- fied or recognized in any particular way (perhaps, though this is controversial, in any way whatsoever). One can see a cat on the sofa and mistake it for a rumpled sweater; see a man (in camouflage or at a distance, for instance) and take him for a tree. People have believed all manner of superstitious things about the eclipses they observed. See- ing objects and events is, in this sense, non-epistemic: one can see O without knowing or believing that it is O. Per- ceiving facts, on the other hand, is epistemic: one cannot see that there is a cat on the sofa without, thereby, coming to know that there is a cat on the sofa. Seeing a fact is com- ing to know (that this is a fact) in some visual way. Smelling a fact (e.g. that the toast is burning) is coming to know this fact in an olfactory way. In this way, then, thing-perception is cognitively less demanding than fact-perception. Both the dog and the cook can smell the burning toast (a thing), but unless it is a very smart dog (or a very dumb cook), only the cook will be able to smell, thereby coming to know (the fact), that the toast is burning. 688 Peirce, Charles Sanders Other ways of describing what we perceive are vari- ations on these two themes. In seeing where he went, when he left, who went with him, and howhe was dressed we are describing the perception of some fact without revealing exactly what fact it is. One cannot see where he went unless one sees some fact about where he went—that (for instance) he went to the attic. We often describe what facts we have observed (e.g. that Judy was at the ball- game) by mentioning only the thing we observed ( Judy) and where we observed it (at the ball-game). What we end up explicitly saying (that we saw Judy at the game) is non- epistemic (we could see Judy at the game without ever recognizing her, without ever knowing that she was at the game) although what we normally succeed in communi- cating by this form of words (this is called a conversational implication) is something epistemic: that we saw (i.e. came to know by seeing) that Judy was at the game. A great deal of perception (of both things and facts) is indirect. We perceive things on television, in the movies, and on records. One sees that the gas tank is empty by see- ing not the gas tank, but the gas gauge and the fact that it reads ‘empty’. This gives rise to questions about whether there are objects, and facts about those objects, that are seen directly. Direct realists believe that physical objects (some of them anyway) and certain facts (though not all facts) about these objects are seen in some direct, unmedi- ated fashion. One does not see the cup (nor the fact that it is a cup) by perceiving, in some more direct manner, an internal object (a cup-ish *sense-datum) and certain facts about this datum (e.g. that it resembles a coffee-cup). A *representative theory of perception denies this—taking sense-data as the primary objects, and facts about sense- data as the basic facts, of perception. f.d. *body; content, non-conceptual; Honderich. R. Chisholm, Perceiving: A Philosophical Study (Ithaca, NY, 1957). F. Dretske, Seeing and Knowing (Chicago, 1969). T. Gendler and J. Hawthorne (eds.), Perceptual Experience (Oxford, 2005). H. H. Price, Perception (London, 1932). perception, representative theory of: see representative theory of perception. perception, veil of: see veil of perception. percepts. The subjective *experience accompanying *perception of objects and events. Percepts are ordinarily distinguished from *sensations or *sense-data in being cognitively enriched by past experience and memory and by the constancy mechanisms (for shape, size, colour, etc.) that make our experience correspond more closely to the objective state of affairs (the distal stimulus) than to condi- tions at the sensory surfaces (proximal stimulus). Sense- data of round pennies (seen at an oblique angle) may be elliptical, but in normal viewing conditions the percept is supposed to correspond to the known shape (round) of the penny. f.d. R. Firth, ‘Sense-Data and the Percept Theory’, Mind (1949–50). perfectionism. The view that promotion of human excel- lence is one of the factors that should be weighed in judg- ing the political and social worth of a society. Much recent discussion is keyed to the treatment in John Rawls’s A The- ory of Justice. Rawls lumped together thinkers as different as Aristotle and Nietzsche as perfectionists. The rejection of perfectionism follows from Rawls’s stipulation that in the *‘original position’ designers of the political and social order do not have a ‘conception of the good’. Any case for perfectionism must contain two elements. One is an argument that some forms of human activity or experi- ence have special value. The other is that a policy of fur- thering this special value should play a part in some aspects of our conduct toward others, including some social and political decisions. An extreme perfectionism could be used to justify élitist social attitudes, but a mod- erate perfectionism might merely argue that govern- ments should spend modest amounts of tax money on support for the arts and for the kinds of scientific research that are most unlikely to have practical applications. j.j.k. A representative modern perfectionism is to be found in Hastings Rashdall, The Theory of Good and Evil (Oxford, 1907). performative utterances: see linguistic acts. performing arts. The performing arts include music, theatre, opera, dance, mime, and so on. What distin- guishes them as a group is the fact of human performance being involved in the end-stage products of the art. In such art-forms, what we appreciate directly and what we import- antly critically attend to are concrete performances; and in so far as there are works in such art-forms, they are con- ceived as works for performance. Performing arts thus con- trast with arts such as painting, sculpture, etching, and the novel, where the primary product is an object that does not stand in need of performance in order to be experienced directly by a public. Performing arts are all temporal arts, in the sense that performances and experiences of them are necessarily extended in time, but not all temporal arts are performing arts. The art of film provides an obvious excep- tion: films are screened, over a period of time, but they are not performed. The genres of tape music, computer music, and electro-acoustic music are additional examples of temporal yet non-performing arts, since their presenta- tion does not involve human performance. Within the performing arts an important distinction is between art-forms that involve the creation of repeatable works, defined by scripts, scores, or other notational arte- facts, and ones not involving works, but instead perform- ances devised on the spot, or improvised, on every occasion. In the former case it is common to think of the work defined by a notation as a kind of abstract object—a type—whose performances are thus instances—or tokens—of that type. Again, though most performing arts involve instantiable types, it is not true that all arts involv- ing instantiable types are performing arts; witness the arts of poetry, photography, and cinema. performing arts 689 . conclusions expressing the simplicity of the soul, the personality of the soul, the immortality of the soul, and the existence of the external world. In each case, the mistake is to try to derive a tenet. had little to say of ‘feeling’.) He insisted that having the right passions was essential to the virtuous life. The Stoics, too, took an interest in emotion on the way to forming their ethics according to Hobbes, individuals covenant with each other to submit their wills to the will of one who is thereby authorized to act on their behalf. The authority of this Leviathan therefore