where the conclusion of one subargument functions also as a premiss in another. But it is also a little wide, in rela- tion to a sense of ‘argument’ commonly used in philoso- phy, where the term refers to a complex of propositions (usually a quite small and specific set) designated as prem- isses and a conclusion. Also, the definition above can be implemented some- what differently in different conversational contexts, for several types of dispute can be involved. One common sense of ‘argument’ is that of a quarrelsome exchange of verbal attacks and counter-attacks. This is one conversa- tional context of argument, but another context is the more orderly type of exchange where each party has the goal of justifying his or her own thesis, and questioning or refuting the other party’s thesis, by reasoned means, using accepted standards of evidence. Argument of this kind, used to resolve an initial conflict of opinions, takes place in a critical discussion (van Eemeren and Grootendorst, Argumentation, Communication and Fallacies). In contrast, argument to bargain over goods or services takes place in a negotiation. But basically, in an argument, some key proposition is held to be in doubt, in contrast to an explan- ation, for example, where the proposition to be explained is generally taken as granted, or at least not subject to doubt or questioning, as far as the purpose of the explan- ation is concerned. In a deductively valid argument, the link between the premisses and the conclusion is strict in the sense that the conclusion must be true in every case in which the prem- isses are true, barring any exception. In such an argument, the conclusion follows from the premisses by logical necessity. A traditional example is: ‘All men are mortal; Socrates is a man; therefore Socrates is mortal’. The prem- isses don’t have to be true, but if they are, the conclusion has to be true. In an inductively strong argument, the link between the premisses and the conclusion is based on probability, so that if the premisses are true, then it can be said that the conclusion is true with a degree of probability (usually measured as a fraction between 0 and 1, the latter being the value assigned to a deductively valid argument, the limiting case). In a presumptively *plausible argument, the link between the premisses and the conclusion is based on burden of proof, meaning that it is not known whether the conclu- sion is true or not, but if the premisses are true, that is enough of a provisional, practical basis for acting as though the conclusion were true, in the absence of evi- dence showing it to be false. Presumptively plausible arguments are species of arguments from ignorance that should be treated with caution, because of their provi- sional nature, making them subject to default, and even in some cases fallacious (Walton, Plausible Argument in Every- day Conversation). Presumptively plausible arguments are very common in everyday conversation, and their abuse or erroneous use is associated with many of the traditional informal fal- lacies, familiar in logic textbooks. A few of the more com- mon types of presumptively plausible arguments are noted below, along with some traditional types of argu- ment and fallacy. Argument from sign derives a conclusion that some fea- ture of a situation is present, based on some other observed feature that generally indicates its presence. For example, ‘Here are (what appear to be) some bear tracks in the snow; therefore a bear passed this way’. Argument from expert opinion creates a presumption that a proposition is true, based on an appeal to the opinion of a suitably qualified expert who has claimed that it is true. More broadly, arguments are often based on appeals to authority of one kind or another, e.g. judicial authority, other than that of expertise. Locke (in his Essay Concerning Human Understanding) identified a type of argument he called argumentum ad verecundiam (argument from respect or modesty), which is ‘to allege the opinions of men whose parts, learning, eminency, power, or some other cause has gained a name and settled their reputation in the common esteem with some kind of authority’, and use this allegation to support one’s own opinion. Locke does not say this is a fallacy, but he indicates how it could be used as a fallacy by someone who portrays anyone who disagrees with the appeal as insolent or immodest, having insufficient respect for authority. Argument from ethos puts forward a proposition as being more plausible on the ground that it was asserted by a per- son with good character. The negative version of this is the abusive or personal ad hominem argument, which claims that an argument is not plausible on the ground that the arguer who advocated it has a bad character (typ- ically bad character for veracity is emphasized). In the Essay Locke defined the *argumentum ad hominem as the tactic of pressing someone ‘with consequences drawn from his own principles or concessions’. This description is closer to the variant usually called the circumstantial ad hominem argument, where a person’s argument is ques- tioned or refuted on the grounds that his personal circum- stances are inconsistent with what he advocates in his argument. For example, if a politician argues for wage cuts in the public sector, but is unwilling to cut his own high salary, a critic may attack his argument by citing the osten- sible inconsistency. Argumentum ad ignorantiam (argument to ignorance) is the argument that because a particular proposition has not been proved true (false), we may conclude that it is false (true). This is sometimes a legitimate kind of argu- mentation based on burden of proof. For example, in a criminal trial, if it is not proved that the defendant is guilty, it is concluded that she is not guilty. However, if pressed ahead too aggressively, it can be used as a sophistical tac- tic. For example, in the McCarthy hearings in the 1950s, absence of any disproof of communist connections was taken as evidence to show that some people were guilty of being communist sympathizers. Argumentum ad populum is the use of appeal to popular opinion to support a conclusion. It may take the form of appeal to group loyalties, popular trends of one kind or 50 arguments, types of another, or to customary ways of doing things. This type of argumentation is reasonable in many cases, but it can be used as a sophistical tactic to bring pressure against an opponent in argument, or to appeal to group interests or loyalties in an emotional way, in lieu of presenting stronger forms of evidence that should be provided. Argumentum ad misericordiam is the use of appeal to pity to support one’s conclusion. Such appeals are sometimes appropriate, but too often they are used as sophistical tac- tics to evade a burden of proof by diverting the line of argument away from the real issue. d.n.w. *deduction; induction; methods, Mill’s; slingshot, argu- ments; testimony. Charles L. Hamblin, Fallacies (London, 1970). John Locke, An Essay Concerning Human Understanding (1690), ed. P. H. Nidditch (Oxford, 1975). Frans H. van Eemeren and Rob Grootendorst, Argumentation, Communication and Fallacies (Hillsdale, NJ, 1992). Douglas N. Walton, Plausible Argument in Everyday Conversation (Albany, NY, 1992). Aristippus (5th century bc). An associate of Socrates, cele- brated as a defender and exemplar of a life of sensual pleasure. His advocacy of pleasure was taken up by the Cyrenaic school (named after Aristippus’ native city of Cyrene in North Africa), reputedly founded by his grand- son, also called Aristippus. The Cyrenaics maintained that the supreme good is the pleasure of the moment, which they identified with a physical process, a ‘smooth motion of the flesh’. They supported their hedonism by the argu- ment that all creatures pursue pleasure and avoid pain. This concentration on immediate pleasure reflected a general scepticism, according to which only immediate sensations could be known. Concern with past or future caused uncertainty and anxiety, and should therefore be avoided. (*Ataraxia.) c.c.w.t. E. Mannebach, Aristippi et Cyrenaicorum Fragmenta (Leiden, 1961). aristocracy, natural. Rule by the members of a long- established ruling class distinguished by ability, property, and a privileged education which instils a high sense of honour, responsibility, and public duty. Aristocracy is one of the three basic types of govern- ment noted by the Greeks, the others being monarchy (rule by one) and democracy (rule by the people). Aristoc- racies can be based on heredity, wealth (oligarchy), or merit (meritocracy). Some thinkers, especially Burke, believe in the natural aristocracy of those whose place in the social fabric has been established by stable hierarchical values hallowed by time. Such a view finds a friendly envir- onment in some forms of *conservatism and can be seen as the expression of a belief in the value of an *organic soci- ety. It is easy for critics on the left to make fun of the idea because it can be depicted as the expression of entrenched privilege and arbitrary power with no rational basis. Nevertheless, the belief in a natural aristocracy can be combined with constitutional safeguards (as in Burke) and its systematic destruction over the last fifty years by the egalitarianism of the left and the managerialism of the right has not ushered in a glorious new era of public service. r.s.d. E. Burke, Reflections on the Revolution in France (1790), ed. Conor Cruise O’Brien (Harmondsworth, 1968). Aristotelianism. Aristotle’s philosophical influence spans the period from his death in 322 bc to today. It has led to a wide range of different philosophical viewpoints, as his work has been interpreted and reinterpreted to fit differ- ent programmes and serve differing goals. His thought has influenced the terminology of *philosophy itself: ‘syl- logism’, ‘premiss’, ‘conclusion’, ‘substance’, ‘essence’, ‘accident’, ‘metaphysics’, ‘species’, ‘genera’, ‘potentiality’, ‘categories’, ‘akrasia’, ‘dialectic’, and ‘analytic’ are all terms taken over from Aristotle. Many contemporary philosophers working on ethics, philosophy of mind and action, political philosophy, and metaphysics claim that their views are influenced by, or even derived from, Aris- totle’s own writings. Still others define their own position by their rejection of Aristotle’s views on essentialism, metaphysics, and natural science. And this situation is not merely an artefact of current philosophical interests; it is one which has obtained through nearly the whole period of Western philosophy since Aristotle’s death. The history of Aristotelianism has many phases. Imme- diately after his death, his school (the Lyceum) remained a centre for scientific and philosophical study. Theophras- tus succeeded him as its head, expanded on his biological researches by a study of botany, and also wrote a history of physical theories and cosmology, while Eudemus com- posed the first history of mathematics and Aristoxenus wrote on music. Theophrastus and the next head of the Lyceum, Strato, were independent thinkers, prepared to criticize Aristotle’s views, and to develop their own the- ories on basic issues. There were sometimes as many as 2,000 students during this period, and internal debate flourished. Zeno of Citium, the founder of the Stoa, said that Theophrastus’ chorus was larger than his own, but that the voices in his own chorus were in greater har- mony. However, in the third century bc, other philosoph- ical schools emerged—the *Epicureans, *Stoics, and *Sceptics—and took centre-stage, rejecting some of Aris- totle’s views and modifying others, and the influence of the Lyceum itself diminished. In the first century bc, Aristotle’s manuscripts were edited by Andronicus and his writings were widely stud- ied. Between the second and sixth centuries ad a series of scholarly commentators studied Aristotle’s work with care and ingenuity, paying particular attention to his writ- ings on logical, physical, and metaphysical topics. Alexan- der of Aphrodisias (second century ad), Porphyry (third century ad), and Philoponus and Simplicius (sixth century ad) were amongst the most distinguished contributors to this tradition. Some aimed not only to interpret Aristotle’s views, but also to criticize them. Philoponus, in particular, developed a series of fundamental objections to Aristotle’s dynamics and attempted to develop his own account of Aristotelianism 51 change and movement. This first renaissance of Aris- totelianism declined after Justinian closed the schools of philosophy at Athens in ad 529, although Aristotle was actively studied in Constantinople for a longer period. The second great renaissance of Aristotelian thought in western Europe began in the twelfth century ad, and was prompted initially by Syrian and Arabic scholar- philosophers who had discussed and developed Aristotle’s scientific and metaphysical works. Of these, the best known are Avicenna (Ibn Sı¯na¯) and Averroës (Ibn Rushd), ‘the Commentator’, who produced commentaries on nearly all of the works of Aristotle which we now possess. Averroës himself believed that Aristotle both initiated and perfected the study of logic, natural science, and meta- physics. Latin translations of Arabic texts and commen- taries on Aristotle began to reach Europe (via Spain) in this period, and provoked widespread interest. Initially, Aris- totle was seen as a threat to Christian orthodoxy, and in 1210 the Council of Paris banned the study of his natural philosophy and threatened to excommunicate anyone who studied it. However, the study of his writings flour- ished under mild persecution, and was further stimulated by the Crusaders’ discovery in Constantinople of many of Aristotle’s manuscripts (as handed down from the Greek commentators), which subsequently were skilfully trans- lated into Latin and made more generally available. Within a few generations, Aristotle’s writings became one of the mainstays of university life in Europe. This was due mainly to the enthusiasm and ability of two Dominicans, Albert the Great (c.1200–80) and Thomas Aquinas (1224/5–74), who sought to present the basic principles of Aristotle’s philosophy in a systematic fashion and to inte- grate it (as far as possible) with Christian and contempor- ary scientific thought. Albertus aimed to give an account of the whole of nature in Aristotelian terms, to capture what Aristotle would have said had he been alive and well- informed in the thirteenth century ad. Aquinas’s goal was to distinguish what was fundamentally sound in Aris- totle’s philosophical writings from certain of the conclu- sions which he actually drew. For example, while Aquinas (as a Christian) wished to reject Aristotle’s view that the world had no beginning, he argued that it was by revela- tion alone that one could know the relevant facts. Thus, he upheld Aristotle’s criticism of his predecessors’ theor- ies that the world had a beginning on the grounds that no philosophical argument could establish what had in fact occurred. Aquinas aimed to reconcile religion and phil- osophy, and to produce a wide-ranging synthesis of Aris- totelian philosophy, Christianity, and the current scientific thinking of his day. The success of Aquinas’s synthesis ensured that for a time Aristotle held the pre-eminent position in Western philosophy. He was regarded for several centuries as the supreme philosopher, ‘the master of those who know’, as Dante called him. However, the effect of this synthesis was in many ways pernicious. After the thirteenth century Aristotle came to represent the status quo in philosophy and science, and to be identified with dogmatic resistance to further speculation and scientific discovery. Naturally, critics arose: in Oxford, William of Ockham and, in Paris, Jean Buridan and Albert of Saxony amongst others. By the end of the fourteenth century, they had (like Philoponus before them) criticized Aristotle’s dynamics and the astro- nomical theories constructed on this basis. The way was open for Copernicus and Galileo to undermine these parts of Aristotle’s physical theories. Perhaps the nadir of this form of Aristotelianism was reached when Cremonini, a leading Aristotelian in Padua, refused to look through Galileo’s telescope because he suspected that what he saw would conflict with his own theories. In the seventeenth century, Francis Bacon, Galileo, and Boyle developed more general attacks against Aristotelianism, accusing it of a resistance to scientific method and empirical observa- tion. Hobbes complained of Aristotle’s continuing influ- ence with considerable vehemence. ‘I believe that scarce anything can be more absurdly said in natural philosophy, than that which is now called Aristotle’s Metaphysics . . . nor more ignorantly, than a great part of his Ethics’ (Leviathan, iv. xlvi). It is something of a paradox that Aristotle was criticized by John Locke and Francis Bacon for lack of interest in sci- entific method and empirical observation. He had, after all, pioneered the empirical science of biology, and had written at length about the importance of ensuring that one’s theories are true to appearances and consistent with the reputable opinions of the relevant experts. His reputa- tion in natural science suffered because of the narrow- minded attempts of the Aristotelians ofthe seventeenth century to defend every aspect of his physical theory. Their ultra-conservative approach prompted a radical rejection of central contentions of Aristotle’s metaphysics and epistemology. A century later, Bishop Berkeley noted judiciously: ‘In these free-thinking times, many an empty head is shook at Aristotle and Plato, as well as at Holy Scriptures. And the writings of those celebrated ancients are by most men treated on a foot with the dry and bar- barous lucubrations of the Schoolmen.’ In this way, the successful criticism of the most speculative features of Aristotle’s dynamics prompted a major sea-change in the development of Western philosophy. The starting-point for philosophical thinking after Descartes came to be sub- jective experience and the challenge of scepticism, rather than man understood as a distinctive species of animal in a world of substances, essences, and natural kinds with their own causal powers. Indeed, from a post-Cartesian view- point many of Aristotle’s central concepts appeared ungrounded or epistemologically insecure. Aristotle’s influence was not undermined in all areas. At a time when his metaphysical doctrines were under sustained attack, the German educationalist Philip Melanchthon (1497–1560) referred to the Ethics as a sem- inal document, and made it essential reading in German universities. Later in the German philosophical tradition, Hegel and Marx were enthusiastic students of Aristotle. Indeed, Marx was sometimes described as a left-wing Aristotelian. 52 Aristotelianism Aristotle’s Poetics exercised a powerful influence on the seventeenth-century French dramatists Corneille and Racine, who attempted to construct tragedies according to his precepts. Corneille went so far as to say that Aris- totle’s dramatic principles were valid ‘for all peoples and for all times’. In nineteenth-century biology, Darwin was so deeply impressed with Aristotle’s biological observations and theories that he remarked that while ‘Linnaeus and Cuvier have been my gods, they were mere schoolboys to old Aristotle’. However, these remarks were exceptions to an intellectual climate in which Aristotle’s central claims about scientific explanation, metaphysics, and logic were rejected either in whole or in part. Indeed, Darwin’s own work appeared to undermine the need for Aristotle’s style of teleological explanation of biological phenomena. The last two centuries have seen several major devel- opments in Aristotelian studies. In the nineteenth cen- tury, scholars sought to establish a secure text of his surviving books, culminating in the Berlin edition, pub- lished from 1831 onwards. Later writers tended to see Aristotle not as propounding one finished philosophical system, but as developing and modifying his views throughout the treatises. Others focused with increasing rigour on Aristotle’s discussion of particular issues in his Ethics or Metaphysics, or more recently his biological works, without assuming that they all fit perfectly into one package of ideas. There has been, in these respects, an attempt to formulate clear and precise accounts of Aris- totle’s views, rather than to rest content with the ‘Aristotle of legend’. It is perhaps no accident in this context that the last few years have seen renewed scholarly interest in the Greek commentators of the first Aristotelian renaissance. What is the current position of ‘Aristotelianism’ in modern philosophy? In several areas, his influence remains strong and alive. I shall only comment on two. 1. Philosophy of Action, Moral Psychology. Many contempor- ary philosophers have been influenced directly by Aris- totle’s pioneering discussions of a variety of issues. The philosophy of *action contains a variety of questions: What counts as an action? How are actions individuated? What is to count as an intentional action or a rational action? Can there be intentional but irrational actions (*akrasia)? Further issues concern the explanation of intentional action: Is it to be explained causally, or in a dis- tinctive manner (rational explanation)? Are the explanan- tia desires or beliefs, and which are explanatorily more basic? How are such psychological states related to under- lying physical states? On each of these issues, Aristotle has a distinctive and interesting answer. Philosophers as diverse as Austin, Anscombe, von Wright, and Davidson, who reopened these issues in the late twentieth century, have found much to use in Aristotle’s discussions. But his sustained and detailed analysis of these problems repays study on its own account. His interest in ontological issues led him to develop an account of the nature and identity of processes, states, activities, and actions which differs from the alternatives canvassed in modern debates. In analysing intentional action, he gave an important role to efficient causation, but saw this as fully consistent with the recognition of the role of agents’ knowledge and teleological (or rational) explanation. Where modern discussions represent these as rival explanatory schemes, Aristotle portrayed them as complementary. His discussion of akrasia focuses on the issue of how akratic action is possible and how it is to be explained—whether in terms of a failure of intellect or imagination, or in terms of desires not fully integrated into one’s picture of well-being. This discussion stands com- parison with even the best modern work. Aristotle is aiming to account for a wide range of cases (some involving failure of intellect, others separate failures of motivation) in a way which does justice to the variety of the phenom- ena of ordinary experience. But at the same time he seeks to develop a theory of practical reasoning and virtue which shows how the akratic is irrational and to be censured. The range and subtlety of Aristotle’s account is evident throughout his discussion of virtue and self- control, which has received considerable attention from contemporary philosophers (such as John McDowell and Philippa Foot). Similar claims can be made for his discus- sions of the interconnection between psychological and physical states. Aristotle is engaging with precisely the issues which concern contemporary opponents of materi- alist reduction who wish to avoid (Platonic or Cartesian) *dualism. In these areas, Aristotle not only initiated philo- sophical discussion but provided a framework within which much contemporary work can be located and better understood. 2. Metaphysical Issues. Contemporary discussion, mainly prompted by two American philosophers, Saul Kripke and Hilary Putnam, has done much to refocus attention on to the Aristotelian issues of *substance, *essence, and *nat- ural kinds. Kripke and Putnam share a range of assump- tions with Aristotle. Terms such as ‘man’ or ‘gold’ have their significance because they signify a distinct natural kind whenever they are coherently uttered. They could not retain their significance and apply to a different object or kind. Aristotle accepted this as a consequence of his account of signification in which the thoughts (with which these terms are conventionally correlated) are ‘likened’ to objects or kinds in the world. But what makes these kinds and objects the same whenever they were specified? At this point, Aristotle developed his metaphysical theory of substance and essence to answer this question and thus to underwrite and legitimize his account of names. Modern authors have highlighted the linguistic and semantic data from which Aristotle began his account; but few (if any) have attempted to present such a systematic metaphysical basis for their semantic claims. In this respect, his project is at least as detailed and developed as those currently on offer. At the very least it indicates what a systematic the- ory of essence would be like. Aristotle advanced his metaphysical claims apparently untroubled by sceptical doubts of the kind which Aristotelianism 53 undermined the first great period of Aristotelianism (in third-century bc Athens) and the third (in western Europe in the seventeenth century ad). Perhaps it was because he was so little concerned by *scepticism that he was able to develop his metaphysical theory in the way he did. How- ever, from a modern perspective, this may not seem the major mistake it was once taken to be. Aristotle was not disturbed by global scepticism because (in his view) we had to be in cognitive contact with the world for our basic terms (such as ‘man’ or ‘gold’) to make sense. Our thoughts had to be ‘likened’ to objects and kinds in the world for them to be the thoughts they are, or for our terms to make sense to us. From the Aristotelian stand- point, global scepticism seems something of a trick: it assumes that we understand terms with meanings which they could only have if we were in reliable cognitive con- tact with the world, and then proceeds to raise sceptical doubts about the reliability of that cognitive contact. This anti-sceptical feature of Aristotle’s thinking made it unappealing in an earlier age when philosophers raised sceptical doubts with scant concern for the question how our thoughts can have the content they do. But it is precisely this aspect of Aristotle’s philosophy, together with its attendant interest in metaphysical issues, which makes it strikingly relevant today. In these areas, Aris- totle’s influence on contemporary philosophy appears stronger and more benign today than it has been at any time since the anti-Aristotelian revolution of the seventeenth century. d.c. D. Charles, Aristotle’s Philosophy of Action (London, 1984). G. E. R. Lloyd, Aristotle: The Growth and Structure of his Thought (Cambridge, 1968). R. Sorabji, Time, Creation and the Continuum (London, 1983). J. L. Stocks, Aristotelianism (Boston, 1925). Aristotle (384–322 bc). Aristotle was born at Stagira in Chalcidice in northern Greece. His father was a doctor whose patients included Amyntas, King of Macedonia. At the age of 17, Aristotle went to Athens to study under Plato, and remained at the *Academy for nearly twenty years until Plato’s death in 348/7. When Speusippus suc- ceeded Plato as its head, Aristotle left Athens, lived for a while in Assos and Mytilene, and then was invited to return to Macedonia by Philip to tutor Alexander. Aris- totle returned to Athens in 335 at the age of 49, and founded his own philosophical school. He worked there for twelve years until Alexander’s death in 323, when the Athenians in strongly anti-Macedonian mood brought a formal charge of impiety against him. Aristotle escaped with his life to Chalcis, but died there in the following year at the age of 62. He married twice, and had a son, Nicomachus, by his second wife. Aristotle’s philosophical interests covered an extremely wide area. He composed major studies of logic, ethics, and metaphysics, but also wrote on epistemology, physics, biology, meteorology, dynamics, mathematics, psych- ology, rhetoric, dialectic, aesthetics, and politics. Many of his treatises constitute an attempt to see the topics studied through the perspective of one set of fundamental concepts and ideas. All reflect similar virtues: a careful weighing of arguments and considerations, acute insight, a sense of what is philosophically plausible, and a desire to separate and classify distinct issues and phenomena. They also exhibit considerable reflection on the nature of philosophical activity and the goals of philosophy itself. Aristotle’s philosophical development is difficult to determine chronologically. He probably worked on a range of concerns simultaneously, and did not always see clearly how far his thinking on logic or philosophy of sci- ence fitted with his current work on (for example) meta- physics or biology. He may have returned more than once to similar topics, and added to existing drafts in a piece- meal fashion at different times. It is, in general, more fruit- ful to inquire how far different elements in his thinking cohere rather than what preceded what. Further, many of his extant works read more like notebooks of work in progress or notes for discussion than books finished and ready for publication. His writings (like Wittgenstein’s) reflect the activity of thinking itself, uncluttered by rhetoric or stylistic affectation. Their consequent fresh- ness of tone should make one cautious of accepting over- regimented accounts of his overall project: for it may well have been developing as he proceeded. In what follows, I shall aim to introduce a few of Aris- totle’s leading ideas in three areas only: logic and phil- osophy of science, ethics, and metaphysics. While these subjects differ widely, there is considerable overlap of concerns and interests between them. Logic and Philosophy of Science. Aristotle was the first to develop the study of deductive inference. He defined the *syllogism as a ‘discourse in which certain things having been stated, something else follows of necessity from their being so’. Syllogisms are deductively valid arguments, and include both arguments of the form: All as are b, All bs are c, All as are c, and as are red, as are coloured. Both these arguments are perfect syllogisms since nothing needs to be added to make clear what necessarily follows. By contrast, arguments form imperfect syllogisms when more needs to be added beyond the premisses to make clear that the conclusion follows of necessity. It is a dis- tinctive feature of Aristotle’s account that it takes as its starting-point the notion of ‘following of necessity’, which is not itself defined in formal or axiomatic terms. If this notion has a further basis, it lies in Aristotle’s semantical account of the predicate as what affirms that a given property belongs to a substance (and so rests on his meta- physics of substance and property). 54 Aristotelianism Aristotle focused on perfect syllogisms which share a certain form involving three terms: two premisses and a conclusion. Examples of such syllogisms are (reading downwards): All as are b, All as are b, Some as are b, Some as are b, All bs are c,Nobs are c, All bs are c,Nobs are c, All as are c.Noa is c. Some as are c. Not all as are c. He claimed that other syllogisms with a similar form and the same crucial terms (‘all’, ‘some’, ‘none’, ‘not all’) could be expressed using one of these perfect cases if one adds three conversion rules: From No bs are a infer No as are b. From All bs are a infer Some as are b. From Some bs are a infer Some as are b. Finally, he proposed that any deductively valid argument can be expressed in one of the four obvious perfect syllo- gisms specified above or reduced to these by means of the conversion rules. If so, any such argument can be refor- mulated as one of the basic cases of perfect syllogisms in which the conclusion obviously follows of necessity. Aristotle was interested in this logical system in part because he was interested in explanation (or demonstra- tion). Every *demonstration is a syllogism, but not every syllogism is a demonstration. In a demonstration, the aim is to explain why the conclusion is true. Thus, if the con- clusion states that (for example) trees of a given type are deciduous, the premiss of the relevant demonstration will state this is so because their sap solidifies. If no further explanation can be given of why their leaves fall, this premiss states the basic nature of their shedding leaves. Premisses in demonstrations are absolutely prior, when no further explanation can be offered of why they are true. These constitute the starting-points for explanation in a given area. Aristotle’s ideas about the nature of valid inference and explanation form the basis of his account of the form a suc- cessful science should take. In terms of these, he outlined an account of what each thing’s essence is (the feature which provides the fundamental account of its other genu- ine properties), of how things should be defined (in terms of their basic explanatory features), and of the ideal of a complete science in which a set of truths is represented as a sequence of consequences drawn from a few basic pos- tulates or common principles. These ideas, which under- lie his Analytics, determined the course of logic and philosophy of science, and to some extent that of science itself, for two millennia. Aristotle’s system has its own shortcomings and idio- syncrasies. His treatment of the syllogistic does not exhaust all of logic, and not all arguments of a developed science can be formulated into the favoured Aristotelian form. His system was a pioneering one which required supplementation. It was unfortunate, not least for his own subsequent reputation, that it came to be regarded as the complete solution to all the problems it raised. It is important to note that Aristotle’s logical project was directly connected with his metaphysical goals. His aim was to develop a logical theory for a natural language capable of describing the fundamental types of object required for a full understanding of reality (individual sub- stances, species, processes, states, etc.). He had no interest in artificial languages, which speak of entities beyond his favoured metaphysical and epistemological theory. His goal was rather to develop a logical theory ‘of a piece’ with his philosophical conception of what exists in the world and how it can be understood. In this respect, his goals differ markedly from those of metalogicians since Frege, who speak of artificial as well as natural languages, and domains of objects unconstrained by any privileged metaphysics. Ethics and Politics. Aristotle’s Ethics contains several major strands. 1. It aims to give a reflective understanding of *well- being or the good life for humans. 2. It suggests that well-being consists in excellent activ- ity such as intellectual contemplation and virtuous actions stemming from a virtuous character. Virtuous action is what the person with practical wisdom would choose; and the practically wise are those who can deliberate success- fully towards well-being. This might be termed the Aris- totelian circle, as the key terms (well-being, virtue, and practical wisdom) appear to be interdefined. 3. It develops a theory of virtue (*arete¯) which aims to explain the fact that what is good seems so to the virtuous. Aristotle examines the characteristic roles of desire, goals, imagination, emotion, and intuition in the choices and intentional actions of the virtuous, and explains in these terms how virtue differs from self-control, incontinence (*akrasia), and self-indulgence. This is a study in moral psychology and epistemology, involving detailed discus- sion of particular virtues involved in the good life. Each of these is important but controversial, and Aris- totle’s own viewpoint is far from clear. Sometimes it appears that the self-sufficient contemplation (of truth) by the individual sage constitutes the ideal good life, but else- where man is represented as a ‘political animal’ who needs friendship and other-directed virtues (such as courage, generosity, and justice) if he is to achieve human well- being. On occasion, Aristotle seems to found his account of the good life on background assumptions about human nature, but elsewhere bases his account of human nature on what it is good for humans to achieve. He remarks that the virtuous see what is good, but elsewhere writes that what is good is so because it appears good to the virtuous. One way (there are many) to fit these strands together runs as follows. The paradigm case of activity which mani- fests well-being is intellectual contemplation, and every- thing else that is an element in the good life is in some relevant way like intellectual contemplation. Practical wisdom is akin to theoretical activity: both are excellences of the rational intellect, both involve a proper grasp of first principles and the integration of relevant psychological states, and both require a grasp of truth in their respective areas. Intellectual contemplation is the activity which best Aristotle 55 exemplifies what is good for humans; anything else which is good for us in some way resembles it. But what counts as truth in practical matters? Is this is to be understood merely as what seems to be the case to the virtuous agent? Alternatively, practical truth might be taken as a basic notion. Or perhaps the virtuous agent is the proper judge because the virtue she possesses, when allied with practical wisdom, constitutes part of well- being. On this view, the interconnections between virtue and well-being would explain why her practical reasoning is as it is (in a way consistent with reputable and well- established opinion). This preserves the analogy with truth in theoretical matters, where inter-connections between kinds, essences, and causal powers explain why our theoretical reasoning is as it is (in a way consistent with reputable opinion). While the third of these interpret- ations captures substantial parts of Aristotle’s discussion, he proceeds with characteristic caution and appears reluctant to commit himself finally on this issue. Aristotle wrote his Ethics as a prolegomenon to his study of Politics. This too reflects his interest in virtue and well-being, but also contains several other major themes. Thus Aristotle holds the following theses. 1. A city state has as its goal well-being, and the ideal constitution is one in which every citizen achieves well- being. 2. In practice, *democracy is preferable to oligarchy because it is more stable and its judgements are likely to be wiser since individuals when grouped together have more wisdom than a few. 3. The practice of slavery, with regard to both ‘natural’ and ‘non-natural’ slaves required to till the soil and main- tain the state (1330 a 32–3), is justifiable. 4. Plato’s ‘communist’ society of guardians in the Republic is to be condemned because it leads to social dis- turbances, undermines private property and friendship, ‘which is the greatest safeguard against revolution’, and is unobtainable. What holds these diverse views together? Sometimes, Aristotle writes as if his aim is for each citizen to achieve the perfectionist goals set out in the Ethics. However, his commitment to this ideal is mitigated by other factors including the need for stability and social harmony. When these conflict (as in his discussion of non-natural slaves), he does not give authority to perfectionist values in a direct or systematic way. It may be that Aristotle thought that there would be more excellent activity in the long run if considerations of harmony and stability were taken ser- iously. But he fails to spell this out or to specify in detail the distributional policies which are to be implemented by the wise rulers who hold power in his preferred constitution. While the Politics contains many influential remarks, such as those condemning the practice of lending money for profit and analysing the nature of revolutions, it is incom- plete as a work of political theory. It also exhibits some of the less attractive aspects of perfectionist theory: if people lack the abilities required for a life of excellence, they are natural slaves rightfully deprived of the basic freedoms enjoyed by those with higher-grade capacities. Similarly, if children are born with serious physical handicaps, they are to be left to die. Aristotle does not seriously address the intuitions of liberty or equality of treatment which run contrary to the demands of perfectionist theory in these cases. Metaphysics and Biology. Aristotle’s metaphysical pro- posals have a number of different sources. Three of them can be summarized as follows. 1. Aristotle’s logical system (as set out above) required a metaphysical underpinning—an account of species, sub- stances, and essences—to underwrite his treatment of logical necessity and demonstration. The same was true of his semantical discussion of the signification of names and the principle of non-contradiction. Names signify (in his view) substances with essences. ‘Man’ has the significance it does because it signifies the same species on all occasions when it is used. But what makes this the same species is that it possesses a distinctive essence which it cannot lack. The kind occupies its own slot in the intelligible structure of the world in virtue of its possession of this essence. The *essence is the fundamental feature which makes the *substance what it is, and explains the other properties of the substance. Aristotle was faced with two problems: he required a metaphysical account of substances, species, and essence to sustain this view, and a psychological account of how we grasp these substances and kinds. (The latter issue is addressed in De anima, where Aristotle pro- posed that our thoughts and perceptions are of objects and kinds when we are in appropriate causal contact with them, and are thus ‘likened’ to them.) 2. Aristotle was convinced that *teleological explan- ation was the key to the proper study of natural organisms. What determined a thing’s nature was what counted as its successful operation: its achieving what it is good for it to achieve (as is implicit in his ethical writings). These goals, and being organized so as to achieve them, is what makes the species the one it is. Some goals are extrinsic; the goal of an axe is to cut wood, and this explains the arrangement of the metal in the axe. But the teleological goal of man is to live a life of a given kind (e.g. of rational activity), and the rest of his nature is designed so as to achieve this intrin- sic goal. The distinctive goal of each biological kind is what determines its respective essence. 3. Aristotle’s critical study of Plato’s theory of *univer- sals had convinced him that universals could not exist by themselves, but only in particular things. Since substances must be capable of independent existence, it appears that they cannot be universals but must be particulars. However, this generated a dilemma since Aristotle also believed that only universals were definable and the objects of scientific knowledge (in the Analytics model). Thus if substances are knowable, they cannot be particu- lars. But now it looks as if substances cannot exist at all since they cannot be either universals or particulars. Aris- totle’s dilemma arises because he was tempted to regard 56 Aristotle particular substances as ontologically primary, while (at the same time) insisting that understanding and definition are of universals. The latter thought he shared with Plato; but the former is very much his own, and one which led to a fundamentally different account of numbers and univer- sals than the one Plato offered. In addressing the first two issues, Aristotle needed to represent the essences of substances in a way which respected two ideas: (a) that each substance has one fun- damental feature which causes its other features to be as they are, (b) this feature is teleologically basic. Form is the candidate proposed as the relevant essence of substances, composed of form and matter. But is the form particular or universal? How is it related to matter? Is it itself one uni- tary thing? These questions dominate Aristotle’s reflec- tions in the Metaphysics, and parts of his account of the soul in De anima and natural kinds in the biological writings. Aristotle’s discussion of these issues has generated sev- eral major scholarly controversies. First, did he take the notion of one unified substance as basic, and regard its matter and form as abstractions from this basic notion? Or did he regard form and matter as independent starting- points which, when related in a given way, yield a unified substance? Second, if each individual substance’s form is unique, how is the form itself individuated? Is its identity fixed independently of the matter (or the composite) it informs? Or is it rather a distinct form precisely because it is the result of a general form informing certain quantities of matter? Third, did Aristotle regard general forms as abstractions from the forms of particular substances, which served as his basic case? Or is the order of explan- ation reversed, general forms taken as explanatorily prior and forms of particular substances derived from general forms enmattered in particular quantities of matter? One approach (there are again many) takes general forms as explanatorily basic, and construes particular forms as the result of their instantiation in different quan- tities of matter. On this view, Aristotle regards form and matter as prior to the composite substance, while main- taining as a separate thesis that universals cannot exist uninstantiated. Composites such as humans are to be understood as the result of the operation of form on mat- ter. They are composed from arms and legs, composed in turn from flesh and blood, themselves composed from basic elements. At each level above the lowest, the rele- vant entities are defined by representing the matter as serving certain teleological goals. While matter is described as potentiality, this means no more than that it can be informed in favourable conditions. This perspec- tive is at work in The Parts of Animals and De anima, yielding a distinctive picture of the soul and of animal. The teleological operations which introduce such phenomena as desire or perception are not definable in terms of effi- cient causation, but refer essentially to the creature’s own goals, such as well-being or survival. Nor can they be defined as ‘whatever plays a given role in a system of explanation’, as they are genuine entities in their own right with their own causal powers and essential features. On this view, Aristotle is neither offering a reductive account of psychological states, nor regarding them as inexplicable or mysterious (as in Platonic dualism). These scholarly issues remain highly controversial, and are at the centre of current debate. Other more general problems are raised by Aristotle’s discussion. First, is it possible to explain the unity or identity of a particular sub- stance at all? Second, what is the nature of a metaphysical explanation which Aristotle is seeking? He appears to offer a constructive account of higher-order states, in some way intermediate between reductionism and dualism. But is this a genuine alternative, and how is the relevant construction itself constrained? Third, is there always one teleologically basic feature which explains the presence and nature of the other genuine properties of substances? As already indicated, Aristotle made substantial progress with each of these questions in his treatises on psychology and biology. Indeed, much of their philosoph- ical interest lies in tracing how far he succeeded in explaining the nature of the relevant phenomena in terms of his central concepts and favoured methodology. The results, particularly in his psychological writings, are often exciting and compelling but sometimes inconclusive. Aristotle encountered serious difficulties in his study of biological natural kinds. He did not succeed in finding one basic feature to explain the remainder of their genuine properties (as required by the Analytics model). Thus, he saw that fish are so constituted as to fulfil a range of diverse functions—swimming, feeding, reproducing, living in water—which cannot all easily be unified in a unitary essence of the type proposed in the Analytics. The model he had developed to analyse physical pheno-mena (such as thunder) could not be applied without major changes to central aspects of the biological world. Aristotle’s commitment to teleological explanation generated results apparently contrary to the guiding idea of non-complex unifying forms proposed in the Metaphysics. It is not clear whether he believed that these problems could be overcome, or concluded that the model of explanation which applied elsewhere could not successfully analyse biological kinds. He did not succeed in integrating all his beliefs into a complete and unified theory. Aristotle’s writings in metaphysics, morals, biology, and psychology are unified by common interests in *nat- ural kinds, teleology, and essence, but they are not parts of the seamless web of a perfectly unified and finished the- ory. Aristotle was too cautious and scrupulous a thinker to carry through a ‘research programme’ without constant refinement and attention to recalcitrant detail. In this respect his writings seem to reflect the nature of intellec- tual contemplation itself. d.c. *logic, traditional. J. L. Ackrill, Aristotle the Philosopher (Oxford, 1981). J. Barnes (ed.), The Complete Works of Aristotle, i and ii (Princeton, NJ, 1984). —— (ed.), The Cambridge Companion to Aristotle (Cambridge, 1995). Aristotle 57 A. Gotthelf and J. Lennox (eds.), Philosophical Issues in Aristotle’s Biology (Cambridge, 1987). T. H. Irwin, Aristotle’s First Principles (Oxford, 1988). R. Sorabji, Necessity, Cause and Blame (London, 1980). W. D. Ross, Aristotle (Oxford, 1923). arithmetic, foundations of. Arithmetic is the study of the natural numbers—0, 1, 2, 3, and so on. A foundation for arithmetic can serve three interconnected interests: an interest in rigorous axiomatization, an epistemological interest in the source and justification of our knowledge of the *numbers, and an ontological interest in the nature of the numbers. Dedekind, and, following him, Peano, dissected the concept of the progression of the natural numbers and for- mulated an axiomatic foundation for arithmetic, now known, unfairly, as the Peano axioms. The idea behind an axiomatic foundation is to set down a small number of axioms, expressed using a small number of primitive, non-logical terms, from which other sentences can be deduced. The primitive terms used are ‘0’ (0 is the first nat- ural number), ‘successor’ (the successor of 0 is 1, the suc- cessor of 1 is 2, etc.) and ‘natural number’, and the five axioms are: 1. 0 is a natural number. 2. The successor of any natural number is a natural number. 3. No two natural numbers have the same successor. 4. 0 is not the successor of any natural number. 5. For any property P, if (i) 0 has P and (ii) the successor of any natural number which has P also has P, then every natural number has P (the principle of math- ematical induction). This informal axiomatic foundation organizes and regi- ments arithmetical truths within an economical system. It can be formalized by translating the axioms into a formal language from which theorems can be deduced via rigor- ous proofs (though Gödel’s *incompleteness theorem limits the success of any such formal axiomatization). How is our knowledge of arithmetical truths to be explained? An axiomatic foundation provides a partial answer: assuming that the axioms are known, then know- ledge of theorems is logical knowledge of the logical con- sequences of the axioms. The outstanding question is: how do we know the axioms? According to the Euclidean paradigm, we know the axioms because they are self- evident, but this is an unsatisfactory answer because judgements of self-evidence are notoriously fallible. Rather than appeal to self-evidence right away, Frege developed his *logicism. The logicist project has three parts: define the vocabulary of arithmetic solely in terms of the vocabulary of logic, identify the natural numbers with ‘logical objects’, and deduce Peano’s axioms as the logical consequences of logical axioms. Thus the logicist project grounds knowledge of arithmetical truth on knowledge of logical axioms which Frege held to be self- evident. This explanation was ripped apart by *Russell’s paradox which demonstrated that Frege’s logic is incon- sistent and which initiated the vigorous foundational research of the early twentieth century. The very idea of an epistemological foundation for arithmetic can be questioned; for example, ‘2 + 2 = 4’ is more obvious and certain than any recondite set of axioms of logic or set theory from which it may be deduced. Nevertheless, an account of the ontological foundation of arithmetic is compulsory. Prima facie, arithmetical truths are truths about objects—the numbers. What sort of objects are they? They do not seem to be either physical or mental objects because there might not be enough of those to serve as the numbers and because the numbers are thought to be necessary existents unlike physical or mental objects. Thus the numbers appear to be *abstract entities, as the Platonist would have us believe: either a sui generis progression or one drawn from a more extensive kind of abstract object such as sets, but in each case having no causal powers. Now epistemological problems resur- face since there is no agreed account of how our know- ledge of abstract objects is possible. a.d.o. P. Benacerraf and H. Putnam (eds.), Philosophy of Mathematics, 2nd edn. (Cambridge, 1983). G. Frege, The Foundations of Arithmetic, tr. J. L. Austin, 2nd edn. (Oxford, 1953). I. Lakatos, ‘Infinite Regress and the Foundations of Mathemat- ics’, in Mathematics, Science and Epistemology, ed. J. Worral and G. Currie (Cambridge, 1978). M. Potter, Reason’s Nearest Kin: Philosophies of Arithmetic from Kant to Carnap (Oxford, 2002). arkhe¯ . A ‘first thing from which something is, or comes to be, or is known’ (Aristotle, Metaphysics v. 1013 a 18–19). Applied to materials which do not arise out of anything more primitive, to causes of change, to propositions fun- damental in deductive systems, by teleologists to benefits and beneficiaries, and, colloquially, since they are sources of initiatives in states, to governments. Kinds of arkhe¯ are as numerous as ways of explaining or senses of ‘understand’. w.c. *first cause argument. Armstrong, D. M. (1926– ). Australian philosopher, Offi- cer of the Order of Australia, and one of the dominant fig- ures in the school sometimes known as Australian materialism. Armstrong was one of the first to advocate *functionalism as a theory of the mind, and to combine that view with *materialism. In metaphysics, he has defended a distinctive version of realism about *univer- sals. Armstrong’s view is that there are philosophical rea- sons for believing in the existence of universals, but universals do not exist independently of the particulars that instantiate them, and which universals exist is an empirical question. This view has been in the background of his later work on scientific laws, and on the nature of modality. Armstrong’s metaphysical realism, his vigorous defence of empirical metaphysics, and his clear, argument- based philosophical style show the influence of John 58 Aristotle Anderson—of whom Gilbert Ryle reputedly said ‘he thinks there are only brass tacks’. t.c. D. M. Armstrong, A Materialist Theory of the Mind (London, 1968). —— A World of States of Affairs (Cambridge, 1997). Arnauld, Antoine (1612–94). A brilliant philosophical con- troversialist, Arnauld exerted a powerful influence on the development of seventeenth-century thought. When still under 30 he composed a devastating critique of Descartes’s arguments for the distinctness of mind and body, casting doubt on the logical completeness and adequacy of the Cartesian conception of a pure thinking substance (Fourth Set of Objections to the Meditations, 1641). A defender, despite his criticisms, of many aspects of the Cartesian system, he went on to write, with Pierre Nicole, the celebrated La Logique, ou L’Art de penser—the so-called Port-Royal Logic—in 1662. In his early seventies, Arnauld published a detailed refutation of Nicolas Male- branche’s theory of perception in the Traité des vraies et fausses idées (1683). A few years later, in a famous exchange of letters with Leibniz, he argued that the Leibnizian the- ory of individual substance eradicates genuine contin- gency and leads to universal fatalism. j.cot. *Cartesianism; mind–body problem; Port-Royalists. S. M. Nadler, Arnauld and the Cartesian Philosophy of Ideas (Man- chester, 1989). R. C. Sleigh, The Leibniz–Arnauld Correspondence (New Haven, Conn., 1990). Arrow, Kenneth Joseph (1921– ). Leading theorist of social choice, winner of a Nobel Prize in 1972. In Social Choice and Individual Values (1951), Arrow studied the determination of rational choice at the collective level for cases where this choice is to be a function of the prefer- ences of the individuals making up the collective. In this study he proved the general impossibility theorem, which gives rise to *Arrow’s paradox. Assuming that any accept- able function must meet a small number of intuitive con- ditions, Arrow proved that there is no consistent function from individual preferences to collective choice. With Debreu, Arrow also made a major contribution to general equilibrium theory. (In an economy in competitive equi- librium all markets clear simultaneously: there is a balance of supply and demand in all markets.) t.p. C. C. von Weizsacker, ‘Kenneth Arrow’s Contributions to Eco- nomics’, Scandinavian Journal of Economics (1972). Arrow’s paradox. A paradox in social choice theory. Why not devise a function which orders options for a society in terms of the preferences of its individual members? Such a function would have to meet certain conditions on rea- sonableness—such as that (a) an ordering could be obtained from any logically possible set of individuals’ preferences, (b) if everyone prefers a given A to a B, then that Ashould be ordered above that B, (c) no individual can dictate the social ordering—there can be no individual such that whenever he prefers an A to a B, then that A must be ordered above that B, and (d) the ordering of any A and B depends on individuals’ preferences between that A and that B alone. *Arrow proved that there was no consistent function which met all the conditions. t.p. *voting paradox. K. J. Arrow, Social Choice and Individual Values (New Haven, Conn., 1951). art. The idea that various activities such as painting, sculp- ture, architecture, music, and poetry have something essential in common belongs to a particular period begin- ning only in the eighteenth century. It was then that the ‘fine arts’ became separated off from scientific disciplines and more mundane exercises of skill. Later, during the eras of romanticism and modernism, this became trans- muted into the single notion of art. Contemporary philosophers have inherited the notion, but are no longer entirely sure what to do with it. One problem is the difficulty of defining art. Consider what is usually treated as the earliest definition: art as mimesis, or the reproduction of the world in images. For a long time painting and literature could be united under this heading (and a precedent cited in Greek thought). How- ever, if art is to include music and architecture, as well as the non-figurative visual forms of the twentieth century, this definition will not easily suffice. Two notable defin- itions from the early part of this century built on the rejec- tion of representation as a defining feature of art: art as significant form, and art as the expression of emotion. Both play down the artwork’s relation to reality, in favour of perceptible aesthetic qualities of the art object itself, or of the relation between the work and the creative mind in which it originated. Earlier intimations of both can be found in the ideas of *beauty and *genius in Kant’s theory of art. Both object-centred and artist-centred definitions of art could be used to discriminate that which was ‘properly’ art from that which was not, and such ideas helped in their day to explain the value of many progressive forms of art. But each is at best one-sided as a comprehensive definition. Successive waves of the avant-garde, together with increasing knowledge of different cultures, have shown how society’s institutions accommodate radical change in what is recognized as art. It has even been suggested that the very point of the concept of art lies in its open-ended capacity to accept change. Some have offered what is called an institutional definition of art, prompted by the thought that the only common feature among artworks is just their being recognized as art by certain institutions in particular societies. It would presumably be left to history to show what these institutions were, and the various functions or values which the things called art have had within them. While there must remain appropriate stand- ards by which one work can be judged superior to another, it would be hard to deny that the inclusion and exclusion of different activities from the status of art has served other functions in society, such as fostering élitism or class-distinction. art 59 . history of mathematics and Aristoxenus wrote on music. Theophrastus and the next head of the Lyceum, Strato, were independent thinkers, prepared to criticize Aristotle’s views, and to develop their. head, Aristotle left Athens, lived for a while in Assos and Mytilene, and then was invited to return to Macedonia by Philip to tutor Alexander. Aris- totle returned to Athens in 335 at the age. (Oxford, 1 981 ). J. Barnes (ed.), The Complete Works of Aristotle, i and ii (Princeton, NJ, 1 984 ). —— (ed.), The Cambridge Companion to Aristotle (Cambridge, 1995). Aristotle 57 A. Gotthelf and