The Oxford Companion to Philosophy Part 46 potx

Udayana (eleventh century) wrote Flower-Offerings of Arguments, detailing five ways of proving the existence of a God. Atheist objectors offered excellent refutations of his cosmological arguments, like this rejoinder: ‘If the uni- verse requires a maker because it undergoes change, even God needs a maker because he sometimes creates, some- times destroys.’ Almost all classical schools had a fully developed account of change and causality. Four major stands here were: 1. The flux theory of the Buddhists: the cause perishes before the effect arises. 2. The emergence theory of Vais´es . ika: the effect is a new entity emerging as inhering in the material cause even if the cause survives as the stuff. 3. The transformation theory of Sa¯m . khya: the effect slumbers in the material cause, with which it is sub- stantially identical. 4. The illusionism of monistic Veda¯nta: the cause alone is real; the effect is an illusory projection of variety which cannot be unreal or real; change is illusory like magic (ma¯ya¯ ). There was fierce discussion over these rival accounts of causation. For example, arguments for commonsensical emergence theory are: (E1) The perceptibly different lump of clay never does the same work as the pot made out of it. (E2) If the pot was already there in the clay, the potter’s effort must have been in vain, unless it is said to produce something non-pre-existent, namely the pot’s structure. If a structure can be added to real- ity, why not the pot? Against this, the transformation theorists argue: (T1) What is unreal, like a rabbit’s horn, cannot be made to exist. (T2) If a and b are distinct it makes sense to ask ‘Bring a along with b’, but ‘Bring the coat along with the wool with which it was made’ is nonsense. So the coat and the wool must be the same in substance. To T1 the emergence theorist retorts, ‘You are confusing absence with non-being. The future sculpture is absent— and not hidden somewhere in the hunk of marble—but it is not a non-entity.’ A mere nothing does not qualify as a genuine absentee in the Vais´es . ika category system. Specif- ically, this system classifies existents into substances, par- ticular qualities, events, universals, inherence-relation, basic individuators, and absence. The first three have real- ness, which is a universal. Hence, on pain of a vicious regress, universals do not have the universal of realness inhering in them. The first seven classes of existents have positive being. But all seven, including absences, are know- able as well as existent. Thus, the absence of the effect before its emergence should not be looked upon as a mere nothing. In epistemology, knowledge is understood by most sys- tems as a doubt-free awareness-episode matching reality and causing pragmatic success. To meet an ancient trad- ition of tightly argued *scepticism which, by the eleventh century, anticipated Gettier-type counter-examples where truth and justification fell apart, detailed theories of truth and causal routes of knowledge were constructed. Ca¯rva¯ka materialists had attacked inferential knowledge by asking, ‘How do you establish the universal generaliza- tion “Whatever has g has f ”, without which any inference from g to f cannot take off? Perception cannot guarantee such a generalization and to base it on inference again would be circular or lead to regress.’ In response to this attack Buddhists resorted to admitting an analytically or causally necessary relation between being an elm and being a tree, or between smoke and fire, and Nya¯ya spoke of intuitive knowledge of the entire class of g/f through the perceived universals. Apart from questions about per- ception, inference, and verbal testimony, issues about knowing that one has known, knowing other minds, the knowledge–object relationship, the mechanism of per- ceptual error, and doubt and ignorance as cognitive states were hotly debated. The seeing of a snake in a rope was understood by some as an unordinary recollective percep- tion of a past real snake; by others as the seeing of a non- existent object; by yet others as mere failure to see the presented rope’s distinction from the remembered snake. A fine-grained epistemology of illusion, of course, could well be used by friends and foes of the non-dualists’ doctrine that the world is an illusion. In ethics the *Bhagavadgı¯ta¯, a central Hindu religious text, synthesized the life of work and the life of wisdom through its ethics of desireless performance of social duties. Buddhism generally prescribed an ethics of self- lessness and universal compassion for fellow sufferers in a sorry world. The Mı¯ma¯m . sa¯ ritualists developed an elabor- ate taxonomy of hypothetical and categorical imperatives, sometimes claiming that it is only in the context of an action-prescribing sentence that a word has meaning. Out of an ancient tradition of defining drama and poetry, a rich philosophical aesthetics of music, poetic enjoyment, and the emotions developed. Disputes about grades of suggestive meaning and analysis of metaphors exercised generations of aesthetes. Except for the Ca¯rva¯ka naturalists, every classical school believed in *karma and rebirth. Liberation from rebirth was set up as life’s highest ideal, but alternative goals of life like pleasure, prosperity, moral rectitude, or piety were also realistically accepted. A methodologically sophisticated philosophy of bodily health was set out by the medical scriptures called Ayurveda. Though we have focused only on ancient and medieval Indian philosophies, rejuvenated Sanskrit learning, espe- cially of neo-Nya¯ya, with Kantian, Marxian, Wittgenstein- ian, or Heideggerian reinterpretations of the classical theories, along with original philosophical thinking, keep contemporary Indian philosophy as vibrant as it was a thousand years ago when Nya¯ya metaphysicians fought 430 Indian philosophy with Buddhists about the existence of eternal cowness on top of bovine particulars, and Jaina philosophers tried to reconcile realists and anti-realists with their pluralistic per- spective on alternative ways of world-making. a.c. J. Ganeri, Philosophy in Classical India (London, 2001). J. N. Mohanty, Reason and Tradition in Indian Thought (Oxford, 1992). Karl Potter, Presuppositions of India’s Philosophies (Delhi, 1991). Mark Siderits, Indian Philosophy of Language (Deventer, 1991). Ninian Smart, Doctrine and Argument in Indian Philosophy (Leiden, 1992). indifference: see spontaneity and indifference; freedom. indifference, principle of: see probability. indirect discourse. One paradigm of indirect discourse is reported speech: for example, ‘Lambert said that Hume was a great Scottish historian.’ Frege argued that in cases like this the term ‘Hume’ refers to its customary *sense, rather than to Hume: the words after ‘said that’ do not denote a truth-value, but rather convey the thought (proposition) expressed by Lambert. Frege’s account cap- tures the insight that in indirect discourse the sense of a speaker’s remarks can be captured in many different ways. Lambert could have said what is reported without using the name ‘Hume’ at all. a.bre. E. Lepore and H. Cappelen, ‘On an Alleged Connection between Indirect Speech and Theory of Meaning’, Mind and Language (1997). individualism, moral and political. In ethical theory and political philosophy individualism is a view that gives pri- mary moral value to individual human beings. Different interpretations are possible concerning what it is about individual human beings that justifies their being given primary value, and also concerning how it is that individ- uals thus valued are to be treated. In political philosophy, certain forms of libertarian and liberal individualism, for example, are influenced by the Kantian view that individual human beings are *‘ends in themselves’, and thus agree that persons are owed respect for their *autonomy, which is protected by inviolable rights; but while both these views may be anti-paternalistic, they notoriously differ in other recommendations for the political order; for example, *liberalism will endorse certain welfare practices but *libertarianism will not. Even regarding the shared anti-*paternalism, these forms of individualism may dispute whether the prized feature of the given individual human being is an idealized ‘ratio- nal nature’ or his or her actual capacity for choice, marked as this may be by neurosis, character defects, and self- deception. Another form of individualism is influenced by classical *utilitarianism, and so prizes the capacity of the individual human being for pleasure and pain; it may also be anti- paternalistic regarding the activities of the state, but tend to regard social practices and institutions generally as instruments for the achievement of the greatest aggregate happiness possible in the society’s circumstances, rather than as expressions of or protections for rights, except as the latter might be conducive to the aggregate *well- being. Within ethics, the valuing of the person characteristic of individualism is especially problematic for the develop- ment of a normative theory of individual responsibility. One is oneself an individual, and thus to be prized; but others are individuals, and they too are to be prized. How does one reconcile a principled regard for one’s own *rights, self-realization, meaningful relationships, and material well-being with moral respect for these features of the lives and persons of others? The issue may become personally distressing as well as theoretically challenging when the fact is that many millions of people in the world are destitute in one way or other. Does individualism allow one to put oneself first in a world so filled with mis- ery and oppression, or require self-sacrifice in the devo- tion of time, energy, and talent to the needs of others? Individualism prizes individual human beings, and differ- ent forms of individualism offer different accounts of what, morally, is prizeworthy about individual human beings; but what this suggests for the conduct of the responsible agent in a world flawed by destitution and gross disparity in levels of life is not yet settled. A further issue for individualism in both ethical theory and political philosophy is the question how the basic indi- vidual is to be construed. Is the person to be understood as an independent atomic particular whose connections with others are consensual or coerced but not constitutive of the identity of the particular? Or is it instead a being whose make-up includes essentially its relationships, and, indeed, other differentiating factors, such as deep inter- ests, temperament, distinctive activities, or even ethnic or cultural heritage? Construing individuals in these different ways suggests differences in normative content for ethical theory and for political philosophy. ‘Respect for persons’ may differ among liberal, libertarian, or communitarian philosophies resting on different views of the essential make-up of the person. Similarly, these different views can alter an ethical theory’s prescriptions for balancing one’s responsibilities regarding others and oneself. An import- ant element in assessing an ethical theory or political phil- osophy is the adequacy of its basic conception of the individual. n.s.c. Steven Lukes, Individualism (Oxford, 1973). Charles Taylor, Sources of the Self (Cambridge, Mass., 1989). Bernard Williams, ‘Persons, Character, and Morality’, in Moral Luck (Cambridge, 1981). individualism and anti-individualism. Theses in philoso- phy of mind advocating opposed conceptions of the psy- chological subject. The individualist conceives the psychological facts about a person as facts which hold independently of her relation to her physical and social environment. Pressure individualism and anti-individualism 431 is put on this conception by the claims (i) that some men- tal states are world-involving, (ii) that some mental states are linguistic-community-involving. *Twin earth thought experiments are used to argue for (i); thought experiments originating from Burge, in which it is shown that commu- nal standards of correctness prevail where terms are used in ascribing mental states to individuals, are used to argue for (ii). A philosopher who subscribes to a strong anti- individualism takes demonstrations of (i) and (ii) to be symptomatic of the fact that the physical and social environment permeates psychological investigation even where an individual’s psychology is in question. j.horn. *externalism. Tyler Burge, ‘Individualism and the Mental’, in Midwest Studies in Philosophy, iv (1979). individuation. The determining of what constitutes an individual: that is, one of something. Principles of individu- ation are the principles by which things, normally of a kind, are distinguished into single individuals, most often at some given time. The single principle of *counting which a *sortal term ‘F’ supplies is commonly the princi- ple used for distinguishing one F (say one table, tree, or person) from another at one time as opposed to doing so over periods of time. Principles of individuation are correspondingly sometimes contrasted to principles of *identity, which concern counting and being the same F over periods of time. Where there is no single principle for determining how many Xs there are somewhere at some time, it may be said that Xs cannot be individuated. Thus ‘objects’ cannot be individuated as such. And while dodos or aardvaarks could be, the same is not true for their negative counter- parts introduced in some contexts. Supposing there to be not-dodos wherever there are no dodos, not-dodos can- not be individuated, which helps show why these are not entities on a footing with dodos. s.w. *things. P. F. Strawson, Individuals (London, 1959). S. Wolfram, Philosophical Logic (London, 1989), ch. 6.2. indoctrination: see teaching and indoctrinating. induction. Induction has traditionally been defined as the *inference from particular to general. More generally an inductive inference can be characterized as one whose conclusion, while not following deductively from its pre- misses, is in some way supported by them or rendered plausible in the light of them. Scientific reasoning from observations to theories is often held to be a paradigm of inductive reasoning. Most philosophers hold that there is a problem about induction: its classic statement is found in Hume’s Enquiry Concerning Human Understanding. Having observed that all arguments to unobserved matters of fact depend upon the relation of cause and effect, Hume remarks that our knowledge of this relation depends on experience: but, he goes on to argue: all inferences from experience suppose, as their foundation, that the future will resemble the past . . . If there be any suspicion that the course of nature may change, and that the past may be no rule for the future, all experience becomes useless, and can give rise to no inference or conclusion. It is impossible, therefore, that any arguments from experience can prove this resemblance of the past to the future; since all these arguments are founded on the supposition of that resemblance. (iv. ii. 32) Hume does not try to counter these arguments by pre- senting a justification of inductive reasoning; but neither does he suggest that we might eschew inductive reason- ing. If we have observed that flame and heat ‘have always been conjoined together’, our expectation of heat is, he says, ‘the necessary result’ of seeing the flame. This expectation is ‘a species of natural instincts, which no reasoning or process of the thought and understanding is able either to produce or to prevent’ (ibid. v. i. 38). Many philosophers have rejected this disbelief in the rationality of induction. Some have said that, taking deduction as the paradigm of reasoning, Hume has merely noticed that induction is not deduction, arguing against him that it is part of what we mean by rationality to operate in accordance with inductive procedures. Some have suggested that induction is justified inductively by its past successes, and that the circularity here is only appar- ently vicious. Some have proposed what is known as a pragmatic justification: not that inductive procedures will lead to the truth, but that if there is a truth to be known, inductive procedures are the best way of getting to it. None of these supposed justifications is universally accepted, and some philosophers—notably Popper— argue that scientists proceed not by cheerfully inferring the course of the future from past regularities, but by proposing bold generalizations and then seeking to falsify them. Some philosophers have assumed the task not of justify- ing induction, but of setting out principles of inductive inference in a way analogous to that in which the princi- ples of deductive inference have been codified. But there is a major difficulty in any account which seeks to character- ize sound inductive argument in an abstract way. The deductive logician tells us that if all As are Bs and all Bs are Cs then all As are Cs: A, B, and C here might be anything. The trouble with the idea of inductive logic is that whether the fact that all observed As are Bs gives any support at all to the claim that all As are Bs depends on what A and B are. We swallow Hume’s examples—like flame and heat— without noticing that we observe all kinds of regularities that we should not dream of expecting to persist. This is the point of Goodman’s new riddle of induction. m.c. *abduction; deduction. L. J. Cohen, An Introduction to the Philosophy of Induction and Prob- ability (Oxford, 1989). N. Goodman, Fact, Fiction, and Forecast (London, 1983). R. Swinburne (ed.), The Justification of Induction (Oxford, 1974). 432 individualism and anti-individualism inequality. In political and social theory, inequality con- sists in the differences between individuals or groups in the possession of what is desirable or undesirable. The main categories of inequality embodied in a society are political, legal, social, and economic. The clearest forms of political inequality are aristocracy and the exclusion of certain groups—women, racial or religious minorities, or those without property—from voting or political office. Legal inequality is exemplified by differences in liability to criminal prosecution or civil action, or in freedom of con- tract. Social inequality involves differences in status, def- erence, and subordination—systems of racial caste being an extreme example. Class inequalities are both social and economic, marking children with the wealth and profes- sional status of their parents. Some inequalities are politically enforced; others merely arise unless they are prevented. While most mod- ern political theories are opposed to the enforcement of inequalities between groups, they must all face the ques- tion how much should be done to prevent inequalities from developing, between either groups or individuals. Two factors make it impossible to eliminate inequality entirely: first, the need for hierarchies of power in any political and legal system, and in any economic system except the most primitive; second, the fact that there are natural inequalities—of ability, enterprise, and luck— which affect people’s success in life. Left to themselves, some people will accumulate more wealth than others and use it to benefit their children, who will do the same, thus giving rise to a class system. The upper classes will also tend to acquire more legal and political power and a higher social status, even if the system is formally democratic and no groups are legally excluded from these advantages. The moral question is whether a society should be con- cerned to narrow gaps of this sort, on the ground that the losers, and more especially their children, do not deserve their disadvantages. The welfare state—provision of social benefits paid for by taxes—is one way of doing this. Moral radical methods, designed to abolish class hierarchy entirely by legal restrictions on the private accumulation of wealth, seem to entail unacceptable general interfer- ence by the state with personal as well as economic lib- erty, and also tend to undermine economic efficiency. Some people believe that so long as there is legal equality of opportunity—so that no one is prohibited from becom- ing rich and powerful if they can—inequality of results is unobjectionable. But even if it is morally unfortunate, some significant inequality of results probably has to be accepted as a permanent feature of the social world. t.n. *equality; justice; well-being; welfarism. G. A. Cohen, ‘Incentives, Inequality, and Community’, in The Tanner Lectures on Human Values (Cambridge, 1992). F. A. Hayek, The Constitution of Liberty (Chicago, 1960). R. Nozick, Anarchy, State, and Utopia (New York, 1974). inference. Understood as the upgrading or adjustment of belief in the light of the play of new information upon current beliefs, it is customary to recognize at least three modes of inference: deductive, inductive, and abductive, although abduction is often treated as a special case of induction. In deductive theories, an inference is justified if it conforms to a principle of logic or to an argument valid- ated by the principles of logic. In some treatments it is also required that the argument be sound. Most deductive theorists since Frege agree that although inference is a psychological process, the principles which make it deduct- ively correct are valid independently of any psychological fact. This raises the question what justifies the laws of logic. The once dominant view that they are true in virtue of the meanings of (certain of ) their constituent terms is discouraged by present-day scepticism about meaning as a theoretically fruitful notion in philosophy. Some critics doubt whether, even if justified, the rules of logic are good rules of deductive inference. *Modus ponens is a case in point. Asserting that it is always permis- sible to infer B from A and ‘If A then B’, Harman points out that although B is here implied, it would not be correct to accept B for any reasoner who came to notice that B was false. Inductive inferences are those that project beyond the known data, as in the paradigm of generalizing that all emeralds are green. Since Francis Bacon’s day, efforts have been made to formulate an inductive logic which would specify conditions under which such projections are justified. Difficulties lie in wait, chiefly Hume’s prob- lem (*induction) or Goodman’s variation. That all the emeralds we have so far come upon are green is a fact which no more licenses the proposition that they are all green than it licenses the proposition that they are all green if observed before 1 January 2050, and are blue otherwise. What, then, justifies our making the former projection rather than the latter? A further projection problem arises from a puzzle invented by Hempel. If known instances of emeralds sustain the projection that they are all green, they likewise sustain the equivalent proposition that all non-green things are non-emeralds. But any non-green non-emerald will help sustain that generalization and any proposition equivalent to it. It would appear, then, that red sunsets, black cats, and all the other non-green non-emeralds sustain the generaliza- tion that all emeralds are green, which is strikingly implausible. Inductive reasoning is also thought to include prob- abilistic reasoning. It is said that an inference is justified if it conforms to the theorems of the *probability calculus. Against this, it is objected that, if true, a ‘computational explosion’ would ensue. Even cases of modest evidential complexity are ‘too complicated for mere finite beings to make extensive use of probabilities’ (Gilbert Harman, Change in View). Even so, Harman does seem to concede that the rules of the probability calculus might be thought of as normatively correct, that is, as rules which a human inferrer should use to the extent that he satisfies appropri- ate assumptions on computationally ideal reasons. inference 433 *Abduction is recognized in two varieties. In one sense, it is *‘inference to the best explanation’, which is a means of justifying the postulation of unobservable phenomena on the strength of explanations they afford of observable phenomena. In its other variety, abduction is the process of forming generic beliefs from known data. Observations incline us to think that tigers are four-legged, a proposition we hold true even upon discovery of a three-legged tiger. Generic sentences differ from general (i.e. universally quantified) sentences by their accommodation of negative instances, that is, of instances which would falsify general sentences. Attractive though it is, the idea of inference to the best explanation awaits an adequate generalized specification of what ‘best’ consists of. And the idea of generic inference requires a satisfactory account of when negative instances do and do not falsify generic claims. j.w. *deduction; induction; implication. Gilbert Harman, Change in View (Cambridge, Mass., 1986). Nelson Goodman, Fact, Fiction, and Forecast, 4th edn. (Cam- bridge, Mass., 1983). inference, immediate. The name in traditional logic for drawing a conclusion from a single premiss, as opposed to the two premisses of the *syllogism. Thus the move from ‘Everything human is corrupt’ (‘All S are P’) to ‘Nothing human is not corrupt’ (‘No S are not P’) is a valid immedi- ate inference, while that from the regretful ‘Only good Indians are dead Indians’ (‘All S are P’) to the genocidal ‘The only good Indian is a dead Indian’ (‘All P are S’) is an invalid immediate inference. c.w. *logic, traditional. L. S. Stebbing, A Modern Introduction to Logic (London, 1930), ch. 5. inference to the best explanation. Accepting a state- ment because it is the best available *explanation of one’s evidence; deriving the conclusion that best explains one’s premisses. According to Gilbert Harman, who uses the phrase in many publications, acceptable inductive infer- ences are all inferences to the best explanation. One can also use this notion in a response to *scepticism. Do you know you are looking at a reference book right now rather than, say, having your brain intricately stimulated by a mad scientist? The sceptic carefully describes this alterna- tive so that no experiment can refute it. The conclusion that you really are looking at a book, however, explains the aggregate of your experiences better than the mad sci- entist hypothesis or any other competing view. A sceptic who disagrees with this, instead of telling still more stories in which we cannot distinguish radically different situ- ations, needs to address fresh issues about explanation. d.h.s. *explanationism. Gilbert Harman, ‘The Inference to the Best Explanation’, Philo- sophical Review (1965). P. Lipton, Inference to the Best Explanation, 2nd edn. (London, 2003). infima species. Literally, lowest form (sort, species). According to traditional Aristotelianism each individual can be pictured as lying permanently within a finite set of circles of genus, subgenera, and species, whose circumfer- ences do not cross; the outermost circle is the individual’s summum genus, the innermost its infima species. The idea makes some sense in biology, but less obviously else- where (e.g. what is the infima species of Mount Kenya, or Alpha Centauri, or the Vienna Philharmonic Orchestra?). On the other hand certain scholastics thought that indi- vidual angels must each be aninfima species, and some have found the same thing implied in Aristotle’s souls and Leib- niz’s monads. c.a.k. *genus and species. infinite, traversal of the: see traversal of the infinite. infinite regress. Suppose we define a voluntary act as one caused by an act of will: if acts of will are themselves vol- untary then the definition requires that they themselves be caused by prior acts of will. But there is no limit to the number of times this train of reasoning can be reiterated: so either the definition is wrong or acts of will are not vol- untary. The argument—deployed by Ryle in The Concept of Mind—shows that the proposed analysis of what it is for acts to be voluntary involves an infinite regress. m.c. infinitesimals. *Numbers greater than 0 but less than ½, ⅓, etc. In mainstream mathematics infinitesimals do not exist, though Leibniz suggested inventing infinitesimals, written dx, dy, etc. as fictions to help in the differential and integral calculus. In 1960 Abraham Robinson used math- ematical logic to introduce and justify non-standard analy- sis, an approach to calculus which allows us to use infinitesimals systematically in proofs and thus recapture Leibniz’s intuitions. w.a.h. Abraham Robinson, ‘The Metaphysics of the Calculus’, in Jaakko Hintikka (ed.), The Philosophy of Mathematics (Oxford, 1969). infinity. *Zeno’s paradoxes were the first problems of infinity to vex philosophers, provoking Anaxagoras to hold that there was no smallest quantity of anything, and the Greek atomists to the opposite opinion. But the atom- ists showed no fear of the infinitely large, as they posited an infinite universe with innumerable worlds in it. Aris- totle, however, held that there was nothing ‘actually’ infi- nite, either infinitely small or infinitely large or infinitely numerous; for him, all infinity was merely ‘potential’. Many philosophers since have been wary of infinity. Most famously, Kant argued that it was beyond the reach of rea- son, and the source of insoluble *antinomies. In practice the infinitely large (in space or time) has not been troublesome. The change from Aristotle’s finite uni- verse to the infinite space of Newton’s cosmology, though unsettling in other ways, did not tax the mathematician’s understanding. (The real numbers are very naturally 434 inference correlated with the points of an infinite line, and hence triples of real numbers are naturally correlated with the points of an infinite three-dimensional space.) The infinitely small proved more difficult. The Greek mathematicians had avoided it, by their elegant method of exhaustion, but when the differential calculus was intro- duced in the seventeenth century, it did seem to need the puzzling notion of an *infinitesimal, i.e. a quantity smaller than any finite quantity but greater than zero. This puzzle persisted for nearly two centuries, until Cauchy (1789–1857) and then Weierstrass (1815–97) showed how the awkward notion could be eliminated. The infinitely numerous was first seriously studied by Cantor, whose work led directly to the *paradoxes of logic, and thence to modern *set theory. It is easily seen that two finite sets have the same number of members if and only if there is a relation which correlates their mem- bers one to one. Cantor’s basic idea was to extend this cri- terion to infinite sets, introducing infinite cardinal numbers to number their members. It follows from this criterion that an infinite set is not increased by adding to it any finite number of new members, nor decreased by sub- tracting from it any finite number of members. (For example, we can correlate all the positive integers with integers greater than 100 just by correlating x withx + 100.) Thus, where κ is an infinite cardinal and n a finite cardinal, we have κ + n = κ – n = κ. Similarly κ · n = κ and κ n = κ. But Cantor was able to prove the inequality 2 κ > κ, for any cardinal κ whatever, from which it follows that the series of infinite cardinal numbers is itself an infinite series. The set of all finite cardinals is said to have the cardinal number ℵ 0 (aleph null), which is the smallest infinite cardinal. The next is ℵ 1 (aleph one), and so on. Cantor’s *continuum hypothesis states that ℵ 1 is the number of the real num- bers. It is now known that the hypothesis can be neither proved nor disproved from the currently accepted axioms of set theory. Cantor also introduced infinite ordinal numbers, which are in fact more important to modern set theory than the infinite cardinals. But there is no space to describe them here. d.b. *numbers. G. Cantor, Contributions to the Founding of the Theory of Transfinite Numbers, tr. P. E. B. Jourdain (New York, 1955). M. Hallett, Cantorian Set Theory and Limitation of Size (Oxford, 1984). A. W. Moore, The Infinite (London, 1990). infinity, axiom of. An axiom of standard set theories. It is required to ensure the existence of a *set which has infi- nitely many members. A set has infinitely many members just in case there is no natural number n such that the set has exactly n members. An example of such a set is the set S containing the empty set (the set with no members) and the unit sets (sets with just one member) of any sets which S contains; S contains the empty set, the unit set of the empty set, the unit set of the unit set of the empty set, and so on. The axiom of infinity is required for set-theoretical constructions such as the definition of the real numbers as infinite sequences of rational numbers. a.d.o. W. V. Quine, Set Theory and its Logic (Cambridge, Mass., 1963), sect. 39. informal logic: see logic, informal. Ingarden, Roman (1893–1970). Polish phenomenologist with a realist leaning. Studied in Lvov, Vienna, and Göt- tingen, and in Freiburg with Husserl. Professor in Lvov and Cracow. His works, written in Polish and German, deal with various problems of aesthetics (Das literarische Kunstwerk (1931) is perhaps the best known of his works outside Poland), and with metaphysics and epistemology (including Vom formalen Aufbau destindividuellen Gegen- standes (1935) and The Controversy about the Existence of the World, 2 vols., 1947–9, in Polish). He accepted the method of eidetic reduction but utterly rejected the transcenden- tal idealism of the late Husserl; he argued that a realist ontology may be built on a phenomenological basis which provides a method to classify various modalities of being, including specific existence forms of the objects of aes- thetic perception. He was a consistent critic of positivism, nominalism, physicalism, and idealism. l.k. *phenomenology. A. T. Tymieniecka, Essence et existence: Essai sur la philosophie de N. Hartman et R. Ingarden (1957). in-itself: see for-itself and in-itself. innate ideas. These are *ideas that exist in the mind with- out having been derived from previous experience. Plato held that all of our ideas are innate, although we do not clearly grasp them; learning consists of remembering these ideas and we develop a clearer understanding of them through the process of Socratic questioning and dialectic. There is a close relation between a philosopher’s views on innate ideas, *a priori knowledge, and *neces- sary truths. Rationalists typically hold that the mind has a set of innate ideas that provide the source of a priori knowledge of a wide variety of necessary truths. Empiri- cists deny that there are any innate ideas and limit a priori knowledge and our grasp of necessary truths to *tautolo- gies and propositions derived from arbitrary *definitions of words. There has been little agreement about the exact nature of innate ideas among either their defenders or their detractors. Descartes allows for a wide variety of innate ideas and principles; sometimes he suggests that virtually all our ideas are innate, at least potentially. He also describes our thinking faculty as an innate idea, and con- siders the idea of God to be innate, although he also argues that this idea must have been put into our minds by God. Locke held that the mind of an infant is like a blank paper and that all of our ideas are imprinted on the mind by experience. He treated the mind as having a number of inherent powers, such as remembering and imagining, innate ideas 435 but held that our ideas of these powers are not innate. Locke also denied that there are any innate principles in the mind because (among other reasons) such principles would require innate ideas. Leibniz replied that the mind is more like a block of marble with veins which limit what can be sculpted from the block, rather than like a blank paper. On this view, innate ideas are natural tendencies of the mind and we need not be explicitly conscious of them or of the necessary truths that are based on them; we require experience and thought to determine which of our ideas are innate. Thus Leibniz accepted Locke’s claim that much of our learning is from experience, but denied that this shows that the ideas and propositions we learn are not innate. Ultimately Leibniz agreed with Plato that all of our ideas are innate and that all learning is actually the exfoli- ation of ideas that were always present in our minds. It can be argued that Kant’s *categories are innate ideas on a Leibnizian model. The categories are concepts that are internal to the nature of reason and that provide an a priori framework for all of our experience. Because the categories are imposed on experience by our minds, those aspects of experience that derive from the categories are necessary features of experience and we can know a priori that they will characterize all our experience. Since innate ideas would provide universal features of human thought and experience, the debate over whether such ideas exist continued to rage in twentieth-century anthropology. Defenders of innate ideas also include Chomsky, who postulates a universal innate *grammar in human beings to account for our ability to learn language and our ability to distinguish an unlimited number of grammatical from ungrammatical expressions in a lan- guage we have mastered. The debate over the existence of innate ideas has been superseded by the debate over which aspects of human knowledge (if any) are innate and which are learned; there is no clear resolution of this ques- tion at the present time. h.i.b. *empiricism; ideas; rationalism. N. Chomsky, Aspects of the Theory of Syntax (Cambridge, Mass., 1965). G. W. Leibniz, New Essays on Human Understanding, tr. and ed. P. Remnant and J. Bennett (Cambridge, 1985). J. Locke, An Essay Concerning Human Understanding, ed. P. Nidditch (Oxford, 1984). inner sense. Regarded by Locke and Kant as a faculty of the mind whereby it is introspectively aware of its own contents in a manner which is analogous to the perception of external objects. More recent supporters of this notion have argued that the best model for inner sense is bodily perception, that is, one’s awareness ‘from the inside’ of the position and movement of one’s own body. One difficulty with this proposal, from a Kantian perspective, is that bod- ily perception is of something spatial, whereas the objects of Kantian inner sense are supposed to be temporally but not spatially ordered. q.c. *introspection. D. M. Armstrong, ‘Consciousness and Causality’, in D. M. Arm- strong and Norman Malcolm, Consciousness and Causality: A Debate on the Nature of the Mind (Oxford, 1984). S. Shoemaker, The First-Person Perspective and Other Essays (Cambridge, 1996). instrumentalism. The doctrine that scientific theories are not true descriptions of an unobservable reality, but merely useful instruments which enable us to order and anticipate the observable world. Traditional versions of instrumentalism were influenced by verificationist the- ories of meaning, and held that theoretical claims about unobservables cannot be regarded as literally meaningful. More recent versions of instrumentalism are motivated by sceptical rather than semantic arguments: they allow that scientists can make meaningful claims about an unob- servable world, but deny that we should believe those claims. One motivation for this kind of sceptical instru- mentalism is the ‘underdetermination of theory by evi- dence’. However, realist opponents of instrumentalism can respond that the compatibility of different theories with the observational evidence does not mean those the- ories are all equally well supported by that evidence. A bet- ter argument for sceptical instrumentalism is probably the ‘pessimistic meta-induction’, which argues that, since past scientific theories have all proved false, we can expect pre- sent and future theories to prove false too. d.p. *verification principle. P. Churchland and C. Hooker (eds.), Images of Science (Chicago, 1985). B. van Fraassen, The Scientific Image (Oxford, 1980). instrumental value. Some item has instrumental *value just to the extent that it lends itself (fortuitously or by design) effectively to the achievement of some desired or valued purpose. It is that which is ‘good as a means to . . . ’. Hammers, chisels, and tools of all kinds are palmary instances of instrumentally valued items. Aristotle described slaves as living tools. In contrast, we think all humans have intrinsic value (or inherent value). Kant’s dictum that one should treat all persons ‘as ends’ expresses this thought. Instrumental and other forms of value are discussed in G. H. von Wright, The Varieties of Goodness (London, 1963). n.j.h.d. *ends and means. insufficient reason, principle of. The principle of insuffi- cient reason states that equal probabilities must be assigned to each of competing assertions if there is no positive reason for assigning them different probabilities. Keynes is the chief figure in discussion of this principle, which he preferred to call the principle of indifference. His own definition is ‘if there is no known reason for predicating of our subject one rather than another of several alternatives, then relatively to such knowledge the assertions of each of these alternatives have an equal probability’. He devoted an entire chapter of his 436 innate ideas book on *probability to a vehement refutation of the principle. The principle is of interest in the theory of rational choice. It has been shown to generate paradoxes (e.g. *Bertrand’s paradox) and to create difficulties for induct- ivist theories such as Carnap’s, where its employment has to be sharply constrained to prevent the problem that if all a priori probabilities are equal, as Wittgenstein claimed in the Tractatus, the possibility of learning from experience is excluded. a.c.g. J. M. Keynes, A Treatise of Probability (1921), ch. 9. integrity. The quality of a person who can be counted upon to give precedence to moral considerations, even when there is strong inducement to let self-interest or some clamant desire override them, or where the betrayal of moral principle might pass undetected. To have integrity is to have unconditional and steady commitment to moral values and obligations. For such a person, the fundamental question whether to conduct life on the plane of self-concern or of moral seriousness has been decisively resolved, though particular life situations will doubtless continue to put that commitment to strenuous test. This moral commitment becomes a crucial compon- ent in his or her sense of identity as a person: it confers a unity (integration) of *character, and even a simplicity upon the man or woman of integrity. What integrity can- not guarantee is the soundness of the value-judgements themselves, which form the core of that person’s commitment. r.w.h. *conscience. A. Campbell Garnett, ‘Conscience and Conscientiousness’, in J. Feinberg (ed.), Moral Concepts (Oxford, 1969), ch. 7. J. J. C. Smart and B. Williams, Utilitarianism, For and Against (Cambridge, 1973). intellectual virtues: see virtues; virtues, doxastic. intelligence. A family of intellectual traits, virtues, and abilities occurring in varying degrees and concentrations. An intelligent creature is one capable of coping with the unexpected. An intelligent person is one in whom memory and the capacity to grasp relations and to solve problems with speed and originality are especially pronounced. Despite much study, psychologists have yet to settle on a precise characterization of intelligence. This has not damp- ened enthusiasm for the design and application of tests pur- porting to measure intelligence, however, and E. G. Boring’s remark that ‘intelligence is what the tests test’ is apposite. In recent years, debates have raged between those who regard intelligence as genetically fixed, and those who take it to be a product of social, cultural, and educational factors. Undoubtedly, heredity and environ- ment contribute in ways difficult to untangle. j.heil *rationality; reason. R. J. Sternberg, Metaphors of Mind: Conceptions of the Nature of Intel- ligence (Cambridge, 1990). intension: see extension and intension. intensionality. A context or form of words is intensional if its truth is dependent on the *meanings, and not just the *reference, of its component words, or on the meanings, and not just the truth-value, of any of its subclauses. So, ‘He coughed because he smoked’ is intensional, since there is no guarantee that truth is preserved if ‘he smoked’ is replaced by some other true sentence. More problem- atic are such contexts as ‘The sales assistant thought that the customer was wrong’, which supposedly may not be true if ‘the customer’ is replaced by the person’s name, or by some other mode of reference, as ‘The sales assistant thought that your cousin was wrong’. On the one hand, it has been maintained that we may enlist only referential terms which could have been used by the person whose thought is being reported, so that if the sales assistant was unaware that the customer was cousin to the person addressed, this second variant would be false. On the other hand, our ordinary practice would suggest that choice of referential terms is dictated more by what secures reference for those currently addressed, a correct mode of reference giving rise at worst to an inapposite form of words, not to a falsehood. b.b.r. *opacity. B. Rundle, Grammar in Philosophy (Oxford, 1979). intention. Phenomenon, of intending to do something, treated in philosophy of mind and action, and in jurispru- dence, and of importance in moral philosophy, e.g. in connection with *akrasia. Some notion of intention has seemed to be a crucial ingredient in an account of *action: the adverb ‘intention- ally’ may be put to work in marking out a class of actions; and the verb ‘intend’ introduces a state of mind of a per- son’s intending to do something, which may be present even where the person does not actually do the thing, but which is directed towards action even so. (Whether some- one can do something intentionally without having intended to do it is controversial.) Some philosophers have distinguished between inten- tions directed at particular pieces of present behaviour, and intentions directed at future action. The former sort, called ‘act-related’, may be thought to be present wher- ever something is done intentionally; these are sometimes said to be the things of which we have an experience in acting, so that they may be used to account for the distinct- ive phenomenology of agency. (*Agent.) It is the latter sort, the ‘future-directed’, with which accounts of intention are usually primarily concerned. One aim of an account of intention is to connect the concept with related ones, so as to see how a person’s intending to do something features in her practical delib- eration and in action. An account may start from the ques- tion whether intention can be reduced to desire and belief. (Since the idea of having a reason for action can be explicated in terms of desire and belief, these two are often thought intention 437 of as the two primary psychological attitudes, so that, if a reduction were possible, intentions would not need to be recognized as mental states sui generis.) One suggested reduction says that a person intends to do something if and only if she desires to do it and believes that she will do it. But the recent literature contains many arguments against any such reduction. It also contains arguments against the assimilation of intending to either desiring or believing. Like desire, intention moves people to action; but whereas you may desire what you think you cannot achieve, you cannot intend what you think is impossible of attainment. Like belief, intention sets constraints on what is done; but intentions, unlike beliefs, are not straightforwardly evaluable as true or false, and an account of what it is for one intention to be consistent with another is different from an account of what it is for one belief to be consistent with another. Intention, it seems, must be treated neither as an affective state (like desire) nor as a cognitive one (like belief ), but as a distinct- ively practical state, subject to its own ‘rationality requirements’. Michael E. Bratman has developed a planning theory of intention. His approach is initially a functional one: given believing, desiring creatures, who have limited time for deliberation, whose lives are coherent and co-ordinated with others’, what would be the features of states of mind that would assist in making them effective agents? Well, those states must carry commitments to practice, and in doing so be such as to control conduct and be available to new episodes of practical reason. Being in such states is what it is for agents to have plans. And plans are typically decomposable into elements, which are intentions. The idea of ‘oblique’ intention is sometimes introduced in jurisprudence, following Bentham: roughly, foreseen consequences of actions, although not directly intended, are obliquely so. Recognizing oblique intention intro- duces a class of things which people may be answerable for doing which is wider than the class of intended things. j.horn. *volition. Michael E. Bratman, Intention, Plans, and Practical Reason (Cam- bridge, Mass., 1987). Donald Davidson, ‘Intending’, in Essays on Actions and Events (Oxford, 1980). J. R. Searle, Intentionality (Cambridge, 1983), ch. 3. intentional fallacy. The alleged mistake of interpreting or evaluating a work of art on the basis of the artist’s inten- tions (or other states of mind), instead of properties ‘intrin- sic’ to the work itself. The idea was favoured by proponents of the post-war ‘new criticism’, but succumbs to two main objections: historical features of a work’s pro- duction commonly do affect interpretation, and inten- tions may be manifest in the work, rather than wholly external to it. c.j. W. Wimsatt and M. Beardsley, ‘The Intentional Fallacy’, in D. Newton de Molina (ed.), On Literary Intention (Edinburgh, 1976). intentionality. Technical term for a distinguishing fea- ture of states of mind: the fact that they are ‘about’ or rep- resent things. The term derives from the medieval Latin intentio, a scholastic term for the ideas or representations of things formed by the mind. The term was revived in 1874 by Franz Brentano for ‘the direction of the mind on an object’. Brentano’s idea was that intentionality is the mark of the mental: all and only mental states are inten- tional. This idea, often known as Brentano’s thesis, can be expressed by saying that one cannot believe, wish, or hope without believing or wishing something. Beliefs, wishes, desires, hopes, and the like are therefore often called ‘intentional states’. (*Propositional attitudes.) Contempor- ary philosophers sometimes describe the intentionality of mental states as their ‘aboutness’. Used in this way, ‘intentionality’ does not necessarily involve the idea of intention—in the sense that actions are intentional (though somewhat confusingly, intentions are intentional states in the sense under discussion). The term should also be distinguished from the logical notion of *intensionality. Intensionality is a feature of certain logical and linguistic contexts which exhibit the following fea- tures: (i) they are referentially opaque—substitution of co-referring expressions in a sentence may change the truth-value of the sentence; (ii) they do not license exist- ential generalization—from ‘Fa’ we cannot infer ‘There exists an x such that Fx’. Ascriptions of intentional states certainly can exhibit intensionality in this sense. If I believe that Aristotle wrote the Posterior Analytics, it doesn’t follow that I believe that Alexander’s teacher wrote the Posterior Analytics, since I might not believe that Aristotle was Alexander’s teacher. So ascriptions of intentionality can be opaque. Also, if I want to visit the lost city of Atlantis, it does not follow that something exists which I want to visit. So ascriptions of intentionality do not license existential generalization. But other non-psychological contexts exhibit intensional- ity too—notably, those contexts involving the ideas of necessity and possibility. (*Modality.) Thus while ‘Neces- sarily Aristotle is Aristotle’ is true, ‘Necessarily, Aristotle was the teacher of Alexander’ is (on the face of it) false. So treating intensionality as the mark of intentionality will not yield intentionality as the mark of the mental. (In fact, most contemporary philosophers deny that all men- tal phenomena are intentional in any case, on the grounds that sensations like pains are not ‘directed’ on anything.) Moreover, it is arguable that there are ascriptions of inten- tionality (in the sense of ‘aboutness’) which do not exhibit intensionality. If I see the Pope, and the Pope is a Polish man, then it plausibly follows that I see a Polish man. There is also a sense in which if I see something, there is something that I see. So there seem to be cases of ascrip- tions of intentionality which are not intensional. Most contemporary philosophers therefore treat inten- sional contexts as a general phenomenon of which some of those attributing intentionality are a special case. However, those like Quine who are suspicious of inten- sionality will use this suspicion as grounds for attacking 438 intention the psychological notion of intentionality, in the course of attacking intensionality generally. The intensionality of psychological ascriptions does, however, indicate a number of troublesome features of the idea of intentionality. Intentional states can be about objects that do not exist and they seem to be individuated in many cases not merely by the objects thought about but by the way they are thought about. (*Representation; *sense and reference.) How can such a peculiar phenom- enon as intentionality be part of the natural order of the world? Contemporary answers to this question—the problem of intentionality—have thus been concerned with ‘naturalizing’ intentionality. This usually takes the form of giving some account of how intentional states are causally related to the things they are about. t.c. *belief and desire; mind, syntax, and semantics; inten- tional relation. Franz Brentano, Psychology from an Empirical Standpoint (London, 1973). H. Field, ‘Mental Representation’, Erkenntnis (1978). W. Lyons, Approaches to Intentionality (Oxford, 1995). Roger Scruton, ‘Intensional and Intentional Objects’, Proceedings of the Aristotelian Society (1970–1). John Searle, Intentionality (Cambridge, 1983). intentional relation. Brentano’s thesis of *intentionality, that every mental phenomenon has a direction toward an object, creates the most difficult problem for the philoso- phy of mind. It leads immediately to the following dilemma. Either a mind is somehow related to what is before it—to what it perceives, desires, fears, asserts, imagines, etc.—or it is not. If one chooses the second horn, then one must give a non-relational account of intentionality. But there is at the present time no plausible non-relational account. If one embraces the first horn, then one is immediately faced with a second dilemma. Since a mind can perceive what does not exist, desire what shall never come to pass, assert what is not the case, etc., either an intentional relation must hold in such cases between a mind that exists and something that does not exist, or else these objects of the mind do exist, contrary to our firm conviction. If we accept the first alternative, then we are forced to hold that there is a relation, totally differ- ent from ‘ordinary’ ones, which connects with what does not exist. If we embrace the second alternative, then we must assume that, say, the golden mountain and the round square do after all exist. We are forced, in other words, to accept either the existence of a ‘weird’ relation or the existence of non-existent objects. It will not do, one must realize, to try to escape from this dilemma by claiming that the golden mountain and the round square, though they do not exist, have some sort of lesser being, and that the intentional relation can hold between a mind and things with this kind of ‘watered-down’ being. For, in this case, the fact remains that one has acknowledged the existence of what I just called a ‘weird’ relation. The inten- tional relation is still weird in that it is now believed to hold on occasion between an existent mind and something that does not exist, but has some sort of being. In addition, of course, this attempt to escape from the dilemma has to make sense of the notion of ‘watered- down’ being. If the thesis of intentionality in this fashion leads to a dilemma piled on top of a dilemma, it is to be expected that philosophers, in order to avoid the resulting difficul- ties, will adopt a materialistic (or physicalistic or behav- iouristic) attitude. Intentionality disappears, if there are no minds (mental acts). Therefore, the dilemmas disappear, if there are no minds. Perhaps materialistic treatments of philosophical problems are so popular at the present time, because they promise escape from the dilemmas. r.g. *behaviourism; materialism; physicalism. F. Brentano, Psychology from an Empirical Standpoint (London, 1973). K. Twardowski, On the Content and Object of Representations (The Hague, 1977). intentional stance: see Dennett. interactionism. The view that some mental events cause some physical events and some physical events cause mental events, closely related to the commonsense idea that thoughts and desires cause various physical events, such as limb movements, and some physical events cause visual experiences and the like. The view is therefore dif- ferent from epiphenomenalism, which regards all mental events as causally inefficacious themselves and as effects of physical events. It is also different from and does not entail a philosophically commoner view which takes each mental event to be nomically connected with a neural event. It is also different from identity theories. It is neces- sarily dualistic in character, but need not involve the view held by many pre-twentieth-century philosophers, most famously Descartes, and wisely regarded as a crucial tenet of theism, that mind and matter are two distinct substances. n.l. *dualism; epiphenomenalism; mind–body problem; psychophysical laws. K. R. Popper and J. C. Eccles, The Self and its Brain (Berlin, 1977). internal and external relations: see relations, internal and external. international law. Term coined in Latin (ius inter gentes) in the sixteenth-century renovation of natural law theory after the breakdown of unitary secular-ecclesiastical Christendom, and Englished perhaps by *Bentham. But what it denotes was understood until the mid or late twentieth century as law governing relations between states, rather than nations or peoples. In the absence of standing legislative and judicial institutions, its sources remain largely agreement between states (treaties) and those elements of state practice (custom) that manifest a judgement that, in the relevant domain, general adher- ence to a common rule of action is desirable (opinio iuris). international law 439 . fact more important to modern set theory than the infinite cardinals. But there is no space to describe them here. d.b. *numbers. G. Cantor, Contributions to the Founding of the Theory of Transfinite Numbers,. provoking Anaxagoras to hold that there was no smallest quantity of anything, and the Greek atomists to the opposite opinion. But the atom- ists showed no fear of the infinitely large, as they posited an. theory and political philosophy is the question how the basic indi- vidual is to be construed. Is the person to be understood as an independent atomic particular whose connections with others are consensual