as well as concept-laden, acculturated activities. Speaking a language is part of a form of life (a culture) and to imagine a language is to imagine a form of life. What has to be accepted, the given, is not the empiricist’s mythical sense-data constituting the foundations of knowledge, but forms of life that lie beyond being justified or unjustified. p.m.s.h. G. P. Baker and P. M. S. Hacker, An Analytical Commentary on the Philosophical Investigations, ii: Wittgenstein: Rules, Grammar and Necessity (Oxford, 1985), 238–43. Forms, Platonic. The word ‘Form’ is used to translate Plato’s Greek word idea, which is sometimes transliter- ated into English as ‘Idea’. From an etymological point of view the Greek word means the look of a thing, but it was commonly extended to mean a sort, kind, or type of thing. (Compare the Latin word species.) What is called Plato’s theory of Forms (or Ideas) is a theory about sorts, kinds, or types, and its main claim is that a type exists independently of whether or not there are things of that type. It appears that Plato was led to the theory in the first place by con- sidering such types as the type of person who is virtuous, but he then extended it to many other types. d.b. *Aristotle; cave, analogy of; metaphysics, the history of; phenomena and noumena; Plato; Platonism; third-man argument; transcendentalism. Almost any book on Plato will say something of his theory of Forms. A classic treatment is W. D. Ross, Plato’s Theory of Ideas (Oxford, 1951). formula. The word has no very rigid meaning, but in logic it is customarily applied to written expressions that are strings of symbols containing no words. A formal lan- guage consists of a vocabulary of symbols—e.g. ‘P’, ‘x’, ‘∀’, ‘(’—together with rules determining which strings of them are well formed. The well-formed formulae may then be manipulated mathematically; or they may be ‘interpreted’ (e.g. as *schemas, or as having meanings); or both. c.a.k. Foucault, Michel (1926–84). French intellectual whose politically as well as philosophically motivated examin- ations of obscure historical materials were aimed at diagnosing the present. He called his early books archae- ologies. Although they appear concerned with origins, Foucault insisted that his topic was the implicit know- ledge that underlay and made possible specific practices, institutions, and theories: Madness and Civilization (1961), on the birth of the asylum, offered an archaeology of how the exchange between madness and reason was silenced; The Birth of the Clinic (1963) was ‘An Archaeology of the Medical Gaze’; and The Order of Things (1966) was ‘An Archaeology of the Human Sciences’. In his theoretical manifesto, The Archaeology of Knowledge (1969), Foucault redefined archaeology as the set of discourses that consti- tute ‘the archive’. Foucault’s inaugural lecture at the Collège de France, ‘The Discourse on Language’ (1971), was a transitional text in which he subordinated archaeology to the critical analysis of forms of exclusion and to the genealogical study of the formation of *discourse. Out of concern for prison reform, Foucault returned to the history of prac- tices in Discipline and Punish (1975) with a study of the birth of the nineteenth-century prison. He developed its account of the interaction of knowledge and *power fur- ther in The Will to Knowledge (1976), the first volume of a projected six-volume History of Sexuality. Foucault ultimately came to recognize that what inter- ested him about power was how it produced the subject. The History of Sexuality was redesigned to present a genealogy of the desiring subject, conceived on the model of Nietzsche’s Genealogy of Morals; The Use of Pleasure and The Care of the Self studied Greek and Roman texts on the art of living. The theory of historical discontinuity that is still often associated with Foucault’s name does not apply to these works and really applies only to The Order of Things. r.l.b. J. W. Bernauer, Michel Foucault’s Force of Flight (Atlantic High- lands, NJ, 1990). G. Deleuze, Foucault (Minneapolis, 1988). foundationalism. The theory that *knowledge of the world rests on a foundation of indubitable beliefs from which further propositions can be inferred to produce a superstructure of known truths. Traditionally, it is beliefs about our sense experience that have formed the founda- tion, with beliefs about the external world forming the superstructure. However, the assumption that beliefs about sense experience are infallible has come in for heavy criticism, witness Sellars’s attack on the ‘myth of the *given’. o.r.j. *boat, Neurath’s. Jonathan Dancy, Introduction to Contemporary Epistemology (Oxford, 1985). Wilfrid Sellars, Science, Perception and Reality (London, 1963), ch. 5, sects. 3–11. foundationalism in mathematics. Foundationalism is the view that a body of knowledge, such as mathematics (or one of its branches such as arithmetic or analysis), ought to be built on an absolutely secure epistemic foun- dation. The foundationalist begins with axioms that are self-evident, or, failing that, axioms that are as certain as possible. One might argue, for example, that the truth of the axioms is presupposed by all thought: they cannot be doubted if one is to think at all. The foundationalist derives the truths of the area of knowledge from the axioms using absolutely reliable inferences, a logic which is self-evidently valid. General foundationalism, traced to rationalists like *Descartes, is not widely held any more, but the mathematical version survived well into the twen- tieth century, if not beyond, motivated in part by the logical and semantic paradoxes. *Gödel’s incompleteness theorems dealt a blow to foundationalism concerning mathematics. If a mathematical theory is sufficiently rich, and if the set of axioms and the consequence relation used 310 form of life in the derivations are both effective, then either some truths cannot be derived, or some non-truths can be derived (assuming bivalence). At best, the foundationalist can only claim to have secured the basic truths of math- ematics. s.s. Stewart Shapiro, Foundations without Foundationalism: A Case for Second-Order Logic (Oxford, 1991). Four Freedoms. Asserted in their canonical form by US President Franklin Delano Roosevelt on 6 January 1941 in his State of the Union address to Congress as the ‘four essential human freedoms’: freedom of speech and expres- sion, freedom of every person to worship God in his own way, freedom from want, and freedom from fear. They are usually cited in abbreviated form as freedom of speech and of religion, and freedom from want and from fear. Widely regarded during the Second World War as a suc- cinct statement of the Allied war aims, despite notable fail- ures to achieve these ‘freedoms’ among the Allies. The Four Freedoms are a concise anticipation of what would later become the various ‘human rights’ declared by the United Nations General Assembly in its 1948 Declaration of Human Rights. h.a.b. *freedom; liberty. Four Noble Truths: see Buddhist philosophy. four-term fallacy. A *syllogism with four, rather than three, terms commits this fallacy. Since the requirement that it must have three terms is generally specified in the definition of a syllogism, it is pointless to regard four terms as a fallacy, and arbitrary to specify four as opposed to any number other than three. This is probably why the four- term fallacy has often been conflated with the ‘fallacy of equivocation’, i.e. *ambiguity. c.w. C. L. Hamblin, Fallacies (London, 1970), 44–5, 197–9. frame problem. An important feature of human intelli- gence is that people are able to make selective topical use of long-stored background knowledge, and know how to adjust their thinking or behaviour appropriately in the light of new information. They know when to ignore new information as irrelevant, and when and how to take it into account in determining how to proceed. It is difficult to see how exercising these abilities can just be a matter of following a predetermined routine or set of rules, of the sort that might be embodied in a computer programme. For example, although it may be possible to reduce to a set of rules the behaviour typically involved in ordering a meal in a restaurant, people do not slavishly follow such rules, because one’s actual behaviour in a restaurant is always sensitive to unforeseen contingencies, such as the unexpected arrival of an old friend or, more alarmingly, the occurrence of an earthquake. The difficulty which this presents for any attempt to replicate or mimic human intelligence by means of a computer programme is known as the frame problem. e.j.l. Z. W. Pylyshyn (ed.), The Robot’s Dilemma: The Frame Problem of Artificial Intelligence (Norwood, NJ, 1987). Frankena, William K. (1908–94). Influential American philosopher, at the University of Michigan for more than forty years. His first published paper was a telling critique of G. E. Moore’s notion of the *naturalistic fallacy. By his own account (‘Concluding More or Less Philosophical Postscript’) Frankena in his earliest period was ‘cognitivis- tic’, combining naturalism about ‘good’ and intuitionism about ‘ought’. Subsequently, he became less satisfied with this position, and took up a greater variety of topics. He absorbed some emotivist ideas, did work on the relation between ethics and religion (sympathetic to religion), and wrote on philosophy of education. Frankena’s way of doing conceptual analysis and normative justification has provided a model in some respects for many American philosophers working in ethics. e.t.s. William K. Frankena, ‘Concluding More or Less Philosophical Postscript’, in Kenneth E. Goodpaster (ed.), Perspectives on Morality: Essays by William K. Frankena (Notre Dame, Ind., 1976). Frankfurt, Harry (1929– ). Professor of Philosophy at Princeton (1990– ), he formerly taught at Yale (1976–89) and Rockefeller University (1965–76). His early work revived the debate over the alleged circularity of Descartes’s defence of reason. His essay ‘Freedom of the Will and the Concept of a Person’ (1971) argued for the special significance of the capacity for reflective self- evaluation apparently unique to human beings that is manifested in the formation of what he labelled ‘second- order desires’, i.e. the capacity not merely to have desires, preferences, or motives (which capacity human beings share with certain animals) but also to want to have (or not to have) certain desires, preferences, or motives. His recent work develops the implications of his view that volition is more pertinent even than reason to our experience of ourselves. In The Importance of what we Care About (Cambridge, 1988), he explores various forms of necessity, our being unable to avoid willing some things, our being unable to will other things. Such facts simulta- neously limit our *autonomy and make autonomy possible. r.p.g. Frankfurt School. A German philosophical and socio- logical movement associated with the Institute for Social Research founded within Frankfurt University in 1923. One of its founders, and in 1930 its director, was Max Horkheimer (1895–1973). In the 1930s he expounded the *‘critical theory’ of the school in its journal, Zeitschrift für Sozialforschung (Critical Theory: Selected Essays, (1968; tr. New York, 1972)). Only a radical change in theory and practice can cure the ills of modern society, especially unbridled technology. Every one-sided doctrine is to be subjected to criticism, including Marxism: an emancipat- ing proletarian revolution is not inevitable, and thought or theory is relatively, though not wholly, independent of Frankfurt School 311 social and economic forces. But since theory and its con- cepts are a product of social processes, critical theory must trace their origins, and not, like empiricism and posi- tivism, accept them and thereby indirectly endorse the processes themselves. Horkheimer also contributed to the sociological work Authority and Family (1936). In 1934 the institute closed, Horkheimer and other leading members, such as Adorno and Marcuse, emi- grated, and it was re-established in New York as the New School for Social Research. Several important works appeared during the period of exile: Marcuse’s Reason and Revolution (1941), Adorno and Horkheimer’s Dialectic of Enlightenment (1947; tr. New York, 1972), Adorno’s wide- ranging and aphoristic Minima Moralia (1951; tr. London, 1974), and the collective work by Adorno and others The Authoritarian Personality (New York, 1950). The institute returned to Frankfurt in the early 1950s, and, while Mar- cuse and others remained in the USA, Horkheimer and Adorno also returned. Adorno was its director from 1958 until his death in 1969. The leading member of the school in its recent history is Jurgen Habermas (1929– ), whose Theory and Practice (1963; tr. Boston, 1973) and Knowledge and Human Interests (1968; tr. Boston, 1971) argue that the sciences depend on ideological assumptions and interests, and that enlighten- ment reason has become an instrument of oppression. In contrast to this, he projects the ideal of a communication which involves all rational subjects and is entirely free of domination and error-inducing interest. Like other mem- bers of the school, such as Marcuse (Eros and Civilization (Boston, 1955)), Habermas is interested in psychoanalysis and other non-Marxian types of liberation. Since the school in general believes that science and *positivism are riddled with non-theoretical interests and that reason has become repressive, they cannot accept without qualification Weber’s view that the sciences should be value-free, avoiding value-judgements about the people and institutions they study. They argue, for example, that science already embodies value-judgements, such as the desirability of the technological domination of nature, which, though in fact questionable, seem so self-evident that they appear not to be value-judgements at all, but simply disinterested devotion to science. The postulate of value-freedom in effect insulates such well-entrenched value-judgements from criticism by dis- qualifying potential competitors. Adorno and Habermas debated this issue with Popper and his followers in T. W. Adorno et al., The Positivist Dispute in German Sociology (1969; tr. London, 1976). m.j.i. A. Arato and E. Gebhardt, The Essential Frankfurt School Reader (Oxford, 1978). R. Geuss, The Idea of a Critical Theory (Cambridge, 1981). M. Jay, The Dialectical Imagination (London, 1973). Franklin, Benjamin (1706–90). American statesman and diplomat, scientist and inventor, printer and author. He is honoured as one of the architects of the political independence of the United States and remembered for his experimental and applied science, especially concern- ing the nature of electricity. In his own lifetime, however, he also secured international recognition and domestic popularity as a political philosopher and moralist. His Autobiography and the aphorisms of Poor Richard’s Almanac described and reflected his distinctive blend of *perfec- tionism, *utilitarianism, and Aristotelian *virtue theory. He recommended specific rules of conduct and practical aids to the formation of good habits, insisting that an individual’s development of these virtuous habits would secure private happiness and prosperity, together with a capacity for and devotion to civic improvement. k.h. Charles L. Sanford (ed.), Benjamin Franklin and the American Char- acter (Boston, 1955). fraternity. Relationship between those collectively engaged on a common purpose. The philosophically neglected third child of *revolution, fraternity has been regarded as involving an emotional bond variously relat- ing those who share a common nationalism or, under Marxism, the members of the working class or even, under some *liberalism, all mankind. Fraternity is valued much like *community, and, as with *friendship, for rea- sons that are not instrumental. p.g. *friendship. R. S. Peters, Ethics and Education (London, 1966), ch. 8. Frede, Michael (1940– ). Professor of the History of Phil- osophy in the University of Oxford. Historian of ancient philosophy who is sensitive to the methodological distinc- tion between writing history of philosophy as history and writing history of philosophy as philosophy. His approach entails locating ancient texts in a causal network of other ‘histories’: medicine, law, religion, politics, for example, and attempts to exhibit philosophical problems as they were conceived and treated by the ancients them- selves. His first book, Prädikation und Existenzaussage (1967), initiated a debate over Plato’s Sophist. Die Stoische Logik (1974) provided new ways of understanding Stoic logic. Frede is co-author (with Günther Patzig) of a Ger- man translation and commentary on Aristotle’s Meta- physics Z (1988) and author of many papers. Some of these have been usefully collected in Essays in Ancient Philosophy (1987). s.p. free, freedom: see two groups of entries: (1) freedom and determinism; determinism; scientific determinism; liber- tarianism; origination; the will; autonomy; voluntariness; embraced and reluctant desires; spontaneity and indiffer- ence; compatibilism and incompatibilism; responsibility; fatalism; destiny; (2) political freedom; liberty; liberalism; freedom through reason and goodness; freedom of goodness and reason; self-determination; right to a home- land; hegemony; Four Freedoms; freedom of speech; imperialism. 312 Frankfurt School freedom, academic: see academic freedom. freedom, political. The problem of political freedom can be seen as that of reconciling the value of freedom with the restrictions which seem to be a necessary feature of life in a political society. One natural approach is to view the task as that of effecting a compromise: some degree of freedom must be sacrificed, but it must not be too much. The problem then becomes one of where to draw the line. A popular answer has been to appeal to the idea of basic human *rights (sometimes called *‘natural rights’) and to suggest that these are the freedoms which ought to be safeguarded in any society. Favourite examples are rights to freedom of speech and freedom of assembly, or to free- dom of contract, or the right to ownership and control of one’s own body and therefore to the products of one’s own labour. Any such list of rights, however, is controver- sial, and it is difficult to find any objective way of deter- mining what basic rights people have. One philosophical tradition which has tried to provide a way of dealing with this problem is social contract the- ory. (*Contract, social.) In a *‘state of nature’, it is sup- posed, men enjoy what is in one sense an absolute liberty, since there is no government to command them, but each individual’s liberty is in practice restricted by every other individual’s exercise of liberty. Justifiable restrictions on liberty are therefore those restrictions imposed by the contract which is needed to set up a social order. Thus Hobbes supposes that the state of nature would be one of perpetual war, and that in order to preserve the peace the contract must give the sovereign an absolute power of life and death over every subject. Locke takes a more benign view of the state of nature; it is not, he supposes, a condi- tion of war, but a more settled state of affairs in which men have natural rights to life, liberty, and property, and the power of governments must therefore be limited by respect for those rights and by the consent of the gov- erned. Rousseau’s view of the state of nature is more posi- tive still; ‘man is born free’, and if he is nevertheless ‘everywhere in chains’ the only thing which can make this authority legitimate is a contract which combines the wills of individuals into a ‘general will’ in which everyone par- ticipates. By such a contract the individual loses his ‘nat- ural liberty’ but gains a ‘civil’ and ‘moral’ liberty which ‘makes him truly master of himself’. It is clear, then, that the account of political freedom given by social contract theorists depends on their view of what a state of nature would be like, and since this state of nature is a hypothet- ical condition which has never actually existed, there are obvious difficulties in using the notion to resolve the prob- lem of freedom. An alternative approach is the utilitarian idea put for- ward in John Stuart Mill’s essay On Liberty that freedom should be limited only by the ‘harm’ principle: individuals should be free to do anything which does not harm others, but actions which do harm others may properly be restricted by society. Mill especially emphasizes the bene- fits of freedom of speech. He also maintains that freedom of action should extend to those acts by which individuals might harm themselves, provided they do not thereby harm others. His critics have suggested that this distinc- tion is difficult to sustain, since in harming myself I inevitably make myself a less useful member of society and make demands on shared resources (for example, medical resources), thereby harming others. A more fundamental criticism of this approach has been that it assumes a purely negative and individualistic view of freedom, as simply the absence of restriction or coer- cion. In contrast, philosophers such as Hegel and his fol- lowers have maintained that individuals are truly free not when they act on this or that arbitrary caprice, but when they have rational control over their lives. They have fur- ther suggested that this is possible only through active involvement in the life of a society. Hegel thinks that the duties of political life give an objective rational content to the lives of individuals. Others have suggested that it is through participation in a democratic political system that people can effectively control their lives. A further variant on this approach is the emphasis to be found in Marx and the Marxist tradition on the economic dimension of free- dom: to be free, people must be able to employ the mater- ial resources which they need to give effect to their choices, and this is possible only through collective con- trol over the productive powers of society. All of these suggestions call into question the idea with which we began, of a compromise between the freedom of the indi- vidual and the power of society, since they imply that only as social beings are people capable of exercising freedom in the first place. Underlying these philosophical differ- ences is the continuing debate over whether the concept of *liberty is more properly to be understood in negative or positive terms. r.j.n. John Stuart Mill, On Liberty, various edns., e.g. in Utilitarianism, ed. Mary Warnock (London, 1962). David Miller (ed.), Liberty (Oxford, 1991). Peter Singer, Hegel (Oxford, 1983), ch. 3. freedom and determinism. The great problem of free- dom and determinism is really two problems, one of them metaphysical and empirical in kind, the other ethical and in other ways attitudinal in kind. The first problem is that of whether human choices and actions are causally deter- mined or are in a way free. The second problem is that of the implications of determinism for our moral, personal, and social lives. *Determinism in the context of these problems, to be more specific, is usually the thesis that all our mental states and acts, including choices and decisions, and all our actions are effects necessitated by preceding causes. Thus our futures are in fact fixed and unalterable in much the same way that the past is. The truth or falsity of the thesis depends upon our natures, including our physical natures, and not at all upon our desires or hopes or other feelings. What freedom comes to with these problems is much disputed. Different concepts enter into both the factual and the attitudinal problem. Metaphysical freedom or freedom and determinism 313 *origination, one of the two main kinds, involves not being completely governed by deterministic causal laws. Those who support it say there are no laws, whether of mind or brain or both, that completely settle what we will choose and do. Metaphysical freedom also involves not just the absence of such laws but also our having a kind of power to choose which path the future will take. Let us start with the second problem to the fore (they are a little hard to keep apart). In everyday life, we suppose that free actions in some sense or other are the only ones for which we can hold persons morally responsible, or for which we can appropriately feel gratitude or resentment (Strawson). Ordinary morality says that we are excused for doing something that would otherwise be blame- worthy if we can establish that in some sense or other we had no choice in the matter, that in some sense or other we could not have done otherwise. Some philosophers, incompatibilists, believe that determinism if true destroys *moral responsibility, under- mines interpersonal relations, and destroys our life-hopes by making all actions unfree. Freedom and determinism are incompatible. Incompatibilists who also believe that determinism is false, and hence that some actions are morally responsible, are often called *libertarians. Incom- patibilists who also believe, differently, that determinism is true, and moral responsibility is therefore an illusion, are sometimes called, following William James, hard determinists. Other philosophers, compatibilists, deny that deter- minism has any such effect on freedom and moral respon- sibility. Freedom and determinism are compatible. They are sometimes called soft determinists, but this descrip- tion has the unfortunate effect of officially conflating the problems of the truth of determinism (the first problem) and our appropriate response to it (the second problem). In fact some of these philosophers do not believe in deter- minism, and maybe not in the denial of determinism, but only believe that if it is true, this does not have the upshot that we are not free and responsible. (Another logically possible position—determinism is false but moral respon- sibility still fails to exist—has no advocates and no name. Perhaps we should call it libertinism.) Compatibilists rest their argument on the claim that the sense of ‘free’ in which actions must be free in order to be morally responsible is not the sense that involves origin- ation and is opposed to ‘caused’ or ‘determined’. We only need to be free in the sense in which ‘free’ is opposed to ‘compelled’ or ‘coerced’. We only need to be voluntary in this sense. All we need is voluntariness. (Think of what men in prison lack, or anyone who is subject to a serious addiction.) In G. E. Moore’s famous analysis, I am free in performing an action if I could have done otherwise, but this latter proposition is to be understood as I would have done otherwise if I had chosen. So I could have done otherwise even if determinism is true. Moore’s analysis seems to capture much of the pre- theoretical or everyday-life distinction between excused and unexcused infractions of the moral law. Its essential notion is that some actions result from effective choices by the actor, and hence are free, and some do not result from such choices, and are not free. Moore’s analysis, neverthe- less, seems beside the point to libertarians, because, as they say, if determinism is true, I could not have chosen otherwise in the right sense, and therefore could not have done otherwise. I could not have originated anything. Thus, they say, moral responsibility collapses. Honderich has argued persuasively that the long- running compatibilism–incompatibilism controversy springs from what it overlooks, the systematic ambiguity of talk of freedom. We each have two conceptions of freedom, not one. One involves both origination and voluntariness, while the other involves voluntariness alone. If this is so, compatibilism and incompatibilism are both false—both claim that we have just one conception of freedom or that there is one correct conception of it. For Honderich, something of moral responsibility and much else must change if determinism is true, but not everything must change. The problem is more attitudinal than conceptual. Some of our present attitudes and responses, which depend on ideas of origination, are impossible if determinism is true. But other kinds of them are possible. Certain kinds of ‘life-hopes, personal feelings, knowledge, moral responsibility, the rightness of actions and the moral standing of persons . . . persist, and our lives do not become dark, but remain open to celebration’. To focus on the factual question, one historical argu- ment against the truth of determinism has to do with our common experiences of choosing and deciding. In a genu- ine case now of choosing or deciding, according to liber- tarians, I am directly aware of my freedom to realize either alternative—I know that whatever has happened before now, or whatever is the case now, I can now raise my arm or refrain from raising my arm. This freedom of origin- ation, of which I am indubitably aware, is inconsistent with determinism. Therefore determinism is false. John Stuart Mill responded that this supposed awareness of mine is only a memory of and mistaken inference from past occa- sions, some occasions on which we took something like the first alternative and some occasions on which we took something like the second alternative. But on all such occasions, Mill argued, we followed our strongest motive, and in the present case we must do so as well. Our sup- posed awareness of origination may be of a type with awareness of a metaphysical self—universally accepted among philosophers until Hume said, in short, ‘I can’t find it’, and seemed to be right. It has been argued, in this vein, that *libertarianism does not give us an explanation of human action. It gives us a blank where an explanation should be. And, one might add, it would take a very odd something to fill in the blank. The desired entity—whether called mind, soul, self, agent, or originator—must be sufficiently connected to the past to constitute a continuing locus of personal responsibility, but sufficiently disconnected so that its past does not determine its present. It must be sufficiently con- nected to the causal chain to be able to interrupt it, but 314 freedom and determinism sufficiently disconnected not to get trapped. It must be susceptible to being shaped and maybe governed by motives, threats, punishments, and desires, but not totally controlled by them. It resembles very much the river god, who serves as an explanation for what seems to be the free behaviour of the river—the explanation of its surges and whatever else happens—until a better explanation comes along through physical geography, meteorology, and physics. The mind or originator or whatever is, you might think, a lot worse than what Gilbert Ryle disparaged as ‘the ghost in the machine’. If indeterminists seem dated in their description of what fundamental thing is free (Strawson spoke of their ‘obscure and panicky metaphysics’), they can be up to date in their arguments that something or other is free. The weight and intellectual respectability of physical science are claimed to be on their side. *Quantum mechanics is said to have rejected causal determinism. But the kind of indeterminism involved in quantum mechanics is ran- domness, pure chance. If my arm randomly jerks and strikes someone, that is just the kind of thing that excuses me from moral responsibility. Indeed, there must be some causal link between my action and my past life for it to make sense to think of it as my action. Libertarianism needs to steer a course between the Scylla of randomness and the Charybdis of determinism. Maybe there isn’t any such course. r.c.w. *agent causation. J. C. Eccles and K. R. Popper, The Self and its Brain (Berlin, 1977). T. Honderich, A Theory of Determinism: The Mind, Neuroscience, and Life-Hopes (Oxford, 1988). —— How Free Are You?, 2nd edn. (Oxford, 2002). R. Kane (ed.), The Oxford Handbook of Free Will (New York, 2001). G. E. Moore, Ethics (London, 1912). P. F. Strawson, ‘Freedom and Resentment’, in Studies in the Phil- osophy of Thought and Action (Oxford, 1968). R. Weatherford, The Implications of Determinism (London, 1991). freedom and liberty. These two words are often used interchangeably, except inasmuch as *‘freedom’ exists in the form of an adjective (‘free’) and *‘liberty’ does not. Thus, we talk of ‘free will’ and ‘free action’. Occasionally, more through stipulation than reflection of ordinary usage, the use of one term rather than the other is appro- priate. On these occasions, ‘freedom’ refers to the ability of people to act. Thus in discussions of *freedom and deter- minism, it is the freedom of the will that is at issue. There are a number of conceptions of ‘liberty’. Perhaps the clear- est refers to the fact that the relevant political or judicial system gives people permission to do something: that is, they have no duty not to do that thing. Thus it is possible that people might have permission to do something they do not have the ability to do (perhaps because of impair- ment), and the ability to do something they do not have permission to do. In this respect, freedom and liberty can vary independently. d.m. J. Feinberg, Rights, Justice and the Bounds of Liberty (Princeton, NJ, 1980). freedom of goodness and reason. The view that a good and reasonable man is free, even though he be a slave, is famously associated with the *Stoics, but it pre-dated them and has long outlived them. Many have thought that to talk of ‘freedom’ in this way is to part company entirely with established usage, and therefore to render meaning- ful disagreement impossible. However, if ‘freedom’ can mean the opposite of ‘enslaved’, then it is at least mean- ingful to describe it as threatened by enslavement to bad or unreasonable desires. With the conception of freedom as the capacity to will what is reasonable and good, the problem of *freedom and determinism disappears, since if one is caused to act reasonably and is free in virtue of that, having the capacity to act otherwise, in the indeterminist sense, is otiose. k.m. M. J. Adler, The Idea of Freedom (New York, 1958). freedom of speech. Celebrated as first among *civil liber- ties, freedom of speech (conceived broadly as the expres- sion of verbal as well as non-verbal utterance) is both an instrumental and intrinsic good; instrumental as a neces- sary condition of inquiry and of intrinsic value as an elem- ent in individual well-being and self-fulfilment. Legitimate grounds for limitations on free speech fall into two categories: procedural, concerning restrictions of time, place, and manner on the form and forums of its exercise; and substantive, involving restrictions on con- tent, such as libel, slander, incitement to riot, etc. Even in the latter cases, however, prior restraints (as distinct from civil or criminal responses after the fact) are rarely justi- fied. Some would argue that speech can offend or annoy but never harm; others would concede that it can harm but that the harms are generally outweighed by the bene- fits and by avoidance of the harms its suppression would entail. Still others would favour censorship of pornog- raphy and obscenity because of the harm they do to vul- nerable classes of persons generally. As with other freedoms, the value of freedom of speech must be contrasted with its worth; without opportunities that wealth and power confer, one’s freedom of speech even in a liberal society may be worth very little. In any case, it will be distributed unequally even if equality of freedom of speech is otherwise guaranteed by law. h.a.b. Frederick Schauer, Free Speech: A Philosophical Inquiry (Cam- bridge, 1982). Freedoms, Four: see Four Freedoms. free logics. Logical systems in which existential commit- ment is not assumed, in which names and predicates need not refer to anything, or in which sentences may not be made true or false by what does or does not exist. So, in free predicate logic, ( ∃x) (Fx), ‘There exists at least one x that is F’, does not have to follow from Fa, ‘a is F’. Free logic is called ‘free logic’ because, in contrast with free logics 315 standard predicate calculus, the use of names is free from commitment to the existence of a referent. Arguably, free logics do justice to the intuitive view that from the fact that the concept of something exists it does not follow that that thing exists: from ‘A unicorn has a sin- gle horn’ it does not follow that there are any unicorns. The intuitive view is not beyond question. Arguably, uni- corns do exist but are fictional objects or exist in story- books or people’s imaginations. ‘Exists’ does not mean the same as ‘is a four-dimensional publicly observable object’. Arguably, in a world in which unicorns did not exist, story- books and people’s imaginations would differ from the actual world. There exists both modal and non-modal free logic. In free modal logic, the use of a name implies commitment to existence in at least one possible world, but this is com- mitment only to the possible existence of a referent, not to the existence of a referent. s.p. Ermanno Bencivenga, ‘Free Logics’, in Dov A. Gabbay and Franz Guenthner (eds.), Handbook of Philosophical Logic, vol. 3 (Dor- drecht, 1986). Graeme Forbes, Modern Logic (Oxford, 1994). Mark Sainsbury, Logical Forms (Oxford, 1991). free riders. Usually unintended beneficiaries of a socially provided public good for which they have made no con- tribution—a public good being one the consumption or use of which by one individual or group does not diminish or prevent its consumption or use by others, e.g. radio broadcasts and street lights. The ‘free rider problem’ is that of whether those who benefit in this way do so unjustly and whether, if so, they can rightly be forced to make a contribution. j.hal. *equality; well-being; welfarism. A. de Jasay, Social Contract and Free Ride: A Study of the Public Goods Problem (Oxford, 1989). free will: see freedom and determinism; origination. Frege, Gottlob (1848–1925). The founder of modern mathematical logic. As a logician and philosopher of logic he ranks with Aristotle; as a philosopher of mathematics he has had no peer throughout the history of the subject. After taking his doctorate in philosophy at Göttingen, he taught at the University of Jena from 1874 until his retire- ment in 1918; apart from his intellectual activity his life was uneventful and secluded. His work was little read in his lifetime, and for a long time his influence in philosophy was exercised mainly through the writings of others. Frege had an influence on analytic philosophy through Russell and on continental philosophy through Husserl. He is often thought of as a philosophers’ philosopher, but it was his genius that made possible the work of writers who have caught the attention of the general public, such as Wittgenstein and Chomsky; and his invention of math- ematical logic was one of the major contributions to the developments in many disciplines which resulted in the invention of computers. Frege’s productive career began in 1879 with the publi- cation of a pamphlet with the title Begriffsschrift, which we can render into English as ‘Concept Script’. The pamphlet marked an epoch in the history of logic, for within some hundred pages it set forth a new calculus which has a per- manent place at the heart of modern logic. The concept script which gave the book its title was a new symbolism designed to bring out with clarity logical relationships which were concealed in ordinary language. For generations now the curriculum in formal logic has begun with the study of the *propositional calculus. This is the branch of logic that deals with those inferences which depend on the force of negation, conjunction, dis- junction, etc. when applied to sentences as wholes. Its fun- damental principle is to treat the truth-value (i.e. the truth or falsehood) of sentences which contain connectives such as ‘and’, ‘if’, ‘or’ as being determined solely by the truth-values of the component sentences which are linked by the connectives. Frege’s Begriffsschrift contains the first systematic formulation of the propositional calculus; it is presented in an axiomatic manner in which all laws of logic are derived, by specified rules of inference, from a number of primitive principles. Frege’s symbolism, though elegant, is difficult to print, and is no longer used; but the operations which it expresses continue to be fun- damental in mathematical logic. Frege’s greatest contribution to logic was his invention of quantification theory: a method of symbolizing and rig- orously displaying those inferences that depend for their validity on expressions such as ‘all’ or ‘some’, ‘any’ or ‘every’, ‘no’ or ‘none’. Using a novel notation for quantifi- cation, he presented a first-order *predicate calculus which laid the basis for all recent developments in logic and formalized the theory of inference in a way more rig- orous and more general than the traditional Aristotelian syllogistic which up to the time of Kant was looked on as the be-all and end-all of logic. After Frege, for the first time, formal logic could handle arguments which involved sentences with multiple quantification, such as ‘Nobody knows everybody’ and ‘Any schoolchild can master any language’. In the course of his work Frege developed other branches of logic, including second-order predicate calcu- lus and a version of naïve *set theory. He did not explore the areas of logic known as modal logic (that part of logic that deals with necessity, possibility, and kindred notions) or tense logic (the logic of temporal or significantly tensed statements). These branches of logic had been studied in the Middle Ages, and have been studied again in the pre- sent century in the light of his innovations. In the Begriffsschrift and its sequels Frege was not inter- ested in logic for its own sake. His motive in constructing the new concept script was to assist him in the philosophy of mathematics. (It was his predominantly mathematical agenda which made him comparatively uninterested in the branches of logic which concern inferences about the transient and the changing.) The question which above all he wanted to answer was this: Do proofs in arithmetic rest 316 free logics on pure logic, being based solely upon general laws opera- tive in every sphere of knowledge, or do they need sup- port from empirical facts? To answer this question, Frege set himself the task of seeing ‘how far one could get in arithmetic by means of logical deductions alone, sup- ported only by the laws of thought’. Not only did Frege show how to conduct logic in a mathematical manner: he believed that arithmetic itself could be shown to be a branch of logic in the sense that it could be formalized without the use of any non-logical notions or axioms. It was in the Grundlagen der Arithmetik (1884) that Frege first set out to establish this thesis, which is known by the name of *‘logicism’. The Grundlagen begins with an attack on the ideas of Frege’s predecessors and contemporaries (including Kant and J. S. Mill) on the nature of numbers and of mathemat- ical truth. Kant had maintained that the truths of math- ematics were *synthetic a priori, and that our knowledge of them depended on intuition. Mill, on the contrary, saw mathematical truths as a posteriori, empirical generaliza- tions widely applicable and widely confirmed. Frege maintained that the truths of arithmetic were not syn- thetic at all, neither a priori nor a posteriori. Unlike geom- etry—which, he agreed with Kant, rested on a priori intuition—arithmetic was analytic, that is to say, it could be defined in purely logical terms and proved from purely logical principles. The arithmetical notion of number in Frege’s system is replaced by the logical notion of *‘class’: the cardinal num- bers can be defined as classes of classes with the same number of members; thus the number two is the class of pairs, and the number three the class of trios. Despite appearances, this definition is not circular, because we can say what is meant by two classes having the same number of members without making use of the notion of number: thus, for instance, a waiter may know that there are as many knives as there are plates on a table without know- ing how many of each there are, if he observes that there is just one knife to the right of each plate. Two classes have the same number of members if they can be mapped one- to-one on to each other. We can define the number zero in purely logical terms as the class of all classes with the same number of members as the class of objects which are not identical with themselves. In order to pass from a definition of zero to the defin- ition of the other natural numbers, Frege has to define the notion of ‘successor’ in the sense in which the natural numbers succeed each other in the number series. He defines ‘n immediately succeeds m’ as ‘There exists a con- cept F, and an object falling under it x, such that the num- ber of Fs is n, and the number of Fs not identical with x is m’. With the aid of this definition the other numbers (one, which is the successor of zero, two, which is the successor of one, and so on) can, like zero, be defined without using any notions other than logical ones such as identity, class, and class-equivalence. In the Grundlagen there are two theses to which Frege attaches great importance. One is that each individual number is a self-subsistent object; the other is that the con- tent of a statement assigning a number is an assertion about a concept. At first sight these theses may seem to conflict, but if we understand what Frege meant by ‘con- cept’ and ‘object’ we see that they are complementary. In saying that a number is an object, Frege is not suggesting that a number is something tangible like a tree or a table; rather, he is denying that number is a property belonging to anything, whether an individual or a collection; he is also denying that it is anything subjective, any mental item or any property of a mental item. Concepts are, for Frege, mind-independent, and so there is no contradiction between the thesis that numbers are objective, and the thesis that number-statements are statements about concepts. Frege illustrates this latter thesis with two examples. ‘If I say “Venus has 0 moons”, there simply does not exist any moon or agglomeration of moons for anything to be asserted of; but what happens is that a property is assigned to the concept “moon of Venus”, namely that of including nothing under it. If I say “the King’s carriage is drawn by four horses”, then I assign the number four to the concept “horse that draws the King’s carriage”.’ But if number-statements of this kind are statements about concepts, what kind of object is a number itself? Frege’s answer is that a number is the extension of a con- cept. The number which belongs to the concept F, he says, is the extension of the concept ‘like-numbered to the con- cept F’. This is equivalent to saying that it is the class of all classes which have the same number of members as the class of Fs, as was explained above. So Frege’s theory that numbers are objects depends on the possibility of taking classes as objects. It will be seen that Frege’s philosophy of mathematics is closely linked to his understanding of several key terms of logic and of philosophy; and indeed in the Begriffsschrift and the Grundlagen Frege not only founded modern logic, but also founded the modern philosophical discipline of philosophy of logic. He did so by making a sharp distinc- tion between the philosophical treatment of logic and, on the one hand, psychology (with which it had often been confused by philosophers in the empiricist tradition) and, on the other hand, epistemology (with which it was some- times conflated by philosophers in the *Cartesian trad- ition). In this he was in line with a yet older tradition originating with Aristotle’s De interpretatione: but in the Begriffsschrift and the Grundlagen he investigates such notions as name, sentence, predicate with a scope and sub- tlety greater than Aristotle’s. One of Frege’s most fertile devices was the application of the mathematical notions of *function and *argument to replace the analysis of sentences in ordinary language in terms of subject and predicate. Consider a sentence such as ‘William defeated Harold’—a laconic description, per- haps, of the battle of Hastings. Traditional grammar will say that ‘William’ is the subject, and ‘defeated Harold’ the predicate. To say—as Frege did—that we should look on ‘William’ as an argument, and ‘defeated Harold’ as a Frege, Gottlob 317 function, may at first look as if it is simply an alternative terminology—and indeed, for much of his life, Frege was willing to call an expression such as ‘defeated Harold’ a predicate. But to treat a predicate as a function involves a profound change in the understanding of the construction of sentences. To see this, suppose that we take the sentence ‘William defeated Harold’ and put into it, in place of the word ‘Harold’, the word ‘Canute’. Clearly this alters the sense of the sentence, and indeed it turns it from a true one into a false one. We can think of the sentence as in this way con- sisting of a constant component ‘William defeated’ and a symbol ‘Harold’ replaceable by other similar symbols— names naming other people, in the way that ‘Harold’ names Harold. If we think of a sentence in this way, Frege will call the first component a function, and the second its argument: he is making an extension of the mathematical terminology in accordance with which 6 is the value of the function x × 3 for the argument 2, and 9 is the value of the same function for the argument 3. The sentence ‘William defeated Harold’ is the result of completing the expression ‘William defeated’ with the name ‘Harold’, and the sentence ‘William defeated Canute’ is the result of com- pleting the same expression with the name ‘Canute’. That is to say, in the terminology of Begriffsschrift, ‘William defeated Harold’ is the value of the function ‘William defeated’ for the argument ‘Harold’, and ‘William defeated Canute’ is the value of the same function for the argument ‘Canute’. The sentence ‘William defeated Harold’ is, of course, also the value of the function ‘defeated Harold’ for the argument ‘William’. In the same way, 6 is not only the value of the function x × 3 for the argument 2, but also the value of the function 2 × x for the argument 3. Every sentence, for Frege, can be analysed into argument and function in at least one way, but many can be analysed in more than one way. Corresponding to the distinction in language between functions of this kind and their arguments, Frege main- tained, a systematic distinction must be made between concepts and objects, which are their ontological counter- parts. Objects are what proper names stand for: they are of many kinds, ranging from human beings to numbers. Concepts are items which have a fundamental incom- pleteness, corresponding to the gappiness of a predicate as understood by Frege (i.e. a sentence with a proper name removed from it). Where other philosophers talk ambigu- ously of the meaning of an expression, Frege introduced a distinction between the *reference of an expression (the object to which it refers, as the planet Venus is the refer- ence of ‘the Morning Star’) and the *sense of an expression. (‘The Evening Star’ differs in sense from ‘the Morning Star’ though it too, as astronomers discovered, refers to Venus.) These theories of philosophical logic were worked out by Frege in a series of articles in the early 1890s: ‘Funktion und Begriff’ (Function and Concept, 1891), ‘Begriff und Gegenstand’ (Concept and Object, 1892), ‘Sinn und Bedeutung’ (Sense and Reference, 1892). The most con- troversial application of Frege’s distinction between sense and reference was his theory that the reference of a sen- tence was its truth-value (i.e. the True, or the False), and the connected theses that in a scientifically respectable lan- guage every term must have a reference and every sen- tence must be either true or false. These theses lead to many difficulties. In the last years of his life, between 1918 and his death, Frege attempted to write a full treatise of philosophical logic. All that was completed was a series of articles (Logis- che Untersuchungen, 1919–23) in which he returns to the relationship between logic and philosophical psychology or philosophy of mind, and discusses the nature of thought and inference. His work in this area has been largely superseded by the later writings of Wittgenstein, a philosopher much influenced throughout his life, as he himself avowed, by Frege’s agenda and Frege’s structures of thought. The climax of Frege’s career as a philosopher should have been the publication of the two volumes of Die Grundgesetze der Arithmetik (1893– 1903), in which he set out to present in formal manner the logicist construction of arithmetic on the basis of pure logic and set theory. This work was to execute the task which had been sketched in the earlier books on the philosophy of mathematics: it was to enunciate a set of axioms which would be recognizably truths of logic, to propound a set of undoubtedly sound rules of inference, and then to present, one by one, deriv- ations by these rules from these axioms of the standard truths of arithmetic. The magnificent project aborted before it was ever completed. The first volume was published in 1893; the second volume did not appear until 1903 and while it was in the press Frege received a letter from Russell pointing out that the fifth of the initial axioms made the whole sys- tem inconsistent. This was the axiom which, in Frege’s words, allowed ‘the transition from a concept to its exten- sion’, the transition which was essential if it was to be established that numbers were logical objects. Frege’s sys- tem, with this axiom, permitted the formation of the class of all classes that are not members of themselves. But the formation of such a class, Russell pointed out, leads to paradox: if it is a member of itself then it is not a member of itself; if it is not a member of itself, then it is a member of itself. A system which leads to such paradox cannot be logically sound. With good reason, Frege was utterly downcast by this discovery, though he strove to patch his system by weak- ening the guilty axiom. We now know that his logicist programme cannot ever be successfully carried out. The path from the axioms of logic to the theorems of arith- metic is barred at two points. First, as Russell’s paradox showed, the naïve set theory which was part of Frege’s logical basis was inconsistent in itself, and the remedies which Frege proposed for this proved ineffective. Thus, the axioms of arithmetic cannot be derived from purely logical axioms in the way he hoped. Secondly, the notion 318 Frege, Gottlob of ‘axioms of arithmetic’ was itself later called in question when Gödel showed that it was impossible to give arith- metic a complete and consistent axiomatization. None the less, the concepts and insights developed by Frege in the course of expounding his logicist thesis have a permanent interest which is unimpaired by the defeat of that pro- gramme at the hands of Russell and Gödel. Wittgenstein once described to Geach his final meeting with Frege. ‘The last time I saw Frege, as we were waiting at the station for my train, I said to him “Don’t you ever find any difficulty in your theory that numbers are objects?” He replied “Sometimes I seem to see a diffi- culty—but then again I don’t see it.”’ a.j.p.k. *logic, history of; logic, modern. G. E. M. Anscombe and P. Geach, Three Philosophers (Oxford, 1961). M. Dummett, Frege: Philosophy of Language (London, 1973). —— Frege: Philosophy of Mathematics (London, 1991). G. W. Frege, Collected Papers on Mathematics, Logic and Philosophy, ed. B. McGuinness (Oxford, 1984). —— Conceptual Notation and Related Articles, ed. T. W. Bynum (Oxford, 1972). —— The Foundations of Arithmetic, tr. J. L. Austin (Oxford, 1950). —— The Frege Reader, ed. M. Beaney (Oxford, 1997). A. Kenny, Frege: An Introduction to the Founder of Modern Analytic Philosophy (Oxford, 2000). C. Wright, Frege’s Conception of Numbers as Objects (Aberdeen, 1983). French philosophy. Although the literary scepticism of François Rabelais (1494–1553) and Michel de Montaigne (1533–92) expresses thought that is in part recognizably philosophical, Descartes is the earliest French philosopher because before him no one systematically attempted to solve philosophical problems and write the results in French. French philosophy since Descartes can be cor- rectly viewed as a series of endorsements and repudiations of *Cartesianism but is still more usefully viewed as essen- tially oscillating between optimism and pessimism about the powers of reason. Pascal’s famous distinction between two mistakes—to deny reason and to allow only reason— arguably applies nowhere more appropriately than to French philosophy over its four centuries. In the seventeenth century Cartesian optimism about the metaphysical role of reason was subject to two kinds of critique; one metaphysical and theological, the other empiricist. Blaise Pascal maintained that putative meta- physical and theological knowledge acquired by the exer- cise of the intellect was essentially incomplete and a non-rational leap of faith was required to supplement it. Pierre Gassendi (1592–1655) maintained, against Descartes, the empiricist thesis that the exercise of the senses is the best guide to the nature of reality and that the correct role of reason is confined to drawing inferences from the findings of sense experience. Although the eighteenth-century *Enlightenment endorsed an empiricist respect for the natural sciences and a burgeoning social anthropology (evident, for example, in the work of Voltaire, Holbach, La Mettrie, Mon- tesquieu, and Condillac), it is a return to optimism about the powers of reason, not this time in any metaphysical employment, but in a naturalistic and human role. The Encyclopédie of Diderot and d’Alembert relies on the opti- mistic principle that no aspect of reality is in principle opaque to human inquiry. The uses of the senses and the intellect are singularly necessary and in principle jointly sufficient for complete knowledge. No single philosophical thesis is common to all and only those thinkers called the *‘philosophes’, but most of them combined atheism and anti-clericalism with a respect for science and urged a liberal politics which rec- ommended a constitutional monarchy on the English model (rather than republicanism) against the prevalent absolute monarchy of most European states. Most shared, too, a concern for non-religious education and a synthesis of arts and sciences. In Rousseau and Maine de Biran the Enlightenment was subject to two kinds of anti-rationalist reaction. Although Rousseau’s concept of the general will, which putatively reconciles the freedom of the individual with political society, is consistent with the philosophes’ cri- tique of the absolutism of the ancien régime, his moral and epistemological attack on the sciences and his postulation of God, freedom, and the immortality of the soul consti- tute a spiritualist and metaphysical reaction against Enlightenment humanism. In Maine de Biran too, in his emphasis on the spiritual nature of inner experience, there is a pessimism about the power of reason to solve meta- physical problems. The *positivism of the late nineteenth and early twenti- eth centuries is essentially anti-metaphysical and anti- theological in its insistence that any problem may, in principle, be solved using the methods of the natural sci- ences or mathematics (a view endorsed, famously, by Comte). However, the rather empiricist foundations of French positivism are subjected to quasi-Kantian criticism by Poincaré. He argues that science cannot be derived merely from the findings of sense experience, but is also intellectually constructed through the imposition of a set of a priori conventions on those findings. Although Poincaré suggests a synthesis between ration- alism and empiricism, Bergson is the only major French thinker since Descartes who seriously integrates the scien- tific and the non-rational into his philosophy. Although the living subjective flux of the ‘durée réelle’ (‘real dura- tion’) cannot be explained scientifically, it makes the whole of knowledge (and, a fortiori, the whole of science) possible. Bergson’s philosophy enjoyed a vogue in France after the First World War comparable to that of Sartre’s existentialism after the Second. Bergson is neglected at the time of writing, even though his philosophy has the rare merit of taking seriously both science and the subjective reality of lived experience. French philosophy since Bergson has been dominated by five philosophical movements: *phenomenology, *existen- tialism, *Marxism, *structuralism, and *post-structuralism. French philosophy 319 . of the History of Phil- osophy in the University of Oxford. Historian of ancient philosophy who is sensitive to the methodological distinc- tion between writing history of philosophy as history. appears that Plato was led to the theory in the first place by con- sidering such types as the type of person who is virtuous, but he then extended it to many other types. d.b. *Aristotle; cave,. definition of zero to the defin- ition of the other natural numbers, Frege has to define the notion of ‘successor’ in the sense in which the natural numbers succeed each other in the number series.