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four terms, fallacy of (quaternio terminorum)

The formal fallacy committed in a categorical syllogism that is invalid because it employs more than three distinct categorical terms.

Example: "All managers are politicians, and all sybarites are administrators, so all sybarites are politicians."

Also see FF and GLF.

Fourier, Jean-Baptiste Joseph (1768-1830)

French Egyptologist and mathematician. In his Théorie analytique de la chaleur (The Analytical Theory of Heat) (1822) Fourier demonstrated the use of infinite series for calculation of the conduction of heat. Accompanying Napolean's army into Egypt, he devoted his later years to archaeological research and occasional essays.

Recommended Reading: John Herivel, Joseph Fourier: The Man and the Physicist (Clarendon, 1984); Who Is Fourier?: A Mathematical Adventure, tr. by Alan Gleason (Blackwell, 1995); Morris Kline, Mathematical Thought from Ancient to Modern Times (Oxford, 1990); M. J. Lighthill, An introduction to Fourier analysis and generalized functions (Cambridge, 1958).

Also see EB, David Wilkins, MMT, and WSB.

Frankfurt School
Institut für Sozialforschung

A community of German thinkers in the Institut für Sozialforschung (Institute for Social Research) who developed the methodology of critical theory. Prominent members include Horkheimer, Adorno, Benjamin, Marcuse, Fromm, and Habermas.

Recommended Reading: The Essential Frankfurt School Reader, ed. by Andrew Arato and Eike Gebhardt (Continuum, 1982); Martin Jay, The Dialectical Imagination: A History of the Frankfurt School and the Institute of Social Research 1923-1950 (California, 1996); and Rolf Wiggerhaus, The Frankfurt School: Its History, Theories, and Political Significance, tr. by Michael Robertson (MIT, 1995).

Also see Douglas Kellner.

freedom {Lat. libertas Ger. Freiheit}}

The human capacity to act (or not to act) as we choose or prefer, without any external compulsion or restraint. Freedom in this sense is usually regarded as a presupposition of moral responsibility: the actions for which I may be praised or blamed, rewarded or punished, are just those which I perform freely.

The further question of whether choice—the volition or will to act—is itself free or subject to ordinary causality raises the issue of determinism in human conduct. But most modern philosophers have held that (internal) determination of the will by desire or impulse does not diminish the relevant sense of moral responsibility.

Recommended Reading: Free Will, ed. by Gary Watson (Oxford, 1983); Ilham Dilman, Free Will: An Historical and Philosophical Introduction (Routledge, 1999); Derk Pereboom, Living Without Free Will (Cambridge, 2001); Philip Pettit, A Theory of Freedom: From the Psychology to the Politics of Agency (Oxford, 2001); Robert Kane, The Significance of Free Will (Oxford, 1998); Laura Waddell Ekstrom, Free Will: A Philosophical Study (Westview, 2000); Nancy J. Hirschmann, The Subject of Liberty: Toward a Feminist Theory of Freedom (Princeton, 2003); Graham McFee, Free Will (McGill, 2001); and Daniel C. Dennett, Elbow Room (MIT, 1984).

Also see SEP on free will, incompatibilism, and freedom of speech, Donna Summerfield, David Thompson, and Michael Maher.

Frege, Gottlob (1848-1925)

German mathematician and philosopher who tried to develop effective ways of representing human thought in language and symbols. Frege was an early exponent of the view that arithmetical truth could be established on purely logical grounds. To that end, he developed a formal symbolic language for the expression of truth in Begriffsschrift (Concept-notation) (1879), which introduced quantifiers as logical operators, and employed this symbolic method in Die Grundlagen der Arithmetik (The Foundations of Arithmetic) (1884) and both volumes of Grundgesetze der Arithmetik (The Basic Laws of Arithmetic) (1893, 1903). In "Über Sinn und Bedeutung" ("On Sense and Reference") (1892), Frege proposed a strict distinction between the sense and the reference of terms as a way of avoiding difficult epistemological paradoxes about informative statements of identity.

Recommended Reading: The Frege Reader, ed. by Michael Beaney (Blackwell, 1997); Joan Weiner, Frege (Oxford, 1999); Michael Dummett, The Interpretation of Frege's Philosophy (Harvard, 1981); Michael Dummett, Frege and Other Philosophers (Oxford, 1996); Anthony Kenny, Frege: An Introduction to the Founder of Modern Analytic Philosophy (Blackwell, 2000); Hans D. Sluga, Gottlob Frege (Routledge, 1999); Wolfgang Carl, Frege's Theory of Sense and Reference: Its Origins and Scope (Cambridge, 1994); and R.M. Sainsbury, Departing From Frege: Essays in the Philosophy of Language (Routledge, 2002).

Also see EB, SEP on Frege and the foundations of arithmetic, IEP, and Edward Zalta, MMT, Andy Blunden, DPM, and ELC.


Name given by medieval logicians to any categorical syllogism whose standard form may be designated as EIO-4.

Example: Since no fish are mammals while some animals that live in water are mammals, it follows that some animals that live in water are not fish.

This is one of the fifteen forms in which syllogisms are always valid.

Freud, Sigmund (1856-1939)

Austrian physician and psychoanalyst. Freud offered a series of extended accounts of the mechanism of repression, by means of which the motives of human behavior are unrecognizably disguised even from their agents. A series of lectures entitled Vorlesungen zur Einführung in die Psychoanalyse (The Origin and Development of Psychoanalysis) (1917) offer a summary of his methods and results. In Die Traumdeutung (The Interpretation of Dreams) (1900) , Freud proposed the analysis of dreams as a method of discovering the substantive content of the individual unconscious. In Die Zukunft einer Illusion (The Future of an Illusion) , he offered a naturalistic account of religious belief.

Recommended Reading: The Basic Writings of Sigmund Freud, ed. by A. A. Brill (Modern Library, 1995); The Freud Reader, ed. by Peter Gay (Norton, 1995); The Cambridge Companion to Freud, ed. by Jerome Neu (Cambridge, 1992); Paul Ricoeur, Freud and Philosophy: An Essay on Interpretation, tr. by Denis Savage (Yale, 1986); Anthony Storr, Freud (Oxford, 1989); and Donald Levy, Freud Among the Philosophers: The Psychoanalytic Unconscious and Its Philosophical Critics (Yale, 1996).

Also see IEP, EB, C. George Boeree, Andrew Brook, ELC, Andy Blunden, and Austria-Forum.

Fuller, (Sarah) Margaret (1810-1850)

American journalist and social reformer. In Woman in the Nineteenth Century (1845), Fuller advocated political equality and intellectual opportunity for women. She died in a shipwreck off the coast of New York during her return from work as a newspaper correspondent in Italy. The posthumously-published Life Without and Life Within (1869) includes essays on several key intellectual figures of the nineteenth century.

Recommended Reading: The Essential Margaret Fuller, ed. by Jeffrey Steele (Rutgers, 1992); The Portable Margaret Fuller, ed. by Mary Kelley (Penguin, 1994); and Bell Gale Chevigny, The Woman and the Myth: Margaret Fuller's Life and Writings (Northeastern, 1994).

Also see EB and ELC.


An approach to the philosophy of mind that analyzes mental states in terms of what they do, rather than of what they are. This focus on activities performed instead of on intrinsic features, often taken to parallel the difference between software and hardware in a Turing machine, may help to avoid many thorny problems.

Recommended Reading: The Nature of Mind, ed. by David M. Rosenthal (Oxford, 1991); William G. Lycan, Consciousness (Bradford, 1995); , ed. by Ariew, Cummins, and Perlman (Oxford, 2002); Sydney Shoemaker, The First-Person Perspective and Other Essays (Cambridge, 1996); and The Nature of Consciousness: Philosophical Debates, ed. by Ned Joel Block and Owen Flanagan (MIT, 1997).

Also see SEP, Ned Block, IEP, and DPM.

fuzzy logic

Non-classical system of reasoning in which propositions may have many degrees of truth or falsity. Developed by Lotfi Zadeh as a method of providing for vagueness in the application of predicates, fuzzy logic has found a number of significant practical applications in the design and operation of control-systems.

Recommended Reading: Computing With Words in Information/Intelligent Systems, ed. by Lotfi Asker Zadeh and Janusz Kacprzyk (Springer Verlag, 1999); Susan Haack, Deviant Logic, Fuzzy Logic: Beyond the Formalism (Chicago, 1996); Bart Kosko, Fuzzy Thinking: The New Science of Fuzzy Logic (Hyperion, 1994); Matthew Friedman, Fuzzy Logic (Vehicule, 1998); and George J. Klir and Bo Yuan, Fuzzy Sets and Fuzzy Logic: Theory and Applications (Prentice-Hall, 1995).

Also see EB and SEP.


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