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Polish notation

An alternative representation for symbolic logic, introduced by Jan Lukasiewicz. Use of the basic notation is illustrated in the following table:

Npnegation~ p
Kpqconjunctionp · q
Apqdisjunctionp Ú q
Cpqmaterial implicationp É q
Epq     material equivalence     p º q
PxFxuniversal quantifier(x)Fx
SxGxexistential quantifier($x)Gx
Polish notation eliminates any need for parenthetical bracketing by relying upon a rigorous principle of order. Thus, for example,
can be expressed in Polish notation as CKAprKCpNqCrsANqs.

Recommended Reading: Philosophical Logic in Poland, ed. by Jan Wolenski (Kluwer, 1994) {at} and Jan Lukasiewicz, Aristotle's Syllogistic from the Standpoint of Modern Formal Logic (Clarendon, 1957) {at}.


What pertains to the life of the city {Gk. poliV [polis]} or state. Hence, study of citizenship or the art of governance generally. Political philosophers, including Plato, Aristotle, Machiavelli, Hobbes, Locke, Rousseau, Mill, Marx, and MacKinnon examine the origins, forms, and limits of political power as exercised in practical life.

Recommended Reading: Political Philosophy, ed. by Anthony Quinton (Oxford, 1989) {at}; Jene M. Porter and John Hallowell, Political Philosophy: The Search for Humanity and Order (Prentice Hall, 1997) {at}; Tudor Jones, Introduction to Political Concepts (Routledge, 2001) {at}; Classics of Moral and Political Theory, ed. by Michael L. Morgan (Hackett, 1997) {at}; Dudley Knowles, (McGill, 2001) {at}; History of Political Philosophy, ed. by Leo Strauss and Joseph Cropsey (Chicago, 1987) {at}; and The Routledge Dictionary of Twentieth Century Political Thinkers, ed. by Robert Benewick and Philip Green (Routledge, 1998) {at}.

Also see Richard Hooker, ColE, John V. Strang, and PP.

Polya, George (1887-1985)

Hungarian-American mathematician whose books How to Solve It (1957) {at} and Mathematical Discovery (1962) {at} offered an interesting variety of heuristics for the solution of mathematical and logical problems and contributed significantly to a transformation in the methods for teaching mathematics.

Recommended Reading: George Polya, Mathematics and Plausible Reasoning (Princeton, 1990) {at} and Gerald L. Alexanderson, The Random Walks of George Polya (Math. Assn. of Am., 2000) {at}.

Also see MMT and BIO.

Popper, Karl Raimund (1902-1994)

Austrian philosopher of science and political thinker. According to Popper in Logik der Forschung (The Logic of Scientific Discovery) (1935) {at}, knowledge of the natural world never advances by direct confirmation of scientific theories—which cannot occur—but only indirectly, through the systematic falsification of their alternatives by reference to our experience. He defended a realistic epistemology in Objective Knowledge (1966) {at}. Applying the same methods to political science in The Open Society and its Enemies (1945) vol. 1 {at} and vol. 2 {at}, Popper argued that the unintended harmful consequences of social planning outweigh its benefits and that citizens, therefore, must always retain an absolute right to change their form of government.

Recommended Reading: Karl Raimund Popper, Poverty of Historicism (Routledge, 1993) {at}; Karl Raimund Popper, Conjectures and Refutations: The Growth of Scientific Knowledge (Routledge, 1992) {at}; Roberta Corvi, An Introduction to the Thought of Karl Popper, tr. by Patrick Camiller (Routledge, 1996) {at}; Bryan Magee, Philosophy and the Real World: An Introduction to Karl Popper (Open Court, 1985) {at}; and Frederic Raphael, Popper (Routledge, 1999) {at}.

Also see SEP, Ray Scott Percival , Dan Bucsescu, ColE, ELC, BIO, and Österreich-Lexikon.

populum, argumentum ad

An attempt to persuade by reference to commonplace sentiments; see appeal to emotion.

Recommended Reading: Douglas Walton, Appeal to Popular Opinion (Penn. State, 1999) {at}.

Porphyry (232-304)

Phoenecian philosopher. A disciple of Plotinus, Porphyry defended the neo-platonic philosophy in Peri agalmaton (On Images) and several commentaries on the logic of Aristotle, including an influential exposition of the Categories {at}.

Recommended Reading: Porphyry, Life of Plotinus (Holmes 1983) {at} and Five Texts on the Mediaeval Problem of Universals, ed. by Paul Vincent Spade (Hackett, 1994) {at}.

Also see R. J. Kilcullen, ColE, The Ecole Initiative, ELC, and BIO.


Monastery outside Paris that fostered Jansenism during the seventeenth century. During its heyday, Port-Royal hosted Antoine Arnauld (whose sister Angélique was its abbess), Pierre Nicole, and Blaise Pascal, along with Jean Racine.

Recommended Reading: Antoine Arnauld and Pierre Nicole, Logic or the Art of Thinking: Containing, Besides Common Rules, Several New Observations Appropriate for Forming Judgement, ed. by Jill V. Buroker (Cambridge, 1996) {at}; Marc Escholier, Port-Royal: The Drama of the Jansenists (Hawthorn, 1968) {at}; and William Doyle, Jansenism: Catholic Resistance to Authority from the Reformation to the French Revolution (Palgrave, 2000) {at}.

Also see ColE.


Belief that natural science, based on observation, comprises the whole of human knowledge. Positivists like Auguste Comte, then, reject as meaningless the claims of theology and metaphysics. The most influential twentieth-century version is logical positivism.

Recommended Reading: Auguste Comte, The Positive Philosophy (AMS, 1987) {at}; A. J. Ayer, Logical Positivism (Free Press, 1966) {at}; and Jonathan H. Turner, Classical Sociological Theory: A Positivist's Perspective (Burnham, 1993) {at}.

Also see ColE and ISM.

post hoc, ergo propter hoc

Latin phrase meaning "After this, therefore because of this." Thus, mistaken reliance upon temporal succession alone as enough to establish the presence of a causal relationship between two events.


Most generally, abandonment of Enlightenment confidence in the achievement objective human knowledge through reliance upon reason in pursuit of foundationalism, essentialism, and realism. In philosophy, postmodernists typically express grave doubt about the possibility of universal objective truth, reject artificially sharp dichotomies, and delight in the inherent irony and particularity of language and life. Various themes and implications of postmodern thought are explored by Foucault, Derrida, Lyotard, Rorty, Haraway, and Cixous.

Recommended Reading: Postmodernism: A Reader, ed. by Patricia Waught (Edward Arnold, 1992) {at}; Jean-Francois Lyotard, The Postmodern Condition: A Report on Knowledge, tr. by Brian Massumi (Minnesota, 1985) {at}; Steven Best and Douglas Kellner, Postmodern Theory (Guilford, 1991) {at}; Paul Cilliers, Complexity and Postmodernism: Understanding Complex Systems (Routledge, 1998) {at}; The Routledge Critical Dictionary of Postmodern Thought, ed. by Stuart Sim (Routledge, 1999) {at}; and James N. Powell, Postmodernism for Beginners (Writers and Readers, 1998) {at}.

Also see Reinhardt Düßel, Thomas Csordas, ColE, and G.K. Parish-Philp.


A proposition assumed to be true without any appeal to evidentiary support, especially when it is then used to derive further statements in a formal system or general theory.

potentiality {Gr. dunamiV [dynamis]}

What might have been or could be, as opposed to what is the case. Hence, for Aristotle, a disposition or tendency to manifest itself.

See actuality / potentiality.

pragmatic theory of truth

Belief that a proposition is true when acting upon it yields satisfactory practical results. As formulated by William James, the pragmatic theory promises (in the long term) a convergence of human opinions upon a stable body of scientific propostions that have been shown in experience to be successful principles for human action.

Recommended Reading: William James, Pragmatism and the Meaning of Truth (Harvard, 1978) {at}; Alan R. White, Truth (Anchor, 1970) {at}; and Richard L. Kirkham, Theories of Truth: A Critical Introduction (Bradford, 1995) {at}.


An indigenous American philosophical theory that explains both meaning and truth in terms of the application of ideas or beliefs to the performance of actions that have observable practical outcomes. Prominent pragmatists in the tradition include Peirce, James, Mead, Addams, and Dewey. More recently, such analytic philosophers as Quine, Putnam, and Rorty have expressed sympathy with various portions of the pragmatic program.

Recommended Reading: Pragmatism: A Reader, ed. by Louis Menand (Vintage, 1997) {at}; H. Standish Thayer, Meaning and Action: A Critical History of Pragmatism (Hackett, 1981) {at}; Louis Menand, The Metaphysical Club: A Story of Ideas in America (Farrar, Straus, &l Giroux, 2001) {at}; Howard Mounce, The Two Pragmatisms: From Peirce to Rorty (Routledge, 1997) {at}; Charlene Haddock Seigfried, Pragmatism and Feminism: Reweaving the Social Fabric (Chicago, 1996) {at}; Bruce Kuklick, A History of Philosophy in America 1720-2000 (Oxford, 2001) {at}; Cornel West, The American Evasion of Philosophy: A Genealogy of Pragmatism (Wisconsin, 1989) {at}; and Richard Shusterman, Practicing Philosophy: Pragmatism and the Philosophical Life (Routledge, 1997) {at}.

Also see ISM and ColE.

praxiV [praxis]

Greek term for action or doing, as opposed to creative production (poihsiV [poiêsis]). According to Aristotle, actions are subject to moral valuation if they result from deliberate choice.

Recommended Reading: F. E. Peters, Greek Philosophical Terms: A Historical Lexicon (NYU, 1967) {at}.

Also see PP.

precising definition

A careful effort to reduce the vagueness of a term by stipulating features not included in its lexical definition.

predicate calculus

A formal logical system constructed to symbolize assertions that individual things have features; see quantification theory.

Recommended Reading: Graeme Forbes, Modern Logic: A Text in Elementary Symbolic Logic (Oxford, 1994) {at}; Joseph Bessie and Stuart Glennan, Elements of Deductive Inference: An Introduction to Symbolic Logic (Wadsworth, 1999) {at}; and Merrie Bergmann, James Moor, and Jack Nelson, The Logic Book (McGraw-Hill, 1997) {at}.

predicate constant

A symbol (usually uppercase letters such as F, G, H, etc.) used to represent a specific feature or property in quantification theory.


The explanation of an event that has not yet occurred by reference to observed regularities in the natural world.

Recommended Reading: Wesley C. Salmon, Causality and Explanation (Oxford, 1997) {at}; Peter Spirtes, Clark Glymour, and Richard Scheines, Causation, Prediction, and Search (MIT, 2001) {at}; Judea Pearl, Causality: Models, Reasoning, and Inference (Cambridge, 2001) {at}; and Karl Raimund Popper, Conjectures and Refutations: The Growth of Scientific Knowledge (Routledge, 1992) {at}.


A statement whose truth is used to infer that of others; see argument.


R. M. Hare's contention that the use of moral language conveys an implicit commitment to act accordingly. Thus, for example, saying that "Murder is wrong" not only entails acceptance of a universalizable obligation not to kill, but also leads to avoidance of the act of killing.

Recommended Reading: R. M. Hare, The Language of Morals (Clarendon, 1991) {at}; R. M. Hare, Moral Thinking: Its Levels, Methods, and Point (Oxford, 1982) {at}; and R. M. Hare, Objective Prescriptions: and Other Essays (Oxford, 1999) {at}.

presocratic philosophers

Greek philosophers of the sixth and fifth centuries B.C.E., many of them known to us only through fragmentary reports by later writers, whose speculative and practical thought predates the development of critical philosophy by Socrates and Plato. Prominent presocratics include: Thales, Anaximander, Anaximenes, Pythagoras, Heraclitus, Xenophanes, Parmenides, Zeno of Elea, Empedocles, Anaxagoras, Protagoras, Hippias, Leucippus, Democritus, and the Sophists.

Recommended Reading: Kathleen Freeman, Ancilla to the Pre-Socratic Philosophers (Harvard, 1983) {at}; G. S. Kirk and J. E. Raven, The Presocratic Philosophers: A Critical History With a Selection of Texts (Cambridge, 1988) {at}; Jonathan Barnes, The Presocratic Philosophers (Routledge, 1982) {at}; and The Cambridge Companion to Early Greek Philosophy, ed. by A. A. Long (Cambridge, 1999) {at}.

Also see IEP, Ricardo Nirenberg, and PP.


What is implicitly involved in making an assertion. Hence, according to P.F. Strawson, a presupposition is a necessary condition for either the truth or the falsity of the statement that presupposes it. Thus, for example, "My grand-daughter is a smart baby"—whether or not she exhibits intelligent behavior—presupposes that I do, in fact, have at least one female grand-child.

Recommended Reading: Douglas N. Walton, Argumentation Schemes for Presumptive Reasoning (Erlbaum, 1995) {at}; Nirit Kadmon, Formal Pragmatics: Semantics, Pragmatics, Presupposition, and Focus (Blackwell, 2001) {at}; and Gennaro Chierchia, Dynamics of Meaning: Anaphora, Presupposition, and the Theory of Grammar (Chicago, 1995) {at}.


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Last modified 9 August 2002.
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