Paradoxes
- LAST REVIEWED: 24 July 2013
- LAST MODIFIED: 24 July 2013
- DOI: 10.1093/obo/9780195396577-0201
- LAST REVIEWED: 24 July 2013
- LAST MODIFIED: 24 July 2013
- DOI: 10.1093/obo/9780195396577-0201
Introduction
Many paradoxes are best construed as inferences from plausible premises to an implausible conclusion. The sorites paradox, or paradox of the heap, is like this: A pile of 10,000 grains is a heap. For any number n greater than 1, if a pile of n grains is a heap then so is a pile of n – 1 grains. So one grain is a heap. Even if all paradoxes can be forced into this mold, they are not naturally presented in this way. Semantic paradoxes like the liar and set-theoretic paradoxes like Russell’s typically yield contradictions. In some paradoxes, we are faced with a dilemma. Which of two ships, for example, is identical with Theseus’s original ship, the ship with its planks replaced or the ship reconstituted from the old planks? In other paradoxes, there are parallel arguments for conflicting verdicts. But a common theme is the conflict with our ordinary belief.
The Nature of Paradoxes
Quine 1966 is a classic. Clark 2012 on paradox is a general discussion. Sainsbury 2009 characterizes paradox as “an apparently unacceptable conclusion derived by apparently acceptable reasoning from apparently acceptable premises,” and recognizes degrees, some paradoxes being deeper than others. Passeau 2013 offers a precise treatment of such degrees. Both Lycan 2010 and Rescher 2001 treat paradoxes as, in Lycan’s words, “inconsistent sets of propositions, each of which is very plausible.” Whereas Sainsbury 2009 picks out certain propositions as premises, the latter treat Sainsbury’s premises and conclusion on a par. Logically, the accounts are equivalent, but Sainsbury’s account is often more natural (say for the sorites). Sorensen 1988 aims to show how many paradoxes, like the unexpected examination, exhibit a “master cognitive flaw.” Sorensen 2003 contains a technical criticism of Sainsbury 2009.
Clark, Michael. Paradoxes from A to Z. 3d ed. London: Routledge, 2012.
The entry on paradox is a general discussion.
Lycan, William. “What, Exactly, Is a Paradox?” Analysis 70 (2010): 615–622.
An alternative account to Sainsbury 2009, and similar to Rescher 2001. Available online for purchase or by subscription.
Passeau, Alexander. “An Exact Measure of Paradox.” Analysis 73.1 (2013): 17–26.
The paper is a precise treatment of degrees of paradoxicality, given in formal symbolic terms, with a sensitive discussion. Available online for purchase or by subscription.
Quine, W. V. “The Ways of Paradox.” In The Ways of Paradox and Other Essays. By W. V. Quine, 3–20. New York: Random House, 1966.
This is a classic paper, which distinguishes “veridical” from “falsidical” paradoxes.
Rescher, Nicholas. Paradoxes: Their Roots, Range, and Resolution. Chicago: Open Court, 2001.
This gives an alternative account to Sainsbury 2009, and is similar to Lycan 2010. See especially chapter 1.
Sainsbury, R. M. “Introduction.” In Paradoxes. 3d ed. By R. M. Sainsbury, 1–2. Cambridge, UK: Cambridge University Press, 2009.
DOI: 10.1017/CBO9780511812576.002
This is an influential account. It recognizes degrees, so that some paradoxes are deeper than others.
Sorensen, Roy. Blindspots. Oxford: Clarendon, 1988.
The book illustrates the “master cognitive flaw” in such examples as the unexpected examination and similar paradoxes of the author’s own invention.
Sorensen, Roy. A Brief History of the Paradox: Philosophy and the Labyrinths of the Mind. Oxford: Oxford University Press, 2003.
These few pages criticize Sainsbury 2009. The criticism, though sound, does not show that Sainsbury is fundamentally wrong. See pp. 104–107.
Users without a subscription are not able to see the full content on this page. Please subscribe or login.
How to Subscribe
Oxford Bibliographies Online is available by subscription and perpetual access to institutions. For more information or to contact an Oxford Sales Representative click here.
Article
- A Priori Knowledge
- Abduction and Explanatory Reasoning
- Ability
- Abortion
- Abstract Objects
- Action
- Addams, Jane
- Adorno, Theodor
- Aesthetic Hedonism
- Aesthetics, Analytic Approaches to
- Aesthetics, Continental
- Aesthetics, Environmental
- Aesthetics, History of
- African Philosophy, Contemporary
- Alexander, Samuel
- Analytic/Synthetic Distinction
- Anarchism, Philosophical
- Animal Rights
- Anscombe, G. E. M.
- Anthropic Principle, The
- Anti-Natalism
- Applied Ethics
- Aquinas, Thomas
- Argument Mapping
- Art and Emotion
- Art and Knowledge
- Art and Morality
- Artifacts
- Assertion
- Astell, Mary
- Atheism
- Augustine
- Aurelius, Marcus
- Austin, J. L.
- Autonomy
- Bacon, Francis
- Bayesianism
- Beauty
- Belief
- Bergson, Henri
- Berkeley, George
- Biology, Philosophy of
- Bolzano, Bernard
- Boredom, Philosophy of
- British Idealism
- Buber, Martin
- Buddhist Philosophy
- Burge, Tyler
- Business Ethics
- Camus, Albert
- Canterbury, Anselm of
- Carnap, Rudolf
- Causation
- Cavendish, Margaret
- Certainty
- Chemistry, Philosophy of
- Childhood, Philosophy of
- Chinese Philosophy
- Cognitive Ability
- Cognitive Phenomenology
- Cognitive Science, Philosophy of
- Coherentism
- Color
- Communitarianism
- Computational Science
- Computer Science, Philosophy of
- Computer Simulations
- Comte, Auguste
- Concepts
- Conceptual Role Semantics
- Conditionals
- Confirmation
- Confucius
- Connectionism
- Consciousness
- Constructive Empiricism
- Contemporary Hylomorphism
- Contextualism
- Contrastivism
- Cook Wilson, John
- Cosmology, Philosophy of
- Critical Theory
- Culture and Cognition
- Daoism and Philosophy
- Davidson, Donald
- de Beauvoir, Simone
- de Montaigne, Michel
- Death
- Decision Theory
- Deleuze, Gilles
- Democracy
- Depiction
- Derrida, Jacques
- Descartes, René
- Descartes, René: Sensory Representations
- Descriptions
- Dewey, John
- Dialetheism
- Disability
- Disagreement, Epistemology of
- Disjunctivism
- Dispositions
- Divine Command Theory
- Doing and Allowing
- du Châtelet, Emilie
- Dummett, Michael
- Dutch Book Arguments
- Early Modern Philosophy, 1600-1750
- Eastern Orthodox Philosophical Thought
- Education, Philosophy of
- Emotion
- Engineering, Philosophy and Ethics of
- Environmental Philosophy
- Epicurus
- Epistemic Basing Relation
- Epistemic Defeat
- Epistemic Injustice
- Epistemic Justification
- Epistemic Philosophy of Logic
- Epistemology
- Epistemology and Active Externalism
- Epistemology, Bayesian
- Epistemology, Feminist
- Epistemology, Internalism and Externalism in
- Epistemology, Moral
- Epistemology of Education
- Ethical Consequentialism
- Ethical Deontology
- Ethical Intuitionism
- Eugenics and Philosophy
- Events, The Philosophy of
- Evidence
- Evidence-Based Medicine, Philosophy of
- Evidential Support Relation In Epistemology, The
- Evil
- Evolutionary Debunking Arguments in Ethics
- Evolutionary Epistemology
- Experimental Philosophy
- Explanations of Religion
- Extended Mind Thesis, The
- Externalism and Internalism in the Philosophy of Mind
- Faith, Conceptions of
- Fatalism
- Feminist Aesthetics and Feminist Philosophy of Art
- Feminist Philosophy
- Feyerabend, Paul
- Fichte, Johann Gottlieb
- Fiction
- Fictionalism
- Fictionalism in the Philosophy of Mathematics
- Film, Philosophy of
- Foot, Philippa
- Foreknowledge
- Forgiveness
- Formal Epistemology
- Foucault, Michel
- Free Will
- Frege, Gottlob
- Gadamer, Hans-Georg
- Generics
- Geometry, Epistemology of
- God and Possible Worlds
- God, Arguments for the Existence of
- God, The Existence and Attributes of
- Grice, Paul
- Habermas, Jürgen
- Hart, H. L. A.
- Heaven and Hell
- Hegel, Georg Wilhelm Friedrich: Aesthetics
- Hegel, Georg Wilhelm Friedrich: Metaphysics
- Hegel, Georg Wilhelm Friedrich: Philosophy of History
- Hegel, Georg Wilhelm Friedrich: Philosophy of Politics
- Heidegger, Martin: Early Works
- Hermeneutics
- Higher Education, Philosophy of
- History, Philosophy of
- Hobbes, Thomas
- Horkheimer, Max
- Human Rights
- Hume, David: Aesthetics
- Hume, David: Moral and Political Philosophy
- Husserl, Edmund
- Idealizations in Science
- Identity in Physics
- Images
- Imagination
- Imagination and Belief
- Immanuel Kant: Political and Legal Philosophy
- Impossible Worlds
- Incommensurability in Science
- Indian Philosophy
- Indispensability of Mathematics
- Inductive Reasoning
- Infinitism
- Instruments in Science
- Intellectual Humility
- Intentionality, Collective
- Intuitions
- James, William
- Japanese Philosophy
- Kant and the Laws of Nature
- Kant, Immanuel: Aesthetics and Teleology
- Kant, Immanuel: Ethics
- Kant, Immanuel: Theoretical Philosophy
- Kierkegaard, Søren
- Knowledge
- Knowledge-first Epistemology
- Knowledge-How
- Kristeva, Julia
- Kuhn, Thomas S.
- Lacan, Jacques
- Lakatos, Imre
- Langer, Susanne
- Language of Thought
- Language, Philosophy of
- Latin American Philosophy
- Laws of Nature
- Legal Epistemology
- Legal Philosophy
- Legal Positivism
- Leibniz, Gottfried Wilhelm
- Levinas, Emmanuel
- Lewis, C. I.
- Liberty
- Literature, Philosophy of
- Locke, John
- Locke, John: Identity, Persons, and Personal Identity
- Logic
- Lottery and Preface Paradoxes, The
- Lucretius
- Machiavelli, Niccolò
- Martin Heidegger: Later Works
- Martin Heidegger: Middle Works
- Marx, Karl
- Material Constitution
- Mathematical Explanation
- Mathematical Pluralism
- Mathematical Structuralism
- Mathematics, Ontology of
- Mathematics, Philosophy of
- Mathematics, Visual Thinking in
- McDowell, John
- McTaggart, John
- Meaning of Life, The
- Mechanisms in Science
- Medically Assisted Dying
- Medicine, Contemporary Philosophy of
- Medieval Logic
- Medieval Philosophy
- Memory
- Mental Causation
- Mereology
- Merleau-Ponty, Maurice
- Meta-epistemological Skepticism
- Metaepistemology
- Metaethics
- Metametaphysics
- Metaphilosophy
- Metaphor
- Metaphysical Grounding
- Metaphysics, Contemporary
- Metaphysics, Feminist
- Midgley, Mary
- Mill, John Stuart
- Mind, Metaphysics of
- Modal Epistemology
- Modality
- Models and Theories in Science
- Modularity
- Montesquieu
- Moore, G. E.
- Moral Contractualism
- Moral Naturalism and Nonnaturalism
- Moral Responsibility
- Multiculturalism
- Murdoch, Iris
- Music, Analytic Philosophy of
- Nationalism
- Natural Kinds
- Naturalism in the Philosophy of Mathematics
- Naïve Realism
- Neo-Confucianism
- Neuroscience, Philosophy of
- Nietzsche, Friedrich
- Nonexistent Objects
- Normative Ethics
- Normative Foundations, Philosophy of Law:
- Normativity and Social Explanation
- Objectivity
- Occasionalism
- Olfaction
- Ontological Dependence
- Ontology of Art
- Ordinary Objects
- Other Minds
- Pacifism
- Pain
- Panpsychism
- Paradoxes
- Particularism in Ethics
- Pascal, Blaise
- Paternalism
- Patriotism
- Peirce, Charles Sanders
- Perception, Cognition, Action
- Perception, The Problem of
- Perfectionism
- Persistence
- Personal Identity
- Phenomenal Concepts
- Phenomenal Conservatism
- Phenomenology
- Philosophy for Children
- Photography, Analytic Philosophy of
- Physicalism
- Physicalism and Metaphysical Naturalism
- Physics, Experiments in
- Plato
- Plotinus
- Political Epistemology
- Political Obligation
- Political Philosophy
- Popper, Karl
- Pornography and Objectification, Analytic Approaches to
- Practical Knowledge
- Practical Moral Skepticism
- Practical Reason
- Pragmatics
- Pragmatism
- Probabilistic Representations of Belief
- Probability, Interpretations of
- Problem of Divine Hiddenness, The
- Problem of Evil, The
- Propositions
- Psychology, Philosophy of
- Punishment
- Pyrrhonism
- Qualia
- Quietism
- Quine, W. V. O.
- Race
- Racist Jokes
- Rationalism
- Rationality
- Rawls, John: Moral and Political Philosophy
- Realism and Anti-Realism
- Realization
- Reasons in Epistemology
- Reductionism in Biology
- Reference, Theory of
- Reid, Thomas
- Relativism
- Reliabilism
- Religion, Philosophy of
- Religious Belief, Epistemology of
- Religious Experience
- Religious Pluralism
- Ricoeur, Paul
- Rights
- Risk, Philosophy of
- Rorty, Richard
- Rousseau, Jean-Jacques
- Rule-Following
- Russell, Bertrand
- Ryle, Gilbert
- Sartre, Jean-Paul
- Schopenhauer, Arthur
- Science and Religion
- Science, Theoretical Virtues in
- Scientific Explanation
- Scientific Progress
- Scientific Realism
- Scientific Representation
- Scientific Revolutions
- Scotus, Duns
- Self-Knowledge
- Sellars, Wilfrid
- Semantic Externalism
- Semantic Minimalism
- Semiotics
- Seneca
- Senses, The
- Sensitivity Principle in Epistemology
- Shepherd, Mary
- Singular Thought
- Situated Cognition
- Situationism and Virtue Theory
- Skepticism, Contemporary
- Skepticism, History of
- Slurs, Pejoratives, and Hate Speech
- Smith, Adam: Moral and Political Philosophy
- Social Aspects of Scientific Knowledge
- Social Epistemology
- Social Identity
- Sounds and Auditory Perception
- Space and Time
- Speech Acts
- Spinoza, Baruch
- Stebbing, Susan
- Strawson, P. F.
- Structural Realism
- Suicide
- Supererogation
- Supervenience
- Tarski, Alfred
- Technology, Philosophy of
- Testimony, Epistemology of
- Theoretical Terms in Science
- Thomas Aquinas' Philosophy of Religion
- Thought Experiments
- Time and Tense
- Time Travel
- Toleration
- Torture
- Transcendental Arguments
- Tropes
- Trust
- Truth
- Truth and the Aim of Belief
- Truthmaking
- Turing Test
- Two-Dimensional Semantics
- Understanding
- Uniqueness and Permissiveness in Epistemology
- Utilitarianism
- Vagueness
- Value of Knowledge
- Vienna Circle
- Virtue Epistemology
- Virtue Ethics
- Virtues, Epistemic
- Virtues, Intellectual
- Voluntarism, Doxastic
- War
- Weakness of Will
- Weil, Simone
- Well-Being
- William of Ockham
- Williams, Bernard
- Wisdom
- Wittgenstein, Ludwig: Early Works
- Wittgenstein, Ludwig: Later Works
- Wittgenstein, Ludwig: Middle Works
- Wollstonecraft, Mary