In philosophy, an antinomy (; Ancient Greek: antí 'against' + nómos 'law') is a real or apparent contradiction between two conclusions, both of which seem justified. It is a term used in logic and epistemology, particularly in the philosophy of Immanuel Kant.
The argument from free will, also called the paradox of free will or theological fatalism, contends that omniscience and free will are incompatible and that any conception of God that incorporates both properties is therefore inconceivable. See the various controversies over claims of God's omniscience, in particular the critical notion of foreknowledge.
The Ross–Littlewood paradox (also known as the balls and vase problem or the ping pong ball problem) is a hypothetical problem in abstract mathematics and logic designed to illustrate the paradoxical, or at least non-intuitive, nature of infinity. More specifically, like the Thomson's lamp paradox, the Ross–Littlewood paradox tries to illustrate the conceptual difficulties with the notion of a supertask, in which an
The barbershop paradox was proposed by Lewis Carroll in a three-page essay titled 'A Logical Paradox', which appeared in the July 1894 issue of Mind. The name comes from the 'ornamental' short story that Carroll uses in the article to illustrate the paradox.
Bentley's paradox (named after Richard Bentley) points to a problem occurring when Newton's theory of gravitation is applied to cosmology. This cosmological paradox states that if all the stars are drawn to each other by gravitation, they should collapse into a single point.
The 'Big Book' is a thought experiment developed by Ludwig Wittgenstein about the nature of ethics and the verifiability of ethical knowledge. This account is given by him in an early work, the 1929 Lecture on Ethics, and it matches also his position given in the early Tractatus Logico-Philosophicus (Proposition 6.41).
In linguistic morphology, the bracketing paradox concerns morphologically complex words which have more than one analysis, or bracketing, e.g., one for phonology and one for semantics, and the two are not compatible, or brackets do not align.
A catch-22 is a paradoxical situation from which an individual cannot escape because of contradictory rules or limitations. The term was first used by Joseph Heller in his 1961 novel Catch-22.
In social choice theory, Condorcet's voting paradox (also called Condorcet's paradox or the Condorcet paradox) is a fundamental discovery by the Marquis de Condorcet that majority rule is inherently self-contradictory. The result implies that it is logically impossible for any voting system to guarantee that a winner will have support from a majority of voters; for example, there can be rock-paper-scissors scenarios
In traditional logic, a contradiction involves a proposition conflicting either with itself or established fact. It is often used as a tool to detect disingenuous beliefs and bias.
The crocodile paradox, also known as crocodile sophism, is a paradox in logic in the same family of paradoxes as the liar paradox. The premise states that a crocodile, who has stolen a child, promises the parent that their child will be returned if and only if they correctly predict what the crocodile will do next.
Curry's paradox is a paradox in which an arbitrary claim F is proved from the mere existence of a sentence C that says of itself 'If C, then F'. The paradox requires only a few apparently-innocuous logical deduction rules.
Deductive reasoning is the process of drawing valid inferences. An inference is valid if its conclusion follows logically from its premises, meaning that it is impossible for the premises to be true and the conclusion to be false.
The drinker paradox (also known as the drinker's theorem, the drinker's principle, or the drinking principle) is a theorem of classical predicate logic that can be stated as 'There is someone in the pub such that, if he or she is drinking, then everyone in the pub is drinking.' It was popularised by the mathematical logician Raymond Smullyan, who called it the 'drinking principle' in his 1978 book What Is the Name of
The Epicurean paradox is a logical dilemma about the problem of evil attributed to the Greek philosopher Epicurus, who argued against the existence of a god who is simultaneously omniscient, omnipotent, and omnibenevolent.
The so-called Epimenides paradox has to do with self-reference in logic. It is named after the Cretan philosopher Epimenides of Knossos (alive circa 600 BC) who said: 'Cretans, liars always, evil beasts, idle bellies'.
A paradox is a logically self-contradictory statement or a statement that runs contrary to one's expectation. It is a statement that, despite apparently valid reasoning from true or apparently true premises, leads to a seemingly self-contradictory or a logically unacceptable conclusion.
Fitch's paradox of knowability is a puzzle of epistemic logic. It provides a challenge to the knowability thesis, which states that every truth is, in principle, knowable.
The French paradox is an apparently paradoxical epidemiological observation that French people have a relatively low incidence of coronary heart disease (CHD), while having a diet relatively rich in saturated fats, in apparent contradiction to the widely held belief that the high consumption of such fats is a risk factor for CHD. The paradox is that if the thesis linking saturated fats to CHD is valid, the French oug
The new riddle of induction was presented by Nelson Goodman in Fact, Fiction, and Forecast as a successor to Hume's original problem. It presents the logical predicates grue and bleen which are unusual due to their time-dependence.
The Hispanic paradox is an epidemiological finding that Hispanic Americans tend to have health outcomes that paradoxically are comparable to, or in some cases better than, those of their U.S. non-Hispanic White counterparts, even though Hispanics have lower average income and education, higher rates of disability, as well as a higher incidence of various cardiovascular risk factors and metabolic diseases. Low socioec
Hormesis is a two-phased dose-response relationship whereby low-dose exposures have a beneficial effect and high-dose amounts are either inhibitory to function or toxic. Within the hormetic zone, the biological response to low-dose amounts of some stressors is generally favorable.
Inferences are steps in logical reasoning, moving from premises to logical consequences; etymologically, the word infer means to 'carry forward'. Inference is theoretically traditionally divided into deduction and induction, a distinction that dates at least to Aristotle (300s BC).
The Israeli paradox was an apparently paradoxical epidemiological observation that Israeli Jews have a relatively high incidence of coronary heart disease (CHD), despite having a diet relatively low in saturated fats, in apparent contradiction to the widely held belief that the high consumption of such fats is a risk factor for CHD. The paradox was that if the thesis linking saturated fats to CHD is valid, the Israel
In economics, the Jevons paradox, or Jevons effect, is said to occur when technological improvements that increase the efficiency of a resource's use lead to a rise, rather than a fall, in total consumption of that resource. Greater efficiency reduces the amount of the resource needed per application, lowering its effective cost; if demand is sufficiently price elastic, this induces demand such that the per-unit savi
In mathematics, the Kleene–Rosser paradox is a paradox that shows that certain systems of formal logic are inconsistent, in particular the version of Haskell Curry's combinatory logic introduced in 1930, and Alonzo Church's original lambda calculus, introduced in 1932–1933, both originally intended as systems of formal logic. The paradox was exhibited by Stephen Kleene and J. B. Rosser in 1935.
In philosophy and logic, the classical liar paradox or liar's paradox or antinomy of the liar is the statement of a liar that they are lying: for instance, declaring that 'I am lying'. If the liar is indeed lying, then the liar is telling the truth, which means the liar just lied.
The liberal paradox, also Sen paradox or Sen's paradox, is a logical paradox proposed by Amartya Sen which shows that no means of aggregating individual preferences into a single, social choice, can simultaneously fulfill the following, seemingly mild conditions: The unrestrictedness condition, or U: every possible ranking of each individual's preferences and all outcomes of every possible voting rule will be conside
The psychology of eating meat is an area of study seeking to illuminate the confluence of morality, emotions, cognition, and personality characteristics in the phenomenon of the consumption of meat. Research into the psychological and cultural factors of meat-eating suggests correlations with masculinity, support for hierarchical values, and reduced openness to experience.
In logic and probability theory, two events (or propositions) are mutually exclusive or disjoint if they cannot both occur at the same time. A clear example is the set of outcomes of a single coin toss, which can result in either heads or tails, but not both.
In logic and mathematics, necessity and sufficiency are terms used to describe a conditional or implicational relationship between two statements. For example, in the conditional statement: 'If P then Q', Q is necessary for P, because the truth of Q is 'necessarily' guaranteed by the truth of P. (Equivalently, it is impossible to have P without Q, or the falsity of Q ensures the falsity of P.) Similarly, P is suffici
The new riddle of induction was presented by Nelson Goodman in Fact, Fiction, and Forecast as a successor to Hume's original problem. It presents the logical predicates grue and bleen which are unusual due to their time-dependence.
The omnipotence paradox is a family of paradoxes that arise with some understandings of the term omnipotent. The paradox arises, for example, if one assumes that an omnipotent being has no limits and is capable of realizing any outcome, even a logically contradictory one such as creating a square circle.
A paradox is a logically self-contradictory statement or a statement that runs contrary to one's expectation. It is a statement that, despite apparently valid reasoning from true or apparently true premises, leads to a seemingly self-contradictory or a logically unacceptable conclusion.
Free choice is a phenomenon in natural language where a linguistic disjunction appears to receive a logical conjunctive interpretation when it interacts with a modal operator. For example, the following English sentences can be interpreted to mean that the addressee can watch a movie and that they can also play video games, depending on their preference: You can watch a movie or play video games.
This article contains a discussion of paradoxes of set theory. As with most mathematical paradoxes, they generally reveal surprising and counter-intuitive mathematical results, rather than actual logical contradictions within modern axiomatic set theory.
Understood in a narrow sense, philosophical logic is the area of logic that studies the application of logical methods to philosophical problems, often in the form of extended logical systems like modal logic. Some theorists conceive of philosophical logic in a broader sense as the study of the scope and nature of logic in general.
Philosophy of logic is the branch of philosophy that studies the scope and nature of logic. It investigates the philosophical problems raised by logic, such as the presuppositions often implicitly at work in theories of logic and in their application.
The Pinocchio paradox arises in the hypothetical situation when Pinocchio says 'My nose will grow' and is a version of the liar paradox. The liar paradox is defined in philosophy and logic as the statement 'This sentence is false.' Any attempts to assign a classical binary truth value to this statement lead to a contradiction, or paradox.
In logic, reductio ad absurdum (Latin for 'reduction to absurdity'), also known as argumentum ad absurdum, (Latin for 'argument to absurdity') apagogical argument, or proof by contradiction is the form of argument that attempts to establish a claim by showing that following the logic of a contrary proposition or argument would lead to absurdity or contradiction. Although it is quite freely used in mathematical proofs
A puzzle is a game, problem, or toy that tests a person's ingenuity or knowledge. In a puzzle, the solver is expected to put pieces together (or take them apart) in a logical way, in order to find the solution of the puzzle.
In logic, reductio ad absurdum (Latin for 'reduction to absurdity'), also known as argumentum ad absurdum, (Latin for 'argument to absurdity') apagogical argument, or proof by contradiction is the form of argument that attempts to establish a claim by showing that following the logic of a contrary proposition or argument would lead to absurdity or contradiction. Although it is quite freely used in mathematical proofs
The region-beta paradox is the phenomenon that people can sometimes recover more quickly from more distressing experiences than from less distressing ones. The hypothesized reason is that intense states trigger psychological defense processes that reduce the distress, while less intense states do not trigger the same psychological defense processes and, therefore, less effective attenuation of the stress occurs.
In logic, Richard's paradox is a semantical antinomy of set theory and natural language first described by the French mathematician Jules Richard in 1905. The paradox is ordinarily used to motivate the importance of distinguishing carefully between mathematics and metamathematics.
The Ross–Littlewood paradox (also known as the balls and vase problem or the ping pong ball problem) is a hypothetical problem in abstract mathematics and logic designed to illustrate the paradoxical, or at least non-intuitive, nature of infinity. More specifically, like the Thomson's lamp paradox, the Ross–Littlewood paradox tries to illustrate the conceptual difficulties with the notion of a supertask, in which an
Imperative logic is the field of logic concerned with imperatives. In contrast to declaratives, it is not clear whether imperatives denote propositions or more generally what role truth and falsity play in their semantics.
In mathematical logic, Russell's paradox (also known as Russell's antinomy) is a set-theoretic paradox published by the British philosopher and mathematician, Bertrand Russell, in 1901. Russell's paradox shows that every set theory that contains an unrestricted comprehension principle leads to contradictions.
Quantitative structure–activity relationship (QSAR) models are regression or classification models used in the chemical and biological sciences and engineering. In QSAR regression models relate a set of 'predictor' variables (X) to the potency of the response variable (Y), while classification QSAR models relate the predictor variables to a categorical value of the response variable.
Science fiction (often shortened to sci-fi or abbreviated SF) is the genre of speculative, science-based fiction that imagines advanced and futuristic scientific or technological progress. The elements of science fiction have evolved over time: from space exploration, extraterrestrial life, time travel, and robotics; to parallel universes, dystopian societies, and biological manipulations; and, most lately, to inform
The self-absorption paradox describes the contradictory association whereby higher levels of self-awareness are simultaneously associated with higher levels of psychological distress and with psychological well-being. In 1999 Trapnell and Campbell explored the self-absorption paradox in relation to private self-consciousness or attention to internal aspects of the self.
Self-reference is a concept that involves referring to oneself or one's own attributes, characteristics, or actions. It can occur in language, logic, mathematics, philosophy, and other fields.
In mathematical logic and philosophy, Skolem's paradox is the apparent contradiction that a countable model of first-order set theory could contain an uncountable set. The paradox arises from part of the Löwenheim–Skolem theorem; Thoralf Skolem was the first to discuss the seemingly contradictory aspects of the theorem, and to discover the relativity of set-theoretic notions now known as non-absoluteness.
Tarski's undefinability theorem, stated and proved by Alfred Tarski in 1933, is an important limitative result in mathematical logic, the foundations of mathematics, and in formal semantics. Informally, the theorem states that 'arithmetical truth cannot be defined in arithmetic'.
The term boundary paradox refers to the conflict between traditional, rank-based classification of life and evolutionary thinking. In the hierarchy of ranked categories it is implicitly assumed that the morphological gap is growing along with increasing ranks: two species from the same genus are more similar than other two species from different genera in the same family, these latter two species are more similar tha
The Temperature paradox or Partee's paradox is a classic puzzle in formal semantics and philosophical logic. Formulated by Barbara Partee in the 1970s, it consists of the following argument, which speakers of English judge as wildly invalid.
Twin Earth is a thought experiment proposed by philosopher Hilary Putnam in his papers 'Meaning and Reference' (1973) and 'The Meaning of 'Meaning'' (1975). It is meant to serve as an illustration of his argument for semantic externalism, or the view that the meanings of words are not purely psychological.
In logic, specifically in deductive reasoning, an argument is valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. It is not required for a valid argument to have premises that are actually true, but to have premises that, if they were true, would guarantee the truth of the argument's conclusion.
A paradox is a logically self-contradictory statement or a statement that runs contrary to one's expectation. It is a statement that, despite apparently valid reasoning from true or apparently true premises, leads to a seemingly self-contradictory or a logically unacceptable conclusion.
In social choice theory, Condorcet's voting paradox (also called Condorcet's paradox or the Condorcet paradox) is a fundamental discovery by the Marquis de Condorcet that majority rule is inherently self-contradictory. The result implies that it is logically impossible for any voting system to guarantee that a winner will have support from a majority of voters; for example, there can be rock-paper-scissors scenarios
What the Tortoise Said to Achilles', written by Lewis Carroll in 1895 for the philosophical journal Mind, is a brief allegorical dialogue on the foundations of logic. The title alludes to one of Zeno's paradoxes of motion, in which Achilles could never overtake the tortoise in a race.