A

A System of Logic ''A System of Logic, Ratiocinative and Inductive'' is an 1843 book by English philosopher John Stuart Mill. Overview In this work, he formulated the five principles of inductive reasoning that are known as Mill's Methods. This work is important ...

A priori and a posteriori ("from the earlier") and ("from the later") are Latin phrases used in philosophy to distinguish types of knowledge, justification, or argument by their reliance on empirical evidence or experience. knowledge is independent from current ...

-- Abacus logic -- Abduction (logic) -- Abductive validation -- Academia Analitica -- Accuracy and precision -- Ad captandum -- Ad hoc hypothesis -- Ad hominem --

Affine logic Affine logic is a substructural logic whose proof theory rejects the structural rule of contraction. It can also be characterized as linear logic with weakening. The name "affine logic" is associated with linear logic, to which it differs by all ...

-- Affirming the antecedent --

Affirming the consequent Affirming the consequent, sometimes called converse error, fallacy of the converse, or confusion of necessity and sufficiency, is a formal fallacy of taking a true conditional statement (e.g., "If the lamp were broken, then the room would be dar ...

-- Algebraic logic -- Ambiguity --

Analysis Analysis ( : analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (3 ...

-- Analysis (journal) -- Analytic reasoning --

Analytic–synthetic distinction The analytic–synthetic distinction is a semantic distinction, used primarily in philosophy to distinguish between propositions (in particular, statements that are affirmative subject–predicate judgments) that are of two types: analytic propos ...

Anangeon Anangeon ( grc-gre, ἀναγκαῖον, "necessary"), also known as dicaeologia (, "a plea in defense"),
is a specious method ...

-- Anecdotal evidence --

Antecedent (logic) An antecedent is the first half of a hypothetical proposition, whenever the if-clause precedes the then-clause. In some contexts the antecedent is called the ''protasis''. Examples: * If P, then Q. This is a nonlogical formulation of a hypotheti ...

-- Antepredicament --

Anti-psychologism In logic, anti-psychologism (also logical objectivism or logical realism) is a theory about the nature of logical truth, that it does not depend upon the contents of human ideas but exists independent of human ideas. Overview The anti-psychologisti ...

-- Antinomy --

Apophasis Apophasis (; , ) is a rhetorical device wherein the speaker or writer brings up a subject by either denying it, or denying that it should be brought up. Accordingly, it can be seen as a rhetorical relative of irony. The device is also called p ...

-- Appeal to probability --

Appeal to ridicule Appeal to ridicule (also called appeal to mockery, ''ad absurdo'', or the horse laugh) is an informal fallacy which presents an opponent's argument as absurd, ridiculous, or humorous, and therefore not worthy of serious consideration. Appeal to ...

-- Archive for Mathematical Logic -- Arché -- Argument -- Argument by example -- Argument form --

Argument from authority An argument from authority (''argumentum ab auctoritate''), also called an appeal to authority, or argumentum ad verecundiam, is a form of argument in which the opinion of an authority on a topic is used as evidence to support an argument. Some con ...

Argument map An argument map or argument diagram is a visual representation of the structure of an argument. An argument map typically includes the key components of the argument, traditionally called the '' conclusion'' and the ''premises'', also called ''con ...

Argumentation theory Argumentation theory, or argumentation, is the interdisciplinary study of how conclusions can be supported or undermined by premises through logical reasoning. With historical origins in logic, dialectic, and rhetoric, argumentation theory, incl ...

Argumentum ad baculum ''Argumentum ad baculum'' (Latin for "argument to the cudgel" or "appeal to the stick") is the fallacy committed when one makes an appeal to force to bring about the acceptance of a conclusion.John Woods: ''Argumentum ad baculum.'' In: ''Argume ...

Argumentum e contrario In logic, an ' (Latin: 'argument from the contrary'; also ''a contrario'' or ''ex contrario''https://tieteentermipankki.fi/wiki/Oikeustiede:vastakohtaisp%C3%A4%C3%A4telm%C3%A4), also known as appeal from the contrary, denotes any proposition that ...

-- Ariadne's thread (logic) -- Aristotelian logic --

Aristotle Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of ph ...

-- Association for Informal Logic and Critical Thinking -- Association for Logic, Language and Information --

Association for Symbolic Logic The Association for Symbolic Logic (ASL) is an international organization of specialists in mathematical logic and philosophical logic. The ASL was founded in 1936, and its first president was Alonzo Church. The current president of the ASL is ...

Attacking Faulty Reasoning ''Attacking Faulty Reasoning'' is a textbook on logical fallacies by T. Edward Damer that has been used for many years in a number of college courses on logic, critical thinking, argumentation, and philosophy. It explains 60 of the most commonl ...

-- Australasian Association for Logic -- Axiom -- Axiom independence --

Axiom of reducibility The axiom of reducibility was introduced by Bertrand Russell in the early 20th century as part of his ramified theory of types. Russell devised and introduced the axiom in an attempt to manage the contradictions he had discovered in his analysis ...

Axiomatic system In mathematics and logic, an axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems. A theory is a consistent, relatively-self-contained body of knowledge which usually contains ...

-- Axiomatization --

B

Backward chaining --

Barcan formula In quantified modal logic, the Barcan formula and the converse Barcan formula (more accurately, schemata rather than formulas) (i) syntactically state principles of interchange between quantifiers and modalities; (ii) semantically state a relation ...

-- Begging the question --

Begriffsschrift ''Begriffsschrift'' (German for, roughly, "concept-script") is a book on logic by Gottlob Frege, published in 1879, and the formal system set out in that book. ''Begriffsschrift'' is usually translated as ''concept writing'' or ''concept notatio ...

Belief A belief is an attitude that something is the case, or that some proposition is true. In epistemology, philosophers use the term "belief" to refer to attitudes about the world which can be either true or false. To believe something is to take ...

Belief bias Belief bias is the tendency to judge the strength of arguments based on the plausibility of their conclusion rather than how strongly they support that conclusion. A person is more likely to accept an argument that supports a conclusion that alig ...

Belief revision Belief revision is the process of changing beliefs to take into account a new piece of information. The logical formalization of belief revision is researched in philosophy, in databases, and in artificial intelligence for the design of rational ag ...

Benson Mates Benson Mates (May 19, 1919 in Portland, Oregon – May 14, 2009 in Berkeley, California) was an American philosopher, noted for his work in logic, the history of philosophy, and skepticism. Mates studied philosophy and mathematics at the Un ...

-- Bertrand Russell Society --

Biconditional elimination Biconditional elimination is the name of two valid rules of inference of propositional logic. It allows for one to infer a conditional from a biconditional. If P \leftrightarrow Q is true, then one may infer that P \to Q is true, and also th ...

Biconditional introduction In propositional calculus, propositional logic, biconditional introductionCopi and Cohen is a Validity (logic), valid rule of inference. It allows for one to inference, infer a Logical biconditional, biconditional from two Material conditional, ...

-- Bivalence and related laws -- Blue and Brown Books -- Boole's syllogistic -- Boolean algebra (logic) -- Boolean algebra (structure) -- Boolean network --

C

Canonical form In mathematics and computer science, a canonical, normal, or standard form of a mathematical object is a standard way of presenting that object as a mathematical expression. Often, it is one which provides the simplest representation of an ...

-- Canonical form (Boolean algebra) --

Cartesian circle The Cartesian circle is a potential mistake in reasoning attributed to French philosopher René Descartes. The argument Descartes argues – for example, in the third of his '' Meditations on First Philosophy'' – that whatever one clearly and ...

Case-based reasoning In artificial intelligence and philosophy, case-based reasoning (CBR), broadly construed, is the process of solving new problems based on the solutions of similar past problems. In everyday life, an auto mechanic who fixes an engine by recallin ...

Categorical logic __NOTOC__ Categorical logic is the branch of mathematics in which tools and concepts from category theory are applied to the study of mathematical logic. It is also notable for its connections to theoretical computer science. In broad terms, categ ...

Categories (Aristotle) The ''Categories'' ( Greek Κατηγορίαι ''Katēgoriai''; Latin ''Categoriae'' or ''Praedicamenta'') is a text from Aristotle's '' Organon'' that enumerates all the possible kinds of things that can be the subject or the predicate of a p ...

Categories (Peirce) On May 14, 1867, the 27–year-old Charles Sanders Peirce, who eventually founded pragmatism, presented a paper entitled " On a New List of Categories" to the American Academy of Arts and Sciences. Among other things, this paper outlined a theory ...

Category mistake A category mistake, or category error, or categorical mistake, or mistake of category, is a semantic or ontological error in which things belonging to a particular category are presented as if they belong to a different category, or, alternativ ...

Catuṣkoṭi ''Catuṣkoṭi'' (Sanskrit; Devanagari: चतुष्कोटि, , Sinhalese:චතුස්කෝටිකය) is a logical argument(s) of a 'suite of four discrete functions' or 'an indivisible quaternity' that has multiple applications an ...

-- Circular definition -- Circular reasoning --

Circular reference A circular reference is a series of references where the last object references the first, resulting in a closed loop. In language A circular reference is not to be confused with the logical fallacy of a circular argument. Although a circula ...

Circular reporting Circular reporting, or false confirmation, is a situation in source criticism where a piece of information appears to come from multiple independent sources, but in reality comes from only one source. In many cases, the problem happens mistaken ...

Circumscription (logic) Circumscription is a non-monotonic logic created by John McCarthy to formalize the common sense assumption that things are as expected unless otherwise specified. Circumscription was later used by McCarthy in an attempt to solve the frame probl ...

-- Circumscription (taxonomy) -- Classical logic --

Clocked logic In computing, the clock rate or clock speed typically refers to the frequency at which the clock generator of a processor can generate pulses, which are used to synchronize the operations of its components, and is used as an indicator of the pro ...

-- Cognitive bias --

Cointerpretability In mathematical logic, cointerpretability is a binary relation on formal theories: a formal theory ''T'' is cointerpretable in another such theory ''S'', when the language of ''S'' can be translated into the language of ''T'' in such a way that ''S ...

-- Colorless green ideas sleep furiously --

Combinational logic In automata theory, combinational logic (also referred to as time-independent logic or combinatorial logic) is a type of digital logic which is implemented by Boolean circuits, where the output is a pure function of the present input only. This ...

-- Combinatory logic -- Combs method -- Common knowledge (logic) -- Commutativity of conjunction --

Completeness (logic) In mathematical logic and metalogic, a formal system is called complete with respect to a particular property (philosophy), property if every Well-formed formula, formula having the property can be formal proof, derived using that system, i.e. is ...

Composition of Causes The Composition of Causes was a set of philosophical laws advanced by John Stuart Mill in his watershed essay ''A System of Logic''. These laws outlined Mill's view of the epistemological components of emergentism, a school of philosophical laws ...

-- Compossibility -- Comprehension (logic) -- Computability logic --

Concept Concepts are defined as abstract ideas. They are understood to be the fundamental building blocks of the concept behind principles, thoughts and beliefs. They play an important role in all aspects of cognition. As such, concepts are studied by ...

Conceptualism In metaphysics, conceptualism is a theory that explains universality of particulars as conceptualized frameworks situated within the thinking mind. Intermediate between nominalism and realism, the conceptualist view approaches the metaphysical co ...

-- Condensed detachment -- Conditional disjunction --

Conditional probability In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event (by assumption, presumption, assertion or evidence) has already occurred. This particular method relies on event B occu ...

Conditional proof A conditional proof is a proof that takes the form of asserting a conditional, and proving that the antecedent of the conditional necessarily leads to the consequent. Overview The assumed antecedent of a conditional proof is called the conditio ...

-- Conditional quantifier -- Confirmation bias --

Conflation Conflation is the merging of two or more sets of information, texts, ideas, opinions, etc., into one, often in error. Conflation is often misunderstood. It originally meant to fuse or blend, but has since come to mean the same as equate, treati ...

-- Confusion of the inverse --

Conjunction elimination In propositional logic, conjunction elimination (also called ''and'' elimination, ∧ elimination, or simplification)Hurley is a valid immediate inference, argument form and rule of inference which makes the inference that, if the conjunction ' ...

Conjunction fallacy The conjunction fallacy (also known as the Linda problem) is an inference from an array of particulars, in violation of the laws of probability, that a conjoint set of two or more conclusions is likelier than any single member of that same set. It ...

Conjunction introduction Conjunction introduction (often abbreviated simply as conjunction and also called and introduction or adjunction) is a valid rule of inference of propositional logic. The rule makes it possible to introduce a conjunction into a logical proof. I ...

Conjunctive normal form In Boolean logic, a formula is in conjunctive normal form (CNF) or clausal normal form if it is a conjunction of one or more clauses, where a clause is a disjunction of literals; otherwise put, it is a product of sums or an AND of ORs. As a cano ...

Connexive logic Connexive logic names one class of alternative, or non-classical, logics designed to exclude the paradoxes of material implication. The characteristic that separates connexive logic from other non-classical logics is its acceptance of Aristotle's t ...

-- Connotation --

Consequent A consequent is the second half of a hypothetical proposition. In the standard form of such a proposition, it is the part that follows "then". In an implication, if ''P'' implies ''Q'', then ''P'' is called the antecedent and ''Q'' is called ...

Consistency In classical deductive logic, a consistent theory is one that does not lead to a logical contradiction. The lack of contradiction can be defined in either semantic or syntactic terms. The semantic definition states that a theory is consistent ...

Constructive dilemma Constructive dilemmaCopi and Cohen is a valid rule of inference of propositional logic. It is the inference that, if ''P'' implies ''Q'' and ''R'' implies ''S'' and either ''P'' or ''R'' is true, then either ''Q or S'' has to be true. In sum, ...

-- Contra principia negantem non est disputandum --

Contradiction In traditional logic, a contradiction occurs when a proposition conflicts either with itself or established fact. It is often used as a tool to detect disingenuous beliefs and bias. Illustrating a general tendency in applied logic, Aristotle's ...

Contrapositive In logic and mathematics, contraposition refers to the inference of going from a conditional statement into its logically equivalent contrapositive, and an associated proof method known as proof by contraposition. The contrapositive of a statem ...

Control logic Control logic is a key part of a software program that controls the operations of the program. The control logic responds to commands from the user, and it also acts on its own to perform automated tasks that have been structured into the program. ...

Conventionalism Conventionalism is the philosophical attitude that fundamental principles of a certain kind are grounded on (explicit or implicit) agreements in society, rather than on external reality. Unspoken rules play a key role in the philosophy's structur ...

Converse (logic) In logic and mathematics, the converse of a categorical or implicational statement is the result of reversing its two constituent statements. For the implication ''P'' → ''Q'', the converse is ''Q'' → ''P''. For the categorical propositi ...

-- Converse Barcan formula -- Correlative-based fallacies --

Counterexample A counterexample is any exception to a generalization. In logic a counterexample disproves the generalization, and does so rigorously in the fields of mathematics and philosophy. For example, the fact that "John Smith is not a lazy student" is a ...

Counterfactual conditional Counterfactual conditionals (also ''subjunctive'' or ''X-marked'') are conditional sentences which discuss what would have been true under different circumstances, e.g. "If Peter believed in ghosts, he would be afraid to be here." Counterfactua ...

Counterintuitive 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 premises, leads to a seemingly self-contradictory or a logically u ...

Cratylism Cratylism as a philosophical theory reflects the teachings of the Athenian Cratylus ( grc, Κρατύλος, also transliterated as Kratylos), fl. mid to late 5th century BCE. Cratylism holds that there is a natural relationship between words and w ...

-- Credibility --

Criteria of truth In epistemology, criteria of truth (or tests of truth) are standards and rules used to judge the accuracy of statements and claims. They are tools of verification, and as in the problem of the criterion, the reliability of these tools is disputed ...

-- Critical-Creative Thinking and Behavioral Research Laboratory --

Critical pedagogy Critical pedagogy is a philosophy of education and social movement that developed and applied concepts from critical theory and related traditions to the field of education and the study of culture. It insists that issues of social justice and de ...

Critical reading Critical reading is a form of language analysis that does not take the given text at face value, but involves a deeper examination of the claims put forth as well as the supporting points and possible counterarguments. The ability to reinterpret ...

-- Critical thinking -- Critique of Pure Reason --

Curry's paradox 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''", requiring only a few apparently innocuous logical deduction rules. Since ''F'' is arbi ...

-- Cyclic negation --

D

Dagfinn Føllesdal Dagfinn Føllesdal (born 22 June 1932) is a Norwegian-American philosopher. He is the Clarence Irving Lewis Professor of Philosophy Emeritus at Stanford University, and professor emeritus at the University of Oslo. Biography and career Følles ...

-- De Interpretatione --

De Morgan's laws In propositional logic and Boolean algebra, De Morgan's laws, also known as De Morgan's theorem, are a pair of transformation rules that are both valid rules of inference. They are named after Augustus De Morgan, a 19th-century British math ...

Decidability (logic) In logic, a true/false decision problem is decidable if there exists an effective method for deriving the correct answer. Zeroth-order logic (propositional logic) is decidable, whereas first-order and higher-order logic are not. Logical systems ar ...

-- Decidophobia -- Decision making --

Decisional balance sheet A decisional balance sheet or decision balance sheet is a tabular method for representing the pros and cons of different choices and for helping someone decide what to do in a certain circumstance. It is often used in working with ambivalence in p ...

Deductive closure In mathematical logic, a set of logical formulae is deductively closed if it contains every formula that can be logically deduced from , formally: if always implies . If is a set of formulae, the deductive closure of is its smallest superse ...

Deduction theorem In mathematical logic, a deduction theorem is a metatheorem that justifies doing conditional proofs—to prove an implication ''A'' → ''B'', assume ''A'' as an hypothesis and then proceed to derive ''B''—in systems that do not have an ...

-- Deductive fallacy -- Deductive reasoning --

Default logic Default logic is a non-monotonic logic proposed by Raymond Reiter to formalize reasoning with default assumptions. Default logic can express facts like “by default, something is true”; by contrast, standard logic can only express that somethi ...

-- Defeasible logic --

Defeasible reasoning In philosophical logic, defeasible reasoning is a kind of reasoning that is rationally compelling, though not deductive reasoning, deductively valid. It usually occurs when a rule is given, but there may be specific exceptions to the rule, or su ...

Definable set In mathematical logic, a definable set is an ''n''-ary relation on the domain of a structure whose elements satisfy some formula in the first-order language of that structure. A set can be defined with or without parameters, which are elements ...

Definist fallacy The definist fallacy (sometimes called the Socratic fallacy, after Socrates)William J. Prior, "Plato and the 'Socratic Fallacy'", ''Phronesis'' 43(2) (1998), pp. 97–113. is a logical fallacy, identified by William Frankena in 1939, that involves ...

-- Definition -- Definitions of logic -- Degree of truth --

Denying the antecedent Denying the antecedent, sometimes also called inverse error or fallacy of the inverse, is a formal fallacy of inferring the inverse from the original statement. It is committed by reasoning in the form: :If ''P'', then ''Q''. :Therefore, if not ...

-- Denying the correlative --

Deontic logic Deontic logic is the field of philosophical logic that is concerned with obligation, permission, and related concepts. Alternatively, a deontic logic is a formal system that attempts to capture the essential logical features of these concepts. It ...

Description Description is the pattern of narrative development that aims to make vivid a place, object, character, or group. Description is one of four rhetorical modes (also known as ''modes of discourse''), along with exposition, argumentation, and narra ...

-- Description logic -- Descriptive fallacy --

Deviant logic Deviant logic is a type of logic incompatible with classical logic. Philosopher Susan Haack uses the term ''deviant logic'' to describe certain non-classical systems of logic. In these logics: * the set of well-formed formulas generated equals th ...

Dharmakirti Dharmakīrti (fl. c. 6th or 7th century; Tibetan: ཆོས་ཀྱི་གྲགས་པ་; Wylie: ''chos kyi grags pa''), was an influential Indian Buddhist philosopher who worked at Nālandā.Tom Tillemans (2011)Dharmakirti Stanford ...

-- Diagrammatic reasoning --

Dialectica ''Dialectica'' is a quarterly philosophy journal published by Blackwell between 2004 and 2019. As of 2020, Dialectica is published in full open access. The journal was founded in 1947 by Gaston Bachelard, Paul Bernays and Ferdinand Gonseth. ...

Dialectica space Dialectica spaces are a categorical way of constructing models of linear logic. They were introduced by Valeria de Paiva, Martin Hyland's student, in her doctoral thesis, as a way of modeling both linear logic and Gödel's Dialectica interpretat ...

Dialetheism Dialetheism (from Greek 'twice' and 'truth') is the view that there are statements that are both true and false. More precisely, it is the belief that there can be a true statement whose negation is also true. Such statements are called "true ...

-- Dichotomy --

Difference (philosophy) Difference is a key concept of philosophy, denoting the process or set of properties by which one entity is distinguished from another within a relational field or a given conceptual system. In the Western philosophical system, difference is trad ...

-- Digital timing diagram --

Dignāga Dignāga (a.k.a. ''Diṅnāga'', c. 480 – c. 540 CE) was an Indian Buddhist scholar and one of the Buddhist founders of Indian logic (''hetu vidyā''). Dignāga's work laid the groundwork for the development of deductive logic in India and ...

Dilemma A dilemma ( grc-gre, δίλημμα "double proposition") is a problem offering two possibilities, neither of which is unambiguously acceptable or preferable. The possibilities are termed the ''horns'' of the dilemma, a clichéd usage, but dist ...

Disjunction elimination In propositional logic, disjunction elimination (sometimes named proof by cases, case analysis, or or elimination), is the valid argument form and rule of inference that allows one to eliminate a disjunctive statement from a logical proof. It ...

Disjunction introduction Disjunction introduction or addition (also called or introduction) is a rule of inference of propositional logic and almost every other deduction system. The rule makes it possible to introduce disjunctions to logical proofs. It is the infer ...

Disjunctive normal form In boolean logic, a disjunctive normal form (DNF) is a canonical normal form of a logical formula consisting of a disjunction of conjunctions; it can also be described as an OR of ANDs, a sum of products, or (in philosophical logic) a ''cluster c ...

Disjunctive syllogism In classical logic, disjunctive syllogism (historically known as ''modus tollendo ponens'' (MTP), Latin for "mode that affirms by denying") is a valid argument form which is a syllogism having a disjunctive statement for one of its premise ...

-- Dispositional and occurrent belief --

Disquotational principle The disquotational principle is a philosophical principle which holds that a rational speaker will accept "''p''" if and only if he or she believes ''p''. The quotes indicate that the statement ''p'' is being treated as a sentence, and not as a ...

-- Dissoi logoi -- Division of Logic, Methodology, and Philosophy of Science --

Don't-care term In digital logic, a don't-care term (abbreviated DC, historically also known as ''redundancies'', ''irrelevancies'', ''optional entries'', ''invalid combinations'', ''vacuous combinations'', ''forbidden combinations'', ''unused states'' or ''l ...

Donald Davidson (philosopher) Donald Herbert Davidson (March 6, 1917 – August 30, 2003) was an American philosopher. He served as Slusser Professor of Philosophy at the University of California, Berkeley, from 1981 to 2003 after having also held teaching appointments a ...

-- Double counting (fallacy) --

Double negation In propositional logic, double negation is the theorem that states that "If a statement is true, then it is not the case that the statement is not true." This is expressed by saying that a proposition ''A'' is logically equivalent to ''not (not ...

-- Double negative --

Double negation elimination In propositional logic, double negation is the theorem that states that "If a statement is true, then it is not the case that the statement is not true." This is expressed by saying that a proposition ''A'' is logically equivalent to ''not (not ...

Doxa Doxa (; from verb ) Liddell, Henry George, and Robert Scott. 1940.δοκέω" In ''A Greek-English Lexicon'', edited by H. S. Jones and R. McKenzie. Oxford. Clarendon Press. – via Perseus Project. is a common belief or popular opinion. In cla ...

Drinking the Kool-Aid "Drinking the Kool-Aid" is an expression used to refer to a person who believes in a possibly doomed or dangerous idea because of perceived potential high rewards. The phrase typically carries a negative connotation. It can also be used ironicall ...

E

EL++ --

Ecological fallacy An ecological fallacy (also ecological ''inference'' fallacy or population fallacy) is a formal fallacy in the interpretation of statistical data that occurs when inferences about the nature of individuals are deduced from inferences about the g ...

Effective method In logic, mathematics and computer science, especially metalogic and computability theory, an effective method Hunter, Geoffrey, ''Metalogic: An Introduction to the Metatheory of Standard First-Order Logic'', University of California Press, 1971 or ...

Elimination rule In logic and proof theory, natural deduction is a kind of proof calculus in which logical reasoning is expressed by inference rules closely related to the "natural" way of reasoning. This contrasts with Hilbert-style systems, which instead use axio ...

Emotional reasoning Emotional reasoning is a cognitive process by which an individual concludes that their emotional reaction proves something is true, despite contrary empirical evidence. Emotional reasoning creates an 'emotional truth', which may be in direct c ...

-- Emotions in decision-making --

Empty name In metaphysics and the philosophy of language, an empty name is a proper name that has no referent. The problem of empty names is the idea that empty names have a meaning when it seems they should not have. The name " Pegasus" is empty; there is ...

Encyclopedia of the Philosophical Sciences The ''Encyclopaedia of the Philosophical Sciences'' (abbreviated as ''EPS'' or simply ''Encyclopaedia''; german: Enzyklopädie der philosophischen Wissenschaften im Grundrisse, ''EPW'', translated as ''Encyclopedia of the Philosophical Sciences ...

-- End term --

Engineered language Engineered languages (often abbreviated to engelangs, or, less commonly, engilangs) are constructed languages devised to test or prove some hypotheses about how languages work or might work. There are at least three subcategories, philosophical ...

Entailment Logical consequence (also entailment) is a fundamental concept in logic, which describes the relationship between statements that hold true when one statement logically ''follows from'' one or more statements. A valid logical argument is one ...

Entitative graph An entitative graph is an element of the diagrammatic syntax for logic that Charles Sanders Peirce developed under the name of qualitative logic beginning in the 1880s, taking the coverage of the formalism only as far as the propositional or ...

-- Enumerative definition -- Epicureanism --

Epilogism Epilogism is a style of inference used by the ancient Empiric school of medicine. It is a theory-free method that looks at history through the accumulation of facts without major generalization and with consideration of the consequences of making ca ...

Epistemic closure Epistemic closure is a property of some belief systems. It is the principle that if a subject S knows p, and S knows that p entails q, then S can thereby come to know q. Most epistemological theories involve a closure principle and many skepti ...

Equisatisfiability In Mathematical logic (a subtopic within the field of formal logic), two formulae are equisatisfiable if the first formula is satisfiable whenever the second is and vice versa; in other words, either both formulae are satisfiable or both are not. E ...

Erotetics Erotetics or erotetic logic is a part of logic, devoted to logical analysis of questions. It is sometimes called the logic of questions and answers. Overview The idea was originally developed by Richard Whately. For example, he noted the ambiguity ...

-- Eternal statement --

Etymological fallacy An etymological fallacy is committed when an argument makes a claim about the present meaning of a word based exclusively on that word's etymology. It is a genetic fallacy that holds a word's historical meaning to be its sole valid meaning and th ...

European Summer School in Logic, Language and Information The European Summer School in Logic, Language and Information (ESSLLI) is an annual academic conference organized by the European Association for Logic, Language and Information. The focus of study is the "interface between linguistics, logic and ...

-- Evidence --

Exclusive nor Logical equality is a logical operator that corresponds to equality in Boolean algebra and to the logical biconditional in propositional calculus. It gives the functional value ''true'' if both functional arguments have the same logical val ...

Exclusive or Exclusive or or exclusive disjunction is a logical operation that is true if and only if its arguments differ (one is true, the other is false). It is symbolized by the prefix operator J and by the infix operators XOR ( or ), EOR, EXOR, , ...

Existential fallacy The existential fallacy, or existential instantiation, is a formal fallacy. In the existential fallacy, one presupposes that a class has members when one is not supposed to do so; i.e., when one should not assume existential import. Not to be c ...

Existential graph An existential graph is a type of diagrammatic or visual notation for logical expressions, proposed by Charles Sanders Peirce, who wrote on graphical logic as early as 1882,Peirce, C. S., " n Junctures and Fractures in Logic (editors' title for ...

Existential quantification In predicate logic, an existential quantification is a type of quantifier, a logical constant which is interpreted as "there exists", "there is at least one", or "for some". It is usually denoted by the logical operator symbol ∃, which, ...

-- Expert --

Explanandum An explanandum (a Latin term) is a sentence describing a phenomenon that is to be explained, and the explanans are the sentences adduced as explanations of that phenomenon. For example, one person may pose an ''explanandum'' by asking "Why is there ...

Explanation An explanation is a set of statements usually constructed to describe a set of facts which clarifies the causes, context, and consequences of those facts. It may establish rules or laws, and may clarify the existing rules or laws in relatio ...

Explanatory power Explanatory power is the ability of a hypothesis or theory to explain the subject matter effectively to which it pertains. Its opposite is ''explanatory impotence''. In the past, various criteria or measures for explanatory power have been prop ...

Extension (semantics) In any of several fields of study that treat the use of signs — for example, in linguistics, logic, mathematics, semantics, semiotics, and philosophy of language — the extension of a concept, idea, or sign consists of the things to which it app ...

-- Extensional context -- Extensional definition --

F

Fa (concept) Fa (;) is a concept in Chinese philosophy that covers ethics, logic, and law. It can be translated as "law" in some contexts, but more often as "model" or "standard." First gaining importance in the Mohist school of thought, the concept was princip ...

-- Fact -- Fallacies of definition -- Fallacy -- Fallacy of distribution --

Fallacy of four terms The fallacy of four terms ( la, quaternio terminorum) is the formal fallacy that occurs when a syllogism has four (or more) terms rather than the requisite three, rendering it invalid. Definition Categorical syllogisms always have three terms: ...

Fallacy of quoting out of context Quoting out of context (sometimes referred to as contextomy or quote mining) is an informal fallacy in which a passage is removed from its surrounding matter in such a way as to distort its intended meaning. Contextomies may be either intentional o ...

-- Fallacy of the four terms --

False attribution False attribution can refer to: * Misattribution in general, when a quotation or work is accidentally, traditionally, or based on bad information attributed to the wrong person or group * A specific fallacy where an advocate appeals to an irrelevan ...

-- False dilemma --

False equivalence False equivalence is an informal fallacy in which an equivalence is drawn between two subjects based on flawed or false reasoning. This fallacy is categorized as a fallacy of inconsistency. Colloquially, a false equivalence is often called "com ...

False premise A false premise is an incorrect proposition that forms the basis of an argument or syllogism. Since the premise (proposition, or assumption) is not correct, the conclusion drawn may be in error. However, the logical validity of an argument is ...

Fictionalism Fictionalism is the view in philosophy according to which statements that appear to be descriptions of the world should not be construed as such, but should instead be understood as cases of "make believe", of pretending to treat something as liter ...

Finitary relation In mathematics, a finitary relation over sets is a subset of the Cartesian product ; that is, it is a set of ''n''-tuples consisting of elements ''x'i'' in ''X'i''. Typically, the relation describes a possible connection between the elemen ...

-- Finite model property --

First-order logic First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantifie ...

First-order predicate In mathematical logic, a first-order predicate is a predicate that takes only individual(s) constants or variables as argument(s).. Compare second-order predicate and higher-order predicate. This is not to be confused with a one-place predicate o ...

First-order predicate calculus First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quan ...

First-order resolution In mathematical logic and automated theorem proving, resolution is a rule of inference leading to a refutation complete theorem-proving technique for sentences in propositional logic and first-order logic. For propositional logic, systematically ...

Fitch-style calculus Fitch notation, also known as Fitch diagrams (named after Frederic Fitch), is a notational system for constructing formal proofs used in sentential logics and predicate logics. Fitch-style proofs arrange the sequence of sentences that make up the ...

Fluidic logic Fluidics, or fluidic logic, is the use of a fluid to perform analog or digital operations similar to those performed with electronics. The physical basis of fluidics is pneumatics and hydraulics, based on the theoretical foundation of fluid dyn ...

Fluidics Fluidics, or fluidic logic, is the use of a fluid to perform analog or digital operations similar to those performed with electronics. The physical basis of fluidics is pneumatics and hydraulics, based on the theoretical foundation of fluid dyna ...

Formal fallacy In philosophy, a formal fallacy, deductive fallacy, logical fallacy or non sequitur (; Latin for " tdoes not follow") is a pattern of reasoning rendered invalid by a flaw in its logical structure that can neatly be expressed in a standard logic syst ...

Formal ontology In philosophy, the term formal ontology is used to refer to an ontology defined by axioms in a formal language with the goal to provide an unbiased (domain- and application-independent) view on reality, which can help the modeler of domain- or a ...

Formal system A formal system is an abstract structure used for inferring theorems from axioms according to a set of rules. These rules, which are used for carrying out the inference of theorems from axioms, are the logical calculus of the formal system. A form ...

Formalism (philosophy) The term ''formalism'' describes an emphasis on form over content or meaning in the arts, literature, or philosophy. A practitioner of formalism is called a ''formalist''. A formalist, with respect to some discipline, holds that there is no transc ...

Forward chaining Forward chaining (or forward reasoning) is one of the two main methods of reasoning when using an inference engine and can be described logically as repeated application of ''modus ponens''. Forward chaining is a popular implementation strategy ...

-- Free logic --

Free variables and bound variables In mathematics, and in other disciplines involving formal languages, including mathematical logic and computer science, a free variable is a notation (symbol) that specifies places in an expression where substitution may take place and is not ...

-- Function and Concept -- Fuzzy logic --

G

Game semantics Game semantics (german: dialogische Logik, translated as ''dialogical logic'') is an approach to Formal semantics (logic), formal semantics that grounds the concepts of truth or Validity (logic), validity on game theory, game-theoretic concepts, su ...

-- Ganto's Ax -- Geometry of interaction -- Gilles-Gaston Granger --

Gongsun Long Gongsun Long (, BCLiu 2004, p. 336), courtesy name Zibing (子秉), was a Chinese philosopher and writer who was a member of the School of Names (Logicians) of ancient Chinese philosophy. He also ran a school and enjoyed the support of rulers, ...

-- Grammaticality --

Greedy reductionism Greedy reductionism, identified by Daniel Dennett, in his 1995 book ''Darwin's Dangerous Idea'', is a kind of erroneous reductionism. Whereas "good" reductionism means explaining a thing in terms of what it reduces to (for example, its parts and t ...

Grundlagen der Mathematik ''Grundlagen der Mathematik'' (English: ''Foundations of Mathematics'') is a two-volume work by David Hilbert and Paul Bernays. Originally published in 1934 and 1939, it presents fundamental mathematical ideas and introduced second-order arithme ...

H

HPO formalism --

Halo effect The halo effect (sometimes called the halo error) is the tendency for positive impressions of a person, company, brand, or product in one area to positively influence one's opinion or feelings in other areas. Halo effect is “the name given to t ...

Handbook of Automated Reasoning The ''Handbook of Automated Reasoning'' (, 2128 pages) is a collection of survey articles on the field of automated reasoning. Published in June 2001 by MIT Press, it is edited by John Alan Robinson and Andrei Voronkov. Volume 1 describes methods ...

-- Hanlon's razor --

Hasty generalization A faulty generalization is an informal fallacy wherein a conclusion is drawn about all or many instances of a phenomenon on the basis of one or a few instances of that phenomenon. It is similar to a proof by example in mathematics. It is an examp ...

Herbrandization {{Short description, Proof of Herbrand's theorem The Herbrandization of a logical formula (named after Jacques Herbrand) is a construction that is dual to the Skolemization of a formula. Thoralf Skolem had considered the Skolemizations of formul ...

-- Hetucakra --

Heyting algebra In mathematics, a Heyting algebra (also known as pseudo-Boolean algebra) is a bounded lattice (with join and meet operations written ∨ and ∧ and with least element 0 and greatest element 1) equipped with a binary operation ''a'' → ''b'' of '' ...

-- Higher-order predicate --

Higher-order thinking Higher-order thinking, known as higher order thinking skills (HOTS), is a concept of education reform based on learning taxonomies (such as Bloom's taxonomy). The idea is that some types of learning require more cognitive processing than others, ...

Historian's fallacy The historian's fallacy is an informal fallacy that occurs when one assumes that decision makers of the past viewed events from the same perspective and having the same information as those subsequently analyzing the decision. It is not to be confu ...

-- Historical fallacy --

History of logic The history of logic deals with the study of the development of the science of valid inference (logic). Formal logics developed in ancient times in India, China, and Greece. Greek methods, particularly Aristotelian logic (or term logic) as found ...

History of the function concept The mathematical concept of a function emerged in the 17th century in connection with the development of the calculus; for example, the slope \operatorname\!y/\operatorname\!x of a graph at a point was regarded as a function of the ''x''-coordina ...

Hold come what may Hold come what may is a phrase popularized by logician Willard Van Orman Quine. Beliefs that are "held come what may" are beliefs one is unwilling to give up, regardless of any evidence with which one might be presented. Quine held that any belief ...

Homunculus argument The homunculus argument is an informal fallacy whereby a concept is explained in terms of the concept itself, recursion, recursively, without first defining or explaining the original concept. This fallacy arises most commonly in the theory of ...

Horn clause In mathematical logic and logic programming, a Horn clause is a logical formula of a particular rule-like form which gives it useful properties for use in logic programming, formal specification, and model theory. Horn clauses are named for the log ...

-- Hume's fork --

Hume's principle Hume's principle or HP says that the number of ''F''s is equal to the number of ''G''s if and only if there is a one-to-one correspondence (a bijection) between the ''F''s and the ''G''s. HP can be stated formally in systems of second-order logic. ...

Hypothetical syllogism In classical logic, a hypothetical syllogism is a valid argument form, a syllogism with a conditional statement for one or both of its premises. An example in English: :If I do not wake up, then I cannot go to work. :If I cannot go to work, then ...

I

Identity (philosophy) --

Identity of indiscernibles The identity of indiscernibles is an ontological principle that states that there cannot be separate objects or entities that have all their properties in common. That is, entities ''x'' and ''y'' are identical if every predicate possessed by ''x'' ...

Idola fori ''Idola fori'' (singular ''Idolum fori''), sometimes translated as "Idols of the Market Place" or "Idols of the Forum", are a category of logical fallacy which results from the imperfect correspondences between the word definitions in human lang ...

Idola specus ''Idola specus'' (singular ''Idolum specus''), normally translated as "Idols of the Cave" (or "Idols of the Den"), is a type of logical fallacy whereby the peculiar biases of individuals lead them to errors. This Latin term was coined by Sir Fra ...

Idola theatri ''Idola theatri'' (singular ''Idolum theatri'') is a type of tendency towards logical fallacy or error, normally translated as "idols of the theatre". The Latin was coined by Sir Francis Bacon in his ''Novum Organum''—one of the earliest t ...

Idola tribus ''Idola tribus'' (singular ''Idolum tribus'') is a category of logical fallacy, normally translated as "Idols of the Tribe", which refers to a tendency of human nature to prefer certain types of incorrect conclusions. It is a Latin term, coined ...

If-by-whiskey Noah S. "Soggy" Sweat Jr. (October 2, 1922February 23, 1996) was an American judge, law professor, and state representative in Mississippi, notable for his 1952 speech on the floor of the Mississippi state legislature concerning whiskey. Reporte ...

Iff In logic and related fields such as mathematics and philosophy, "if and only if" (shortened as "iff") is a biconditional logical connective between statements, where either both statements are true or both are false. The connective is bicon ...

Illicit major Illicit major is a formal fallacy committed in a categorical syllogism that is invalid because its major term is undistributed in the major premise but distributed in the conclusion. This fallacy has the following argument form: #''All A are B' ...

Illicit minor Illicit minor is a formal fallacy committed in a categorical syllogism that is invalid because its minor term is undistributed in the minor premise but distributed in the conclusion. This fallacy has the following argument form: :All A are B. : ...

Illuminationism Illuminationism (Persian حكمت اشراق ''hekmat-e eshrāq'', Arabic: حكمة الإشراق ''ḥikmat al-ishrāq'', both meaning "Wisdom of the Rising Light"), also known as ''Ishrāqiyyun'' or simply ''Ishrāqi'' (Persian اشراق, Arab ...

-- Immutable truth --

Imperative logic 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. Thus, there is almost n ...

-- Implicant --

Inclusion (logic) In logic and mathematics, inclusion is the concept that all the contents of one object are also contained within a second object. For example, if ''m'' and ''n'' are two logical matrix, logical matrices, then :m \subset n \quad \text \quad \forall ...

-- Incomplete comparison -- Inconsistent comparison -- Inconsistent triad --

Independence-friendly logic Independence-friendly logic (IF logic; proposed by Jaakko Hintikka and in 1989) is an extension of classical first-order logic (FOL) by means of slashed quantifiers of the form (\exists v/V) and (\forall v/V), where V is a finite set of variables. ...

Indian logic The development of Indian logic dates back to the ''anviksiki'' of Medhatithi Gautama (c. 6th century BCE); the Sanskrit grammar rules of Pāṇini (c. 5th century BCE); the Vaisheshika school's analysis of atomism (c. 6th century BCE to 2nd centu ...

Inductive logic Inductive reasoning is a method of reasoning in which a general principle is derived from a body of observations. It consists of making broad generalizations based on specific observations. Inductive reasoning is distinct from ''deductive'' rea ...

-- Inductive logic programming -- Inference -- Inference procedure --

Inference rule In the philosophy of logic, a rule of inference, inference rule or transformation rule is a logical form consisting of a function which takes premises, analyzes their syntax, and returns a conclusion (or conclusions). For example, the rule of ...

-- Inferential role semantics --

Infinitary logic An infinitary logic is a logic that allows infinitely long statements and/or infinitely long proofs. Some infinitary logics may have different properties from those of standard first-order logic. In particular, infinitary logics may fail to be co ...

Infinite regress An infinite regress is an infinite series of entities governed by a recursive principle that determines how each entity in the series depends on or is produced by its predecessor. In the epistemic regress, for example, a belief is justified beca ...

-- Infinity --

Informal fallacy Informal fallacies are a type of incorrect argument in natural language. The source of the error is not just due to the ''form'' of the argument, as is the case for formal fallacies, but can also be due to their ''content'' and ''context''. Fall ...

-- Informal logic -- Inquiry -- Inquiry (philosophy journal) --

Insolubilia In the Middle Ages, variations on the liar paradox were studied under the name of ''insolubilia'' ("insolubles"). Overview Although the liar paradox was well known in antiquity, interest seems to have lapsed until the twelfth century, when it ap ...

Institute for Logic, Language and Computation The Institute for Logic, Language and Computation (ILLC) is a research institute of the University of Amsterdam, in which researchers from the Faculty of Science and the Faculty of Humanities collaborate. The ILLC's central research area is the st ...

Intellectual responsibility Intellectual responsibility (also known as epistemic responsibility) is a philosophical concept related to that of epistemic justification. According to Frederick F. Schmitt, "the conception of justified belief as epistemically responsible belief h ...

Intended interpretation An interpretation is an assignment of meaning to the symbols of a formal language. Many formal languages used in mathematics, logic, and theoretical computer science are defined in solely syntactic terms, and as such do not have any meaning until ...

-- Intension -- Intensional fallacy --

Intensional logic Intensional logic is an approach to predicate logic that extends first-order logic, which has quantifiers that range over the individuals of a universe (''extensions''), by additional quantifiers that range over terms that may have such individuals ...

Intensional statement In linguistics, logic, philosophy, and other fields, an intension is any property or quality connoted by a word, phrase, or another symbol. In the case of a word, the word's definition often implies an intension. For instance, the intensions o ...

-- Intentional Logic --

Intermediate logic In mathematical logic, a superintuitionistic logic is a propositional logic extending intuitionistic logic. Classical logic is the strongest consistent superintuitionistic logic; thus, consistent superintuitionistic logics are called intermediate l ...

Interpretability In mathematical logic, interpretability is a relation between formal theories that expresses the possibility of interpreting or translating one into the other. Informal definition Assume ''T'' and ''S'' are formal theories. Slightly simplified, '' ...

Interpretability logic Interpretability logics comprise a family of modal logics that extend provability logic to describe interpretability or various related metamathematical properties and relations such as weak interpretability, Π1-conservativity, cointerpretability ...

-- Interpretive discussion -- Introduction rule -- Introduction to Mathematical Philosophy -- Intuitionistic linear logic --

Intuitionistic logic Intuitionistic logic, sometimes more generally called constructive logic, refers to systems of symbolic logic that differ from the systems used for classical logic by more closely mirroring the notion of constructive proof. In particular, systems ...

-- Invalid proof --

Inventor's paradox The inventor's paradox is a phenomenon that occurs in seeking a solution to a given problem. Instead of solving a specific type of problem, which would seem intuitively easier, it can be easier to solve a more general problem, which covers the spec ...

Inverse (logic) In logic, an inverse is a type of conditional sentence which is an immediate inference made from another conditional sentence. More specifically, given a conditional sentence of the form P \rightarrow Q , the inverse refers to the sentence \neg P ...

-- Inverse consequences --

Irreducibility In philosophy, systems theory, science, and art, emergence occurs when an entity is observed to have properties its parts do not have on their own, properties or behaviors that emerge only when the parts interact in a wider whole. Emergence ...

-- Is Logic Empirical? --

Isagoge The ''Isagoge'' ( el, Εἰσαγωγή, ''Eisagōgḗ''; ) or "Introduction" to Aristotle's "Categories", written by Porphyry in Greek and translated into Latin by Boethius, was the standard textbook on logic for at least a millennium after his ...

-- Ivor Grattan-Guinness --

J

Jacobus Naveros --

Jayanta Bhatta Jayanta Bhatta ( CE – CE) was a Kashmiri poet, teacher, logician, and an advisor to King Sankaravarman. He was a philosopher of the Nyaya school of Hindu philosophy. He authored three works on Nyāya philosophy: one of which is not known ...

-- Jingle-jangle fallacies --

John Corcoran (logician) John Corcoran ( ; 20 March 1937 - 8 January 2021) was an American logician, philosopher, mathematician, and historian of logic. He is best known for his philosophical work on concepts such as the nature of inference, relations between condition ...

-- John W. Dawson, Jr -- Journal of Applied Non-Classical Logics -- Journal of Automated Reasoning --

Journal of Logic, Language and Information The ''Journal of Logic, Language and Information'' is a quarterly peer-reviewed academic journal covering research on "natural, formal, and programming languages". It is the official journal of the European Association for Logic, Language and Infor ...

-- Journal of Logic and Computation --

Journal of Mathematical Logic The ''Journal of Mathematical Logic'' was established in 2001 and is published by World Scientific. It covers the field of mathematical logic and its applications. Abstracting and indexing The journal is abstracted and indexed in: * Current Math ...

Journal of Philosophical Logic The ''Journal of Philosophical Logic'' is a bimonthly peer-reviewed academic journal covering all aspects of logic. It was established in 1972 and is published by Springer Science+Business Media. The editors-in-chief are Rosalie Iemhoff (Utrecht ...

Journal of Symbolic Logic The '' Journal of Symbolic Logic'' is a peer-reviewed mathematics journal published quarterly by Association for Symbolic Logic. It was established in 1936 and covers mathematical logic. The journal is indexed by ''Mathematical Reviews'', Zentralb ...

Judgment (mathematical logic) In mathematical logic, a judgment (or judgement) or assertion is a statement or enunciation in a metalanguage. For example, typical judgments in first-order logic would be ''that a string is a well-formed formula'', or ''that a proposition is tru ...

Judgmental language Judgmental language is a subset of red herring fallacies. It employs insulting, compromising or pejorative language to influence the recipient's judgment. Examples :''The surgeon general says that smoking is harmful to your health. Nowhere in t ...

Just-so story In science and philosophy, a just-so story is an untestable narrative explanation for a cultural practice, a biological trait, or behavior of humans or other animals. The pejorative nature of the expression is an implicit criticism that remind ...

K

Karnaugh map The Karnaugh map (KM or K-map) is a method of simplifying Boolean algebra expressions. Maurice Karnaugh introduced it in 1953 as a refinement of Edward W. Veitch's 1952 Veitch chart, which was a rediscovery of Allan Marquand's 1881 ''logi ...

-- Kinetic logic --

Knowing and the Known ''Knowing and the Known'' is a 1949 book by John Dewey and Arthur Bentley. Overview As well as a Preface, an Introduction and an Index, the book consists of 12 chapters, or papers, as the authors call them in their introduction. Chapters 1 (Vag ...

Kripke semantics Kripke semantics (also known as relational semantics or frame semantics, and often confused with possible world semantics) is a formal semantics for non-classical logic systems created in the late 1950s and early 1960s by Saul Kripke and André Jo ...

Kurt Gödel Society The Kurt Gödel Society was founded in Vienna, Austria in 1987. It is an international organization aimed at promoting research primarily on logic, philosophy and the history of mathematics, with special attention to connections with Kurt Gödel, ...

L

Language Language is a structured system of communication. The structure of a language is its grammar and the free components are its vocabulary. Languages are the primary means by which humans communicate, and may be conveyed through a variety of ...

Language, Proof and Logic Language, Proof and Logic is an educational software package, devised and written by Jon Barwise and John Etchemendy, geared to teaching formal logic through the use of a tight integration between a textbook (same name as the package) and four sof ...

Lateral thinking Lateral thinking is a manner of solving problems using an indirect and creative approach via reasoning that is not immediately obvious. It involves ideas that may not be obtainable using only traditional step-by-step logic. The term was first u ...

Law of excluded middle In logic, the law of excluded middle (or the principle of excluded middle) states that for every proposition, either this proposition or its negation is true. It is one of the so-called three laws of thought, along with the law of noncontradi ...

Law of identity In logic, the law of identity states that each thing is identical with itself. It is the first of the historical three laws of thought, along with the law of noncontradiction, and the law of excluded middle. However, few systems of logic are bui ...

Law of non-contradiction In logic, the law of non-contradiction (LNC) (also known as the law of contradiction, principle of non-contradiction (PNC), or the principle of contradiction) states that contradictory propositions cannot both be true in the same sense at the sa ...

Law of noncontradiction In logic, the law of non-contradiction (LNC) (also known as the law of contradiction, principle of non-contradiction (PNC), or the principle of contradiction) states that contradictory propositions cannot both be true in the same sense at the sa ...

Law of thought The laws of thought are fundamental axiomatic rules upon which rational discourse itself is often considered to be based. The formulation and clarification of such rules have a long tradition in the history of philosophy and logic. Generally they ...

Laws of Form ''Laws of Form'' (hereinafter ''LoF'') is a book by G. Spencer-Brown, published in 1969, that straddles the boundary between mathematics and philosophy. ''LoF'' describes three distinct logical systems: * The "primary arithmetic" (described in C ...

-- Laws of logic --

Leap of faith A leap of faith, in its most commonly used meaning, is the act of believing in or accepting something outside the boundaries of reason. Overview The phrase is commonly attributed to Søren Kierkegaard; however, he never used the term, as he ...

Lemma (logic) In mathematics, informal logic and argument mapping, a lemma (plural lemmas or lemmata) is a generally minor, proven proposition which is used as a stepping stone to a larger result. For that reason, it is also known as a "helping theorem" or ...

Lexical definition The lexical definition of a term, also known as the dictionary definition, is the definition closely matching the meaning of the term in common usage. As its other name implies, this is the sort of definition one is likely to find in the dictiona ...

-- Linear logic -- Linguistic and Philosophical Investigations --

Linguistics and Philosophy ''Linguistics and Philosophy'' is a peer-reviewed journal addressing "structure and meaning in natural language". This journal, along with '' Studies in Language'', is a continuation of the journal ''Foundations of Language'' (1965 to 1976). The ...

List of fallacies A fallacy is reasoning that is logically invalid, or that undermines the logical validity of an argument. All forms of human communication can contain fallacies. Because of their variety, fallacies are challenging to classify. They can be classif ...

-- List of incomplete proofs -- List of logic journals --

List of paradoxes This list includes well known paradoxes, grouped thematically. The grouping is approximate, as paradoxes may fit into more than one category. This list collects only scenarios that have been called a paradox by at least one source and have their ...

Logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premise ...

Logic Lane __NOTOC__ Logic Lane is a small historic cobbled lane that runs through University College in Oxford, England, so called because it was the location of a school of logicians. It links the High Street at the front of the college with Merton Str ...

-- Logic Spectacles -- Logic gate --

Logic in China Formal logic in China has a special place in the history of logic due to its length of and relative isolation to the strong ancient adoption and continued current of development of the study of logic in Europe, India, and the Islamic world. Mohis ...

Logic in Islamic philosophy Early Islamic law placed importance on formulating standards of argument, which gave rise to a "novel approach to logic" ( ''manṭiq'' "speech, eloquence") in Kalam (Islamic scholasticism). However, with the rise of the Mu'tazili philosophers, wh ...

-- Logic of class --

Logic of information The logic of information, or the logical theory of information, considers the information content of logical signs and expressions along the lines initially developed by Charles Sanders Peirce. In this line of work, the concept of information serve ...

Logic programming Logic programming is a programming paradigm which is largely based on formal logic. Any program written in a logic programming language is a set of sentences in logical form, expressing facts and rules about some problem domain. Major logic pro ...

Logica Universalis ''Logica Universalis'' is a peer-reviewed academic journal which covers research related to universal logic Originally the expression ''Universal logic'' was coined by analogy with the expression ''Universal algebra''. The first idea was to dev ...

-- Logica nova -- Logical Analysis and History of Philosophy --

Logical Investigations (Husserl) The ''Logical Investigations'' (german: Logische Untersuchungen) (1900–1901; second edition 1913) are a two-volume work by the philosopher Edmund Husserl, in which the author discusses the philosophy of logic and criticizes psychologism, the vie ...

-- Logical Methods in Computer Science -- Logical abacus -- Logical argument --

Logical assertion In mathematical logic, a judgment (or judgement) or assertion is a statement or enunciation in a metalanguage. For example, typical judgments in first-order logic would be ''that a string is a well-formed formula'', or ''that a proposition is tru ...

Logical atomism Logical atomism is a philosophical view that originated in the early 20th century with the development of analytic philosophy. Its principal exponent was the British philosopher Bertrand Russell. It is also widely held that the early works of his ...

Logical biconditional In logic and mathematics, the logical biconditional, sometimes known as the material biconditional, is the logical connective (\leftrightarrow) used to conjoin two statements and to form the statement " if and only if ", where is known as th ...

Logical conditional Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises ...

Logical conjunction In logic, mathematics and linguistics, And (\wedge) is the truth-functional operator of logical conjunction; the ''and'' of a set of operands is true if and only if ''all'' of its operands are true. The logical connective that represents thi ...

Logical constant In logic, a logical constant of a language \mathcal is a symbol that has the same semantic value under every interpretation of \mathcal. Two important types of logical constants are logical connectives and quantifiers. The equality predicate (us ...

Logical disjunction In logic, disjunction is a logical connective typically notated as \lor and read aloud as "or". For instance, the English language sentence "it is raining or it is snowing" can be represented in logic using the disjunctive formula R \lor ...

Logical equality Logical equality is a logical operator that corresponds to equality in Boolean algebra and to the logical biconditional in propositional calculus. It gives the functional value ''true'' if both functional arguments have the same logical valu ...

Logical equivalence In logic and mathematics, statements p and q are said to be logically equivalent if they have the same truth value in every model. The logical equivalence of p and q is sometimes expressed as p \equiv q, p :: q, \textsfpq, or p \iff q, depending o ...

-- Logical extreme --

Logical form In logic, logical form of a statement is a precisely-specified semantic version of that statement in a formal system. Informally, the logical form attempts to formalize a possibly ambiguous statement into a statement with a precise, unambiguou ...

Logical harmony Logical harmony, a name coined by Michael Dummett, is a supposed constraint on the rules of inference that can be used in a given logical system. Overview The logician Gerhard Gentzen proposed that the meanings of logical connectives could be given ...

-- Logical holism --

Logical NAND In Boolean functions and propositional calculus, the Sheffer stroke denotes a logical operation that is equivalent to the negation of the conjunction operation, expressed in ordinary language as "not both". It is also called nand ("not and") or ...

-- Logical NOR --

Logical operator In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a logical constant. They can be used to connect logical formulas. For instance in the syntax of propositional logic, the binary ...

-- Logical quality --

Logical truth Logical truth is one of the most fundamental concepts in logic. Broadly speaking, a logical truth is a statement which is true regardless of the truth or falsity of its constituent propositions. In other words, a logical truth is a statement whic ...

Logicism In the philosophy of mathematics, logicism is a programme comprising one or more of the theses that — for some coherent meaning of 'logic' — mathematics is an extension of logic, some or all of mathematics is reducible to logic, or some or all ...

-- Logico-linguistic modeling --

Logos ''Logos'' (, ; grc, λόγος, lógos, lit=word, discourse, or reason) is a term used in Western philosophy, psychology and rhetoric and refers to the appeal to reason that relies on logic or reason, inductive and deductive reasoning. Ari ...

-- Loosely associated statements -- Łoś–Tarski preservation theorem --

Ludic fallacy The ludic fallacy, proposed by Nassim Nicholas Taleb in his book '' The Black Swan'' ( 2007), is "the misuse of games to model real-life situations". Taleb explains the fallacy as "basing studies of chance on the narrow world of games and dice". ...

-- Lwów–Warsaw school of logic --

M

Main contention --

Major term A syllogism ( grc-gre, συλλογισμός, ''syllogismos'', 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true ...

Markov's principle Markov's principle, named after Andrey Markov Jr, is a conditional existence statement for which there are many equivalent formulations, as discussed below. The principle is logically valid classically, but not in intuitionistic constructive m ...

-- Martin Gardner bibliography --

Masked-man fallacy In philosophical logic, the masked-man fallacy (also known as the intensional fallacy or epistemic fallacy) is committed when one makes an illicit use of Leibniz's law in an argument. Leibniz's law states that if A and B are the same object, the ...

Material conditional The material conditional (also known as material implication) is an operation commonly used in logic. When the conditional symbol \rightarrow is interpreted as material implication, a formula P \rightarrow Q is true unless P is true and Q i ...

Mathematical fallacy In mathematics, certain kinds of mistaken proof are often exhibited, and sometimes collected, as illustrations of a concept called mathematical fallacy. There is a distinction between a simple ''mistake'' and a ''mathematical fallacy'' in a proo ...

Mathematical logic Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of formal ...

Meaning (linguistics) Semantics (from grc, σημαντικός ''sēmantikós'', "significant") is the study of reference, meaning, or truth. The term can be used to refer to subfields of several distinct disciplines, including philosophy, linguistics and comput ...

Meaning (non-linguistic) Non-linguistic (or pre-linguistic) meaning is a type of meaning not mediated or perceived through linguistic signs. In linguistics, the concept is used in discussions about whether such meaning is different from meaning expressed through languag ...

Meaning (philosophy of language) In semantics, semiotics, philosophy of language, metaphysics, and metasemantics, meaning "is a relationship between two sorts of things: signs and the kinds of things they intend, express, or signify". The types of meanings vary according to the ...

-- Meaningless statement --

Megarian school The Megarian school of philosophy, which flourished in the 4th century BC, was founded by Euclides of Megara, one of the pupils of Socrates. Its ethical teachings were derived from Socrates, recognizing a single good, which was apparently combin ...

Mental model theory of reasoning The mental model theory of reasoning was developed by Philip Johnson-Laird and Ruth M.J. Byrne (Johnson-Laird and Byrne, 1991). It has been applied to the main domains of deductive inference including relational inferences such as spatial and temp ...

-- Mereology --

Meta-communication Meta-communication is a secondary communication (including indirect cues) about how a piece of information is meant to be interpreted. It is based on the idea that the same message accompanied by different meta-communication can mean something entir ...

-- Metalanguage --

Metalogic Metalogic is the study of the metatheory of logic. Whereas ''logic'' studies how logical systems can be used to construct valid and sound arguments, metalogic studies the properties of logical systems.Harry GenslerIntroduction to Logic Routledge, ...

-- Metamathematics --

Metasyntactic variable A metasyntactic variable is a specific word or set of words identified as a placeholder in computer science and specifically computer programming. These words are commonly found in source code and are intended to be modified or substituted before ...

Metatheorem In logic, a metatheorem is a statement about a formal system proven in a metalanguage. Unlike theorems proved within a given formal system, a metatheorem is proved within a metatheory, and may reference concepts that are present in the metathe ...

Metavariable In logic, a metavariable (also metalinguistic variable or syntactical variable) is a symbol or symbol string which belongs to a metalanguage and stands for elements of some object language. For instance, in the sentence :''Let A and B be two sente ...

Middle term In logic, a middle term is a term that appears (as a subject or predicate of a categorical proposition) in both premises but not in the conclusion of a categorical syllogism. Example: :Major premise: All men are mortal. :Minor premise A syllogi ...

Minimal axioms for Boolean algebra In mathematical logic, minimal axioms for Boolean algebra are assumptions which are equivalent to the axioms of Boolean algebra (or propositional calculus), chosen to be as short as possible. For example, if one chooses to take commutativity for gra ...

Minimal logic Minimal logic, or minimal calculus, is a symbolic logic system originally developed by Ingebrigt Johansson. It is an intuitionistic and paraconsistent logic, that rejects both the law of the excluded middle as well as the principle of explosion ...

Minor premise A syllogism ( grc-gre, συλλογισμός, ''syllogismos'', 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true ...

-- Miscellanea Logica -- Missing dollar riddle -- Modal fallacy -- Modal fictionalism -- Modal logic -- Model theory -- Modus ponens --

Modus tollens In propositional logic, ''modus tollens'' () (MT), also known as ''modus tollendo tollens'' (Latin for "method of removing by taking away") and denying the consequent, is a deductive argument form and a rule of inference. ''Modus tollens' ...

Moral reasoning Moral reasoning is the study of how people think about right and wrong and how they acquire and apply moral rules. It is a subdiscipline of moral psychology that overlaps with moral philosophy, and is the foundation of descriptive ethics. Descri ...

Motivated reasoning Motivated reasoning is the phenomenon in cognitive science and social psychology in which emotional biases lead to justifications or decisions based on their desirability rather than an accurate reflection of the evidence. It is the "tendency to ...

Moving the goalposts Moving the goalposts (or shifting the goalposts) is a metaphor, derived from goal-based sports, that means to change the rule or criterion (goal) of a process or competition while it is still in progress, in such a way that the new goal offers one ...

Multigrade predicate In mathematics and logic, plural quantification is the theory that an individual variable x may take on ''plural'', as well as singular, values. As well as substituting individual objects such as Alice, the number 1, the tallest building in London ...

Multi-valued logic Many-valued logic (also multi- or multiple-valued logic) refers to a propositional calculus in which there are more than two truth values. Traditionally, in Aristotle's logical calculus, there were only two possible values (i.e., "true" and "false ...

Multiple-conclusion logic A multiple-conclusion logic is one in which logical consequence is a relation, \vdash, between two sets of sentences (or propositions). \Gamma \vdash \Delta is typically interpreted as meaning that whenever each element of \Gamma is true, some ...

Mutatis mutandis ''Mutatis mutandis'' is a Medieval Latin phrase meaning "with things changed that should be changed" or "once the necessary changes have been made". It remains unnaturalized in English and is therefore usually italicized in writing. It is used ...

Mutual knowledge (logic) Mutual knowledge is a fundamental concept about information in game theory, (epistemic) logic, and epistemology. An event is mutual knowledge if all agents know that the event occurred.Osborne, Martin J., and Ariel Rubinstein. ''A Course in Game Th ...

Mutually exclusive events 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 ...

Münchhausen trilemma In epistemology, the Münchhausen trilemma, also commonly known as the Agrippan trilemma, is a thought experiment intended to demonstrate the theoretical impossibility of proving any truth, even in the fields of logic and mathematics, without a ...

N

Naive set theory -- Name -- Narrative logic --

Natural deduction In logic and proof theory, natural deduction is a kind of proof calculus in which logical reasoning is expressed by inference rules closely related to the "natural" way of reasoning. This contrasts with Hilbert-style systems, which instead use ax ...

Natural kind "Natural kind" is an intellectual grouping, or categorizing of things, in a manner that is reflective of the actual world and not just human interests. Some treat it as a classification identifying some structure of truth and reality that exists wh ...

-- Natural language --

Necessary and sufficient 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 then ", is necessary for , because the truth of ...

Necessity and sufficiency 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 then ", is necessary for , because the truth of ...

-- Negation --

Neutrality (philosophy) Neutrality is the tendency not to ''side'' in a conflict (physical or ideological), which may not suggest neutral parties do not have a side or are not a side themselves. In colloquial use ''neutral'' can be synonymous with ''unbiased''. However, ...

Nirvana fallacy The nirvana fallacy is the informal fallacy of comparing actual things with unrealistic, idealized alternatives. It can also refer to the tendency to assume there is a perfect solution to a particular problem. A closely related concept is the "per ...

-- Nixon diamond --

No true Scotsman No True Scotsman, or appeal to purity, is an informal fallacy in which one attempts to protect their universal generalization from a falsifying counterexample by excluding the counterexample improperly.Antony Flew, ''God & Philosophy''p. 104 Hutc ...

-- Nominal identity -- Non-Aristotelian logic --

Non-classical logic Non-classical logics (and sometimes alternative logics) are formal systems that differ in a significant way from standard logical systems such as propositional and predicate logic. There are several ways in which this is done, including by way of ...

Non-monotonic logic A non-monotonic logic is a formal logic whose conclusion relation is not monotonic. In other words, non-monotonic logics are devised to capture and represent defeasible inferences (cf. defeasible reasoning), i.e., a kind of inference in which re ...

-- Non-rigid designator --

Non sequitur (logic) In philosophy, a formal fallacy, deductive fallacy, logical fallacy or non sequitur (; Latin for " tdoes not follow") is a pattern of reasoning rendered invalid by a flaw in its logical structure that can neatly be expressed in a standard logic syst ...

-- Noneism --

Nonfirstorderizability In formal logic, nonfirstorderizability is the inability of a natural-language statement to be adequately captured by a formula of first-order logic. Specifically, a statement is nonfirstorderizable if there is no formula of first-order logic whic ...

-- Nordic Journal of Philosophical Logic -- Normal form (natural deduction) --

Novum Organum The ''Novum Organum'', fully ''Novum Organum, sive Indicia Vera de Interpretatione Naturae'' ("New organon, or true directions concerning the interpretation of nature") or ''Instaurationis Magnae, Pars II'' ("Part II of The Great Instauration ...

-- Nyaya --

Nyāya Sūtras The ''Nyāya Sūtras'' is an ancient Indian Sanskrit text composed by , and the foundational text of the Nyaya school of Hindu philosophy. The date when the text was composed, and the biography of its author is unknown, but variously esti ...

O

Object of the mind An object of the mind is an object that exists in the imagination, but which, in the real world, can only be represented or modeled. Some such objects are abstractions, literary concepts, or fictional scenarios. Closely related are intentional o ...

-- Occam's razor --

On Formally Undecidable Propositions of Principia Mathematica and Related Systems "Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I" ("On Formally Undecidable Propositions of Principia Mathematica and Related Systems I") is a paper in mathematical logic by Kurt Gödel. Submitted November ...

One-sided argument Cherry picking, suppressing evidence, or the fallacy of incomplete evidence is the act of pointing to individual cases or data that seem to confirm a particular position while ignoring a significant portion of related and similar cases or data th ...

Ontological commitment An ontological commitment of a language is one or more objects postulated to exist by that language. The 'existence' referred to need not be 'real', but exist only in a universe of discourse. As an example, legal systems use vocabulary referring t ...

Open sentence An open formula is a formula that contains at least one free variable. An open formula does not have a truth value assigned to it, in contrast with a closed formula which constitutes a proposition and thus can have a truth value like ''true'' or ...

-- Opinion -- Opposing Viewpoints series -- Ordered logic --

Organon The ''Organon'' ( grc, Ὄργανον, meaning "instrument, tool, organ") is the standard collection of Aristotle's six works on logical analysis and dialectic. The name ''Organon'' was given by Aristotle's followers, the Peripatetics. The six ...

Original proof of Gödel's completeness theorem The proof of Gödel's completeness theorem given by Kurt Gödel in his doctoral dissertation of 1929 (and a shorter version of the proof, published as an article in 1930, titled "The completeness of the axioms of the functional calculus of logic" ( ...

-- Osmund Lewry -- Ostensive definition --

Outline of logic Logic is the formal science of using reason and is considered a branch of both philosophy and mathematics and to a lesser extent computer science. Logic investigates and classifies the structure of statements and arguments, both through the stu ...

-- Overbelief --

P

Package-deal fallacy -- Panlogism -- Paraconsistent logic --

Paraconsistent logics A paraconsistent logic is an attempt at a logical system to deal with contradictions in a discriminating way. Alternatively, paraconsistent logic is the subfield of logic that is concerned with studying and developing "inconsistency-tolerant" syste ...

Parade of horribles A parade of horribles can either refer to a type of parade where people wear grotesque costumes, or a rhetorical device where one argues against taking a certain course of action by listing a number of extremely undesirable events that would result ...

Paradox 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 premises, leads to a seemingly self-contradictory or a logically u ...

-- Pars destruens/pars construens --

Pathetic fallacy The phrase pathetic fallacy is a literary term for the attribution of human emotion and conduct to things found in nature that are not human. It is a kind of personification that occurs in poetic descriptions, when, for example, clouds seem sullen ...

Persuasive definition A persuasive definition is a form of stipulative definition which purports to describe the true or commonly accepted meaning of a term, while in reality stipulating an uncommon or altered use, usually to support an argument for some view, or to cr ...

Peter Simons (academic) Peter M. Simons, (born 23 March 1950) is a British philosopher and a retired professor of philosophy at Trinity College Dublin. He is known for his work with Kevin Mulligan and Barry Smith on metaphysics and the history of Austrian philoso ...

Philosophia Mathematica ''Philosophia Mathematica'' is a philosophical journal devoted to the philosophy of mathematics, published by Oxford University Press Oxford University Press (OUP) is the university press of the University of Oxford. It is the largest univers ...

-- Philosophical logic --

Philosophy of logic Philosophy of logic is the area 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 ...

Peirce's law In logic, Peirce's law is named after the philosopher and logician Charles Sanders Peirce. It was taken as an axiom in his first axiomatisation of propositional logic. It can be thought of as the law of excluded middle written in a form that i ...

Plural quantification In mathematics and logic, plural quantification is the theory that an individual variable x may take on ''plural'', as well as singular, values. As well as substituting individual objects such as Alice, the number 1, the tallest building in London ...

Poisoning the well Poisoning the well (or attempting to poison the well) is a type of informal fallacy where adverse information about a target is preemptively presented to an audience, with the intention of discrediting or ridiculing something that the target per ...

Polarity item In linguistics, a polarity item is a lexical item that is associated with affirmation or negation. An affirmation is a positive polarity item, abbreviated PPI or AFF. A negation is a negative polarity item, abbreviated NPI or NEG. The linguisti ...

-- Polish Logic --

Polish notation Polish notation (PN), also known as normal Polish notation (NPN), Łukasiewicz notation, Warsaw notation, Polish prefix notation or simply prefix notation, is a mathematical notation in which operators ''precede'' their operands, in contrast ...

-- Politician's syllogism --

Polychotomous key Polychotomous key refers to the number of alternatives which a decision point may have in a non-temporal hierarchy of independent variables. The number of alternatives are equivalent to the root or nth root of a mathematical or logical variable. D ...

-- Polylogism -- Polysyllogism --

Port-Royal Logic ''Port-Royal Logic'', or ''Logique de Port-Royal'', is the common name of ''La logique, ou l'art de penser'', an important textbook on logic first published anonymously in 1662 by Antoine Arnauld and Pierre Nicole, two prominent members of the Jan ...

Possible world A possible world is a complete and consistent way the world is or could have been. Possible worlds are widely used as a formal device in logic, philosophy, and linguistics in order to provide a semantics for intensional and modal logic. Their me ...

-- Post's lattice -- Post disputation argument --

Post hoc ergo propter hoc ''Post hoc ergo propter hoc'' (Latin: 'after this, therefore because of this') is an informal fallacy that states: "Since event Y ''followed'' event X, event Y must have been ''caused'' by event X." It is often shortened simply to ''post hoc fal ...

-- Posterior Analytics -- Practical syllogism -- Pragmatic mapping --

Pragmatic maxim {{C. S. Peirce articles, abbreviations=no The pragmatic maxim, also known as the maxim of pragmatism or the maxim of pragmaticism, is a maxim of logic formulated by Charles Sanders Peirce. Serving as a normative recommendation or a regulative princ ...

Pragmatic theory of truth A pragmatic theory of truth is a theory of truth within the philosophies of pragmatism and pragmaticism. Pragmatic theories of truth were first posited by Charles Sanders Peirce, William James, and John Dewey. The common features of these theories ...

-- Pramāṇa -- Pramāṇa-samuccaya --

Precising definition A precising definition is a definition that contracts or reduces the scope of the lexical definition of a term for a specific purpose by including additional criteria that narrow down the set of things meeting the definition. For example, a dict ...

-- Precision questioning --

Predicable Predicable (Lat. praedicabilis, that which may be stated or affirmed, sometimes called ''quinque voces'' or ''five words'') is, in scholastic logic, a term applied to a classification of the possible relations in which a predicate may stand to it ...

Predicate (logic) In logic, a predicate is a symbol which represents a property or a relation. For instance, in the first order formula P(a), the symbol P is a predicate which applies to the individual constant a. Similarly, in the formula R(a,b), R is a predicat ...

Predicate abstraction In logic, predicate abstraction is the result of creating a predicate from a sentence. If Q is any formula then the predicate abstract formed from that sentence is (λy.Q), where λ is an abstraction operator and in which every occurrence of y occ ...

Predicate logic First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantifie ...

-- Preferential entailment --

Preintuitionism In the philosophy of mathematics, the pre-intuitionists were a small but influential group who informally shared similar philosophies on the nature of mathematics. The term itself was used by L. E. J. Brouwer, who in his 1951 lectures at Cambridge ...

-- Prescriptivity --

Presentism (literary and historical analysis) In literary and historical analysis, presentism is the anachronistic introduction of present-day ideas and perspectives into depictions or interpretations of the past. Some modern historians seek to avoid presentism in their work because they con ...

-- Presupposition --

Principia Mathematica The ''Principia Mathematica'' (often abbreviated ''PM'') is a three-volume work on the foundations of mathematics written by mathematician–philosophers Alfred North Whitehead and Bertrand Russell and published in 1910, 1912, and 1913. ...

Principle of bivalence In logic, the semantic principle (or law) of bivalence states that every declarative sentence expressing a proposition (of a theory under inspection) has exactly one truth value, either true or false. A logic satisfying this principle is called ...

Principle of explosion In classical logic, intuitionistic logic and similar logical systems, the principle of explosion (, 'from falsehood, anything ollows; or ), or the principle of Pseudo-Scotus, is the law according to which any statement can be proven from a ...

-- Principle of nonvacuous contrast --

Principle of sufficient reason The principle of sufficient reason states that everything must have a reason or a cause. The principle was articulated and made prominent by Gottfried Wilhelm Leibniz, with many antecedents, and was further used and developed by Arthur Schopenhau ...

-- Principles of Mathematical Logic -- Prior Analytics -- Private Eye Project -- Pro hominem --

Probabilistic logic Probabilistic logic (also probability logic and probabilistic reasoning) involves the use of probability and logic to deal with uncertain situations. Probabilistic logic extends traditional logic truth tables with probabilistic expressions. A diffic ...

Probabilistic logic network A probabilistic logic network (PLN) is a conceptual, mathematical, and computational approach to uncertain inference; inspired by logic programming, but using probabilities in place of crisp (true/false) truth values, and fractional uncertainty i ...

Problem of future contingents Future contingent propositions (or simply, future contingents) are statements about states of affairs in the future that are '' contingent:'' neither necessarily true nor necessarily false. The problem of future contingents seems to have been fi ...

-- Problem of induction --

Process of elimination Process of elimination is a logical method to identify an entity of interest among several ones by excluding all other entities. In educational testing, it is a process of deleting options whereby the possibility of an option being correct is clos ...

Project Reason Samuel Benjamin Harris (born April 9, 1967) is an American philosopher, neuroscientist, author, and podcast host. His work touches on a range of topics, including rationality, religion, ethics, free will, neuroscience, meditation, psychedelic ...

Proof-theoretic semantics Proof-theoretic semantics is an approach to the semantics of logic that attempts to locate the meaning of propositions and logical connectives not in terms of interpretations, as in Tarskian approaches to semantics, but in the role that the propo ...

-- Proof (truth) --

Proof by assertion Proof by assertion, sometimes informally referred to as proof by repeated assertion, is an informal fallacy in which a proposition is repeatedly restated regardless of contradiction and refutation.Austin J. Freeley, David L. Steinberg, ''Argumentat ...

-- Proof theory --

Propaganda techniques A number of propaganda techniques based on social psychology, social psychological research are used to generate propaganda. Many of these same techniques can be classified as Informal fallacy, logical fallacies, since propagandists use arguments ...

Proposition In logic and linguistics, a proposition is the meaning of a declarative sentence. In philosophy, " meaning" is understood to be a non-linguistic entity which is shared by all sentences with the same meaning. Equivalently, a proposition is the no ...

Propositional calculus Propositional calculus is a branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes zeroth-order logic. It deals with propositions (which can be true or false) and relations ...

Propositional function In propositional calculus, a propositional function or a predicate is a sentence expressed in a way that would assume the value of true or false, except that within the sentence there is a variable (''x'') that is not defined or specified (thus be ...

-- Propositional representation --

Propositional variable In mathematical logic, a propositional variable (also called a sentential variable or sentential letter) is an input variable (that can either be true or false) of a truth function. Propositional variables are the basic building-blocks of proposit ...

Prosecutor's fallacy The prosecutor's fallacy is a fallacy of statistical reasoning involving a test for an occurrence, such as a DNA match. A positive result in the test may paradoxically be more likely to be an erroneous result than an actual occurrence, even i ...

Provability logic Provability logic is a modal logic, in which the box (or "necessity") operator is interpreted as 'it is provable that'. The point is to capture the notion of a proof predicate of a reasonably rich formal theory, such as Peano arithmetic. Examples ...

-- Proving too much -- Prudence --

Pseudophilosophy Pseudophilosophy is a term applied to a philosophical idea or system which does not meet an expected set of philosophical standards. There is no universally accepted set of standards, but there are similarities and some common ground. Definitions ...

Psychologism Psychologism is a family of philosophical positions, according to which certain psychological facts, laws, or entities play a central role in grounding or explaining certain non-psychological facts, laws, or entities. The word was coined by Johan ...

Psychologist's fallacy The psychologist's fallacy is an informal fallacy that occurs when an observer assumes that his or her subjective experience reflects the true nature of an event. The fallacy was named by William James in the 19th century: Alternative statement ...

Q

Q.E.D. -- Quantification --

Quantization (linguistics) In formal semantics, a predicate is quantized if it being true of an entity requires that it is ''not'' true of any proper subparts of that entity. For example, if something is an "apple", then no proper subpart of that thing is an "apple". If some ...

Quantum logic In the mathematical study of logic and the physical analysis of quantum foundations, quantum logic is a set of rules for manipulation of propositions inspired by the structure of quantum theory. The field takes as its starting point an observ ...

R

Ramism Ramism was a collection of theories on rhetoric, logic, and pedagogy based on the teachings of Petrus Ramus, a French academic, philosopher, and Huguenot convert, who was murdered during the St. Bartholomew's Day massacre in August 1572. Accord ...

-- Rationality --

Razor (philosophy) In philosophy, a razor is a principle or rule of thumb that allows one to eliminate ("shave off") unlikely explanations for a phenomenon, or avoid unnecessary actions. Razors include: *Occam's razor: Simpler explanations are more likely to be corr ...

Reason Reason is the capacity of consciously applying logic by drawing conclusions from new or existing information, with the aim of seeking the truth. It is closely associated with such characteristically human activities as philosophy, science, ...

Reductio ad absurdum In logic, (Latin for "reduction to absurdity"), also known as (Latin for "argument to absurdity") or ''apagogical arguments'', is the form of argument that attempts to establish a claim by showing that the opposite scenario would lead to absu ...

Reference Reference is a relationship between objects in which one object designates, or acts as a means by which to connect to or link to, another object. The first object in this relation is said to ''refer to'' the second object. It is called a '' name'' ...

Reflective equilibrium Reflective equilibrium is a state of balance or coherence among a set of beliefs arrived at by a process of deliberative mutual adjustment among general principles and particular judgements. Although he did not use the term, philosopher Nelson G ...

Regression fallacy The regression (or regressive) fallacy is an informal fallacy. It assumes that something has returned to normal because of corrective actions taken while it was abnormal. This fails to account for natural fluctuations. It is frequently a special ki ...

Regular modal logic In modal logic, a regular modal logic is a modal logic containing (as axiom or theorem) the duality of the modal operators: \Diamond A \leftrightarrow \lnot\Box\lnot A and closed under the rule \frac. Every normal modal logic In logic, a norma ...

-- Reification (fallacy) -- Relativist fallacy --

Relevance Relevance is the concept of one topic being connected to another topic in a way that makes it useful to consider the second topic when considering the first. The concept of relevance is studied in many different fields, including cognitive sci ...

Relevance logic Relevance logic, also called relevant logic, is a kind of non-classical logic requiring the antecedent and consequent of implications to be relevantly related. They may be viewed as a family of substructural or modal logics. It is generally, but ...

Relevant logic Relevance logic, also called relevant logic, is a kind of non-classical logic requiring the antecedent and consequent of implications to be relevantly related. They may be viewed as a family of substructural or modal logics. It is generally, but ...

-- Remarks on the Foundations of Mathematics --

Retroduction Abductive reasoning (also called abduction,For example: abductive inference, or retroduction) is a form of logical inference formulated and advanced by American philosopher Charles Sanders Peirce beginning in the last third of the 19th century ...

-- Retrospective determinism --

Revolutions in Mathematics {{italic title ''Revolutions in Mathematics'' is a 1992 collection of essays in the history and philosophy of mathematics. Contents *Michael J. Crowe, Ten "laws" concerning patterns of change in the history of mathematics (1975) (15–20); *Herbe ...

-- Rhetoric --

Rigour Rigour (British English) or rigor (American English; see spelling differences) describes a condition of stiffness or strictness. These constraints may be environmentally imposed, such as "the rigours of famine"; logically imposed, such as ma ...

Rolandas Pavilionis Rolandas Pavilionis (July 3, 1944, Šiauliai – May 10, 2006, Vilnius) was a Lithuanian philosopher, politician and Member of the European Parliament (MEP) for the Liberal Democratic Party; part of the Union for a Europe of Nations. Biograph ...

Round square copula In metaphysics and the philosophy of language, the round square copula is a common example of the dual copula strategy used in reference to the problem of nonexistent objects as well as their relation to problems in modern philosophy of language. ...

-- Rudolf Carnap -- Rule of inference -- Rvachev function --

S

SEE-I -- Salva congruitate -- Salva veritate --

Satisfiability In mathematical logic, a formula is ''satisfiable'' if it is true under some assignment of values to its variables. For example, the formula x+3=y is satisfiable because it is true when x=3 and y=6, while the formula x+1=x is not satisfiable over ...

Scholastic logic In philosophy, term logic, also known as traditional logic, syllogistic logic or Aristotelian logic, is a loose name for an approach to formal logic that began with Aristotle and was developed further in ancient history mostly by his followers, ...

School of Names The School of Names (), sometimes called the School of Forms and Names (), was a school of Chinese philosophy that grew out of Mohism during the Warring States period in 479–221 BCE. The followers of the School of Names were sometimes called the ...

Science of Logic ''Science of Logic'' (''SL''; german: Wissenschaft der Logik, ''WdL''), first published between 1812 and 1816, is the work in which Georg Wilhelm Friedrich Hegel outlined his vision of logic. Hegel's logic is a system of '' dialectics'', i.e., ...

-- Scientific temper -- Second-order predicate -- Segment addition postulate -- Self-reference --

Self-refuting idea A self-refuting idea or self-defeating idea is an idea or statement whose falsehood is a logical consequence of the act or situation of holding them to be true. Many ideas are called self-refuting by their detractors, and such accusations are ther ...

-- Self-verifying theories --

Semantic theory of truth A semantic theory of truth is a theory of truth in the philosophy of language which holds that truth is a property of sentences. Origin The semantic conception of truth, which is related in different ways to both the correspondence and deflati ...

Semantics Semantics (from grc, σημαντικός ''sēmantikós'', "significant") is the study of reference, meaning, or truth. The term can be used to refer to subfields of several distinct disciplines, including philosophy, linguistics and comp ...

Sense and reference In the philosophy of language, the distinction between sense and reference was an idea of the German philosopher and mathematician Gottlob Frege in 1892 (in his paper "On Sense and Reference"; German: "Über Sinn und Bedeutung"), reflecting the ...

Sequent In mathematical logic, a sequent is a very general kind of conditional assertion. : A_1,\,\dots,A_m \,\vdash\, B_1,\,\dots,B_n. A sequent may have any number ''m'' of condition formulas ''Ai'' (called " antecedents") and any number ''n'' of ass ...

Sequent calculus In mathematical logic, sequent calculus is a style of formal logical argumentation in which every line of a proof is a conditional tautology (called a sequent by Gerhard Gentzen) instead of an unconditional tautology. Each conditional tautology i ...

Sequential logic In automata theory, sequential logic is a type of logic circuit whose output depends on the present value of its input signals and on the sequence of past inputs, the input history. This is in contrast to ''combinational logic'', whose output i ...

Set (mathematics) A set is the mathematical model for a collection of different things; a set contains '' elements'' or ''members'', which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or ...

Seven Types of Ambiguity (Empson) ''Seven Types of Ambiguity'' is a work of literary criticism by William Empson which was first published in 1930. It was one of the most influential critical works of the 20th century and was a key foundation work in the formation of the New Crit ...

Sheffer stroke In Boolean functions and propositional calculus, the Sheffer stroke denotes a logical operation that is equivalent to the negation of the conjunction operation, expressed in ordinary language as "not both". It is also called nand ("not and") ...

Ship of Theseus The Ship of Theseus is a thought experiment about whether an object that has had all of its original components replaced remains the same object. According to legend, Theseus, the mythical Greek founder-king of Athens, had rescued the children ...

-- Simple non-inferential passage --

Singular term A singular term is a paradigmatic referring device in a language. Singular terms are of philosophical importance for philosophers of language, because they ''refer'' to things in the world, and the ability of words to refer calls for scrutiny. Ove ...

-- Situation --

Situational analysis Situational logic (also situational analysis) is a concept advanced by Karl Popper in his ''The Poverty of Historicism''. Situational logic is a process by which a social scientist tries to reconstruct the problem situation confronting an agent in ...

Skeptic's Toolbox The Skeptic's Toolbox is an annual four-day workshop devoted to scientific skepticism. It was formed by psychologist and now-retired University of Oregon professor Ray Hyman, has been held every August since 1992, and is sponsored by the Committ ...

Slingshot argument In philosophical logic, a slingshot argument is one of a group of arguments claiming to show that all true sentences stand for the same thing. This type of argument was dubbed the " slingshot" by philosophers Jon Barwise and John Perry (1981) ...

-- Social software (social procedure) --

Socratic questioning Socratic questioning (or Socratic maieutics) was named after Socrates. He used an educational method that focused on discovering answers by asking questions from his students. According to Plato, who was one of his students, Socrates believed t ...

Soku hi Soku-hi ( ja, 即非) means "is and is not". The term is primarily used by the representatives of the Kyoto School of Eastern philosophy. The logic of soku-hi or "is and is not" represents a balanced logic of symbolization reflecting sensitivity ...

Some Remarks on Logical Form "Some Remarks on Logical Form" (1929) was the only academic paper ever published by Ludwig Wittgenstein, and contained Wittgenstein's thinking on logic and the philosophy of mathematics immediately before the rupture that divided the early Wittgenst ...

Sophism A sophist ( el, σοφιστής, sophistes) was a teacher in ancient Greece in the fifth and fourth centuries BC. Sophists specialized in one or more subject areas, such as philosophy, rhetoric, music, athletics, and mathematics. They taught ' ...

Sophistical Refutations ''Sophistical Refutations'' ( el, Σοφιστικοὶ Ἔλεγχοι, Sophistikoi Elenchoi; la, De Sophisticis Elenchis) is a text in Aristotle's ''Organon'' in which he identified thirteen fallacies.Sometimes listed as twelve. According to A ...

Soundness In logic or, more precisely, deductive reasoning, an argument is sound if it is both valid in form and its premises are true. Soundness also has a related meaning in mathematical logic, wherein logical systems are sound if and only if every formu ...

-- Source credibility -- Source criticism --

Special case In logic, especially as applied in mathematics, concept is a special case or specialization of concept precisely if every instance of is also an instance of but not vice versa, or equivalently, if is a generalization of . A limiting case i ...

Specialization (logic) Specialization or Specialized may refer to: Academia * Academic specialization, may be a course of study or major at an academic institution or may refer to the field in which a specialist practices * Specialty (medicine), a branch of medical ...

Speculative reason Speculative reason, sometimes called theoretical reason or pure reason, is theoretical (or logical, deductive) thought, as opposed to practical (active, willing) thought. The distinction between the two goes at least as far back as the ancient ...

Spurious relationship In statistics, a spurious relationship or spurious correlation is a mathematical relationship in which two or more events or variables are associated but '' not'' causally related, due to either coincidence or the presence of a certain third, u ...

-- Square of opposition --

State of affairs (philosophy) In philosophy, a state of affairs (german: Sachverhalt), also known as a situation, is a way the actual world must be in order to make some given ''proposition'' about the actual world true; in other words, a state of affairs is a ''truth-maker'', w ...

-- Statement (logic) -- Straight and Crooked Thinking -- Straight face test --

Straw man A straw man (sometimes written as strawman) is a form of argument and an informal fallacy of having the impression of refuting an argument, whereas the real subject of the argument was not addressed or refuted, but instead replaced with a false o ...

Strength (mathematical logic) The relative strength of two systems of formal logic can be defined via model theory. Specifically, a logic \alpha is said to be as strong as a logic \beta if every elementary class in \beta is an elementary class in \alpha.Heinz-Dieter Ebbinghaus ...

Strict conditional In logic, a strict conditional (symbol: \Box, or ⥽) is a conditional governed by a modal operator, that is, a logical connective of modal logic. It is logically equivalent to the material conditional of classical logic, combined with the necess ...

-- Strict implication -- Strict logic -- Structural rule --

Studia Logica ''Studia Logica'' (full name: Studia Logica, An International Journal for Symbolic Logic), is a scienific journal publishing papers employing formal tools from Mathematics and Logic. The scope of papers published in Studia Logica covers all scient ...

-- Studies in Logic, Grammar and Rhetoric -- Subjective logic --

Substitution (logic) Substitution is a fundamental concept in logic. A substitution is a syntactic transformation on formal expressions. To apply a substitution to an expression means to consistently replace its variable, or placeholder, symbols by other expressions. ...

Substructural logic In logic, a substructural logic is a logic lacking one of the usual structural rules (e.g. of classical and intuitionistic logic), such as weakening, contraction, exchange or associativity. Two of the more significant substructural logics are r ...

-- Sufficient condition -- Sum of Logic --

Sunk costs In economics and business decision-making, a sunk cost (also known as retrospective cost) is a cost that has already been incurred and cannot be recovered. Sunk costs are contrasted with '' prospective costs'', which are future costs that may be ...

Supertask In philosophy, a supertask is a countably infinite sequence of operations that occur sequentially within a finite interval of time. Supertasks are called hypertasks when the number of operations becomes uncountably infinite. A hypertask that in ...

Supervaluationism In philosophical logic, supervaluationism is a semantics for dealing with irreferential singular terms and vagueness. It allows one to apply the tautologies of propositional logic in cases where truth values are undefined. According to super ...

Supposition theory Supposition theory was a branch of medieval logic that was probably aimed at giving accounts of issues similar to modern accounts of reference, plurality, tense, and modality, within an Aristotelian context. Philosophers such as John Buridan, W ...

-- Survivorship bias -- Syllogism --

Syllogistic fallacy A syllogism ( grc-gre, συλλογισμός, ''syllogismos'', 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true. ...

Symbol (formal) A logical symbol is a fundamental concept in logic, tokens of which may be marks or a configuration of marks which form a particular pattern. Although the term "symbol" in common use refers at some times to the idea being symbolized, and at other ...

-- Syntactic Structures -- Syntax (logic) --

Synthese ''Synthese'' () is a scholarly periodical specializing in papers in epistemology, methodology, and philosophy of science, and related issues. Its subject area is divided into four specialties, with a focus on the first three: (1) "epistemology, me ...

-- Systems of Logic Based on Ordinals --

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T-schema The T-schema ("truth schema", not to be confused with " Convention T") is used to check if an inductive definition of truth is valid, which lies at the heart of any realisation of Alfred Tarski's semantic theory of truth. Some authors refer to it ...

Tacit assumption A tacit assumption or implicit assumption is an assumption that underlies a logical argument, course of action, decision, or judgment that is not explicitly voiced nor necessarily understood by the decision maker or judge. These assumptions may b ...

Tarski's undefinability theorem 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 ...

Tautology (logic) In mathematical logic, a tautology (from el, ταυτολογία) is a formula or assertion that is true in every possible interpretation. An example is "x=y or x≠y". Similarly, "either the ball is green, or the ball is not green" is always ...

Temporal logic In logic, temporal logic is any system of rules and symbolism for representing, and reasoning about, propositions qualified in terms of time (for example, "I am ''always'' hungry", "I will ''eventually'' be hungry", or "I will be hungry ''until'' I ...

Temporal parts In contemporary metaphysics, temporal parts are the parts of an object that exist in time. A temporal part would be something like "the first year of a person's life", or "all of a table from between 10:00 a.m. on June 21, 1994 to 11:00 p.m. on Ju ...

Teorema (journal) ''Teorema'' is a triannual Peer review, peer-reviewed academic journal of philosophy, published in Spain. History It was established in 1971 by Manuel Garrido (*1925-†(2015) and published without interruption until 1986. ''Teorema'' also or ...

Term (argumentation) In argumentation theory, a term is that part of a statement in an argument which refers to a specific thing. Usually, but not always expressed as a noun, one of the requirements to informally prove a conclusion with a deductive argument is for all ...

Term logic In philosophy, term logic, also known as traditional logic, syllogistic logic or Aristotelian logic, is a loose name for an approach to formal logic that began with Aristotle and was developed further in ancient history mostly by his followers, ...

Ternary logic In logic, a three-valued logic (also trinary logic, trivalent, ternary, or trilean, sometimes abbreviated 3VL) is any of several many-valued logic systems in which there are three truth values indicating ''true'', ''false'' and some indeterminat ...

Testability Testability is a primary aspect of Science and the Scientific Method and is a property applying to an empirical hypothesis, involves two components: #Falsifiability or defeasibility, which means that counterexamples to the hypothesis are logicall ...

Tetralemma The tetralemma is a figure that features prominently in the logic of India. Definition It states that with reference to any a logical proposition X, there are four possibilities: : X (affirmation) : \neg X (negation) : X \land\neg X (both) : \n ...

-- Textual case based reasoning -- The False Subtlety of the Four Syllogistic Figures --

The Foundations of Arithmetic ''The Foundations of Arithmetic'' (german: Die Grundlagen der Arithmetik) is a book by Gottlob Frege, published in 1884, which investigates the philosophical foundations of arithmetic. Frege refutes other theories of number and develops his own t ...

-- The Geography of Thought --

The Laws of Thought ''An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities'' by George Boole, published in 1854, is the second of Boole's two monographs on algebraic logic. Boole was a professor of mathem ...

The Paradoxes of the Infinite ''Paradoxes of the Infinite'' (German title: ''Paradoxien des Unendlichen'') is a mathematical work by Bernard Bolzano on the theory of sets. It was published by a friend and student, František Přihonský, in 1851, three years after Bolzano's d ...

Theorem In mathematics, a theorem is a statement that has been proved, or can be proved. The ''proof'' of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of t ...

Theoretical definition A theoretical definition defines a term in an academic discipline, functioning as a proposal to see a phenomenon in a certain way. A theoretical definition is a proposed way of thinking about potentially related events. Theoretical definitions cont ...

Theory and Decision Theory and Decision is a peer-reviewed multidisciplinary journal of decision science published quarterly by Springer Science+Business Media. It was first published in 1970. The current editor-in-chief is Mohammed Abdellaoui. The journal publishe ...

Theory of justification Justification (also called epistemic justification) is the property of belief that qualifies it as knowledge rather than mere opinion. Epistemology is the study of reasons that someone holds a rationally admissible belief (although the term is a ...

-- Theory of obligationes -- Third-cause fallacy -- Three men make a tiger --

Tolerance (in logic) In mathematical logic, a tolerant sequence is a sequence :T_1,...,T_n of formal theories such that there are consistent extensions :S_1,...,S_n of these theories with each S_{i+1} interpretable in S_i. Tolerance naturally generalizes from ...

-- Topical logic --

Topics (Aristotle) The ''Topics'' ( grc-gre, Τοπικά; la, Topica) is the name given to one of Aristotle's six works on logic collectively known as the '' Organon''. The treatise presents the art of dialectic — the invention and discovery of arguments in whi ...

Tractatus Logico-Philosophicus The ''Tractatus Logico-Philosophicus'' (widely abbreviated and cited as TLP) is a book-length philosophical work by the Austrian philosopher Ludwig Wittgenstein which deals with the relationship between language and reality and aims to define th ...

Train of thought The train of thought or track of thought refers to the interconnection in the sequence of ideas expressed during a connected discourse or thought, as well as the sequence itself, especially in discussion how this sequence leads from one idea to ...

-- Trairūpya --

Transferable belief model The transferable belief model (TBM) is an elaboration on the Dempster–Shafer theory (DST), which is a mathematical model used to evaluate the probability that a given proposition is true from other propositions which are assigned probabilities. ...

Transparent Intensional Logic Transparent intensional logic (frequently abbreviated as TIL) is a logical system created by Pavel Tichý. Due to its rich ''procedural semantics'' TIL is in particular apt for the logical analysis of natural language. From the formal point of vie ...

-- TregoED --

Trikonic Trikonic, is a technique of triadic analysis-synthesis which has been developed by Gary Richmond based on the original idea of a possible applied science making three categorial distinctions, which philosopher Charles Sanders Peirce, its creator, ...

Trilemma A trilemma is a difficult choice from three options, each of which is (or appears) unacceptable or unfavourable. There are two logically equivalent ways in which to express a trilemma: it can be expressed as a choice among three unfavourable option ...

Trivial objections Trivial objections (also referred to as hair-splitting, nothing but objections, barrage of objections and banal objections) is an informal logical fallacy where irrelevant and sometimes frivolous objections are made to divert the attention away fro ...

Trivialism Trivialism is the logical theory that all statements (also known as propositions) are true and that all contradictions of the form "p and not p" (e.g. the ball is red and not red) are true. In accordance with this, a trivialist is a person who b ...

Truth Truth is the property of being in accord with fact or reality.Merriam-Webster's Online Dictionarytruth 2005 In everyday language, truth is typically ascribed to things that aim to represent reality or otherwise correspond to it, such as belie ...

Truth-bearer A truth-bearer is an entity that is said to be either true or false and nothing else. The thesis that some things are true while others are false has led to different theories about the nature of these entities. Since there is divergence of o ...

Truth condition In semantics and pragmatics, a truth condition is the condition under which a sentence is true. For example, "It is snowing in Nebraska" is true precisely when it is snowing in Nebraska. Truth conditions of a sentence do not necessarily reflect cu ...

Truth function In logic, a truth function is a function that accepts truth values as input and produces a unique truth value as output. In other words: The input and output of a truth function are all truth values; a truth function will always output exactly o ...

Truth value In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth, which in classical logic has only two possible values ('' true'' or '' false''). Computing In some pro ...

Truthiness Truthiness is the belief or assertion that a particular statement is true based on the intuition or perceptions of some individual or individuals, without regard to evidence, logic, intellectual examination, or facts. Truthiness can range from i ...

Truthmaker Truthmaker theory is "the branch of metaphysics that explores the relationships between what is true and what exists". The basic intuition behind truthmaker theory is that truth depends on being. For example, a perceptual experience of a green tre ...

Type (model theory) In model theory and related areas of mathematics, a type is an object that describes how a (real or possible) element or finite collection of elements in a mathematical structure might behave. More precisely, it is a set of first-order formulas in ...

Type theory In mathematics, logic, and computer science, a type theory is the formal presentation of a specific type system, and in general type theory is the academic study of type systems. Some type theories serve as alternatives to set theory as a fou ...

Type–token distinction The type–token distinction is the difference between naming a ''class'' (type) of objects and naming the individual ''instances'' (tokens) of that class. Since each type may be exemplified by multiple tokens, there are generally more tokens than ...

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Ultrafinitism In the philosophy of mathematics, ultrafinitism (also known as ultraintuitionism,International Workshop on Logic and Computational Complexity, ''Logic and Computational Complexity'', Springer, 1995, p. 31. strict formalism,St. Iwan (2000),On the U ...

Unification (computer science) In logic and computer science, unification is an algorithmic process of solving equations between symbolic expressions. Depending on which expressions (also called ''terms'') are allowed to occur in an equation set (also called ''unification prob ...

Unifying theories in mathematics There have been several attempts in history to reach a unified theory of mathematics. Some of the most respected mathematicians in the academia have expressed views that the whole subject should be fitted into one theory. Historical perspective T ...

Uniqueness quantification In mathematics and logic, the term "uniqueness" refers to the property of being the one and only object satisfying a certain condition. This sort of quantification is known as uniqueness quantification or unique existential quantification, and ...

Universal logic Originally the expression ''Universal logic'' was coined by analogy with the expression ''Universal algebra''. The first idea was to develop Universal logic as a field of logic that studies the features common to all logical systems, aiming to be ...

Universal quantification In mathematical logic, a universal quantification is a type of quantifier, a logical constant which is interpreted as "given any" or "for all". It expresses that a predicate can be satisfied by every member of a domain of discourse. In other ...

Univocity Univocity of being is the idea that words describing the properties of God mean the same thing as when they apply to people or things. It is associated with the doctrines of the Scholasticism, Scholastic theologian John Duns Scotus. Scotus In med ...

Unspoken rule Unwritten rules (synonyms: Unspoken rules) are behavioral constraints imposed in organizations or societies that are not typically voiced or written down. They usually exist in unspoken and unwritten format because they form a part of the logical ...

Use–mention distinction The use–mention distinction is a foundational concept of analytic philosophy, according to which it is necessary to make a distinction between a word (or phrase) and it.Devitt and Sterelny (1999) pp. 40–1W.V. Quine (1940) p. 24 Many philos ...

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Vacuous truth In mathematics and logic, a vacuous truth is a conditional or universal statement (a universal statement that can be converted to a conditional statement) that is true because the antecedent cannot be satisfied. For example, the statement "she d ...

-- Vagrant predicate --

Vagueness In linguistics and philosophy, a vague predicate is one which gives rise to borderline cases. For example, the English adjective "tall" is vague since it is not clearly true or false for someone of middling height. By contrast, the word "prime" is ...

-- Validity -- Valuation-based system -- Van Gogh fallacy --

Venn diagram A Venn diagram is a widely used diagram style that shows the logical relation between sets, popularized by John Venn (1834–1923) in the 1880s. The diagrams are used to teach elementary set theory, and to illustrate simple set relationships ...

-- Vicious circle principle --

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Warnier/Orr diagram --

Well-formed formula In mathematical logic, propositional logic and predicate logic, a well-formed formula, abbreviated WFF or wff, often simply formula, is a finite sequence of symbols from a given alphabet that is part of a formal language. A formal language can ...

-- What the Tortoise Said to Achilles --

Willard Van Orman Quine Willard Van Orman Quine (; known to his friends as "Van"; June 25, 1908 – December 25, 2000) was an American philosopher and logician in the analytic tradition, recognized as "one of the most influential philosophers of the twentieth century" ...

William Kneale William Calvert Kneale (22 June 1906 – 24 June 1990) was an English logician best known for his 1962 book ''The Development of Logic'', a history of logic from its beginnings in Ancient Greece written with his wife Martha. Kneale was also ...

-- Window operator -- Wisdom of repugnance -- Witness (mathematics) -- Word sense --

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Zhegalkin polynomial --

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