Following the developments in Formal logic

Formal logic

Classical or traditional system of determining the validity or invalidity of a conclusion deduced from two or more statements...

 with symbolic logic in the late nineteenth century and mathematical logic

Mathematical logic

Mathematical logic is a subfield of mathematics with close connections to foundations of mathematics, theoretical computer science and philosophical logic. The field includes both the mathematical study of logic and the applications of formal logic to other areas of mathematics...

 in the twentieth, topics traditionally treated by logic

Logic

In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...

 not being part of formal logic have tended to be termed either philosophy of logic or philosophical logic if no longer simply logic.

Compared to the history of logic the demarcation between philosophy of logic and philosophical logic

Philosophical logic

Philosophical logic is a term introduced by Bertrand Russell to represent his idea that the workings of natural language and thought can only be adequately represented by an artificial language; essentially it was his formalization program for the natural language...

 is of recent coinage and not always entirely clear. Characterisations include

• Philosophy of logic is the arena of philosophy devoted to examining the scope and nature of logic.
• Philosophy of logic is the investigation, critical analysis and intellectual reflection on issues arising in logic
  Logic
  In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...
  
  . The field is considered to be distinct from philosophical logic
  Philosophical logic
  Philosophical logic is a term introduced by Bertrand Russell to represent his idea that the workings of natural language and thought can only be adequately represented by an artificial language; essentially it was his formalization program for the natural language...
  
  .
• Philosophical logic is the branch of logic
  Logic
  In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...
  
   concerning aspects other than or outside of formal logic.
• Philosophical logic is the application of formal logical techniques to philosophical problems.

This article outlines issues in philosophy of logic or provides links to relevant articles or both.

Introduction

This article makes use the following terms and concepts:

• Type-token distinction
  Type-token distinction
  In disciplines such as philosophy and knowledge representation, the type-token distinction is a distinction that separates an abstract concept from the objects which are particular instances of the concept...
  
  
• Use–mention distinction

Truth

Aristotle said To say that that which is is not or that which is not is, is a falsehood; and to say that which is is and that which is not is not, is true

This apparent truism has not proved unproblematic.

Truthbearers

Logic uses such terms as true, false, inconsistent, valid, and self-contradictory. Questions arise as Strawson (1952) writes

(a) when we use these words of logical appraisal, what is it exactly that we are appraising? and (b) how does logical appraisal become possible?

See also: Sentence

Sentence

Sentence or sentencing may refer to:* Sentence , a grammatical unit of language* Sentence , a formula with no free variables* Sentence , a particular type of musical phrase...

, Statements, Proposition

Proposition

In logic and philosophy, the term proposition refers to either the "content" or "meaning" of a meaningful declarative sentence or the pattern of symbols, marks, or sounds that make up a meaningful declarative sentence...

.

Tarski's definition of Truth

See:-

• Semantic theory of truth#Tarski's Theory
• T-schema
  T-schema
  The T-schema or truth schema is used to give an inductive definition of truth which lies at the heart of any realisation of Alfred Tarski's semantic theory of truth...
  
  
• Stanford Encyclopedia of Philosophy entry on Tarski's Truth Definitions
• Self-reference:2.1 Consequences of the Semantic Paradoxes in Stanford Encyclopedia of Philosophy

Analytic Truths, Logical truth, Validity, Logical consequence and Entailment

Since the use, meaning, if not the meaningfulness, of the terms is part of the debate, it is possible only to give the following working definitions for the purposes of the discussion:

• A necessary truth is one that is true no matter what the state of the world or, as it is sometimes put, in all possible worlds.
• Logical truth
  Logical truth
  Logical truth is one of the most fundamental concepts in logic, and there are different theories on its nature. A logical truth is a statement which is true and remains true under all reinterpretations of its components other than its logical constants. It is a type of analytic statement.Logical...
  
  s are those necessary truths that are necessarily true owing to the meaning of their logical constants only.
• In formal logic a logical truth is just a "statement" (string of symbols in which no variable occurs free) which is true under all possible interpretation
  Interpretation (logic)
  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 they are given some interpretation...
  
  s.
• An analytic truth is one whose predicate concept is contained in its subject concept.

The concept of logical truth is intimately linked with those of validity, logical consequence and entailment

Entailment

In logic, entailment is a relation between a set of sentences and a sentence. Let Γ be a set of one or more sentences; let S1 be the conjunction of the elements of Γ, and let S2 be a sentence: then, Γ entails S2 if and only if S1 and not-S2 are logically inconsistent...

 (as well as self-contradiction, necessarily false &c.).

• If q is a logical truth, then p therefore q will be a valid argument.
• If p1, p2, p3...pn therefore q is a valid argument then its corresponding conditional (logic)
  Corresponding conditional (logic)
  In logic, the corresponding conditional of an argument is a material conditional whose antecedent is the conjunction of the argument's premises and whose consequent is the argument's conclusion. An argument is valid if and only if its corresponding conditional is a logical truth...
  
   will be a logical truth.
• If p1 & p2 & p3...pn entails q then If (p1 & p2 & p3..pn) then q is a logical truth.
• If q is a logical consequence of p1 & p2 & p3...pn if and only if p1 & p2 & p3...pn entails q and if and only if If (p1 & p2 & p3..pn) then q is a logical truth

Issues that arise include:

• If there are truths that must be true, what makes them so?
• Are there analytic truths that are not logical truths?
• Are there necessary truths that are not analytic truths?
• Are there necessary truths that are not logical truths?
• Is the distinction between analytic truth and synthetic truth spurious?

see also http://plato.stanford.edu/entries/logical-truth/

Are Logical Truths a priori or a posteriori knowledge? Synthetic or Analytic?

Ludwig Wittgenstein

Ludwig Wittgenstein

Ludwig Josef Johann Wittgenstein was an Austrian philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language. He was professor in philosophy at the University of Cambridge from 1939 until 1947...

 said that a logical truth was a statement which is true in all possible worlds. This is contrasted with synthetic claim (or fact

Fact

A fact is something that has really occurred or is actually the case. The usual test for a statement of fact is verifiability, that is whether it can be shown to correspond to experience. Standard reference works are often used to check facts...

) which is only true in this world as it has historically unfolded.

Some argue that a "proposition

Proposition

In logic and philosophy, the term proposition refers to either the "content" or "meaning" of a meaningful declarative sentence or the pattern of symbols, marks, or sounds that make up a meaningful declarative sentence...

" such as “If p and q, then p.” and the proposition “All husbands are married.” are logical truths because they are "analytic" true, i.e. because of their meanings

Meaning (linguistics)

In linguistics, meaning is what is expressed by the writer or speaker, and what is conveyed to the reader or listener, provided that they talk about the same thing . In other words if the object and the name of the object and the concepts in their head are the same...

 and not because of any facts of the world, i.e. they are not synthetic.

See

• Is logic empirical?
  Is logic empirical?
  "Is logic empirical?" is the title of two articles that discuss the idea that the algebraic properties of logic may, or should, be empirically determined; in particular, they deal with the question of whether empirical facts about quantum phenomena may provide grounds for revising classical logic...
  
  
• Willard Van Orman Quine: Rejection of the analytic-synthetic distinction
• Analytic-synthetic distinction

Meaning and reference

See

• Sense and reference
  Sense and reference
  Sinn and bedeutung are usually translated, respectively, as sense and reference. Two different aspects of some terms' meanings, a term's reference is the object that the term refers to, while the term's sense is the way that the term refers to that object.Sinn and bedeutung were introduced by...
  
  
• Theory of reference
• Mediated reference theory
  Mediated reference theory
  The mediated reference theory is a semantic theory that posits that words refer to something in the external world, but insists that there is more to the meaning of a name than simply the object to which it refers. It thus stands opposed to the theory of direct reference. Its most famous advocate...
  
  
• Direct reference theory
  Direct reference theory
  A direct reference theory is a theory of meaning that claims that the meaning of an expression lies in what it points out in the world. It stands in contrast to mediated reference theories.- John Stuart Mill :...
  
  
• Causal theory of reference
  Causal theory of reference
  A causal theory of reference is a theory of how terms acquire specific referents. Such theories have been used to describe many referring terms, particularly logical terms, proper names, and natural kind terms...
  
   (section References)
• Descriptivist theory of names
  Descriptivist theory of names
  Descriptivist theory of names is a view of the nature of the meaning and reference of proper names generally attributed to Gottlob Frege and Bertrand Russell...
  
   (section References)
• Saul Kripke
  Saul Kripke
  Saul Aaron Kripke is an American philosopher and logician. He is a professor emeritus at Princeton and teaches as a Distinguished Professor of Philosophy at the CUNY Graduate Center...
  
   (section References)
• Frege's Puzzle
  Frege's Puzzle
  Frege's Puzzle is a puzzle about the semantics of proper names, although the title is also sometimes applied to a related puzzle about indexicals...
  
   (section New Theories of Reference and the Return of Frege's Puzzle)
• Gottlob Frege
  Gottlob Frege
  Friedrich Ludwig Gottlob Frege was a German mathematician, logician and philosopher. He is considered to be one of the founders of modern logic, and made major contributions to the foundations of mathematics. He is generally considered to be the father of analytic philosophy, for his writings on...
  
   (section References)
• Fictional beings and reference failure
  Fictional beings and reference failure
  According to Bertrand Russell's theory of truth, there is only one actual world, and a statement's truth value depends on whether the statement obtains in the actual world. Continuing the tradition of Gottlob Frege, Bertrand Russell posited that a name picks out, or refers to, a real object in the...
  
   (section References)
• Rigid designator
  Rigid designator
  In modal logic and the philosophy of language, a term is said to be a rigid designator when it designates the same thing in all possible worlds in which that thing exists and does not designate anything else in those possible worlds in which that thing does not exist...
  
   (section Causal-Historical Theory of Reference)
• Philosophy of language
  Philosophy of language
  Philosophy of language is the reasoned inquiry into the nature, origins, and usage of language. As a topic, the philosophy of language for analytic philosophers is concerned with four central problems: the nature of meaning, language use, language cognition, and the relationship between language...
  
   (section References)
• Index of philosophy of language articles
  Index of philosophy of language articles
  This is an index of articles in philosophy of language* A.P. Martinich* Aboutness* Absence paradox* Adolph Stöhr* Alexis Kagame* Alfred Jules Ayer* Alphabet of human thought* Ambiguity* Analytic-synthetic distinction* Anaphora* Andrea Bonomì...
  
  
• Supposition theory
  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, from within an Aristotelian context. Philosophers such as John Buridan, William of Ockham, William of Sherwood, Walter...
  
   (section References)
• Referring expression
  Referring expression
  A referring expression , in linguistics, is any noun phrase, or surrogate for a noun phrase, whose function in a text is "pick out" someone an individual person, place, object, or a set of persons, places, objects, etc. The technical terminology for "pick out" differs a great deal from one...
  
  
• Meaning (philosophy of language)
• Denotation
  Denotation
  This word has distinct meanings in other fields: see denotation . For the opposite of Denotation see Connotation.*In logic, linguistics and semiotics, the denotation of a word or phrase is a part of its meaning; however, the part referred to varies by context:** In grammar and literary theory, the...
  
    Connotation
  Connotation
  A connotation is a commonly understood subjective cultural or emotional association that some word or phrase carries, in addition to the word's or phrase's explicit or literal meaning, which is its denotation....
  
  
• Extension
  Extension (semantics)
  In any of several studies that treat the use of signs - for example, in linguistics, logic, mathematics, semantics, and semiotics - the extension of a concept, idea, or sign consists of the things to which it applies, in contrast with its comprehension or intension, which consists very roughly of...
  
    Intension
  Intension
  In linguistics, logic, philosophy, and other fields, an intension is any property or quality connoted by a word, phrase or other symbol. In the case of a word, it is often implied by the word's definition...
  
  
• Extensional definition
  Extensional definition
  An extensional definition of a concept or term formulates its meaning by specifying its extension, that is, every object that falls under the definition of the concept or term in question....
  
  
• Intensional definition
  Intensional definition
  In logic and mathematics, an intensional definition gives the meaning of a term by specifying all the properties required to come to that definition, that is, the necessary and sufficient conditions for belonging to the set being defined....
  
  
• Metacommunicative competence
  Metacommunicative competence
  Metacommunicative competence is the ability to intervene within difficult conversations and to correct communication problems by utilizing the different ways of practical communication:...
  
  
• Absent referent
  Absent referent
  Absent referent is a concept that originated in linguistics, and is the condition of a sign that has an empty, absent, non-existent, paradoxical, hypothetical, supernatural, or undefined referent...
  
  

Names and descriptions

• Fictional beings and reference failure
  Fictional beings and reference failure
  According to Bertrand Russell's theory of truth, there is only one actual world, and a statement's truth value depends on whether the statement obtains in the actual world. Continuing the tradition of Gottlob Frege, Bertrand Russell posited that a name picks out, or refers to, a real object in the...
  
  
• Proper name (philosophy)
• Definite description
  Definite description
  A definite description is a denoting phrase in the form of "the X" where X is a noun-phrase or a singular common noun. The definite description is proper if X applies to a unique individual or object. For example: "the first person in space" and "the 42nd President of the United States of...
  
  
• Descriptivist theory of names
  Descriptivist theory of names
  Descriptivist theory of names is a view of the nature of the meaning and reference of proper names generally attributed to Gottlob Frege and Bertrand Russell...
  
  
• Theory of descriptions
  Theory of descriptions
  The theory of descriptions is the philosopher Bertrand Russell's most significant contribution to the philosophy of language. It is also known as Russell's Theory of Descriptions...
  
  
• Singular term
  Singular term
  There is no really adequate definition of singular term. Here are some definitions proposed by different writers:# A term that tells us which individual is being talked about....
  
  
• Term logic#Singular terms
• Empty name
  Empty name
  In the philosophy of language, an empty name is a proper name that has no referent.The problem of empty names is that empty names have a meaning that it seems they shouldn't have. The name "Pegasus" is empty; there is nothing to which it refers. Yet though there is no Pegasus, we know what the...
  
  
• Bas van Fraassen#Singular Terms, truth-value Gaps, and Free Logic
• The Foundations of Arithmetic#Development of Frege's own view of a number
• Philosophy of language#references
• direct reference
• Mediated reference theory
  Mediated reference theory
  The mediated reference theory is a semantic theory that posits that words refer to something in the external world, but insists that there is more to the meaning of a name than simply the object to which it refers. It thus stands opposed to the theory of direct reference. Its most famous advocate...
  
  

Formal and material consequence

• The problem of the material conditional: see Material conditional
  Material conditional
  The material conditional, also known as material implication, is a binary truth function, such that the compound sentence p→q is logically equivalent to the negative compound: not . A material conditional compound itself is often simply called a conditional...
  
  

Philosophical theories of logic

• Conceptualism
  Conceptualism
  Conceptualism is a philosophical 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 concept of universals from a perspective that denies...
  
  
• Constructivism
  Constructivism (mathematics)
  In the philosophy of mathematics, constructivism asserts that it is necessary to find a mathematical object to prove that it exists. When one assumes that an object does not exist and derives a contradiction from that assumption, one still has not found the object and therefore not proved its...
  
  
• Dialetheism
  Dialetheism
  Dialetheism is the view that some statements can be both true and false simultaneously. More precisely, it is the belief that there can be a true statement whose negation is also true...
  
  
• Fictionalism
  Fictionalism
  Fictionalism is a methodological theory in philosophy that suggests that statements of a certain sort should not be taken to be literally true, but merely as a useful fiction...
  
  
• Finitism
  Finitism
  In the philosophy of mathematics, one of the varieties of finitism is an extreme form of constructivism, according to which a mathematical object does not exist unless it can be constructed from natural numbers in a finite number of steps...
  
  
• Formalism
  Formalism (mathematics)
  In foundations of mathematics, philosophy of mathematics, and philosophy of logic, formalism is a theory that holds that statements of mathematics and logic can be thought of as statements about the consequences of certain string manipulation rules....
  
  
• Intuitionism
  Intuitionism
  In the philosophy of mathematics, intuitionism, or neointuitionism , is an approach to mathematics as the constructive mental activity of humans. That is, mathematics does not consist of analytic activities wherein deep properties of existence are revealed and applied...
  
  
• Logical atomism
  Logical atomism
  Logical atomism is a philosophical belief that originated in the early 20th century with the development of analytic philosophy. Its principal exponents were the British philosopher Bertrand Russell, the early work of his Austrian-born pupil and colleague Ludwig Wittgenstein, and his German...
  
  
• Logicism
  Logicism
  Logicism is one of the schools of thought in the philosophy of mathematics, putting forth the theory that mathematics is an extension of logic and therefore some or all mathematics is reducible to logic. Bertrand Russell and Alfred North Whitehead championed this theory fathered by Richard Dedekind...
  
  
• Nominalism
  Nominalism
  Nominalism is a metaphysical view in philosophy according to which general or abstract terms and predicates exist, while universals or abstract objects, which are sometimes thought to correspond to these terms, do not exist. Thus, there are at least two main versions of nominalism...
  
  
• Realism
  Philosophical realism
  Contemporary philosophical realism is the belief that our reality, or some aspect of it, is ontologically independent of our conceptual schemes, linguistic practices, beliefs, etc....
  
  
• Platonic realism
  Platonic realism
  Platonic realism is a philosophical term usually used to refer to the idea of realism regarding the existence of universals or abstract objects after the Greek philosopher Plato , a student of Socrates. As universals were considered by Plato to be ideal forms, this stance is confusingly also called...
  
  
• Structuralism
  Structuralism
  Structuralism originated in the structural linguistics of Ferdinand de Saussure and the subsequent Prague and Moscow schools of linguistics. Just as structural linguistics was facing serious challenges from the likes of Noam Chomsky and thus fading in importance in linguistics, structuralism...
  
  

Other Topics

• Leibniz's Law: see Identity of indiscernibles
  Identity of indiscernibles
  The identity of indiscernibles is an ontological principle which states that two or more objects or entities are identical if they have all their properties in common. That is, entities x and y are identical if any predicate possessed by x is also possessed by y and vice versa...
  
  
• Vacuous names
• Do predicates have properties?: See Second-order logic
  Second-order logic
  In logic and mathematics second-order logic is an extension of first-order logic, which itself is an extension of propositional logic. Second-order logic is in turn extended by higher-order logic and type theory....
  
  
• Sense, Reference, Connotation, Denotation, Extension, Intension
• The status of the Laws of Logic
• Classical Logic
• Intuitionism
• Realism: see Platonic realism
  Platonic realism
  Platonic realism is a philosophical term usually used to refer to the idea of realism regarding the existence of universals or abstract objects after the Greek philosopher Plato , a student of Socrates. As universals were considered by Plato to be ideal forms, this stance is confusingly also called...
  
  , Philosophical realism
  Philosophical realism
  Contemporary philosophical realism is the belief that our reality, or some aspect of it, is ontologically independent of our conceptual schemes, linguistic practices, beliefs, etc....
  
  
• The Law of Excluded Middle: see Law of excluded middle
  Law of excluded middle
  In logic, the law of excluded middle is the third of the so-called three classic laws of thought. It states that for any proposition, either that proposition is true, or its negation is....
  
  
• Modality, Intensionality and Propositional Attitude
• Counter-factuals

• Psychologism

See also

• Logic
  Logic
  In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...
  
  
• Is logic empirical?
  Is logic empirical?
  "Is logic empirical?" is the title of two articles that discuss the idea that the algebraic properties of logic may, or should, be empirically determined; in particular, they deal with the question of whether empirical facts about quantum phenomena may provide grounds for revising classical logic...
  
  
• Type-token distinction
  Type-token distinction
  In disciplines such as philosophy and knowledge representation, the type-token distinction is a distinction that separates an abstract concept from the objects which are particular instances of the concept...
  
  
• Use–mention distinction

Resources

• Haack, Susan
  Susan Haack
  Susan Haack is an English professor of philosophy and law at the University of Miami in the United States. She has written on logic, the philosophy of language, epistemology, and metaphysics. Her pragmatism follows that of Charles Sanders Peirce.-Career:Haack is a graduate of the University of...
  
  . 1978. Philosophy of Logics. Cambridge University Press
  Cambridge University Press
  Cambridge University Press is the publishing business of the University of Cambridge. Granted letters patent by Henry VIII in 1534, it is the world's oldest publishing house, and the second largest university press in the world...
  
  . (ISBN 0-521-29329-4)
• Quine, W. V. O.  2004. Philosophy of Logic. 2nd ed. Harvard University Press
  Harvard University Press
  Harvard University Press is a publishing house established on January 13, 1913, as a division of Harvard University, and focused on academic publishing. In 2005, it published 220 new titles. It is a member of the Association of American University Presses. Its current director is William P...
  
  . (ISBN 0-674-66563-5)

Important figures

Important figures in the philosophy of logic include (but are not limited to):

• Aristotle
  Aristotle
  Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...
  
  
• George Boole
  George Boole
  George Boole was an English mathematician and philosopher.As the inventor of Boolean logic—the basis of modern digital computer logic—Boole is regarded in hindsight as a founder of the field of computer science. Boole said,...
  
  
• George Boolos
  George Boolos
  George Stephen Boolos was a philosopher and a mathematical logician who taught at the Massachusetts Institute of Technology.- Life :...
  
  
• Rudolf Carnap
  Rudolf Carnap
  Rudolf Carnap was an influential German-born philosopher who was active in Europe before 1935 and in the United States thereafter. He was a major member of the Vienna Circle and an advocate of logical positivism....
  
  
• Gordon Clark
  Gordon Clark
  Gordon Haddon Clark was an American philosopher and Calvinist theologian. He was a primary advocate for the idea of presuppositional apologetics and was chairman of the Philosophy Department at Butler University for 28 years...
  
  
• Alonzo Church
  Alonzo Church
  Alonzo Church was an American mathematician and logician who made major contributions to mathematical logic and the foundations of theoretical computer science. He is best known for the lambda calculus, Church–Turing thesis, Frege–Church ontology, and the Church–Rosser theorem.-Life:Alonzo Church...
  
  
• Augustus De Morgan
  Augustus De Morgan
  Augustus De Morgan was a British mathematician and logician. He formulated De Morgan's laws and introduced the term mathematical induction, making its idea rigorous. The crater De Morgan on the Moon is named after him....
  
  
• Michael Dummett
  Michael Dummett
  Sir Michael Anthony Eardley Dummett FBA D.Litt is a British philosopher. He was, until 1992, Wykeham Professor of Logic at the University of Oxford...
  
  

• Gottlob Frege
  Gottlob Frege
  Friedrich Ludwig Gottlob Frege was a German mathematician, logician and philosopher. He is considered to be one of the founders of modern logic, and made major contributions to the foundations of mathematics. He is generally considered to be the father of analytic philosophy, for his writings on...
  
  
• Kurt Gödel
  Kurt Gödel
  Kurt Friedrich Gödel was an Austrian logician, mathematician and philosopher. Later in his life he emigrated to the United States to escape the effects of World War II. One of the most significant logicians of all time, Gödel made an immense impact upon scientific and philosophical thinking in the...
  
  
• Georg Hegel
• Immanuel Kant
  Immanuel Kant
  Immanuel Kant was a German philosopher from Königsberg , researching, lecturing and writing on philosophy and anthropology at the end of the 18th Century Enlightenment....
  
  
• Gottfried Leibniz
  Gottfried Leibniz
  Gottfried Wilhelm Leibniz was a German philosopher and mathematician. He wrote in different languages, primarily in Latin , French and German ....
  
  
• David Lewis
  David Kellogg Lewis
  David Kellogg Lewis was an American philosopher. Lewis taught briefly at UCLA and then at Princeton from 1970 until his death. He is also closely associated with Australia, whose philosophical community he visited almost annually for more than thirty years...
  
  
• John Stuart Mill
  John Stuart Mill
  John Stuart Mill was a British philosopher, economist and civil servant. An influential contributor to social theory, political theory, and political economy, his conception of liberty justified the freedom of the individual in opposition to unlimited state control. He was a proponent of...
  
  

• Charles Sanders Peirce
• Alvin Plantinga
  Alvin Plantinga
  Alvin Carl Plantinga is an American analytic philosopher and the emeritus John A. O'Brien Professor of Philosophy at the University of Notre Dame. He is known for his work in philosophy of religion, epistemology, metaphysics, and Christian apologetics...
  
  
• Arthur Prior
  Arthur Prior
  Arthur Norman Prior was a noted logician and philosopher. Prior founded tense logic, now also known as temporal logic, and made important contributions to intensional logic, particularly in Prior .-Biography:Prior was entirely educated in New Zealand, where he was fortunate to have come under the...
  
  
• Willard Van Orman Quine
  Willard Van Orman Quine
  Willard Van Orman Quine was an American philosopher and logician in the analytic tradition...
  
  
• Bertrand Russell
  Bertrand Russell
  Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS was a British philosopher, logician, mathematician, historian, and social critic. At various points in his life he considered himself a liberal, a socialist, and a pacifist, but he also admitted that he had never been any of these things...
  
  
• Alfred Tarski
  Alfred Tarski
  Alfred Tarski was a Polish logician and mathematician. Educated at the University of Warsaw and a member of the Lwow-Warsaw School of Logic and the Warsaw School of Mathematics and philosophy, he emigrated to the USA in 1939, and taught and carried out research in mathematics at the University of...
  
  
• Ludwig Wittgenstein
  Ludwig Wittgenstein
  Ludwig Josef Johann Wittgenstein was an Austrian philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language. He was professor in philosophy at the University of Cambridge from 1939 until 1947...
  
  

Philosophers of logic

• W.V.O. Quine
• Bertrand Russell
  Bertrand Russell
  Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS was a British philosopher, logician, mathematician, historian, and social critic. At various points in his life he considered himself a liberal, a socialist, and a pacifist, but he also admitted that he had never been any of these things...
  
  
• Ludwig Wittgenstein
  Ludwig Wittgenstein
  Ludwig Josef Johann Wittgenstein was an Austrian philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language. He was professor in philosophy at the University of Cambridge from 1939 until 1947...
  
  

• Michael Dummett
  Michael Dummett
  Sir Michael Anthony Eardley Dummett FBA D.Litt is a British philosopher. He was, until 1992, Wykeham Professor of Logic at the University of Oxford...
  
  
• Hilary Putnam
  Hilary Putnam
  Hilary Whitehall Putnam is an American philosopher, mathematician and computer scientist, who has been a central figure in analytic philosophy since the 1960s, especially in philosophy of mind, philosophy of language, philosophy of mathematics, and philosophy of science...
  
  
• Saul Kripke
  Saul Kripke
  Saul Aaron Kripke is an American philosopher and logician. He is a professor emeritus at Princeton and teaches as a Distinguished Professor of Philosophy at the CUNY Graduate Center...
  
  

• Charles Sanders Peirce
• Alfred Tarski
  Alfred Tarski
  Alfred Tarski was a Polish logician and mathematician. Educated at the University of Warsaw and a member of the Lwow-Warsaw School of Logic and the Warsaw School of Mathematics and philosophy, he emigrated to the USA in 1939, and taught and carried out research in mathematics at the University of...
  
  
• Donald Davidson
  Donald Davidson (philosopher)
  Donald Herbert Davidson was an American philosopher born in Springfield, Massachusetts, who served as Slusser Professor of Philosophy at the University of California, Berkeley from 1981 to 2003 after having also held teaching appointments at Stanford University, Rockefeller University, Princeton...
  
  

Literature

• Fisher Jennifer, On the Philosophy of Logic, Thomson Wadworth, 2008, ISBN 13 978-0-495-00888-0
• Goble, Lou, ed., 2001. (The Blackwell Guide to) Philosophical Logic. Oxford: Blackwell
  Blackwell Publishing
  Wiley-Blackwell is the international scientific, technical, medical, and scholarly publishing business of John Wiley & Sons. It was formed by the merger of John Wiley's Global Scientific, Technical, and Medical business with Blackwell Publishing, after Wiley took over Blackwell Publishing in...
  
  . ISBN 0-631-20693-0.
• Grayling, A. C.
  A. C. Grayling
  Anthony Clifford Grayling is a British philosopher. In 2011 he founded and became the first Master of New College of the Humanities, a private undergraduate college in London. Until June 2011, he was Professor of Philosophy at Birkbeck, University of London, where he taught from 1991...
  
  , 1997. An Introduction to Philosophical Logic. 3rd ed. Oxford: Blackwell. ISBN 0-631-19982-9.
• Jacquette, Dale, ed., 2002. A Companion to Philosophical Logic. Oxford Blackwell. ISBN 1-4051-4575-7.
• McGinn, Colin, 2000. Logical Properties: Identity, Existence, Predication, Necessity, Truth. Oxford: Oxford University Press
  Oxford University Press
  Oxford University Press is the largest university press in the world. It is a department of the University of Oxford and is governed by a group of 15 academics appointed by the Vice-Chancellor known as the Delegates of the Press. They are headed by the Secretary to the Delegates, who serves as...
  
  . ISBN 0-19-926263-2.
• Sainsbury, Mark, 2001. Logical Forms: An Introduction to Philosophical Logic. 2nd ed. Oxford: Blackwell. ISBN 0-631-21679-0.
• Wolfram, Sybil, 1989. Philosophical Logic: An Introduction. London: Routledge
  Routledge
  Routledge is a British publishing house which has operated under a succession of company names and latterly as an academic imprint. Its origins may be traced back to the 19th-century London bookseller George Routledge...
  
  . 290 pages. ISBN 0415023181, 9780415023184
• Journal of Philosophical Logic, Springer SBM

External links

• Routledge Encyclopedia of Philosophy entry