Following the developments in Formal logic with
symbolic logicSymbolic logic is the area of mathematics which studies the purely formal properties of strings of symbols. The interest in this area springs from two sources. First, the symbols used in symbolic logic can be seen as representing the words used in philosophical logic...
in the late nineteenth century and
mathematical logicMathematical logic is a subfield of mathematics with close connections to 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
logicLogic, from the Greek λογική is the art and science of reasoning. More specifically, it is defined by the Penguin Encyclopedia to be "The formal systematic study of the principles of valid inference and correct reasoning". As a discipline, logic dates back to Aristotle, who established its...
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 logicPhilosophical logic is the study of the more specifically philosophical aspects of logic. The term contrasts with philosophy of logic, metalogic, and mathematical logic; and since the development of mathematical logic in the late nineteenth century, it has come to include most of those topics...
is of recent coinage and not always entirely clear.
Following the developments in Formal logic with
symbolic logicSymbolic logic is the area of mathematics which studies the purely formal properties of strings of symbols. The interest in this area springs from two sources. First, the symbols used in symbolic logic can be seen as representing the words used in philosophical logic...
in the late nineteenth century and
mathematical logicMathematical logic is a subfield of mathematics with close connections to 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
logicLogic, from the Greek λογική is the art and science of reasoning. More specifically, it is defined by the Penguin Encyclopedia to be "The formal systematic study of the principles of valid inference and correct reasoning". As a discipline, logic dates back to Aristotle, who established its...
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 logicPhilosophical logic is the study of the more specifically philosophical aspects of logic. The term contrasts with philosophy of logic, metalogic, and mathematical logic; and since the development of mathematical logic in the late nineteenth century, it has come to include most of those topics...
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, from the Greek λογική is the art and science of reasoning. More specifically, it is defined by the Penguin Encyclopedia to be "The formal systematic study of the principles of valid inference and correct reasoning". As a discipline, logic dates back to Aristotle, who established its...
. The field is considered to be distinct from philosophical logicPhilosophical logic is the study of the more specifically philosophical aspects of logic. The term contrasts with philosophy of logic, metalogic, and mathematical logic; and since the development of mathematical logic in the late nineteenth century, it has come to include most of those topics...
and metalogicMetalogic is the study of the metatheory of logic. While logic is the study of the manner in which logical systems can be used to decide the correctness of arguments, metalogic studies the properties of the logical systems themselves...
.
- Philosophical logic is the branch of logic
Logic, from the Greek λογική is the art and science of reasoning. More specifically, it is defined by the Penguin Encyclopedia to be "The formal systematic study of the principles of valid inference and correct reasoning". As a discipline, logic dates back to Aristotle, who established its...
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
In 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 or sentencing may refer to:* Sentence , a grammatical unit of language* Sentence , a formula with no free variables* Sentence , the smallest period in a musical composition...
, Statements, PropositionA proposition is a sentence expressing something true or false. In philosophy, particularly in logic, a proposition is identified ontologically as an idea, concept, or abstraction whose token instances are patterns of symbols, marks, sounds, or strings of words...
.
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 truths 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
An interpretation is an assignment of "meaning" to the symbols of a 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 consequenceLogical consequence is a fundamental concept in logic. It is the relation that holds between a set of sentences and a sentence when the former "entails" the latter...
and
entailmentIn linguistics, entailment is the relationship between two sentences where the truth of one requires the truth of the other . This relationship is generalized below.As a tool or method to make progress, one might use the entailment concept...
(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 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 WittgensteinLudwig Josef Johann Wittgenstein was an Austrian-British philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language....
said that a
logical truth was a statement which is true in all possible worlds. This is contrasted with
synthetic claim (or
factA fact is a pragmatic truth, a statement that can, at least in theory, be checked and confirmed. Facts are often contrasted with opinions and beliefs, statements which are held to be true, but are not amenable to pragmatic confirmation....
) which is only true in
this world as it has historically unfolded.
Some argue that a "
propositionA proposition is a sentence expressing something true or false. In philosophy, particularly in logic, a proposition is identified ontologically as an idea, concept, or abstraction whose token instances are patterns of symbols, marks, sounds, or strings of words...
" 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
meaning- Theoretic :* Meaning , meaning which is communicated through the use of language* Meaning , extra-linguistic meaning , and natural meaning, where no intentions are involved at all* Meaning has to do with the distribution of signs in sign relations* Meaning as a relationship between...
s and not because of any facts of the world, i.e they are not synthetic.
See
- 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
Formal and material consequence
- The problem of the material conditional: see Material conditional
The material conditional, also known as the material implication or truth functional conditional, expresses a property of certain conditionals in logic. In propositional logic, it expresses a binary truth function from truth-values to truth-values. In predicate logic, it can be viewed as a subset...
Philosophical theories of logic
- Conceptualism
Conceptualism is a doctrine in philosophy intermediate between nominalism and realism that says universals exist only within the mind and have no external or substantial reality.- Conceptualism in scholasticism :...
- Constructivism
In the philosophy of mathematics, constructivism asserts that it is necessary to find a mathematical object to prove that it exists...
- Dialetheism
Dialetheism is the view that there are true contradictions, or dialetheia. More specifically, dialetheists believe that for some sentence or proposition P, both P and its negation, not-P , are true. Dialetheism is not itself a formal logic, but to endorse dialetheism without accepting some...
- 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 a useful fiction...
- Finitism
In the philosophy of mathematics, 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
- 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 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 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 Gottlob Frege...
- 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
Contemporary philosophical realism is the belief in a reality that is completely ontologically independent of our conceptual schemes, linguistic practices, beliefs, etc. Philosophers who profess realism also typically believe that truth consists in a belief's correspondence to reality...
- Platonic realism
Platonic realism is a philosophical term usually used to refer to the idea of realism regarding the existence of universals after the Greek philosopher Plato , a student of Socrates, and the teacher of Aristotle...
- Representationalism
- Structuralism
Structuralism is an approach to the human sciences that attempts to analyze a specific field as a complex system of interrelated parts. It began in linguistics with the work of Ferdinand de Saussure...
Other Topics
- Leibniz's Law: see 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
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 is a philosophical term usually used to refer to the idea of realism regarding the existence of universals after the Greek philosopher Plato , a student of Socrates, and the teacher of Aristotle...
, Philosophical realismContemporary philosophical realism is the belief in a reality that is completely ontologically independent of our conceptual schemes, linguistic practices, beliefs, etc. Philosophers who profess realism also typically believe that truth consists in a belief's correspondence to reality...
- The Law of Excluded Middle: see Law of excluded middle
In logic, The Law of excluded middle, also known as the Principle of excluded middle or Excluded middle is the principle that for any proposition, either that proposition is true, or its negation is. The principle can be expressed in either a logical or a semantical form. The semantical form...
- Modality, Intensionality and Propositional Attitude
- Counter-factuals
See also
- Logic
Logic, from the Greek λογική is the art and science of reasoning. More specifically, it is defined by the Penguin Encyclopedia to be "The formal systematic study of the principles of valid inference and correct reasoning". As a discipline, logic dates back to Aristotle, who established its...
- 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
In 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 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 PressCambridge University Press is a printer and publisher granted a Royal Letters Patent by Henry VIII in 1534. It is the world's oldest continually operating book publisher...
. (ISBN 0-521-29329-4)
- Quine, W. V. O. 2004. Philosophy of Logic. 2nd ed. Harvard University Press
Harvard University Press is a publishing house, a division of Harvard University, that is highly respected in academic publishing. It was established on January 13, 1913. In 2005, it published 220 new titles. It is a member of the Association of American University Presses . The current director...
. (ISBN 0-674-66563-5)
Important figures
Important figures in the philosophy of logic include (but are not limited to):
- Aristotle
Aristotle was a Greek philosopher, a student of Plato and teacher of Alexander the Great. He wrote on many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, politics, government, ethics, biology, and zoology.Together with Plato and Socrates , Aristotle is one of...
- George Boole
George Boole was anEnglish mathematician and philosopher.As the inventor of Boolean logic, which is the basis of modern digital computer logic, Boole is regarded in hindsight as one of the founders of the field of computer science. Boole said,.....
- 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 was an influential German-born philosopher who was active in Europe before 1935 and in the United States thereafter. He was a leading member of the Vienna Circle and a prominent advocate of logical positivism.-Life and work:Carnap was born to a west German family that had been humble...
- 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 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...
- Augustus De Morgan
Augustus De Morgan was a British mathematician and logician. He formulated De Morgan's laws and introduced the term mathematical induction, and made its idea rigorous. The crater De Morgan on the Moon is named after him....
- Michael Dummett
Sir Michael Anthony Eardley Dummett FBA D.Litt is a leading British philosopher. He has both written on the history of analytic philosophy, and made original contributions to the subject, particularly in the areas of philosophy of mathematics, philosophy of logic, philosophy of language and...
- Gottlob Frege
Friedrich Ludwig Gottlob Frege was a German mathematician who became a logician and philosopher. He was one of the founders of modern logic, and made major contributions to the foundations of mathematics. As a philosopher, he is generally considered to be the father of analytic philosophy, for his...
- Kurt Gödel
Kurt Gödel was an Austrian-American logician, mathematician and philosopher. One of the most significant logicians of all time, Gödel made an immense impact upon scientific and philosophical thinking in the 20th century, a time when many, such as Bertrand Russell, A. N...
- Georg Hegel
- Immanuel Kant
Immanuel Kant was an 18th-century German philosopher from the Prussian city of Königsberg...
- Gottfried Leibniz
Gottfried Wilhelm Leibniz was a German philosopher, polymath and mathematician who wrote primarily in Latin and French....
- David Lewis
-Academics:*David Lewis , civil lawyer and first Principal of Jesus College, Oxford*David Lewis , English author and psychologist*David C...
- John Stuart Mill
John Stuart Mill , English philosopher, political theorist, political economist, civil servant and Member of Parliament, was an influential liberal thinker of the 19th century whose works on liberty justified freedom of the individual in opposition to unlimited state control...
- Charles Sanders Peirce
- Alvin Plantinga
Alvin Carl Plantinga is an American philosopher, currently the John A. O'Brien Professor of Philosophy at the University of Notre Dame. He is known for his work in epistemology, metaphysics, and the philosophy of religion, and in particular for applying the methods of analytic philosophy to defend...
- Arthur Prior
Arthur Norman Prior was a noted logician. Prior founded tense logic, now also known as temporal logic, and made important contributions to intensional logic, particularly in Prior ....
- Willard Van Orman Quine
Willard Van Orman Quine was an American philosopher and logician in the analytic tradition...
- Bertrand Russell
Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS was an English philosopher, logician, mathematician, historian, and social critic. Although he spent the majority of his life in England, he was born in Wales, where he also died.Russell led the British "revolt against idealism" in the...
- Alfred Tarski
Alfred Tarski was a Polish logician and mathematician...
- Ludwig Wittgenstein
Ludwig Josef Johann Wittgenstein was an Austrian-British philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language....
Philosophers of logic
- W.V.O. Quine
- Bertrand Russell
Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS was an English philosopher, logician, mathematician, historian, and social critic. Although he spent the majority of his life in England, he was born in Wales, where he also died.Russell led the British "revolt against idealism" in the...
- Ludwig Wittgenstein
Ludwig Josef Johann Wittgenstein was an Austrian-British philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language....
- Michael Dummett
Sir Michael Anthony Eardley Dummett FBA D.Litt is a leading British philosopher. He has both written on the history of analytic philosophy, and made original contributions to the subject, particularly in the areas of philosophy of mathematics, philosophy of logic, philosophy of language and...
- Hilary Putnam
Hilary Whitehall Putnam is an American philosopher who has been a central figure in analytic philosophy since the 1960s, especially in philosophy of mind, philosophy of language, and philosophy of science...
- Saul Kripke
Saul Aaron Kripke is an American philosopher and logician, now emeritus from Princeton. He teaches as distinguished professor of philosophy at CUNY Graduate Center. Since the 1960s Kripke has been a central figure in a number of fields related to logic, philosophy of language, metaphysics,...
- Charles Sanders Peirce
- Alfred Tarski
Alfred Tarski was a Polish logician and mathematician...
- Donald Davidson
Donald Herbert Davidson was an American philosopher who served as Slusser Professor of Philosophy at the University of California, Berkeley from 1981 to 2003 after having also held substantive teaching appointments at Stanford University, Rockefeller University, Princeton University, and the...
Literature
- Goble, Lou, ed., 2001. (The Blackwell Guide to) Philosophical Logic. Oxford: Blackwell
Wiley-Blackwell, formerly Blackwell Publishing, is a learned society publishing company based in Oxford, England. It was formed by the merger of two earlier Blackwell companies in 2001 and was taken over by John Wiley & Sons in 2007...
. ISBN 0-631-20693-0.
- Grayling, A. C.
Anthony Clifford Grayling, FRSA, FRSL is a British philosopher and author. He is Professor of Philosophy at Birkbeck, University of London and a supernumerary fellow of St Anne's College, Oxford...
, 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.
- Sainsbury, Mark, 2001. Logical Forms: An Introduction to Philosophical Logic. 2nd ed. Oxford: Blackwell. ISBN 0-631-21679-0.
- McGinn, Colin. 2000. Logical Properties: Identity, Existence, Predication, Necessity, Truth. Oxford: Oxford University Press
Oxford house 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 OUP's...
. ISBN 0-19-926263-2.
- Wolfram, Sybil, 1989. Philosophical Logic: An Introduction. London: Routledge
Routledge has been a long-standing and respected name in British and academic publishing, both as a publishing house 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, who issued his first...
. 290 pages. ISBN 0415023181, 9780415023184
- Journal of Philosophical Logic, Springer SBM
- Fisher J, On the Philosophy of Logic, Thomson Wadworth, 2008, ISBN 13 978-0-495-00888-0
External links