Alan Ross Anderson (1925–1973) was an American

logician 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 ...

and

professor Professor (commonly abbreviated as Prof.) is an Academy, academic rank at university, universities and other post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin as a "person who pr ...

philosophy Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language. Such questions are often posed as problems to be studied or resolved. Some ...

Yale University Yale University is a private research university in New Haven, Connecticut. Established in 1701 as the Collegiate School, it is the third-oldest institution of higher education in the United States and among the most prestigious in the wo ...

and the

University of Pittsburgh The University of Pittsburgh (Pitt) is a public state-related research university in Pittsburgh, Pennsylvania. The university is composed of 17 undergraduate and graduate schools and colleges at its urban Pittsburgh campus, home to the universit ...

. A frequent collaborator with

Nuel Belnap Nuel Dinsmore Belnap Jr. (; born 1930) is an American logician and philosopher who has made contributions to the philosophy of logic, temporal logic, and structural proof theory. He taught at the University of Pittsburgh from 1963 until his ret ...

, Anderson was instrumental in the development of

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 ...

and

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. I ...

. Anderson died of cancer in 1973.

Relevance logic

Anderson believed that the conclusion of a valid

inference Inferences are steps in reasoning, moving from premises to logical consequences; etymologically, the word '' infer'' means to "carry forward". Inference is theoretically traditionally divided into deduction and induction, a distinction that in ...

ought to have something to do with (i.e. be ''relevant'' to) the

premise A premise or premiss is a true or false statement that helps form the body of an argument, which logically leads to a true or false conclusion. A premise makes a declarative statement about its subject matter which enables a reader to either agre ...

s. Formally, he captured this "

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 ...

condition" with the principle that : ''A'' entails ''B'' only if ''A'' and ''B'' share at least one non-logical constant. As simple as this idea appears, implementing it in 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 ...

requires a radical departure from the

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 Philosophy (f ...

classical logic Classical logic (or standard logic or Frege-Russell logic) is the intensively studied and most widely used class of deductive logic. Classical logic has had much influence on analytic philosophy. Characteristics Each logical system in this class ...

. Anderson and Belnap (with contributions from

J. Michael Dunn J. Michael Dunn (June 19, 1941 – April 5, 2021) was Oscar Ewing Professor Emeritus of Philosophy, Professor Emeritus of Informatics and Computer Science, was twice chair of the Philosophy Department, was Executive Associate Dean of the College o ...

Kit Fine Kit Fine (born 26 March 1946) is a British philosopher, currently university professor and Silver Professor of Philosophy and Mathematics at New York University. Prior to joining the philosophy department of NYU in 1997, he taught at the Uni ...

Alasdair Urquhart Alasdair Ian Fenton Urquhart (; born 20 December 1945) is a Scottish–Canadian philosopher and emeritus professor of philosophy at the University of Toronto. He has made contributions to the field of logic, especially non-classical logic. On ...

Robert K. Meyer The name Robert is an ancient Germanic given name, from Proto-Germanic "fame" and "bright" (''Hrōþiberhtaz''). Compare Old Dutch ''Robrecht'' and Old High German ''Hrodebert'' (a compound of ''Hrōþ, Hruod'' ( non, Hróðr) "fame, glory ...

, Anil Gupta, and others) explored the formal consequences of the relevance condition in great detail in their influential ''Entailment'' books (see references below), which are the most frequently cited works in the field of

. Anderson and Belnap were quick to observe that the concept of relevance had been central to logic since

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 phil ...

, but had been unduly neglected since

Gottlob Frege Friedrich Ludwig Gottlob Frege (; ; 8 November 1848 – 26 July 1925) was a German philosopher, logician, and mathematician. He was a mathematics professor at the University of Jena, and is understood by many to be the father of analytic phil ...

and

George Boole George Boole (; 2 November 1815 – 8 December 1864) was a largely self-taught English mathematician, philosopher, and logician, most of whose short career was spent as the first professor of mathematics at Queen's College, Cork in Ire ...

laid the foundations for what would come to be known, somewhat ironically, as "classical" logic. (For an example of classical logic's failure to satisfy the relevance condition, see the article on the

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 co ...

Deontic logic

Anderson advocated the view that sentences of the form "It ought to be (the case) that ''A''" should be interpreted logically as: * Not-''A'' entails v, where v means something like ''a

norm Naturally occurring radioactive materials (NORM) and technologically enhanced naturally occurring radioactive materials (TENORM) consist of materials, usually industrial wastes or by-products enriched with radioactive elements found in the envir ...

has been violated''. He developed systems of

deontic In moral philosophy, deontological ethics or deontology (from Greek language, Greek: + ) is the normative ethics, normative ethical theory that the morality of an action should be based on whether that action itself is right or wrong under a s ...

relevance logic containing a special constant v (notation varies) for this purpose. Such systems have sometimes been characterized as "reductions" of deontic logic to alethic

modal logic Modal logic is a collection of formal systems developed to represent statements about necessity and possibility. It plays a major role in philosophy of language, epistemology, metaphysics, and natural language semantics. Modal logics extend other ...

. This is misleading at best, however, since alethic modal logics generally do not contain anything like Anderson's special v constant.

Philosophy of logic

Anderson was known for being a

Platonist Platonism is the philosophy of Plato and school of thought, philosophical systems closely derived from it, though contemporary platonists do not necessarily accept all of the doctrines of Plato. Platonism had a profound effect on Western though ...

(or realist, or

monist Monism attributes oneness or singleness (Greek: μόνος) to a concept e.g., existence. Various kinds of monism can be distinguished: * Priority monism states that all existing things go back to a source that is distinct from them; e.g., i ...

) about logic; he believed in "The One True Logic," and he believed that it was a

Bibliography

* Anderson, A. R. 1967. Some nasty problems in the formal logic of ethics. ''Nous'' I(4): 345-60. * Anderson, A. R. and Belnap, N. D. 1975. ''Entailment: The Logic of Relevance and Necessity. Vol. 1.'' Princeton:

Princeton University Press Princeton University Press is an independent publisher with close connections to Princeton University. Its mission is to disseminate scholarship within academia and society at large. The press was founded by Whitney Darrow, with the financial su ...

. * Anderson, A. R., Belnap, N. D., and Dunn, J. M. 1992. ''Entailment: The Logic of Relevance and Necessity. Vol. 2.'' Princeton: Princeton University Press.

Relevance logic

Deontic logic

Philosophy of logic

Bibliography

References

Further reading