Alan Ross Anderson (1925–1973) was an American logician and

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

philosophy Philosophy ('love of wisdom' in Ancient Greek) is a systematic study of general and fundamental questions concerning topics like existence, reason, knowledge, Value (ethics and social sciences), value, mind, and language. It is a rational an ...

Yale University Yale University is a Private university, private Ivy League research university in New Haven, Connecticut, United States. Founded in 1701, Yale is the List of Colonial Colleges, third-oldest institution of higher education in the United Stat ...

and the

University of Pittsburgh The University of Pittsburgh (Pitt) is a Commonwealth System of Higher Education, state-related research university in Pittsburgh, Pennsylvania, United States. The university is composed of seventeen undergraduate and graduate schools and colle ...

. A frequent collaborator with Nuel Belnap, Anderson was instrumental in the development of relevance logic and deontic logic. Anderson died of cancer in 1973.

Relevance logic

Anderson believed that the conclusion of a valid

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

ought to have something to do with (i.e. be ''relevant'' to) the premises. Formally, he captured this " relevance 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 requires a radical departure from the

semantics Semantics is the study of linguistic Meaning (philosophy), meaning. It examines what meaning is, how words get their meaning, and how the meaning of a complex expression depends on its parts. Part of this process involves the distinction betwee ...

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 c ...

. Anderson and Belnap (with contributions from J. Michael Dunn, Kit Fine, Alasdair Urquhart, Robert K. Meyer, 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 relevance logic. Anderson and Belnap were quick to observe that the concept of relevance had been central to logic since

Aristotle Aristotle (; 384–322 BC) was an Ancient Greek philosophy, Ancient Greek philosopher and polymath. His writings cover a broad range of subjects spanning the natural sciences, philosophy, linguistics, economics, politics, psychology, a ...

, 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 philos ...

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 Ireland. H ...

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.)

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 has been violated''. He developed systems of deontic 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. 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 (or realist, or monist) about logic; he believed in "The One True Logic," and he believed that it was a relevance logic.

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 ...

. * 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