Alan Ross Anderson
Encyclopedia
Alan Ross Anderson was an American
logician and professor
of philosophy
at Yale University
and the University of Pittsburgh
.
A frequent collaborator with Nuel Belnap
, Anderson was instrumental in the development of relevance logic
and deontic logic
.
Anderson died of cancer in 1973.
ought to have something to do with (i.e. be relevant to) the premise
s. Formally, he captured this "relevance
condition" with the principle that
As simple as this idea appears, implementing it in a formal system
requires a radical departure from the semantics
of classical logic
. Anderson and Belnap (with contributions from J. Michael Dunn, Kit Fine
, Alasdair Urquhart
, Robert K. Meyer, Anil Gupta (logician), 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
, but had been unduly neglected since Gottlob Frege
and George Boole
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
.)
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.
, or monist) about logic; he believed in "The One True Logic," and he believed that it was a relevance logic.
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
logician and professor
Professor
A professor is a scholarly teacher; the precise meaning of the term varies by country. Literally, professor derives from Latin as a "person who professes" being usually an expert in arts or sciences; a teacher of high rank...
of philosophy
Philosophy
Philosophy is the study of general and fundamental problems, such as those connected with existence, knowledge, values, reason, mind, and language. Philosophy is distinguished from other ways of addressing such problems by its critical, generally systematic approach and its reliance on rational...
at Yale University
Yale University
Yale University is a private, Ivy League university located in New Haven, Connecticut, United States. Founded in 1701 in the Colony of Connecticut, the university is the third-oldest institution of higher education in the United States...
and the University of Pittsburgh
University of Pittsburgh
The University of Pittsburgh, commonly referred to as Pitt, is a state-related research university located in Pittsburgh, Pennsylvania, United States. Founded as Pittsburgh Academy in 1787 on what was then the American frontier, Pitt is one of the oldest continuously chartered institutions of...
.
A frequent collaborator with Nuel Belnap
Nuel Belnap
Nuel D. Belnap, Jr. is an American logician and philosopher who has made many important contributions to the philosophy of logic, temporal logic, and structural proof theory. He has taught at the University of Pittsburgh since 1961; before that he was at Yale University. His best known work is...
, Anderson was instrumental in the development of relevance logic
Relevance logic
Relevance logic, also called relevant logic, is a kind of non-classical logic requiring the antecedent and consequent of implications be relevantly related. They may be viewed as a family of substructural or modal logics...
and deontic logic
Deontic logic
Deontic logic is the field of 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...
.
Anderson died of cancer in 1973.
Relevance logic
Anderson believed that the conclusion of a valid inferenceInference
Inference is the act or process of deriving logical conclusions from premises known or assumed to be true. The conclusion drawn is also called an idiomatic. The laws of valid inference are studied in the field of logic.Human inference Inference is the act or process of deriving logical conclusions...
ought to have something to do with (i.e. be relevant to) the premise
Premise
Premise can refer to:* Premise, a claim that is a reason for, or an objection against, some other claim as part of an argument...
s. Formally, he captured this "relevance
Relevance
-Introduction:The concept of relevance is studied in many different fields, including cognitive sciences, logic and library and information science. Most fundamentally, however, it is studied in epistemology...
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
Formal system
In formal logic, a formal system consists of a formal language and a set of inference rules, used to derive an expression from one or more other premises that are antecedently supposed or derived . The axioms and rules may be called a deductive apparatus...
requires a radical departure from the semantics
Semantics
Semantics is the study of meaning. It focuses on the relation between signifiers, such as words, phrases, signs and symbols, and what they stand for, their denotata....
of classical logic
Classical logic
Classical logic identifies a class of formal logics that have been most intensively studied and most widely used. The class is sometimes called standard logic as well...
. Anderson and Belnap (with contributions from J. Michael Dunn, Kit Fine
Kit Fine
Kit Fine is Silver Professor of Philosophy and Mathematics at New York University. He previously taught for several years at UCLA...
, Alasdair Urquhart
Alasdair Urquhart
Alasdair Ian Fenton Urquhart, born December 20, 1945, is an emeritus Professor of Philosophy at the University of Toronto. He has made notable contributions to the field of logic, especially non-classical logic. One of his most notable achievements is proving the undecidability of the relevance...
, Robert K. Meyer, Anil Gupta (logician), 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
Relevance logic
Relevance logic, also called relevant logic, is a kind of non-classical logic requiring the antecedent and consequent of implications be relevantly related. They may be viewed as a family of substructural or modal logics...
.
Anderson and Belnap were quick to observe that the concept of relevance had been central to logic since 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...
, but had been unduly neglected since 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...
and 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,...
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
Principle of explosion
The principle of explosion, or the principle of Pseudo-Scotus, is the law of classical logic and intuitionistic and similar systems of logic, according to which any statement can be proven from a contradiction...
.)
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
Norm (philosophy)
Norms are concepts of practical import, oriented to effecting an action, rather than conceptual abstractions that describe, explain, and express. Normative sentences imply “ought-to” types of statements and assertions, in distinction to sentences that provide “is” types of statements and assertions...
has been violated. He developed systems of deontic
Deontic logic
Deontic logic is the field of 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...
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 realistPhilosophical 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....
, or monist) about logic; he believed in "The One True Logic," and he believed that it was a relevance logic.
Resources
- 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 PressPrinceton University Press-Further reading:* "". Artforum International, 2005.-External links:* * * * *...
. - Anderson, A. R., Belnap, N. D., and Dunn, J. M. 1992. Entailment: The Logic of Relevance and Necessity. Vol. 2. Princeton: Princeton University Press. ISBN 0-691-07339-2
- Mares, E. D. 1992. Andersonian deontic logic. Theoria 58: 3-20.