- Alan Ross Anderson
Alan Ross Anderson, born 1925, was an American
logicianand professorof philosophyat Yale Universityand the University of Pittsburgh. A frequent collaborator with Nuel Belnap, Anderson was instrumental in the development of relevance logicand deontic logic.
Anderson died of
Anderson believed that the
conclusionof a valid inferenceought to have something to do with (i.e. be "relevant" to) the premises. Formally, he captured this " relevancecondition" with the principle that
: "A" entails "B" only if "A" and "B" share at least one non-logical
As simple as this idea appears, implementing it in a
formal systemrequires a radical departure from the semanticsof 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 Fregeand George Boolelaid 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.)
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.
* 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.
* 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.
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