Information Technology Reference
In-Depth Information
be another ground for preferring the system R and just adding one's favorite
necessity operator(s).
But prominent researchers, even within the Anderson and Belnap community,
havechallengedtheappropriatenessofthename“relevancelogic.”RobertK.Meyer
infactpreferredtotalkof“relevantlogic.”Meyer(1978)containsanopeningsection
titled “Do relevant logics capture relevance.” 1 He then says (p. 3): “The answer to
thequestionwithwhichthissectionopensis'No'.Therelevantlogicsdonotcapture
relevance.Theydonot begin tocapturerelevance... . Despitethesub-titleof Entail-
ment ,there is no 'Logicof relevance'.” Meyer(1985)has a morenuanced discussion
of the issues, and we discuss these below.
2 More of Meyer on Relevance
Setting aside the personal (consistency with his own early usage) and the gram-
matical reason (“relevant” is the adjectival form), Meyer has a variety of more
substantive reasons, none of which he thinks in themselves make the logics E
and R less interesting (though he does have other concerns with E in particu-
lar, hence his title “Farewell to Entailment”). He says (p. 607): “I argue rather
that capturing relevance does not have much to do with the nature or purposes
of Relevant Logics.” Meyer's more substantive reasons include the elusiveness
of the notion of “relevance,” and the thought that (p. 610) “Relevance is not
an ingredient of a theory of logical entailment. Insofar as logical sense can be
assigned to the notion, it is a consequence of holding such a theory.”
Meyer goes on to examine Anderson and Belnap's argument that Entailment
gives a “ 'mathematically satisfactory way' of isolating relevance as a component
of good argument,” saying that there are the “two main strings of its bow.” The
first string is what Anderson and Belnap have labeled the “Variable Sharing
Property,” that is if A
B is a theorem, then there is some sentential variable
p that occurs in both A and B - thereby showing some connection of meaning, or
relevance . Both the logics E and R have this property. The second string is harder
to describe and depends on, as Meyer puts it, “tracking” the assumptions in a
natural-deduction argument to make sure that if A
B is proven by assuming
the antecedent A and showing the consequent B ,that A was actually used in
the derivation. This is supposed to show that A is relevant to B .
Both of these criteria have subtleties in their statement, and this might be
enough to undermine them as a criterion for “relevance.” To give one example,
[
p
( p
q )]
q has the Variable Sharing Property. Also the argument
p
( p
q is classically valid (it is the notorious Disjunctive Syllogism, which
Anderson and Belnap rejected, at least as a relevant implication). And yet the
q )
1 GregRestall(2006)explainswhyhecallsthesubject“relevantlogic,”although“nothing
of substance hangs on this issue: Americans call our topic 'relevance logic,' and people
of Commonwealth countries (primarily Australia and Scotland) call it 'relevant logic.'
ThesplitcomesdowntoadisagreementbetweenNuelBelnapandRobertMeyer.Meyer
brought his favored terminology 'relevant' with him to Australia, where it has stuck.”
 
Search WWH ::




Custom Search