[FOM] Relevance Logic and Tennant
Harvey Friedman
hmflogic at gmail.com
Sat Aug 31 03:03:01 EDT 2013
In communication offline with Neil Tennant, he has pointed out that in his
posting of http://www.cs.nyu.edu/pipermail/fom/2013-August/017528.html , he
has not indicated a rejection of the validity of thinning on the right,
thickening on the left, or related valid inference rules of classical logic.
Various forms of "rejection" on the part of those investigating or
proposing adoption of relevance logic, is reasonably standard. E.g.,
http://plato.stanford.edu/entries/logic-relevance "They claim that these
formulae fail to be valid if we interpret → as representing the concept of
implication that we have before we learn classical logic. Relevance
logicians claim that what is unsettling about these so-called paradoxes is
that in each of them the antecedent seems irrelevant to the consequent.
... In addition, relevance logicians have had qualms about certain
inferences that classical logic makes valid. For example, consider the
classically valid inference ..."
http://rationalwiki.org/wiki/Relevance_logic "Relevance logic attempts to
capture formally this intuitive idea, that the premises must be relevant to
the conclusion for the implication to be true."
http://consequently.org/papers/rle.pdf page 7. "Thus, most notoriously
the disjunctive syllogism (of Section 2) is counted as invalid."
http://johnmacfarlane.net/142/relevance-handout.pdf 2 Options
No one wants to reject ^ elimination. These options have all been tried:
(a) Reject _ Intro (a.k.a. “disjunctive weakening”)
(b) Reject the transitivity of entailment
(c) Reject Disjunctive Syllogism
http://www.st-andrews.ac.uk/~slr/Relevant_Logic.pdf Chapter 6 "Much of
Anderson and Belnap's argument for rejecting ex falso quodlibet
and setting up a logical system in which implication is non-truth-functional
depends on such claims as that `A and not-A' is not relevant to B, and
that relevance is a necessary condition for validity." ... "The idea that
validity requires a relevant connection between premises and
conclusion has a long history."
ALSO, in the case of intuitionistic logic and constructive mathematics,
many of the key figures, such as Brouwer and Bishop, have explicitly
rejected certain classical logic inferences as either invalid or
incoherent.
>From offline, Tennant is clearly putting forth a more nuanced position.
The interesting and relevant(!!) part of my posting is most of it, where I
do not (apparently incorrectly) ascribe views to Tennant. See
http://www.cs.nyu.edu/pipermail/fom/2013-August/017528.html and
http://www.cs.nyu.edu/pipermail/fom/2013-August/017535.html.
Harvey Friedman
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