[FOM] Relevance Logic and Tennant
silver_1 at mindspring.com
Sun Sep 1 13:05:05 EDT 2013
Not knowing as much as I should about Dick Epstein's "Relatedness Logic" doesn't stop me from wondering why it's never mentioned alongside of Relevant (Relevance) Logic(s). Is it considered "fatally flawed"? If you think so, can you, Harvey, or anyone else, provide any details or reference?
On Aug 31, 2013, at 12:03 AM, Harvey Friedman <hmflogic at gmail.com> wrote:
> 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
> FOM mailing list
> FOM at cs.nyu.edu
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