Read, Stephen - Monism: The One True Logic

02/06/2009


In this paper author attacks the logical pluralism of Beall and Restall, which tries to admit to classical, constructionist and situational logics as all equally valid. Author categorizes their argument as follows:
1. Validity (V) is defined as: (V) A conclusion 'A' follows from premises iff in any case the premises are true is also a case when A is true. (here cases are 'worlds' or 'constructions' or 'situations')
2. A 'logic' specifies the cases mentioned in (V)
3. There are at least two different specifications
(pg1)
Author represents Beall & Restall as reconstructing different times when (V) can be specified: in classical logic, (V) is preserved in 'complete and consistent situations' like 'worlds'. Constructive logic specifies (V) in possibly incomplete or indeterminate situations, and finally relevance logic specifies a logic that satisfies (V) in inconsistent situations. (pg1) Author now repeats Graham Priest's challenge to this account: take logic K1 and K2-- in K1 premises P imply conclusion C. In K2, P doesn't imply C. P is true. Is C true? Author argues this challenge forces the position that K1 is superior to K2 (K1 being classical logic here). (pg2-3)

Author believes that Beall & Restall's logical pluralism by trying to preserve truth under (V) will plunge into inconsistency (pg4), a major sticking point being the non-dialetheic paraconsistentist, who belives that Ex Falso Quodlibet (from a contradiction, anything follows) is invalid but also doesn't believe that contradictions can be true. (pg5-6) The Beall & Restall reply is to ask for not just truth-preservation but also relevance-preservation from (V), but author argues this doesn't fit the bill either (pg6).

The problem, author believes, is to try to write the semantics of non-classical logics in 'classical metalanguage'. This puts the classicist in an unfair advantage when evaluating validity (pg7). Author unravels this argument in the pages that follow (pg8-10), by the way examining the claims of Varzi and Yagisawa in trying to establish the coherency of possible impossible worlds. Author offers instead relevance logic as the one true logic and chastises Beall & Restall for 'combining non-classical theory with a classical metatheory' (pg9).