Relevant implication and the case for a weaker logic

Brady, Ross T.

doi:10.1007/bf00247002

Cited by 22 publications

(21 citation statements)

References 34 publications

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“…In contrast, in Brady (1996) and Brady (2006), entailment is conceptualized, in a singular positive way, as meaning containment. Logical contents and ranges of atomic formulae are introduced, to which reasonable properties are added, which in turn enable these contents and ranges to extend to compound formulae.…”

Section: Classical Logic and Classical Negationmentioning

confidence: 99%

“…As in the first alternative, there is the issue of whether classicality applies to abstractions and idealizations on the physical world (see Brady, 1996), and Brady (2006), also, Brady (2007). Certainly, the two-sorted approach requires some domain of classicality for these classical formulae to apply to.…”

Section: Classical Logic and Classical Negationmentioning

confidence: 99%

“…Then, soundness and completeness theorems are proved for the logic MC with respect to the above content semantics. As can be seen in Brady (1996) and Brady (2006), the above axiomatization is very largely pinned down by the content semantics. Each of the axioms, rules, and meta-rule are shown to satisfy the meaning considerations, expressed as logical contents.…”

Section: Classical Logic and Classical Negationmentioning

confidence: 99%

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Four Basic Logical Issues

Brady

Rush

2009

The Review of Symbolic Logic

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The paper addresses what we see as the four major issues in logic. The overriding issue is that of the choice of logic. We start with some discussion of the preliminary issue of whether there is such a 'one true logic,' but we reserve the main discussion for the first issue of 'classical logic versus non-classical logic.' Here, we discuss the role of meaning and truth, the relation between classical logic and classical negation, and whether and, if so, how classical logic should reside at the base world. Given the argument in favor of an overall use of non-classical logic, the second issue is that of the choice of non-classical logic. Brady's logic MC of meaning containment is argued for, with some comparison made with other relevant logics. For the remaining two issues, we make a case for relevant deduction, in comparison with classical deduction, and we explore possibilities for the appropriate meta-logic, comparing classical and non-classical approaches.

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Section: Classical Logic and Classical Negationmentioning

confidence: 99%

Section: Classical Logic and Classical Negationmentioning

confidence: 99%

Section: Classical Logic and Classical Negationmentioning

confidence: 99%

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Four Basic Logical Issues

Brady

Rush

2009

The Review of Symbolic Logic

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“…Let (1.4) and assume inductively that (13) , . From (1.4) and (13), using Definition 8.6, by Corollary 8.4 (62), in (1.4), one can obtain that (14) .…”

Section: Systemmentioning

confidence: 99%

Atomic Entailment and Atomic Inconsistency and Classical Entailment

Stȩpień¹

2015

JMSS

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Abstract:In this paper we put forward a new solution of the well-known problem of relevant logics,i.e., we construct an atomic entailment. Hence, we construct a system of predicate calculus based on the atomic entailment. Next, we establish the definition of atomic inconsistency. The atomic inconsistency establishes an infinite class of inconsistent, but non-trivial systems. In this paper we construct the new definition of the classical entailment, into the bargain.

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“…We draw lit should be entered in the record that there are some workers in relevance logic who consider both Rand E too strong for at least some purposes (see [Routley, 1977], [Routley et al, 1982], and more recently, [Brady, 1996]). We draw lit should be entered in the record that there are some workers in relevance logic who consider both Rand E too strong for at least some purposes (see [Routley, 1977], [Routley et al, 1982], and more recently, [Brady, 1996]).…”

Section: Implication and The Conditionalmentioning

confidence: 99%

Handbook of Philosophical Logic

2002

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Relevant implication and the case for a weaker logic

Cited by 22 publications

References 34 publications

Four Basic Logical Issues

Four Basic Logical Issues

Atomic Entailment and Atomic Inconsistency and Classical Entailment

Handbook of Philosophical Logic

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