In Support of Valerie Plumwood

Abstract

This paper offers general support for what Valerie Plumwood’s paper is trying to achieve by supporting the rejection of each of her four “false laws of logic”: exportation, illegitimate replacement, commutation (aka. permutation) and disjunctive syllogism. We start by considering her general characterizations of entailment, beginning with her stated definition of entailment as the converse of deducibility. However, this applies to a wide range of relevant logics and so is not able to be used as a criterion for deciding what laws to include in a logic. In this context, we examine the two key differences between deduction from premises to conclusion and entailment from antecedent to consequent. We also consider her use of sufficiency as a general characterizing feature. We then discuss Plumwood’s syntactic criteria used to reject the first three of her false laws of logic and add the Relevance Condition in this context. We next consider semantic characterizing criteria for a logic. After making a case against using truth, we introduce Brady’s logic MC of meaning containment. We then examine the content semantics for MC and use it to reject all of Plumwood’s false laws of logic together with some others. We follow with the related Depth Relevance Condition, which is a syntactic cri- terion satisfied by MC. This clearly rejects the first three of these laws and many others, but not the fourth law. We conclude by giving our overall support for her general enterprise.