On inferring

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The teaching of logic in philosophy aims to help us evaluate arguments for formal validity. Standard logics define validity in a way that allows for implication between premises and conclusions, even when they lack a relevant connection. A key example is the rule “Ex-Falso-Quodlibet” (EFQ), which permits inferring any proposition from a contradiction. This tolerance of irrelevance undermines the ability of standard logics to effectively analyze philosophical, scientific, and everyday arguments, often leading to artificial philosophical pseudoproblems, such as those related to disposition predicates or counterfactuals. In response, non-standard systems known as “relevance logics” aim to avoid irrelevance, but their mainstream relational semantics can be unintuitive and overly complex, making them less appealing to many philosophers seeking straightforward methods for argument evaluation. This treatise proposes an alternative “rules semantics” that is easier to understand and apply. Additionally, it aims to extend this semantics to encompass a wide range of logical concepts necessary for everyday analysis, including first-order predicate logic, higher-order logic, identity, definite descriptions, abstraction principles, and modal logic. The content is accessible to anyone with a solid introductory background in classical logic.