Logical Consequence

Abstract

As with his account of truth, Tarski’s account of logical consequence has come in for a great deal of abuse. Characteristic here is Etchemendy’s familiar assessment that Tarski’s “account of logical truth and logical consequence does not capture, or even come close to capturing, any pretheoretic conception of the logical properties” [Etchemendy, 1990, 6]. Tarski’s conception of consequence has likewise been subject to “defenses” that either attempt to make virtues out of its least attractive features or are implausible as readings of what Tarski actually said. Many of these defenses read “On the Concept of Following Logically” through the lens of the lecture “What are Logical Notions?”, a lecture delivered thirty-one years after the original presentation of the conception of consequence. Though there is some basis for this in work contemporary with CLC, e.g. [Tarski, 1983i], the astonishing fact about the literature is that pretty much nobody has bothered to follow up the article’s many references to Carnap’s Logical Syntax in any detail—this despite the fact that the only conception of consequence Tarski mentions is Carnap’s. I will argue that the article intends nothing more than an improvement on Carnap’s conception that consists in replacing Carnap’s reliance on the notion of substitution with Tarski’s treatment of semantics, and transformation rules taken as primitive with the notion of truth-preservation leaving everything else untouched, and that all of the important claims and arguments in the article are directed at Carnap.KeywordsLogical ConsequenceTransformation RuleLogical TruthTrue SentenceIncompleteness TheoremThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.