Lionel Shapiro

Several authors have argued that a version of Curry's paradox involving validity motivates rejecting the structural rule of contraction. This paper criticizes two recently suggested alternative responses to “validity Curry.” There are three salient stages in a validity Curry derivation. Rejecting contraction blocks the first, while the alternative responses focus on the second and third. I show that a distinguishing feature of validity Curry, as contrasted with more familiar forms of Curry's paradox, is that paradox arises already at the first stage. Accordingly, blocking the second or third stages won't suffice for resolving the paradox.

Reichenbach's Philosophy of Space and Time (1928) avoids most of the logical positivist pitfalls it is generally held to exemplify, notably both conventionalism and verificationism. To see why, we must appreciate that Reichenbach's interest lies in how mathematical structures can be used to describe reality, not in how words like 'distance' acquire meaning. Examination of his proposed "coordinative definition" of congruence shows that Reichenbach advocates a reductionist analysis of the relations figuring in physical geometry (contrary to common readings that attribute to him a holistic conventionalism), while embracing a thoroughly holistic understanding of empirical confirmation (contrary to rival operationalist readings).

According to Gupta and Belnap, the “extensional behavior” of ‘true’ matches that of a circularly defined predicate. Besides promising to explain semantic paradoxicality, their general theory of circular predicates significantly liberalizes the framework of truth-conditional semantics. The authors’ discussions of the rationale behind that liberalization invoke two distinct senses in which a circular predicate’s semantic behavior is explained by a “revision rule” carrying hypothetical information about its extension. Neither attempted explanation succeeds. Their theory may however be modified to employ a relativized notion of extension. The resulting contextualist semantics for ‘true’ construes circularity as a pragmatic phenomenon.