Lionel Shapiro

Validity and Truth-Preservation

The revisionary approach to semantic paradox is commonly thought to have a somewhat uncomfortable corollary, viz. that, on pain of triviality, we cannot affirm that all valid arguments preserve truth (Beall 2007, 2009; Field 2008, (2009b). We show that the standard arguments for this conclusion all break down once (i) the structural rule of contraction is restricted and (ii) how the premises can be aggregated—so that they can be said to jointly entail a given conclusion—is appropriately understood. In addition, we briefly rehearse some reasons for restricting structural contraction.

The very idea of a substructural approach to paradox

This paper aims to call into question the customary division of logically revisionary responses to the truth-theoretic paradoxes into those that are “substructural” and those that are “(fully) structural.” I proceed by examining, as a case study, Beall’s recent proposal based on the paraconsistent logic LP. Beall formulates his response to paradox in terms of a consequence relation that obeys all standard structural rules, though at the price of the language’s lacking a detaching conditional. I argue that the same response to paradox can be given using a consequence relation that preserves detachment rules for a conditional, though at the price of restricting structural rules. The question “Is paradox being blocked by invoking a substructural consequence relation?” is thus ill-posed. The lesson of this example, I conclude, is that there is no useful explication of the idea of a substructural approach to paradox.

Sellars on the Function of Semantic Vocabulary

This paper examines two explanations Sellars gives, at successive stages of his career, of how semantic vocabulary (paradigmatically ‘means that … ’ and ‘is true if and only if … ’) lets us relate linguistic expressions to extra-linguistic reality. Despite their differences, both explanations reveal a distinctive pragmatist approach. According to Sellars, we do not use semantic vocabulary to describe language-world relations. Rather, our taking language to relate to the world is implicit in the moves (inferential or non-inferential) licensed by our semantic assertions. I argue that Sellarss discussions of the function of semantic vocabulary point to an overlooked position regarding the relation between the concepts of meaning and truth. According to him, the function of meaning ascriptions cannot be explained independently of the function of truth ascriptions. That is because the function of meaning ascriptions essentially involves licensing claims about the world when combined with truth ascriptions. If he is right, this poses a challenge to deflationary accounts of the function of truth talk.

Intentionality Bifurcated: A Lesson from Early Modern Philosophy?

This paper examines the pressures leading two very different Early Modern philosophers, Descartes and Locke, to invoke two ways in which thought is directed at objects. According to both philosophers, I argue, the same idea can simultaneously count as “of” two different objects—in two different senses of the phrase ‘idea of’. One kind of intentional directedness is invoked in answering the question What is it to think that thus-and-so? The other kind is invoked in answering the question What accounts for the success of our proper methods of inquiry? For Descartes as well as Locke, the two kinds of “ofness” come apart as a result of strong rationalist commitments. However, I will suggest that even if we reject such commitments, we go wrong if we assume that a single kind of intentional directedness suffices to address both questions.

Between Saying and Doing: Towards an Analytic Pragmatism

A central thesis of Robert Brandom’s treatise Making It Explicit can be formulated in terms of a relation between two ‘vocabularies’, one intentional and the other normative-pragmatic. According to Brandom, the facts expressible in the former vocabulary (facts about what discursive subjects say and think) can be constitutively explained using the latter vocabulary (explained, that is, in terms of what it is appropriate for such subjects to do). Issues of use, meaning, and norms remain at the forefront of Brandom’s attention in the present volume, which contains the text of his 2006 John Locke Lectures (augmented by appendices and an afterword). But Brandom’s aim in this consistently inventive, provocative and engaging book is not to further pursue the project of reducing intentional facts to facts that can be specified non-intentionally. Rather, he presents a systematic metatheoretic framework with which to discuss the many ways one might delineate ‘semantic relations’ between two vocabularies. (Here ‘semantic relations’ are ones that hold in virtue of what contents the respective vocabularies can be used to express.) He argues that attending to some of the relations captured by his framework—specifically, relations that rest on consideration of the practices of vocabulary-users—makes room for an ‘analytic pragmatism’ that overcomes the limitations of the ‘classical project of analysis’. And he offers a wealth of highly suggestive applications of analytic pragmatism, with the overall aim of illuminating the mutual relations among logical, modal, normative, and intentional vocabulary. As Brandom views it, the ‘classical project of analysis’ aims to establish either of the following relations between vocabularies V1 and V2 (the terminology is mine, as his own distinctions are finer-grained):