Diversity Reading List

Abstract: Description: This article is a short overview of philosophical and formal issues in the treatment and analysis of logical consequence. The purpose of the paper is to provide a brief introduction to the central issues surrounding two questions: (1) that of the nature of logical consequence and (2) that of the extension of logical consequence. It puts special emphasis in the role played by formal systems in the investigation of logical consequence.

Introduction: Though it is hardly uncontroversial, the thesis that logic is normative enjoys widespread agreement—probably just about as much agreement as one is ever likely to find in philosophy. There is far less agreement, however, on what exactly this thesis amounts to. To begin with, proponents of the
thesis can’t seem to agree on whether the normative authority of logic is robust or weak. If logic is robustly normative, it has a normative authority that is independent of our attitudes or conventions; if it is weakly normative, it has a normative au- thority that is entirely dependent on our attitudes or conventions. This fundamental disagreement about the normative authority of logic seems to leave little room for any point of agreement among the proponents of the thesis. Furthermore, some opponents of the thesis allow that logic is “entangled” with the normative to the extent that it has normative consequences that are instrumental to the achievement of our wider goals (Russell 2017). This makes it difficult to discern any daylight between the views of those who hold that logic is not normative and those who hold that it is only weakly so. In the next section, I will argue that the thesis that unites the proponents and excludes the opponents is that logical statements and the judgments they can be used to express—such as those concerning logical validity or logical entailment—are normative statements and judgments, in the sense that they analytically, semantically, or conceptually have normative consequences. In section 3, I will critically assess whether logical statements and judgments are indeed normative in this sense. I will consider the prospects of various accounts of what the normative consequences of logical statements or judgments might be, and find them all to be wanting. This, I claim, gives us good reason to deny that logic is normative.

Abstract:

Logical Pluralists maintain that there is more than one genuine/true logical consequence relation. This paper seeks to understand what the position could amount to and some of the challenges faced by its formulation and defence. I consider in detail Beall and Restall’s Logical Pluralism—which seeks to accommodate radically different logics by stressing the way that they each fit a general form, the Generalised Tarski Thesis (GTT)—arguing against the claim that different instances of GTT are admissible precisifications of logical consequence. I then consider what it is to endorse a logic within a pluralist framework and criticise the options Beall and Restall entertain. A case study involving many-valued logics is examined. I next turn to issues of the applications of different logics and questions of which logic a pluralist should use in particular contexts. A dilemma regarding the applicability of admissible logics is tackled and it is argued that application is a red herring in relation to both understanding and defending a plausible form of logical pluralism. In the final section, I consider other ways to be and not to be a logical pluralist by examining analogous positions in debates over religious pluralism: this, I maintain, illustrates further limitations and challenges for a very general logical pluralism. Certain less wide-ranging pluralist positions are more plausible in both cases, I suggest, but assessment of those positions needs to be undertaken on a case-by-case basis.

Abstract:

Some writers object to logical pluralism on the grounds that logic is normative. The rough idea is that the relation of logical consequence has consequences for what we ought to think and how we ought to reason, so that pluralism about the consequence relation would result in an incoherent or unattractive pluralism about those things. In this paper I argue that logic isn’t normative. I distinguish three different ways in which a theory – such as a logical theory – can be entangled with the normative and argue that logic is only entangled in the weakest of these ways, one which requires it to have no normativity of its own. I use this view to show what is wrong with three different arguments for the conclusion that logic is normative.

Abstract: Description: Survey article on logical pluralism. The article is divided into three main parts: i) in the first one the author presents the main arguments for logical pluralism with respect to logical consequence; ii) in the second part, the author considers the relation between logical pluralism and Carnap's linguistic pluralism; iii) in the last section, the author considers further kinds of logical pluralism.

Abstract: This paper deals with the adequacy of the model-theoretic definition of logical consequence. Logical consequence is commonly described as a necessary relation that can be determined by the form of the sentences involved. In this paper, necessity is assumed to be a metaphysical notion, and formality is viewed as a means to avoid dealing with complex metaphysical questions in logical investigations. Logical terms are an essential part of the form of sentences and thus have a crucial role in determining logical consequence. Gila Sher and Stewart Shapiro each propose a formal criterion for logical terms within a model-theoretic framework, based on the idea of invariance under isomorphism. The two criteria are formally equivalent, and thus we have a common ground for evaluating and comparing Sher and Shapiro philosophical justification of their criteria. It is argued that Shapiro's blended approach, by which models represent possible worlds under interpretations of the language, is preferable to Sher’s formal-structural view, according to which models represent formal structures. The advantages and disadvantages of both views’ reliance on isomorphism are discussed.