Diversity Reading List

Abstract: In this article I discuss a recent argument due to Dan McArthur, who suggests that the charge that Michael Friedman's relativised a priori leads to irrationality in theory change can be avoided by adopting structural realism. I provide several arguments to show that the conjunction of Friedman?s relativised a priori with structural realism cannot make the former avoid the charge of irrationality. I also explore the extent to which Friedman's view and structural realism are compatible, a presupposition of McArthur's argument. This compatibility is usually questioned, due to the Kantian aspect of Friedman's view, which clashes with the metaphysical premise of scientific realism. I argue that structural realism does not necessarily depend on this premise and as a consequence can be compatible with Friedman's view, but more importantly I question whether Friedman's view really implies mind dependence

Abstract:

Analytic philosophy in the mid-twentieth century underwent a major change of direction when a prior consensus in favour of extensionalism and descriptivism made way for approaches using direct reference, the necessity of identity, and modal logic. All three were first defended, in the analytic tradition, by one woman, Ruth Barcan Marcus. But analytic philosophers now tend to credit them to Kripke, or Kripke and Carnap. I argue that seeing Barcan Marcus in her historical context – one dominated by extensionalism and descriptivism – allows us to see how revolutionary she was, in her work and influence on others. I focus on her debate with Quine, who found himself retreating to softened, and more viable, versions of his anti-modal arguments as a result. I make the case that Barcan's formal logic was philosophically well-motivated, connected to her views on reference, and well-matched to her overall views on ontology. Her nominalism led her to reject posits which could not be directly observed and named, such as possibilia. She conceived of modal calculi as facilitating counterfactual discourse about actual existents. I conclude that her contributions ought to be recognized as the first of their kind. Barcan Marcus must be awarded a central place in the canon of analytic philosophy.

Abstract: This paper takes the form of a critical discussion of Crispin Wright's notion of entitlement of cognitive project. I examine various strategies for defending the claim that entitlement can make acceptance of a proposition epistemically rational, including one which appeals to epistemic consequentialism. Ultimately, I argue, none of these strategies is successful, but the attempt to isolate points of disagreement with Wright issues in some positive proposals as to how an epistemic consequentialist should characterize epistemic rationality.

Abstract: The goal of the research programme I describe in this article is a realist epistemology for arithmetic which respects arithmetic's special epistemic status (the status usually described as a prioricity) yet accommodates naturalistic concerns by remaining funda- mentally empiricist. I argue that the central claims which would allow us to develop such an epistemology are (i) that arithmetical truths are known through an examination of our arithmetical concepts; (ii) that (at least our basic) arithmetical concepts are accurate mental representations of elements of the arithmetical structure of the inde- pendent world; (iii) that (ii) obtains in virtue of the normal functioning of our sensory apparatus. The first of these claims protects arithmetic's special epistemic status relative, for example, to the laws of physics, the second preserves the independence of arithmetical truth, and the third ensures that we remain empiricists.

Abstract: Controversy remains over exactly why Frege aimed to estabish logicism. In this essay, I argue that the most influential interpretations of Frege's motivations fall short because they misunderstand or neglect Frege's claims that axioms must be self-evident. I offer an interpretation of his appeals to self-evidence and attempt to show that they reveal a previously overlooked motivation for establishing logicism, one which has roots in the Euclidean rationalist tradition. More specifically, my view is that Frege had two notions of self-evidence. One notion is that of a truth being foundationally secure, yet not grounded on any other truth. The second notion is that of a truth that requires only clearly grasping its content for rational, a priori justified recognition of its truth. The overarching thesis I develop is that Frege required that axioms be self-evident in both senses, and he relied on judging propositions to be self-evident as part of his fallibilist method for identifying a foundation of arithmetic. Consequently, we must recognize both notions in order to understand how Frege construes ultimate foundational proofs, his methodology for discovering and identifying such proofs, and why he thought the propositions of arithmetic required proof.

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.

Publisher’s Note: Description - This comprehensive introduction presents the fundamentals of symbolic logic clearly, systematically, and in a straightforward style accessible to readers. Each chapter, or unit, is divided into easily comprehended small bites that enable learners to master the material step-by-step, rather than being overwhelmed by masses of information covered too quickly. The book provides extremely detailed explanations of procedures and techniques, and was written in the conviction that anyone can thoroughly master its content. A four-part organization covers sentential logic, monadic predicate logic, relational predicate logic, and extra credit units that glimpse into alternative methods of logic and more advanced topics.

Summary: This article provides the basics of a typical logic, sometimes called 'classical elementary logic' or 'classical first-order logic', in a rigorous yet accessible manner. Section 2 develops a formal language, with a syntax and grammar. Section 3 sets up a deductive system for the language, in the spirit of natural deduction. Section 4 provides a model-theoretic semantics. Section 5 turns to the relationships between the deductive system and the semantics, and in particular, the relationship between derivability and validity. The authors show that an argument is derivable only if it is valid (soundness). Then they establish a converse: that an argument is valid only if it is derivable (completeness). They also briefly indicate other features of the logic, some of which are corollaries to soundness and completeness. The final section, Section 6, is devoted to a brief examination of the philosophical position that classical logic is 'the one right logic'.

Abstract:

This paper presents a new view of logical pluralism. This pluralism takes into account how the logical connectives shift, depending on the context in which they occur. Using the Question-Under-Discussion Framework as formulated by Craige Roberts, I identify the contextual factor that is responsible for this shift. I then provide an account of the meanings of the logical connectives which can accommodate this factor. Finally, I suggest that this new pluralism has a certain Carnapian flavour. Questions about the meanings of the connectives or the best logic outside of a specified context are not legitimate questions.

Abstract:

Logical pluralism is the view that there is more than one right logic. A particular version of the view, what is sometimes called domain-specific logical pluralism, has it that the right logic and connectives depend somehow on the domain of use, or context of use, or the linguistic framework. This type of view has a problem with cross-framework communication, though: it seems that all such communication turns into merely verbal disputes. If two people approach the same domain with different logics as their guide, then they may be using different connectives, and hence talking past each other. In this situation, if we think we are having a conversation about “ ¬ A”, but are using different “ ¬ ”s, then we are not really talking about the same thing. The communication problem prevents legitimate disagreements about logic, which is a bad result. In this paper I articulate a possible solution to this problem, without giving up pluralism, which requires adopting a notion of metalinguistic negotiation, and allows people to communicate and disagree across domains/contexts/frameworks.

Abstract: Several accounts of representation in cognitive systems have recently been proposed. These look for a theory that will establish how a representation comes to have a certain content, and how these representations are used by cognitive systems. Covariation accounts are unsatisfactory, as they make intelligent reasoning and cognition impossible. Cummins' interpretation-based account cannot explain the distinction between cognitive and non-cognitive systems, nor how certain cognitive representations appear to have intrinsic meaning. Cognitive systems can be defined as model-constructers, or systems that use information from interpreted models as arguments in the functions they execute. An account based on this definition solves many of the problems raised by the earlier proposals

Introduction: In increasing numbers, philosophers are coming to read Sellars' "Empiricism and the Philosophy of Mind" (1997, hereafter EPM) as having dealt the definitive death blow to the idea that inner states with epistemic authority could have this authority immediately. EPM purportedly proves that instead, such states necessarily show up already embedded within a web of inferentially articulated conceptual knowledge, and that in order for this to be possible,  the epistemic subject must be a negotiator of a normative space in which standards of justification and correctness are already recognized. [...] In this paper I will attempt to show that Sellars' mythical explanations in EPM employ a very specific and rhetorically complex methodology, and likewise that we will not be in a position to critically assess the paper's arguments unless we give careful attention to its overall textual structure and to the nature of the mythical explanations it employs.

Abstract: In this paper I examine some research on how to diminish or eliminate stereotype threat in mathematics. Some of the successful strategies include: informing our students about stereotype threat, challenging the idea that logical intelligence is an 'innate' ability, making students In threatened groups feel welcomed, and introducing counter-stereotypical role models. The purpose of this paper is to take these strategies that have proven successful and come up with specific ways to incorporate them into introductory logic classes. For example, the possible benefit of presenting logic to our undergraduate students by concentrating on aspects of logic that do not result in a clash of schemas.

Summary: Surveys the opposition between views of mathematics which take mathematics to represent a independent mathematical reality and views which take mathematical axioms to define or circumscribe their subject matter; and defends the latter view against influential objections.

Publisher's Note: Mary Leng offers a defense of mathematical fictionalism, according to which we have no reason to believe that there are any mathematical objects. Perhaps the most pressing challenge to mathematical fictionalism is the indispensability argument for the truth of our mathematical theories (and therefore for the existence of the mathematical objects posited by those theories). According to this argument, if we have reason to believe anything, we have reason to believe that the claims of our best empirical theories are (at least approximately) true. But since claims whose truth would require the existence of mathematical objects are indispensable in formulating our best empirical theories, it follows that we have good reason to believe in the mathematical objects posited by those mathematical theories used in empirical science, and therefore to believe that the mathematical theories utilized in empirical science are true. Previous responses to the indispensability argument have focussed on arguing that mathematical assumptions can be dispensed with in formulating our empirical theories. Leng, by contrast, offers an account of the role of mathematics in empirical science according to which the successful use of mathematics in formulating our empirical theories need not rely on the truth of the mathematics utilized.