Diversity Reading List

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.

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.

Abstract: This talk surveys a range of positions on the fundamental metaphysical and epistemological questions about elementary logic, for example, as a starting point: what is the subject matter of logic - what makes its truths true? how do we come to know the truths of logic? A taxonomy is approached by beginning from well-known schools of thought in the philosophy of mathematics - Logicism, Intuitionism, Formalism, Realism - and sketching roughly corresponding views in the philosophy of logic. Kant, Mill, Frege, Wittgenstein, Carnap, Ayer, Quine, and Putnam are among the philosophers considered along the way.

Abstract:
Val Plumwood charged classical logic not only with the invalidity of some of its laws, but also with the support of systemic oppression through naturalization of the logical structure of dualisms. In this paper I show that the latter charge - unlike the former - can be carried over to classical mathematics, and I propose a new conception of inconsistent mathematics - queer incomaths - as a liberatory activity meant to undermine said naturalization.

Abstract:

Recent works about ecumenical systems, where connectives from classical and intuitionistic logics can co-exist in peace, warmed the discussion on proof systems for combining logics. This discussion has been extended to alethic modalities using Simpson’s meta-logical characterization: necessity is independent of the viewer, while possibility can be either intuitionistic or classical. In this work, we propose a pure, label free calculus for ecumenical modalities, nEK, where exactly one logical operator figures in introduction rules and every basic object of the calculus can be read as a formula in the language of the ecumenical modal logic EK. We prove that nEK is sound and complete w.r.t. the ecumenical birelational semantics and discuss fragments and extensions.

Abstract:

This paper stresses the importance of identifying the nature of an author’s conception of logic when using terms from modern logic in order to avoid, as far as possible, injecting our own conception of logic in the author’s texts. Sundholm (2012) points out that inferences are staged at the epistemic level and are made out of judgments, not propositions. Since it is now standard to read Aristotelian sullogismoi as inferences, I have taken Alexander of Aphrodisias’s commentaries to Aristotle’s logical treatises as a basis for arguing that the premises and conclusions should be read as judgments rather than as propositions. Under this reading, when Alexander speaks of protaseis, we should not read the modern notion of proposition, but rather what we now call judgments. The point is not just a matter of terminology, it is about the conception of logic this terminology conveys. In this regard, insisting on judgments rather than on propositions helps bring to light Alexander’s epistemic conception of logic.

Abstract:

‘Logical Realism’ is taken to mean many different things. I argue that if reality has a privileged structure, then a view I call metaphysical logical realism is true. The view says that, first, there is ‘ One True Logic ’ ; second, that the One True Logic is made true by the mind ‐ and ‐ language ‐ independent world; and third, that the mind ‐ and ‐ language ‐ independent world makes it the case that the One True Logic is better than any other logic at capturing the structure of reality. Along the way, I discuss a few alternatives, and clarify two distinct kinds of metaphysical logical realism.

Abstract:

The chapter is an overview of Indian logic, with a general introduction followed by specialized sections on four different schools: Nyāya logic, Buddhist logic, Jaina logic, and Navya-Nyāya logic.

Publisher’s Note:

This book describes how logical reasoning works and puts it to the test in applications. It is self-contained and presupposes no more than elementary competence in mathematics.