Diversity Reading List

Abstract:

The concept of truth serves in logic not only as an instrument but also as an object of study. Eubulides of Miletus (fl. fourth century BCE), a Megarian logician, discovered the paradox known as ‘the Liar,’ and, ever since his discovery, logicians down the ages - Aristotle and Chrysippus, John Buridan and William Heytesbury, and Alfred Tarski and Saul Kripke, to mention just a few - have tried to understand the puzzling behavior of the concept of truth.

Publisher's Note: The first systematic exposition of all the central topics in the philosophy of logic, Susan Haack's book has established an international reputation (translated into five languages) for its accessibility, clarity, conciseness, orderliness, and range as well as for its thorough scholarship and careful analyses. Haack discusses the scope and purpose of logic, validity, truth-functions, quantification and ontology, names, descriptions, truth, truth-bearers, the set-theoretical and semantic paradoxes, and modality. She also explores the motivations for a whole range of nonclassical systems of logic, including many-valued logics, fuzzy logic, modal and tense logics, and relevance logics.

Abstract: It is often taken for granted by writers who propose - and, for that matter, by writers who oppose - 'justifications' of inductions, that deduction either does not need, or can readily be provided with, justification. The purpose of this paper is to argue that, contrary to this common opinion, problems analogous to those which, notoriously, arise in the attempt to justify induction, also arise in the attempt to justify deduction.

Abstract:

This chapter gives a survey of the field of philosophy where the philosophical foundations of modern logic were discussed and where such themes of logic were discussed that were on the borderline between logic and other branches of the philosophical enterprise, such as metaphysics and epistemology. The contributions made by Gottlob Frege and Charles Peirce are included since their work in logic is closely related to and also strongly motivated by their philosophical views and interests. In addition, the chapter pays attention to a few philosophers to whom logic amounted to traditional Aristotelian logic and to those who commented on the nature of logic from a philosophical perspective without making any significant contribution to the development of formal logic.

Abstract: In recent years, philosophical work directly concerned with the practice of mathematics has intensified, giving rise to a movement known as the philosophy of mathematical practice. In this paper we offer a survey of this movement aimed at mathematics educators. We first describe the core questions philosophers of mathematical practice investigate as well as the philosophical methods they use to tackle them. We then provide a selective overview of work in the philosophy of mathematical practice covering topics including the distinction between formal and informal proofs, visualization and artefacts, mathematical explanation and understanding, value judgments, and mathematical design. We conclude with some remarks on the potential connections between the philosophy of mathematical practice and mathematics education.

Abstract:

Can there be a feminist logic? By most accounts the answer would be no. What l find remarkable is the great difference in the justifications provided for this conclusion. The impossibility of feminist logic is defended, on the one hand, on the grounds that logic itself is most fundamentally a form of domination and so is inimical to feminist aims. Other philosophers, while also defending the impossibility of feminist logic, do so from the conviction that it is feminist theory rather than logic that is the problem. For these thinkers, feminism cannot make any interesting or important contribution to logic because feminist theory is fundamentally shallow or misguided. In this paper I will argue that both positions are mistaken: Logic is neither as totalizing as the one side believes nor is feminist theory as inconsequential for logic as the other pole would have it. In the course of these arguments, I describe the work of several feminist logicians, showing the possibility and value of feminist approaches to logic.

Abstract:

Hass examines chapters devoted to Aristotle in a recent, prominent, and controversial feminist critique of logic, Andrea Nye's Words of Power: A Feminist Reading of the History of Logic. Hass shows that Nye's criticisms of logic in general and of Aristotle in particular are misplaced. What is crucial in Nye's attack are alleged problems caused by overzealous "abstraction." But Hass argues that abstraction is not problematic; instead, it is crucial (and empowering) for feminist political theory. Although she rejects Nye's form of feminist logic critique, Hass finds more that is worthwhile in the criticisms of logic advanced by Luce lrigaray and Val Plumwood. These thinkers call for feminist alternatives to what has come to be standard deductive logic - and interestingly enough, their call is echoed in other contemporary criticisms from within the field of logic itself, for example, from intuitionist or entailment logics. The logical schemes envisaged by lrigaray and Plumwood would encompass more situated and fluid ways of using formal systems to describe and analyse reality and diverse experiences. Hass argues that, in Aristotle's case, we can glimpse something of such an alternative by looking to his account of negation, which is richer and more complex than that allowed by most contemporary formal systems.

Abstract: Hass examines chapters devoted to Aristotle in a recent, prominent, and controversial feminist critique of logic, Andrea Nye's Words of Power: A Feminist Reading of the History of Logic. Hass shows that Nye's criticisms of logic in general and of Aristotle in particular are misplaced. What is crucial in Nye's attack are alleged problems caused by overzealous "abstraction." But Hass argues that abstraction is not problematic; instead, it is crucial (and empowering) for feminist political theory. Although she rejects Nye's form of feminist logic critique, Hass finds more that is worthwhile in the criticisms of logic advanced by Luce lrigaray and Val Plumwood. These thinkers call for feminist alternatives to what has come to be standard deductive logic - and interestingly enough, their call is echoed in other contemporary criticisms from within the field of logic itself, for example, from intuitionist or entailment logics. The logical schemes envisaged by lrigaray and Plumwood would encompass more situated and fluid ways of using formal systems to describe and analyse reality and diverse experiences. Hass argues that, in Aristotle's case, we can glimpse something of such an alternative by looking to his account of negation, which is richer and more complex than that allowed by most contemporary formal systems.

From the Introduction: "Marjorie Hass addresses the limitations of logical concepts, including negation, by illuminating the ongoing critique of these terms in the work of Luce Irigaray. In Hass’s view, Irigaray’s work calls the neutrality of logic into question, suggesting that the standard formalism is capable of expressing only distorted and partial interpretations of negation, identity, and generality. More specifically, in Irigaray’s work, standard symbolic logic is shown to be unable to represent the form of difference proper to sexual difference, the form of identity proper to feminine identity, and the form of generality proper to a feminine generic. Hass interprets and evaluates Irigaray’s critique of logic, arguing that many of Irigaray’s readers have misunderstood its nature and force."

Abstract: Epistemic logic is the logic of knowledge and belief. It provides insight into the properties of individual knowers, has provided a means to model complicated scenarios involving groups of knowers and has improved our understanding of the dynamics of inquiry.

Publisher's Note: A danger of a heavily formalist approach to the structure of science is that it may lose sight of the concrete actualities on which scientific inference is exercised. On the other hand, and excessively descriptive and relativist approach fails to achieve a general systematization of models of inference. This book tries to steer a middle course between these extremes. Hesse first discusses some epistemological problems bequeathed by positivists analyses of science and also considers the problem of inductive justification of theories in relation to evidence. Following Keynes and Carnap she argues that the axioms of probability constitute the best postulate system for a logic of confirmation.

Introduction: Quantum mechanics is, at least at first glance and at least in part, a mathematical machine for predicting the behaviors of microscopic particles - or, at least, of the measuring instruments we use to explore those behaviors - and in that capacity, it is spectacularly successful: in terms of power and precision, head and shoulders above any theory we have ever had. Mathematically, the theory is well understood; we know what its parts are, how they are put together, and why, in the mechanical sense (i.e., in a sense that can be answered by describing the internal grinding of gear against gear), the whole thing performs the way it does, how the information that gets fed in at one end is converted into what comes out the other. The question of what kind of a world it describes, however, is controversial; there is very little agreement, among physicists and among philosophers, about what the world is like according to quantum mechanics. Minimally interpreted, the theory describes a set of facts about the way the microscopic world impinges on the macroscopic one, how it affects our measuring instruments, described in everyday language or the language of classical mechanics. Disagreement centers on the question of what a microscopic world, which affects our apparatuses in the prescribed manner, is, or even could be, like intrinsically; or how those apparatuses could themselves be built out of microscopic parts of the sort the theory describes.

Abstract: There's a long history of discussion of probability in philosophy, but objective chance separated itself off and came into its own as a topic with the advent of a physical theory—quantum mechanics—in which chances play a central, and apparently ineliminable, role. In 1980 David Lewis wrote a paper pointing out that a very broad class of accounts of the nature of chance apparently lead to a contradiction when combined with a principle that expresses the role of chance in guiding belief. There is still no settled agreement on the proper response to the Lewis problem. At the time he wrote the article, Lewis despaired of a solution, but, although he never achieved one that satisfied him completely, by 1994, due to work primarily by Thau and Hall, he had come to think the problem could be disarmed if we fudged a little on the meaning of 'chance'. I'll say more about this below. What I'm going to suggest, however, is that the qualification is unnecessary. The problem depends on an assumption that should be rejected, viz., that using information about chance to guide credence requires one to conditionalize on the theory of chance that one is using. I'm going to propose a general recipe for using information about chance to guide belief that does not require conditionalization on a theory of chance at any stage. Lewis' problem doesn't arise in this setting.

Abstract: Poincare is well known for his conventionalism and structuralism. However, the relationship between these two theses and their place in Poincare's epistemology of science remain puzzling. In this paper I show the scope of Poincare's conventionalism and its position in Poincare's hierarchical approach to scientific theories. I argue that for Poincare scientific knowledge is relational and made possible by synthetic a priori, empirical and conventional elements, which, however, are not chosen arbitrarily. By examining his geometric conventionalism, his hierarchical account of science and defence of continuity in theory change, I argue that Poincare defends a complex structuralist position based on synthetic a priori and conventional elements, the mind-dependence of which precludes epistemic access to mind-independent structures.

Abstract: In this paper I argue that Poincare's acceptance of the atom does not indicate a shift from instrumentalism to scientific realism. I examine the implications of Poincare's acceptance of the existence of the atom for our current understanding of his philosophy of science. Specifically, how can we understand Poincare's acceptance of the atom in structural realist terms? I examine his 1912 paper carefully and suggest that it does not entail scientific realism in the sense of acceptance of the fundamental existence of atoms but rather, argues against fundamental entities. I argue that Poincare's paper motivates a non-fundamentalist view about the world, and that this is compatible with his structuralism.