Diversity Reading List

Publisher's Note: In Frege's Conception of Logic Patricia A. Blanchette explores the relationship between Gottlob Frege's understanding of conceptual analysis and his understanding of logic. She argues that the fruitfulness of Frege's conception of logic, and the illuminating differences between that conception and those more modern views that have largely supplanted it, are best understood against the backdrop of a clear account of the role of conceptual analysis in logical investigation. The first part of the book locates the role of conceptual analysis in Frege's logicist project. Blanchette argues that despite a number of difficulties, Frege's use of analysis in the service of logicism is a powerful and coherent tool. As a result of coming to grips with his use of that tool, we can see that there is, despite appearances, no conflict between Frege's intention to demonstrate the grounds of ordinary arithmetic and the fact that the numerals of his derived sentences fail to co-refer with ordinary numerals. In the second part of the book, Blanchette explores the resulting conception of logic itself, and some of the straightforward ways in which Frege's conception differs from its now-familiar descendants. In particular, Blanchette argues that consistency, as Frege understands it, differs significantly from the kind of consistency demonstrable via the construction of models. To appreciate this difference is to appreciate the extent to which Frege was right in his debate with Hilbert over consistency- and independence-proofs in geometry. For similar reasons, modern results such as the completeness of formal systems and the categoricity of theories do not have for Frege the same importance they are commonly taken to have by his post-Tarskian descendants. These differences, together with the coherence of Frege's position, provide reason for caution with respect to the appeal to formal systems and their properties in the treatment of fundamental logical properties and relations.

Publisher's Note: This paper examines the methodology used by Kepler to discover a quantitative law of refraction. The aim is to argue that this methodology follows a heuristic method based on the following two Pythagorean principles: (1) sameness is made known by sameness, and (2) harmony arises from establishing a limit to what is unlimited. We will analyse some of the author's proposed analogies to find the aforementioned law and argue that the investigation's heuristic pursues such principles.

Publisher's Note: What is mathematics about? Does the subject-matter of mathematics exist independently of the mind or are they mental constructions? How do we know mathematics? Is mathematical knowledge logical knowledge? And how is mathematics applied to the material world? In this introduction to the philosophy of mathematics, Michele Friend examines these and other ontological and epistemological problems raised by the content and practice of mathematics. Aimed at a readership with limited proficiency in mathematics but with some experience of formal logic it seeks to strike a balance between conceptual accessibility and correct representation of the issues. Friend examines the standard theories of mathematics - Platonism, realism, logicism, formalism, constructivism and structuralism - as well as some less standard theories such as psychologism, fictionalism and Meinongian philosophy of mathematics. In each case Friend explains what characterises the position and where the divisions between them lie, including some of the arguments in favour and against each. This book also explores particular questions that occupy present-day philosophers and mathematicians such as the problem of infinity, mathematical intuition and the relationship, if any, between the philosophy of mathematics and the practice of mathematics. Taking in the canonical ideas of Aristotle, Kant, Frege and Whitehead and Russell as well as the challenging and innovative work of recent philosophers like Benacerraf, Hellman, Maddy and Shapiro, Friend provides a balanced and accessible introduction suitable for upper-level undergraduate courses and the non-specialist.

Abstract: Spin is typically thought to be a fundamental property of the electron and other elementary particles. Although it is defined as an internal angular momentum much of our understanding of it is bound up with the mathematics of group theory. This paper traces the development of the concept of spin paying particular attention to the way that quantum mechanics has influenced its interpretation in both theoretical and experimental contexts. The received view is that electron spin was discovered experimentally by Stern and Gerlach in 1921, 5 years prior to its theoretical formulation by Goudsmit and Uhlenbeck. However, neither Goudsmit nor Uhlenbeck, nor any others involved in the debate about spin cited the Stern-Gerlach experiment as corroborating evidence. In fact, Bohr and Pauli were emphatic that the spin of a single electron could not be measured in classical experiments. In recent years experiments designed to refute the Bohr-Pauli thesis and measure electron spin have been carried out. However, a number of ambiguities surround these results - ambiguities that relate not only to the measurements themselves but to the interpretation of the experiments. After discussing these various issues the author raises some philosophical questions about the ontological and epistemic status of spin.

Introduction: An article in The Chronicle of Higher Education of June 30, 1993, reported, “Two decades after it began redefining debates” in many other disciplines, “feminist thinking seems suddenly to have arrived in economics.” Many economists, of course, did not happen to be in the station when this train arrived, belated as it might be. Many who might have heard rumor of its coming have not yet learned just what arguments are involved or what it promises for the refinement of the profession. The purpose of this essay is to provide a low-cost way of gaining some familiarity.