Diversity Reading List

Abstract: The Prisoner’s Dilemma game is one of the classic games discussed in game theory,  the  study  of  strategic  decision  making  in  situations  of conflict,  which  stretches  between  mathematics  and  the  social  sciences. Game theory was  primarily developed  during  the  late  1940s  and  into  the  1960s  at  a number of research sites funded by various arms of the U.S. military establishment as part of their Cold War research.

Abstract:
Prominent mathematician William Thurston was praised by other mathematicians for his intellectual generosity. But what does it mean to say Thurston was intellectually generous? And is being intellectually generous beneficial? To answer these questions I turn to virtue epistemology and, in particular, Roberts and Wood's (2007) analysis of intellectual generosity. By appealing to Thurston's own writings and interviewing mathematicians who knew and worked with him, I argue that Roberts and Wood's analysis nicely captures the sense in which he was intellectually generous. I then argue that intellectual generosity is beneficial because it counteracts negative effects of the reward structure of mathematics that can stymie mathematical progress.

Summary: Uses Maxwell's model of the ether as a case study in accounting for the role of fictions in science. Argues that we should understand idealisation and abstraction as being different from fiction. Fictional models for Morrison are those that are deliberately intended to be such that the relationship between their structure and the structure of the concrete systems they model is not (immediately) apparent. This is different from mere idealisation, where certain structural features are omitted to make calculations more tractable.

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.

Summary: Morrison and Morgan argue for a view of models as 'mediating instruments' whose role in scientific theorising goes beyond applying theory. Models are partially independent of both theories and the world. This autonomy allows for a unified account of their role as instruments that allow for exploration of both theories and the world.

Abstract:

We investigate the truth conditions of knowledge ascriptions for the case of mathematical knowledge. The availability of a formalizable mathematical proof appears to be a natural criterion:

(*) X knows that p is true iff X has available a formalizable proof of p.

Yet, formalizability plays no major role in actual mathematical practice. We present results of an empirical study, which suggest that certain readings of (*) are not necessarily employed by mathematicians when ascribing knowledge. Further, we argue that the concept of mathematical knowledge underlying the actual use of “to know” in mathematical practice is compatible with certain philosophical intuitions, but seems to differ from philosophical knowledge conceptions underlying (*).

Abstract: Teleological theories of mental content try to explain the contents of mental representations by appealing to a teleological notion of function. Take, for example, the thought that blossoms are forming. On a representational theory of thought, this thought involves a representation of blossoms forming. A theory of content aims among other things to tell us why this representation has that content; it aims to say why it is a thought about blossoms forming rather than about the sun shining or pigs flying or nothing at all. In general, a theory of content tries to say why a mental representation counts as representing what it represents. According to teleological theories of content, what a representation represents depends on the functions of the systems that produce or use the representation. The relevant notion of function is said to be the one that is used in biology and neurobiology in attributing functions to components of organisms (as in "the function of the pineal gland is secreting melatonin" and "the function of brain area MT is processing information about motion"). Proponents of teleological theories of content generally understand such functions to be what the thing with the function was selected for, either by ordinary natural selection or by some other natural process of selection.

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.

Publisher's Note: Structural proof theory is a branch of logic that studies the general structure and properties of logical and mathematical proofs. This book is both a concise introduction to the central results and methods of structural proof theory, and a work of research that will be of interest to specialists. The book is designed to be used by students of philosophy, mathematics and computer science. The book contains a wealth of results on proof-theoretical systems, including extensions of such systems from logic to mathematics, and on the connection between the two main forms of structural proof theory - natural deduction and sequent calculus. The authors emphasize the computational content of logical results. A special feature of the volume is a computerized system for developing proofs interactively, downloadable from the web and regularly updated.

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.