Diversity Reading List

Abstract: The argument from multiple realization is currently considered the argument against intertheoretic reduction. Both Little and Kincaid have applied the argument to the individualism-holism debate in support of the antireductionist holist position. The author shows that the tenability of the argument, as applied to the individualism-holism debate, hinges on the descriptive constraints imposed on the individualist position. On a plausible formulation of the individualist position, the argument does not establish that the intertheoretic reduction of social theories is highly unlikely. Nonetheless, the reductive project may run into other potential obstacles. For this reason, it is concluded that the prospect of intertheoretic reduction is uncertain rather than unlikely.

Abstract: Julian Reiss correctly identified a trilemma about economic models: we cannot maintain that they are false, but nevertheless explain and that only true accounts explain. In this reply we give reasons to reject the second premise – that economic models explain. Intuitions to the contrary should be distrusted.

Abstract: Recent philosophy of science has witnessed a shift in focus, in that significantly more consideration is given to how scientists employ models. Attending to the role of models in scientific practice leads to new questions about the representational roles of models, the purpose of idealizations, why multiple models are used for the same phenomenon, and many more besides. In this paper, I suggest that these themes resonate with central topics in feminist epistemology, in particular prominent versions of feminist empiricism, and that model-based science and feminist epistemology each has crucial resources to offer the other's project.

Abstract: This article identifies conditions under which robust predictive modeling results have special epistemic significance---related to truth, confidence, and security---and considers whether those conditions hold in the context of present-day climate modeling. The findings are disappointing. When today's climate models agree that an interesting hypothesis about future climate change is true, it cannot be inferred---via the arguments considered here anyway---that the hypothesis is likely to be true or that scientists' confidence in the hypothesis should be significantly increased or that a claim to have evidence for the hypothesis is now more secure

Abstract: I argue that the propensity interpretation of fitness, properly understood, not only solves the explanatory circularity problem and the mismatch problem, but can also withstand the Pandora's box full of problems that have been thrown at it. Fitness is the propensity (i.e., probabilistic ability, based on heritable physical traits) for organisms or types of organisms to survive and reproduce in particular environments and in particular populations for a specified number of generations; if greater than one generation, 'reproduction' includes descendants of descendants. Fitness values can be described in terms of distributions of propensities to produce varying number of offspring and can be modeled for any number of generations using computer simulations, thus providing both predictive power and a means for comparing the fitness of different phenotypes. Fitness is a causal concept, most notably at the population level, where fitness differences are causally responsible for differences in reproductive success. Relative fitness is ultimately what matters for natural selection.

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.

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.

Abstract: Intentionality is characteristic of many psychological phenomena. It is commonly held by philosophers that intentionality cannot be ascribed to purely physical systems. This view does not merely deny that psychological language can be reduced to physiological language. It also claims that the appropriateness of some psychological explanation excludes the possibility of any underlying physiological or causal account adequate to explain intentional behavior. This is a thesis which I do not accept. I shall argue that physical systems of a specific sort will show the characteristic features of intentionality. Psychological subjects are, under an alternative description, purely physical systems of a certain sort. The intentional description and the physical description are logically distinct, and are not intertranslatable. Nevertheless, the features of intentionality may be explained by a purely causal account, in the sense that they may be shown to be totally dependent upon physical processes.

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.

Abstract: Gottlob Frege's work in logic and the foundations of mathemat- ics centers on claims of logical entailment; most important among these is the claim that arithmetical truths are entailed by purely logical principles. Occupying a less central but nonetheless important role in Frege's work are claims about failures of entailment. Here, the clearest examples are his theses that the truths of geometry are not entailed by the truths of logic or of arithmetic, and that some of them are not entailed by each other. As he, and we, would put it: the truths of Eluclidean geometry are independent of the truths of logic, and some of them are independent of one another.' Frege's talk of independence and related notions sounds familiar to a modern ear: a proposition is independent of a collection of propositions just in case it is not a consequence of that collection, and a proposition or collection of propositions is consistent just in case no contradiction is a consequence of it. But some of Frege's views and procedures are decidedly tinmodern. Despite developing an extremely sophisticated apparattus for demonstrating that one claim is a consequience of others, Frege offers not a single demon- stration that one claim is not a conseqtuence of others. Thus, in par- tictular, he gives no proofs of independence or of consistency. This is no accident. Despite his firm commitment to the independence and consistency claims just mentioned, Frege holds that independence and consistency cannot systematically be demonstrated.2 Frege's view here is particularly striking in light of the fact that his contemporaries had a fruitful and systematic method for proving consistency and independence, a method which was well known to him. One of the clearest applications of this method in Frege's day came in David Hilbert's 1899 Foundations of Geometry,3 in which he es- tablishes via essentially our own modern method the consistency and independence of various axioms and axiom systems for Euclidean geometry. Frege's reaction to Hilbert's work was that it was simply a failure: that its central methods were incapable of demonstrating consistency and independence, and that its usefulness in the founda- tions of mathematics was highly questionable.4 Regarding the general usefulness of the method, it is clear that Frege was wrong; the last one hundred years of work in logic and mathemat- ics gives ample evidence of the fruitfulness of those techniques which grow directly from the Hilbert-style approach. The standard view today is that Frege was also wrong in his claim that Hilbert's methods fail to demonstrate consistency and independence. The view would seem to be that Frege largely missed Hilbert's point, and that a better under- standing of Hilbert's techniques would have revealed to Frege their success. Despite Frege's historic role as the founder of the methods we now use to demonstrate positive consequence-results, he simply failed, on this account, to understand the ways in which Hilbert's methods could be used to demonstrate negative consequence-results. The purpose of this paper is to question this account of the Frege- Hilbert disagreement. By 1899, Frege had a well-developed view of log- ical consequence, consistency, and independence, a view which was central to his foundational work in arithmetic and to the epistemologi- cal significance of that work. Given this understanding of the logical relations, I shall argue, Hilbert's demonstrations do fail. Successful as they were in demonstrating significant metatheoretic results, Hilbert's proofs do not establish the consistency and independence, in Frege's sense, of geometrical axioms. This point is important, I think, both for an understanding of the basis of Frege's epistemological claims about mathematics, and for an understanding of just how different Frege's conception of logic is from the modern model-theoretic conception that has grown out of the Hilbert-style approach to consistency.