Diversity Reading List

Introduction: In Kant’s moral philosophy, the imperative is perched precariously between two realms governed by the indicative form of speech. In the Critique of Pure Reason, it reminds us of an intelligible, rational realm beyond that governed by descriptive causal explanation. But in the Groundwork of the Metaphysics of Morals, it reminds us of the sensible pull of causality that frequently leads us to violate its intelligible principles. Correspondingly, Kant approaches the moral law from two directions in the Groundwork of the Metaphysic of Morals. When he is explaining moral motivation, he describes and refers to the moral law as an imperative, because this is the form it takes for causally enmeshed human beings. But when he is analyzing its rational formal structure and situating it within his broader analysis of reason, he formulates the moral law in the indicative mood, because this is the form it takes for perfectly rational beings. The vast majority of Kant’s actual formulations of the moral law in the Groundwork are not in the imperative. Of 47 formulations to be found in the text, only four are in the strict imperative. Of those four, only the first receives extended analysis. Of the remaining 43, 31 are expressed in the indicative mood. So two-thirds of Kant’s formulations of the moral law in the Groundwork are descriptive rather than prescriptive. These serve to buttress his repeated reminder that for agents as members of the intelligible world, the “I ought” becomes an “I will”. In the Groundwork, Kant usually addresses us as members of that world.

Abstract:

In this paper, we provide a recipe that not only captures the common structure of semantic paradoxes but also captures our intuitions regarding the relations between these paradoxes. Before we unveil our recipe, we first discuss a well-known schema introduced by Graham Priest, namely,the Inclosure Schema. Without rehashing previous arguments against the Inclosure Schema, we contribute different arguments for the same concern that the Inclosure Schema bundles together the wrong paradoxes. That is, we will provide further arguments on why the Inclosure Schema is both too narrow and too broad. We then spell out our recipe. The recipe shows that all of the following paradoxes share the same structure: The Liar, Curry’s paradox, Validity Curry, Provability Liar, Provability Curry, Knower’s paradox, Knower’s Curry, Grelling-Nelson’s paradox, Russell’s paradox in terms of extensions, alternative Liar and alternative Curry, and hitherto unexplored paradoxes.We conclude the paper by stating the lessons that we can learn from the recipe, and what kind of solutions the recipe suggests if we want to adhere to the Principle of Uniform Solution.

Abstract:
Recent criticism of feminist philosophy poses a dilemma. Feminism is taken to be a substantive set of empirical claims and political commitments, whereas philosophy is taken to be a discipline of thought organized by the pursuit of truth, but uncommitted to any particular truth. This paper responds to this dilemma, and defends the project of feminist philosophy.The first task toward understanding the feminist critique of reason, Alcoff argues, is to historically situate it within the rather long tradition of critiquing reason that has existed within the mainstream of philosophy itself.

Abstract: What sort of claims do scientific models make and how do these claims then underwrite empirical successes such as explanations and reliable policy interventions? In this paper I propose answers to these questions for the class of models used throughout the social and biological sciences, namely idealized deductive ones with a causal interpretation. I argue that the two main existing accounts misrepresent how these models are actually used, and propose a new account.

Abstract: Many solutions have been proposed for solving the problem of macroscopic superpositions of wave function ontology. A possible solution is to assume that, while the wave function provides the complete description of the system, its temporal evolution is not given by the Schroedinger equation. The usual Schroedinger evolution is interrupted by random and sudden "collapses". The most promising theory of this kind is the GRW theory, named after the scientists that developed it: Gian Carlo Ghirardi, Alberto Rimini and Tullio Weber. It seems tempting to think that in GRW we can take the wave function ontologically seriously and avoid the problem of macroscopic superpositions just allowing for quantum jumps. In this paper it is argued that such "bare" wave function ontology is not possible, neither for GRW nor for any other quantum theory: quantum mechanics cannot be about the wave function simpliciter. All quantum theories should be regarded as theories in which physical objects are constituted by a primitive ontology. The primitive ontology is mathematically represented in the theory by a mathematical entity in three-dimensional space, or space-time.

Abstract:
This book is intended for the newcomer to formal logic and is designed to provide an introduction for the intelligent general reader as well as for the student in the classroom. Its primary purpose is to present in a clear, natural, and orderly fashion the fundamentals of a subject that has now acquired the status of an exact science... Chapters I through VII are devoted to the exposition of material necessary to the construction of the deductive system of truth-functions... Thanks to the special notation that has come to be characteristic of symbolic logic, it is possible to express the logical material with clarity and exactness and to organize it, as in Chapter VIII, into a deductive system. Chapters IX through XI are given over to the study of general propositions and of forms of inference involving them... Care has been taken to show how Aristotelian logic is accommodated within the framework of the extended, present-day subject: by introducing the reader to quantification theory and to the current notation for expressing forms of general propositions, and finally, by presenting, in Chapter XII, the calculus of classes.

Abstract:

There is something curiously opaque about Wittgenstein's assertions concerning the connection between proof of a proposition p, sense of the sentence " p ", and understanding " p ". The difficulties inherent in his account are apparent, and he has
himself mentioned them, while leaving their resolution obscure. I shall now detail them, so that it will be clear what difficulties must be got round and what clarification is required.

Abstract:

In Remarks on the Foundations of Mathematics, and elsewhere, Wittgenstein made some general statements about mathematical proof which can only be described as paradoxical. What he says is directed to proofs for which there is no general method of solution such as there is for statements of the form a x b = c where a simple calculation is sufficient. His concern is with propositions for which one cannot in advance of proof describe any procedure which will demonstrate them... In an earlier study,' 'Proof and the Theorem Proved', I singled out a group of propositions for which his account of proof seemed correct, and not paradoxical.... But I did not succeed in making his account of deductions of connections between established concepts paradox-free. I should like to return to his account as applied to such demonstrations, with the aim of explaining what justification there is for it, and what his account comes to.

Abstract:
Mathematicians appear to have quite high standards for when they will rely on testimony. Many mathematicians require that a number of experts testify that they have checked the proof of a result p before they will rely on p in their own proofs without checking the proof of p. We examine why this is. We argue that for each expert who testifies that she has checked the proof of p and found no errors, the likelihood that the proof contains no substantial errors increases because different experts will validate the proof in different ways depending on their background knowledge and individual preferences. If this is correct, there is much to be gained for a mathematician from requiring that a number of experts have checked the proof of p before she will rely on p in her own proofs without checking the proof of p. In this way a mathematician can protect her own work and the work of others from errors. Our argument thus provides an explanation for mathematicians’ attitude towards relying on testimony.

Abstract:

We present a case study of how mathematicians write for mathematicians. We have conducted interviews with two research mathematicians, the talented PhD student Adam and his experienced supervisor Thomas, about a research paper they wrote together. Over the course of 2 years, Adam and Thomas revised Adam’s very detailed first draft. At the beginning of this collaboration, Adam was very knowledgeable about the subject of the paper and had good presentational skills but, as a new PhD student, did not yet have experience writing research papers for mathematicians. Thus, one main purpose of revising the paper was to make it take into account the intended audience. For this reason, the changes made to the initial draft and the authors’ purpose in making them provide a window for viewing how mathematicians write for mathematicians. We examined how their paper attracts the interest of the reader and prepares their proofs for validation by the reader. Among other findings, we found that their paper prepares the proofs for two types of validation that the reader can easily switch between.