Diversity Reading List

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.

Summary: The knowledge version of the paradox arises because it appears that we know our lottery ticket (which is not relevantly different from any other) will lose, but we know that one of the tickets sold will win. The rationality version of the paradox arises because it appears that it is rational to believe of each single ticket in, say, a million-ticket lottery that it will not win, and that it is simultaneously rational to believe that one such ticket will win. It seems, then, that we are committed to attributing two rational beliefs to a single agent at a single time, beliefs that, together with a few background assumptions, are inconsistent and can be seen by the agent to be so. This has seemed to many to be a paradoxical result: an agent in possession of two rational beliefs that she sees to be inconsistent. In my paper, I offer a novel solution to the paradox in both its rationality and knowledge versions that emphasizes a special feature of the lottery case, namely, the statistical nature of the evidence available to the agent. On my view, it is neither true that one knows nor that it is rational to believe that a particular ticket will lose. While this might seem surprising at first, it has a natural explanation and lacks the serious disadvantages of competing solutions.

Publisher’s Note:

Is logic masculine? Is women's lack of interest in the "hard core" philosophical disciplines of formal logic and semantics symptomatic of an inadequacy linked to sex? Is the failure of women to excel in pure mathematics and mathematical science a function of their inability to think rationally? Andrea Nye undermines the assumptions that inform these questions, assumptions such as: logic is unitary, logic is independenet of concrete human relations, and logic transcends historical circumstances as well as gender. In a series of studies of the logics of historical figures--Parmenides, Plato, Aristotle, Zeno, Abelard, Ockham, and Frege--she traces the changing interrelationships between logical innovation and oppressive speech strategies, showing that logic is not transcendent truth but abstract forms of language spoken by men, whether Greek ruling citizens, or scientists.

From the Introduction: "Andrea Nye is also concerned with the role of logic in science, linking the adequacy of logic with its applicability in a domain of scientific knowledge. Nye argues that the dominant predicate logic cannot adequately represent the issues surrounding attempts to divide organisms into species. Feminist critiques of the extensional theory of meaning lay the ground for alternative theories of categorization. Without renewed models of categorization, Nye submits, science is in danger of becoming a self-enclosed “logical” system, rather than an instrumental model of reality."

From the Introduction: "Dorothea Olkowski’s chapter offers an analysis of the need to develop a logic of sense. Drawing on the work of Gilles Deleuze, Olkowski defends formal logic against feminist theorists who have urged that we organize thinking around the principles of embodiment. She warns us against the complete merging of bodily functions and sense-making activities. In Olkowski’s view, feminists need to acknowledge the usefulness of logical analyses at the same time that they must insist on formal systems that reflect and are tempered by human and humane values."

Abstract: According to an adequacy-for-purpose view, models should be assessed with respect to their adequacy or fitness for particular purposes. Such a view has been advocated by scientists and philosophers alike. Important details, however, have yet to be spelled out. This article attempts to make progress by addressing three key questions: What does it mean for a model to be adequate-for-purpose? What makes a model adequate-for-purpose? How does assessing a model’s adequacy-for-purpose differ from assessing its representational accuracy? In addition, responses are given to some objections that might be raised against an adequacy-for-purpose view.

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: It seems natural to choose whether to have a child by reflecting on what it would be like to actually have a child. I argue that this natural approach fails. If you choose to become a parent, and your choice is based on projections about what you think it would be like for you to have a child, your choice is not rational. If you choose to remain childless, and your choice is based upon projections about what you think it would be like for you to have a child, your choice is not rational. This suggests we should reject our ordinary conception of how to make this life-changing decision, and raises general questions about how to rationally approach important life choices.

Abstract:

Much has been said about intuitionistic and classical logical systems since Gentzen’s seminal work. Recently, Prawitz and others have been discussing how to put together Gentzen’s systems for classical and intuitionistic logic in a single unified system. We call Prawitz’ proposal the Ecumenical System, following the terminology introduced by Pereira and Rodriguez. In this work we present an Ecumenical sequent calculus, as opposed to the original natural deduction version, and state some proof theoretical properties of the system. We reason that sequent calculi are more amenable to extensive investigation using the tools of proof theory, such as cut-elimination and rule invertibility, hence allowing a full analysis of the notion of Ecumenical entailment. We then present some extensions of the Ecumenical sequent system and show that interesting systems arise when restricting such calculi to specific fragments. This approach of a unified system enabling both classical and intuitionistic features sheds some light not only on the logics themselves, but also on their semantical interpretations as well as on the proof theoretical properties that can arise from combining logical systems.