Philosophy

The book contains innovative contributions to the history and the philosophy of logic and mathematics in the first half of the twentieth century. It is divided into five main sections: history of logic (from Russell to Tarski); foundational issues (Hilbert’s program, constructivity, Wittgenstein, Gödel); mathematics and phenomenology (Weyl, Becker, Mahnke); nominalism (Quine, Tarski); semantics (Tarski, Carnap, Neurath). The treatment exploits extensively untapped archival sources thereby making available a wealth of new material that deepens in significant ways our understanding of the above-mentioned areas. At the same time, the book is a contribution to recent debates on, among other things, the prospects for a successful nominalist reconstruction of mathematics, the nature of finitist intuition, the viability of alternative definitions of logical consequence, and the extent to which phenomenology can hope to account for the exact sciences.

Ascriptions of mental states to oneself and others give rise to many interesting logical and semantic problems. This problem presents an original account of mental state ascriptions that are made using intensional transitive verbs such as ‘want’, ‘seek’, ‘imaginer’, and ‘worship’. This book offers a theory of how such verbs work that draws on ideas from natural language semantics, philosophy of language, and aesthetics.

This book presents an expanded edition of the author's exploration of the nature and limits of thought. Embracing contradiction and challenging traditional logic, the book engages with issues across philosophical borders, from the historical to the modern, from Eastern to Western, and from the continental to the analytic. This edition of the text includes new chapters on European and Indian philosophy, and reflections on responses to the previous edition of the book.

This book proposes a theory of analogical arguments, with special focus on analogies in mathematics and science. The core principle of the theory is that a good analogical argument must articulate a clear relationship capable of generalization. This idea leads to a set of distinct models for the critical analysis of prominent forms of analogical argument, corresponding to different logical, causal and probabilistic relationships that occur in scientific reasoning. The same principle allows us to relate analogical reasoning to broad norms and values of scientific practice, such as symmetry and unification. Elaborating this principle, the book raises questions and proposes answers regarding (1) criteria for evaluating analogical arguments, (2) the philosophical justification for analogical reasoning, and (3) the place of scientific analogies in the context of theoretical confirmation.

This book provides a presentation of views on the relations between metaphysics and logic from Aristotle through twentieth century philosophers who contributed to the return of metaphysics in the analytic tradition. The collection combines interest in logic and its history with interest in analytical metaphysics and the history of metaphysical thought. The focus is on metaphysica generalis, or the systematic study of the most general categories of being. The volume aims at historical coverage of certain influential figures and themes. As the tradition is very rich, some choices between important philosophers and topics cannot be avoided. The volume seeks for a balance between different periods; still, early modern, modern and twentieth century metaphysics are more extensively studied than the pre-modern tradition. Thinkers discussed include Aristotle, Avicenna, Thomas Aquinas, Duns Scotus, William Ockham, Gottfried Wilhelm Leibniz, Immanuel Kant, Georg Wilhelm Friedrich Hegel, Bernard Bolzano, Charles Sanders Peirce, Georg Cantor, Gottlob Frege, Alexius Meinong, Edmund Husserl, Bertrand Russell, G. E. Moore, C. I. Lewis, Martin Heidegger, Ludwig Wittgenstein, Rudolf Carnap, Willard Van Orman Quine, Wilfrid Sellars, Peter F. Strawson, Ruth Barcan Marcus, David Armstrong, Saul Kripke, and David Lewis. Not all of these have a chapter of their own, however, for some figure only in connection with other thinkers and specific themes related with their work. The individual chapters seek to cover more than one philosopher's thought and also to take notice of other periods in the history than what is their main focus.

This account of rational belief revision explains how a rational agent ought to proceed when adopting a new belief — a difficult matter if the new belief contradicts the agent’s old beliefs. Belief systems are modeled as finite dependency networks. So one can attend not only to what the agent believes, but also to the variety of reasons the agent has for so believing. The computational complexity of the revision problem is characterized. Algorithms for belief revision are formulated, and implemented in Prolog. The implementation tests well on a range of simple belief‐revision problems that pose a variety of challenges for any account of belief‐revision. The notion of ‘minimal mutilation’ of a belief system is explicated precisely. The proposed revision methods are invariant across different global justificatory structures (foundationalist, coherentist, etc.). They respect the intuition that, when revising one's beliefs, one should not hold on to any belief that has lost all its former justifications. The limitation to finite dependency networks is shown not to compromise theoretical generality. This account affords a novel way to argue that there is an inviolable core of logical principles. These principles, which form the system of Core Logic, cannot be given up, on pain of not being able to carry out the reasoning involved in rationally revising beliefs. The book ends by comparing and contrasting the new account with some major representatives of earlier alternative approaches, from the fields of formal epistemology, artificial intelligence and mathematical logic.

A theory of collective rationality identifies collective acts that are evaluable for rationality and formulates principles for their evaluation. This book argues that a group's act is evaluable for rationality if it is the product of acts its members freely and fully control. It also argues that such an act is collectively rational if the acts of the group's members are rational. Efficiency is a goal of collective rationality, but not a requirement, except in cases where conditions are ideal for joint action and agents have rationally prepared for coordination. A theory of collective rationality also yields principles concerning solutions to games. One principle requires that a solution constitute an equilibrium among the incentives of the agents in the game. In a cooperative game some agents are coalitions of individuals, and it may be impossible for all agents to pursue all incentives. Because rationality is attainable, the appropriate equilibrium‐standard for cooperative games requires pursuit of an incentive only if it provides a sufficient reason to act. The book's theory of collective rationality supports an attainable equilibrium‐standard for solutions to cooperative games and shows that its realization follows from individuals' rational acts. This book's theory of collective rationality contributes to philosophical projects such as contractarian ethics and to practical projects such as the design of social institutions.

Vagueness is a familiar but deeply puzzling aspect of the relation between language and the world. It is highly controversial what the nature of vagueness is; a feature of the way we represent reality in language, or rather a feature of reality itself? Assuming standard logical principles, Sorites' arguments suggest that vague terms are either inconsistent or have a sharp boundary. The account we give of such paradoxes plays a pivotal role for our understanding of natural languages. If our reasoning involves any vague concepts, is it safe from contradiction? Do vague concepts really lack any sharp boundary? If not, why are we reluctant to accept the existence of any sharp boundary for them? And what rules of inference can we validly apply, if we reason in vague terms? This book presents the latest work towards a clearer understanding of these old puzzles about the nature and logic of vagueness. The collection offers a stimulating series of original chapters on these and related issues by some of the world's leading experts.