Bøger i Logic, Epistemology, and the Unity of Science serien

Ranging from Alan Turing's seminal 1936 paper to the latest work on Kolmogorov complexity and linear logic, this comprehensive new work clarifies the relationship between computability on the one hand and constructivity on the other.

This volume features essays about and by Paul Benacerraf, whose ideas have circulated in the philosophical community since the early nineteen sixties, shaping key areas in the philosophy of mathematics, the philosophy of language, the philosophy of logic, and epistemology. The book started as a workshop held in Paris at the Collège de France in May 2012 with the participation of Paul Benacerraf. The introduction addresses the methodological point of the legitimate use of so-called ¿Princess Margaret Premises¿ in drawing philosophical conclusions from Gödel¿s first incompleteness theorem. The book is then divided into three sections. The first is devoted to an assessment of the improved version of the original dilemma of ¿Mathematical Truth¿ due to Hartry Field: the challenge to the platonist is now to explain the reliability of our mathematical beliefs given the very subject matter of mathematics, either pure or applied. The second addresses the issue of the ontological status of numbers: Frege¿s logicism, fictionalism, structuralism, and Bourbaki¿s theory of structures are called up for an appraisal of Benacerraf¿s negative conclusions of ¿What Numbers Could Not Be.¿ The third is devoted to supertasks and bears witness to the unique standing of Benacerraf¿s first publication: ¿Tasks, Super-Tasks, and Modern Eleatics¿ in debates on Zenös paradox and associated paradoxes, infinitary mathematics, and constructivism and finitism in the philosophy of mathematics.Two yet unpublished essays by Benacerraf have been included in the volume: an early version of ¿Mathematical Truth¿ from 1968 and an essay on ¿What Numbers Could Not Be¿ from the mid 1970¿s. A complete chronological bibliography of Benacerraf¿s work to 2016 is provided.Essays by Jody Azzouni, Paul Benacerraf, Justin Clarke-Doane, Sébastien Gandon, Brice Halimi, Jon Pérez Laraudogoitia, Mary Leng, Antonio León-Sánchez and Ana C. León-Mejía, Marco Panza, Fabrice Pataut, Philippe de Rouilhan, Andrea Sereni, and Stewart Shapiro.

Thirdly, several chapters are dedicated to a discussion of Constructive Type Theory and more generally of the proof-theoretical notion of meaning.Finally, the book brings together studies on the epistemic role of abduction and argumentation theory, both linked to non-monotonic approaches to the dynamics of knowledge.

This book brings together philosophers, mathematicians and logicians to penetrate important problems in the philosophy and foundations of mathematics. The dominant foundational framework for current mathematics is classical logic and set theory with the axiom of choice (ZFC).

While logicians have proposed many technically developed paraconsistent logical systems and contemporary philosophers like Graham Priest have advanced the view that some contradictions can be true, and advocated a paraconsistent logic to deal with them, until recent times these systems have been little understood by philosophers.

Science is a dynamic process in which the assimilation of new phenomena, perspectives, and hypotheses into the scientific corpus takes place slowly. However, a retrospective view of the practical results of the scientific enterprise and of science itself, grants us a clear view of the unity of the human knowledge seeking enterprise.

Ranging from Alan Turing's seminal 1936 paper to the latest work on Kolmogorov complexity and linear logic, this comprehensive new work clarifies the relationship between computability on the one hand and constructivity on the other.

This compelling reevaluation of the relationship between logic and knowledge affirms the key role that the notion of judgement must play in such a review.

onticism is also compared with other, competing theories of vagueness such as semanticism, the view that vagueness exists only in our linguistic representation of the world.Gareth Evans's influential paper of 1978, "Can There Be Vague Objects?" gave a simple but cogent argument against the coherence of ontic vagueness.

In the eyes of the editors, this book will be considered a success if it can convince its readers of the following: that it is warranted to dream of a realistic and full-fledged theory of mathematical practices, in the plural.

Is reality logical and is logic real? The point of convergence lies in the exploration of the connections between reality - social, natural or ideal - and logical structures employed in describing or discovering it.

Under this view, epistemic contents are introduced into the object language as operators yielding propositions from propositions, rather than as metalogical constraints on the notion of inference. The Realism-Antirealism debate has thus had three players: classical logicians, intuitionists and explicit epistemic logicians.

The philosophy of mathematical practice diverges from mainstream philosophy of mathematics in the emphasis it places on what the majority of working mathematicians actually do, rather than on mathematical foundations. The book begins by first challenging the assumption that there is no role for informal logic in mathematics.

One of the most basic problems in the philosophy of science involves determining the extent to which nature is governed by laws. Traditionally, the problem of the unity of science was intimately connected to the problem of understanding the unity of nature.

This compelling reevaluation of the relationship between logic and knowledge affirms the key role that the notion of judgement must play in such a review.

Science is a dynamic process in which the assimilation of new phenomena, perspectives, and hypotheses into the scientific corpus takes place slowly. However, a retrospective view of the practical results of the scientific enterprise and of science itself, grants us a clear view of the unity of the human knowledge seeking enterprise.

Under this view, epistemic contents are introduced into the object language as operators yielding propositions from propositions, rather than as metalogical constraints on the notion of inference. The Realism-Antirealism debate has thus had three players: classical logicians, intuitionists and explicit epistemic logicians.

OndrejMajer,Ahti-VeikkoPietarinen,andTeroTulenheimo 1 Games and logic in philosophy Recent years have witnessed a growing interest in the unifying methodo- gies over what have been perceived as pretty disparate logical 'systems', or else merely an assortment of formal and mathematical 'approaches' to phi- sophical inquiry.

Andinmy haste, I said: "Allmenare Liars" 1 -Psalms 116:11 The Original Lie Philosophical analysis often reveals and seldom solves paradoxes. To quote Stephen Read: A paradox arises when an unacceptable conclusion is supported by a plausible argument from apparently acceptable premises.

Accordingly, the sociological and historical interpretation - volves in fact two kinds of discontinuity which are closely related: the discontinuity of science as such and the discontinuity of the more inclusive political and social context of its development.

This book develops a philosophical and logical interpretation of the concept of information within the formal structure of Constructive Type Theory (CTT), in a manner concurrent with a diverse range of contemporary perspectives on the philosophy of information.

This is the first book to collect essays from philosophers, mathematicians and computer scientists working at the exciting interface of algorithmic learning theory and the epistemology of science and inductive inference.

This book presents formalizations of three important medieval logical theories: supposition, consequence and obligations.

In the last century, developments in mathematics, philosophy, physics, computer science, economics and linguistics have proven important for the development of logic.

Is reality logical and is logic real? The point of convergence lies in the exploration of the connections between reality - social, natural or ideal - and logical structures employed in describing or discovering it.

This volume analyzes how vagueness occurs and matters as a specific problem in the context of theories that are primarily about something else. Topics include vagueness and metaphysics, vagueness and logic, vagueness and linguistics, and vagueness and law.

Some of the leading scholars of Neurath's work, along with many prominent philosophers of science critically examine his place in the history of philosophy of science and evaluate the relevance of his work for contemporary debates concerning the unity of science.

Belief revision theory and philosophy of science both aspire to shed light on the dynamics ofknowledge - on how our view of the world changes (typically) in the light of new evidence.