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Author: Antonio Piccolomini d’Aragona Publisher: Springer Nature ISBN: 3031202945 Category : Philosophy Languages : en Pages : 284
Book Description
This book presents an in-depth and critical reconstruction of Prawitz’s epistemic grounding, and discusses it within the broader field of proof-theoretic semantics. The theory of grounds is also provided with a formal framework, through which several relevant results are proved. Investigating Prawitz’s theory of grounds, this work answers one of the most fundamental questions in logic: why and how do some inferences have the epistemic power to compel us to accept their conclusion, if we have accepted their premises? Prawitz proposes an innovative description of inferential acts, as applications of constructive operations on grounds for the premises, yielding a ground for the conclusion. The book is divided into three parts. In the first, the author discusses the reasons that have led Prawitz to abandon his previous semantics of valid arguments and proofs. The second part presents Prawitz’s grounding as found in his ground-theoretic papers. Finally, in the third part, a formal apparatus is developed, consisting of a class of languages whose terms are equipped with denotation functions associating them to operations and grounds, as well as of a class of systems where important properties of the terms can be proved.
Author: Antonio Piccolomini d’Aragona Publisher: Springer Nature ISBN: 3031202945 Category : Philosophy Languages : en Pages : 284
Book Description
This book presents an in-depth and critical reconstruction of Prawitz’s epistemic grounding, and discusses it within the broader field of proof-theoretic semantics. The theory of grounds is also provided with a formal framework, through which several relevant results are proved. Investigating Prawitz’s theory of grounds, this work answers one of the most fundamental questions in logic: why and how do some inferences have the epistemic power to compel us to accept their conclusion, if we have accepted their premises? Prawitz proposes an innovative description of inferential acts, as applications of constructive operations on grounds for the premises, yielding a ground for the conclusion. The book is divided into three parts. In the first, the author discusses the reasons that have led Prawitz to abandon his previous semantics of valid arguments and proofs. The second part presents Prawitz’s grounding as found in his ground-theoretic papers. Finally, in the third part, a formal apparatus is developed, consisting of a class of languages whose terms are equipped with denotation functions associating them to operations and grounds, as well as of a class of systems where important properties of the terms can be proved.
Author: Antonio Piccolomini d'Aragona Publisher: ISBN: 9783031202957 Category : Languages : en Pages : 0
Book Description
This book presents an in-depth and critical reconstruction of Prawitz's epistemic grounding, and discusses it within the broader field of proof-theoretic semantics. The theory of grounds is also provided with a formal framework, through which several relevant results are proved. Investigating Prawitz's theory of grounds, this work answers one of the most fundamental questions in logic: why and how do some inferences have the epistemic power to compel us to accept their conclusion, if we have accepted their premises? Prawitz proposes an innovative description of inferential acts, as applications of constructive operations on grounds for the premises, yielding a ground for the conclusion. The book is divided into three parts. In the first, the author discusses the reasons that have led Prawitz to abandon his previous semantics of valid arguments and proofs. The second part presents Prawitz's grounding as found in his ground-theoretic papers. Finally, in the third part, a formal apparatus is developed, consisting of a class of languages whose terms are equipped with denotation functions associating them to operations and grounds, as well as of a class of systems where important properties of the terms can be proved.
Author: Heinrich Wansing Publisher: Springer ISBN: 3319110411 Category : Philosophy Languages : en Pages : 469
Book Description
This volume is dedicated to Prof. Dag Prawitz and his outstanding contributions to philosophical and mathematical logic. Prawitz's eminent contributions to structural proof theory, or general proof theory, as he calls it, and inference-based meaning theories have been extremely influential in the development of modern proof theory and anti-realistic semantics. In particular, Prawitz is the main author on natural deduction in addition to Gerhard Gentzen, who defined natural deduction in his PhD thesis published in 1934. The book opens with an introductory paper that surveys Prawitz's numerous contributions to proof theory and proof-theoretic semantics and puts his work into a somewhat broader perspective, both historically and systematically. Chapters include either in-depth studies of certain aspects of Dag Prawitz's work or address open research problems that are concerned with core issues in structural proof theory and range from philosophical essays to papers of a mathematical nature. Investigations into the necessity of thought and the theory of grounds and computational justifications as well as an examination of Prawitz's conception of the validity of inferences in the light of three “dogmas of proof-theoretic semantics” are included. More formal papers deal with the constructive behaviour of fragments of classical logic and fragments of the modal logic S4 among other topics. In addition, there are chapters about inversion principles, normalization of p roofs, and the notion of proof-theoretic harmony and other areas of a more mathematical persuasion. Dag Prawitz also writes a chapter in which he explains his current views on the epistemic dimension of proofs and addresses the question why some inferences succeed in conferring evidence on their conclusions when applied to premises for which one already possesses evidence.
Author: Juan Redmond Publisher: Springer ISBN: 3319265067 Category : Philosophy Languages : en Pages : 554
Book Description
With this volume of the series Logic, Epistemology, and the Unity of Science edited by S. Rahman et al. a challenging dialogue is being continued. The series’ first volume argued that one way to recover the connections between logic, philosophy of sciences, and sciences is to acknowledge the host of alternative logics which are currently being developed. The present volume focuses on four key themes. First of all, several chapters unpack the connection between knowledge and epistemology with particular focus on the notion of knowledge as resulting from interaction. Secondly, new epistemological perspectives on linguistics, the foundations of mathematics and logic, physics, biology and law are a subject of analysis. 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.
Author: Maria van der Schaar Publisher: Springer Science & Business Media ISBN: 9400751370 Category : Philosophy Languages : en Pages : 172
Book Description
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. The commentary repatriates the concept of judgement in the discussion, banished in recent times by the logical positivism of Wittgenstein, Hilbert and Schlick, and the Platonism of Bolzano. The volume commences with the insights of Swedish philosopher Per Martin-Löf, the father of constructive type theory, for whom logic is a demonstrative science in which judgement is a settled feature of the landscape. His paper opens the first of four sections that examine, in turn, historical philosophical assessments of judgement and reason; their place in early modern philosophy; the notion of judgement and logical theory in Wolff, Kant and Neo-Kantians like Windelband; their development in the Husserlian phenomenological paradigm; and the work of Bolzano, Russell and Frege. The papers, whose authors include Per Martin-Löf, Göran Sundholm, Michael Della Rocca and Robin Rollinger, represent a finely judged editorial selection highlighting work on philosophers exercised by the question of whether or not an epistemic notion of judgement has a role to play in logic. The volume will be of profound interest to students and academicians for its application of historical developments in philosophy to the solution of vexatious contemporary issues in the foundation of logic.
Author: Marcos Silva Publisher: Springer ISBN: 331967398X Category : Philosophy Languages : en Pages : 326
Book Description
This edited volume explores the different and seminal ways colours matter to philosophy. Each chapter provides an insightful analysis of one or more cases in which colours raise philosophical problems in different areas and periods of philosophy. This historically informed discussion examines both logical and linguistic aspects, covering such areas as the mind, aesthetics and the foundations of mathematics. The international contributors look at traditional epistemological and metaphysical issues on the subjectivity and objectivity of colours. In addition, they also assess phenomenological problems typical of the continental tradition and contemporary problems in the philosophy of mind. The chapters include coverage of such topics as Newton’s and Goethe’s theory of light and colours, how primary qualities are qualitative and colours are primary, explaining colour phenomenology, and colour in cognition, language and philosophy. "This book beautifully prepares the ground for the next steps in our research on and philosophising about colour" Daniel D. Hutto (University of Wollongong) "It is not an overstatement to say that How Colours to Philosophy is a ground breaking publication" Mazviita Chirimuuta (University of Pittsburgh) "Anyone interested in philosophical issues about color will find it highly stimulating." Martine Nida-Rümelin (Université de Fribourg) "The high quality papers included in this anthology succeed admirably in enriching current philosophical thinking about colour” Erik Myin (University of Antwerp) “This is certainly the most complete collection of philosophical essays on colours ever published” André Leclerc (University of Brasília) “All in all this collections represents a new milestone in the ongoing philosophical debate on colours and colour expressions” Ingolf Max (University of Leipzig)
Author: Gianluigi Oliveri Publisher: Springer Nature ISBN: 3030847063 Category : Science Languages : en Pages : 365
Book Description
This edited collection casts light on central issues within contemporary philosophy of mathematics such as the realism/anti-realism dispute; the relationship between logic and metaphysics; and the question of whether mathematics is a science of objects or structures. The discussions offered in the papers involve an in-depth investigation of, among other things, the notions of mathematical truth, proof, and grounding; and, often, a special emphasis is placed on considerations relating to mathematical practice. A distinguishing feature of the book is the multicultural nature of the community that has produced it. Philosophers, logicians, and mathematicians have all contributed high-quality articles which will prove valuable to researchers and students alike.
Author: Carsten Allefeld Publisher: Nova Publishers ISBN: 9781604560220 Category : Language Arts & Disciplines Languages : en Pages : 344
Book Description
What is the origin of meaning? How does the brain achieve symbolic computation? What are the neural correlates of cognitive processes? These challenging questions at the borderline between neuroscience, cognitive science, nonlinear dynamics, and philosophy are related to the symbol grounding problem: How is the meaning of words and utterances grounded in the dynamics of the brain and in the evolution of beings alive interacting with each other and with their environments? Simply by convention? Or is there an inherent correctness of names, of syllables, or even of sounds? This new book examines these important issues and presents probing analyses of the latest research.
Author: Stefania Centrone Publisher: Springer Nature ISBN: 3030204472 Category : Philosophy Languages : en Pages : 375
Book Description
In a fragment entitled Elementa Nova Matheseos Universalis (1683?) Leibniz writes “the mathesis [...] shall deliver the method through which things that are conceivable can be exactly determined”; in another fragment he takes the mathesis to be “the science of all things that are conceivable.” Leibniz considers all mathematical disciplines as branches of the mathesis and conceives the mathesis as a general science of forms applicable not only to magnitudes but to every object that exists in our imagination, i.e. that is possible at least in principle. As a general science of forms the mathesis investigates possible relations between “arbitrary objects” (“objets quelconques”). It is an abstract theory of combinations and relations among objects whatsoever. In 1810 the mathematician and philosopher Bernard Bolzano published a booklet entitled Contributions to a Better-Grounded Presentation of Mathematics. There is, according to him, a certain objective connection among the truths that are germane to a certain homogeneous field of objects: some truths are the “reasons” (“Gründe”) of others, and the latter are “consequences” (“Folgen”) of the former. The reason-consequence relation seems to be the counterpart of causality at the level of a relation between true propositions. Arigorous proof is characterized in this context as a proof that shows the reason of the proposition that is to be proven. Requirements imposed on rigorous proofs seem to anticipate normalization results in current proof theory. The contributors of Mathesis Universalis, Computability and Proof, leading experts in the fields of computer science, mathematics, logic and philosophy, show the evolution of these and related ideas exploring topics in proof theory, computability theory, intuitionistic logic, constructivism and reverse mathematics, delving deeply into a contextual examination of the relationship between mathematical rigor and demands for simplification.
Author: Antonio Piccolomini d’Aragona
Author: Antonio Piccolomini d’Aragona
Author: Antonio Piccolomini d'Aragona
Author: Heinrich Wansing
Author: Juan Redmond
Author: Maria van der Schaar
Author: Antonio Piccolomini d'Aragona
Author: Marcos Silva
Author: Gianluigi Oliveri
Author: Carsten Allefeld
Author: Stefania Centrone