The Hyperuniverse Project And Maximality
DOWNLOAD
Download The Hyperuniverse Project And Maximality PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get The Hyperuniverse Project And Maximality book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
The Hyperuniverse Project And Maximality
DOWNLOAD
Author : Carolin Antos
language : en
Publisher: Birkhäuser
Release Date : 2018-01-30
The Hyperuniverse Project And Maximality written by Carolin Antos and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-30 with Mathematics categories.
This collection documents the work of the Hyperuniverse Project which is a new approach to set-theoretic truth based on justifiable principles and which leads to the resolution of many questions independent from ZFC. The contributions give an overview of the program, illustrate its mathematical content and implications, and also discuss its philosophical assumptions. It will thus be of wide appeal among mathematicians and philosophers with an interest in the foundations of set theory. The Hyperuniverse Project was supported by the John Templeton Foundation from January 2013 until September 2015
Quine Structure And Ontology
DOWNLOAD
Author : Frederique Janssen-Lauret
language : en
Publisher:
Release Date : 2020
Quine Structure And Ontology written by Frederique Janssen-Lauret and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Philosophy categories.
W.V. Quine, a champion of philosophical naturalism and pioneer of mathematical logic, was one of the most important philosophers of the 20th century. This volume provides a full picture of the development of Quine's views on structure and how it permeates and shapes his attitude to a range of philosophical questions.
Handbook Of The History And Philosophy Of Mathematical Practice
DOWNLOAD
Author : Bharath Sriraman
language : en
Publisher: Springer Nature
Release Date : 2024-04-26
Handbook Of The History And Philosophy Of Mathematical Practice written by Bharath Sriraman and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-26 with Mathematics categories.
The purpose of this unique handbook is to examine the transformation of the philosophy of mathematics from its origins in the history of mathematical practice to the present. It aims to synthesize what is known and what has unfolded so far, as well as to explore directions in which the study of the philosophy of mathematics, as evident in increasingly diverse mathematical practices, is headed. Each section offers insights into the origins, debates, methodologies, and newer perspectives that characterize the discipline today. Contributions are written by scholars from mathematics, history, and philosophy – as well as other disciplines that have contributed to the richness of perspectives abundant in the study of philosophy today – who describe various mathematical practices throughout different time periods and contrast them with the development of philosophy. Editorial Advisory Board Andrew Aberdein, Florida Institute ofTechnology, USA Jody Azzouni, Tufts University, USA Otávio Bueno, University of Miami, USA William Byers, Concordia University, Canada Carlo Cellucci, Sapienza University of Rome, Italy Chandler Davis, University of Toronto, Canada (1926-2022) Paul Ernest, University of Exeter, UK Michele Friend, George Washington University, USA Reuben Hersh, University of New Mexico, USA (1927-2020) Kyeong-Hwa Lee, Seoul National University, South Korea Yuri Manin, Max Planck Institute for Mathematics, Germany (1937-2023) Athanase Papadopoulos, University of Strasbourg, France Ulf Persson, Chalmers University of Technology, Sweden John Stillwell, University of San Francisco, USA David Tall, University of Warwick, UK (1941-2024) This book with its exciting depth and breadth, illuminates us about the history, practice, and the very language of our subject; about the role of abstraction, ofproof and manners of proof; about the interplay of fundamental intuitions; about algebraic thought in contrast to geometric thought. The richness of mathematics and the philosophy encompassing it is splendidly exhibited over the wide range of time these volumes cover---from deep platonic and neoplatonic influences to the most current experimental approaches. Enriched, as well, with vivid biographies and brilliant personal essays written by (and about) people who play an important role in our tradition, this extraordinary collection of essays is fittingly dedicated to the memory of Chandler Davis, Reuben Hersh, and Yuri Manin. ---Barry Mazur, Gerhard Gade University Professor, Harvard University This encyclopedic Handbook will be a treat for all those interested in the history and philosophy of mathematics. Whether one is interested in individuals (from Pythagoras through Newton and Leibniz to Grothendieck), fields (geometry, algebra, number theory, logic, probability, analysis), viewpoints (from Platonism to Intuitionism), or methods (proof, experiment, computer assistance), the reader will find a multitude of chapters that inform and fascinate. ---John Stillwell, Emeritus Professor of Mathematics, University of San Francisco; Recipient of the 2005 Chauvenet Prize Dedicating a volume to the memory of three mathematicians – Chandler Davis, Reuben Hersh, and Yuri Manin –, who went out of their way to show to a broader audience that mathematics is more than what they might think, is an excellent initiative. Gathering authors coming from many different backgrounds but who are very strict about the essays they write was successfully achieved by the editor-in-chief. The result: a great source of potential inspiration! ---Jean-Pierre Bourguignon; Nicolaas Kuiper Honorary Professor at the Institut des Hautes Études Scientifiques
The Forcing Method In Set Theory
DOWNLOAD
Author : Matteo Viale
language : en
Publisher: Springer Nature
Release Date : 2024-11-11
The Forcing Method In Set Theory written by Matteo Viale and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-11 with Mathematics categories.
The main aim of this book is to provide a compact self-contained presentation of the forcing technique devised by Cohen to establish the independence of the continuum hypothesis from the axioms of set theory. The book follows the approach to the forcing technique via Boolean valued semantics independently introduced by Vopenka and Scott/Solovay; it develops out of notes I prepared for several master courses on this and related topics and aims to provide an alternative (and more compact) account of this topic with respect to the available classical textbooks. The aim of the book is to take up a reader with familiarity with logic and set theory at the level of an undergraduate course on both topics (e.g., familiar with most of the content of introductory books on first-order logic and set theory) and bring her/him to page with the use of the forcing method to produce independence (or undecidability results) in mathematics. Familiarity of the reader with general topology would also be quite helpful; however, the book provides a compact account of all the needed results on this matter. Furthermore, the book is organized in such a way that many of its parts can also be read by scholars with almost no familiarity with first-order logic and/or set theory. The book presents the forcing method outlining, in many situations, the intersections of set theory and logic with other mathematical domains. My hope is that this book can be appreciated by scholars in set theory and by readers with a mindset oriented towards areas of mathematics other than logic and a keen interest in the foundations of mathematics.
Philosophy Of Mathematics
DOWNLOAD
Author : Ahmet Cevik
language : en
Publisher: CRC Press
Release Date : 2021-11-09
Philosophy Of Mathematics written by Ahmet Cevik and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-09 with Mathematics categories.
The philosophy of mathematics is an exciting subject. Philosophy of Mathematics: Classic and Contemporary Studies explores the foundations of mathematical thought. The aim of this book is to encourage young mathematicians to think about the philosophical issues behind fundamental concepts and about different views on mathematical objects and mathematical knowledge. With this new approach, the author rekindles an interest in philosophical subjects surrounding the foundations of mathematics. He offers the mathematical motivations behind the topics under debate. He introduces various philosophical positions ranging from the classic views to more contemporary ones, including subjects which are more engaged with mathematical logic. Most books on philosophy of mathematics have little to no focus on the effects of philosophical views on mathematical practice, and no concern on giving crucial mathematical results and their philosophical relevance, consequences, reasons, etc. This book fills this gap. The book can be used as a textbook for a one-semester or even one-year course on philosophy of mathematics. "Other textbooks on the philosophy of mathematics are aimed at philosophers. This book is aimed at mathematicians. Since the author is a mathematician, it is a valuable addition to the literature." - Mark Balaguer, California State University, Los Angeles "There are not many such texts available for mathematics students. I applaud efforts to foster the dialogue between mathematics and philosophy." - Michele Friend, George Washington University and CNRS, Lille, France
Objectivity Realism And Proof
DOWNLOAD
Author : Francesca Boccuni
language : en
Publisher: Springer
Release Date : 2016-07-05
Objectivity Realism And Proof written by Francesca Boccuni and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-05 with Science categories.
This volume covers a wide range of topics in the most recent debates in the philosophy of mathematics, and is dedicated to how semantic, epistemological, ontological and logical issues interact in the attempt to give a satisfactory picture of mathematical knowledge. The essays collected here explore the semantic and epistemic problems raised by different kinds of mathematical objects, by their characterization in terms of axiomatic theories, and by the objectivity of both pure and applied mathematics. They investigate controversial aspects of contemporary theories such as neo-logicist abstractionism, structuralism, or multiversism about sets, by discussing different conceptions of mathematical realism and rival relativistic views on the mathematical universe. They consider fundamental philosophical notions such as set, cardinal number, truth, ground, finiteness and infinity, examining how their informal conceptions can best be captured in formal theories. The philosophy of mathematics is an extremely lively field of inquiry, with extensive reaches in disciplines such as logic and philosophy of logic, semantics, ontology, epistemology, cognitive sciences, as well as history and philosophy of mathematics and science. By bringing together well-known scholars and younger researchers, the essays in this collection – prompted by the meetings of the Italian Network for the Philosophy of Mathematics (FilMat) – show how much valuable research is currently being pursued in this area, and how many roads ahead are still open for promising solutions to long-standing philosophical concerns. Promoted by the Italian Network for the Philosophy of Mathematics – FilMat
Il Teorema Di Dio
DOWNLOAD
Author : Emanuele Gambetta
language : it
Publisher: Gangemi Editore spa
Release Date : 2023-02-26T00:00:00+01:00
Il Teorema Di Dio written by Emanuele Gambetta and has been published by Gangemi Editore spa this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-26T00:00:00+01:00 with Mathematics categories.
Il Teorema di Dio di Gödel nasce da esigenze di carattere esistenziale e religioso. Per comprendere la sua prova ontologica di Dio, occorre tenere a mente come Gödel avesse sempre avuto il desiderio di trovare un ordine logico-matematico da porre a fondamento dell'esistenza dell'universo. Un tale ordine gli sembrava fosse assicurato solo dalla necessità logica dell'esistenza di Dio. L'ente divino doveva essere quella verità che non si basa su calcoli umani ed è, quindi, assoluta e non relativa. Gödel riprende la dimostrazione di Leibniz del seguente condizionale: se l'esistenza di Dio è possibile, allora l'esistenza di Dio è necessaria. Come Leibniz che si discosta dalla prova ontologica di Cartesio dimostrando che l'esistenza di Dio è possibile, cosí il matematico moravo fornisce una prova che Dio forma un sistema logicamente coerente da cui segue per modus ponens che Dio esiste in modo necessario. EMANUELE GAMBETTA ha conseguito il dottorato di Ricerca alla Scuola Normale Superiore di Pisa in Filosofia della Matematica con votazione 70/70 e lode. Poi è stato studente ricercatore all'università di Barcellona dove ha partecipato ai seminari al centro di teoria degli insiemi. In seguito ha fatto visita da ricercatore a molte università in giro per il mondo. Per i tipi della Gangemi Editore ha pubblicato Philosophy of the infinite (2020)
La Logica Del Naturalismo
DOWNLOAD
Author : Fabio Sterpetti
language : it
Publisher: Mimesis
Release Date : 2022-05-17T00:00:00+02:00
La Logica Del Naturalismo written by Fabio Sterpetti and has been published by Mimesis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-17T00:00:00+02:00 with Philosophy categories.
Le concezioni filosofiche tradizionali e predominanti sulla natura della filosofia e della conoscenza affondano le loro radici nel pensiero di pensatori radicalmente antinaturalisti. La logica occupa un posto centrale nella riflessione filosofica e rappresenta un baluardo dell’antinaturalismo. Dunque, dato che la concezione della filosofia che si adotta dipende strettamente dalla concezione della logica che si adotta, fino a quando non si sarà in grado di elaborare una concezione naturalista adeguata della logica, non si sarà in grado di elaborare una posizione naturalista adeguata. Il presente volume intende mostrare come sia possibile elaborare una concezione naturalista in grado di rispondere in modo adeguato alle obiezioni che le vengono mosse dai sostenitori delle concezioni tradizionali solo a patto di accettare di ripensare radicalmente la relazione che sussiste tra la logica, la matematica, le scienze naturali e la filosofia.
Objects Structures And Logics
DOWNLOAD
Author : Gianluigi Oliveri
language : en
Publisher: Springer Nature
Release Date : 2022-03-08
Objects Structures And Logics written by Gianluigi Oliveri and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-08 with Science categories.
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.
Second Philosophy A Naturalistic Method
DOWNLOAD
Author : Penelope Maddy
language : en
Publisher: Clarendon Press
Release Date : 2007-04-19
Second Philosophy A Naturalistic Method written by Penelope Maddy and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-19 with Science categories.
Many philosophers these days consider themselves naturalists, but it's doubtful any two of them intend the same position by the term. In this book, Penelope Maddy describes and practises a particularly austere form of naturalism called 'Second Philosophy'. Without a definitive criterion for what counts as 'science' and what doesn't, Second Philosophy can't be specified directly - 'trust only the methods of science!' or some such thing - so Maddy proceeds instead by illustratingthe behaviours of an idealized inquirer she calls the 'Second Philosopher'. This Second Philosopher begins from perceptual common sense and progresses from there to systematic observation, active experimentation, theory formation and testing, working all the while to assess, correct and improve hermethods as she goes. Second Philosophy is then the result of the Second Philosopher's investigations.Maddy delineates the Second Philosopher's approach by tracing her reactions to various familiar skeptical and transcendental views (Descartes, Kant, Carnap, late Putnam, van Fraassen), comparing her methods to those of other self-described naturalists (especially Quine), and examining a prominent contemporary debate (between disquotationalists and correspondence theorists in the theory of truth) to extract a properly second-philosophical line of thought. She then undertakes to practise SecondPhilosophy in her reflections on the ground of logical truth, the methodology, ontology and epistemology of mathematics, and the general prospects for metaphysics naturalized.