Intuitionistic Proof Versus Classical Truth (eBook)
XIII, 170 Seiten
Springer International Publishing (Verlag)
978-3-319-74357-8 (ISBN)
This book examines the role of acts of choice in classical and intuitionistic mathematics. Featuring fifteen papers - both new and previously published - it offers a fresh analysis of concepts developed by the mathematician and philosopher L.E.J. Brouwer, the founder of intuitionism.
The author explores Brouwer's idealization of the creative subject as the basis for intuitionistic truth, and in the process he also discusses an important, related question: to what extent does the intuitionistic perspective succeed in avoiding the classical realistic notion of truth? The papers detail realistic aspects in the idealization of the creative subject and investigate the hidden role of choice even in classical logic and mathematics, covering such topics as bar theorem, type theory, inductive evidence, Beth models, fallible models, and more. In addition, the author offers a critical analysis of the response of key mathematicians and philosophers to Brouwer's work. These figures include Michael Dummett, Saul Kripke, Per Martin-Löf, and Arend Heyting.
This book appeals to researchers and graduate students with an interest in philosophy of mathematics, linguistics, and mathematics.
Enrico Martino was associated professor (now retired) of Logic and Philosophy of Mathematics in the department of Mathematics and, subsequently of FISPPA of the University of Padua. His main interests are Philosophy of Logic and Mathematics.
Enrico Martino was associated professor (now retired) of Logic and Philosophy of Mathematics in the department of Mathematics and, subsequently of FISPPA of the University of Padua. His main interests are Philosophy of Logic and Mathematics.
Brouwer, Dummett and the bar theorem.- Creative subject and bar theorem.- Natural intuitionistic semantics and generalized Beth semantics.- Connection between the principle of inductive evidence and the bar theorem.- On the Brouwerian concept of negative continuity.- Classical and intuitionistic semantical groundedness.- Brouwer’s equivalence between virtual and inextensible order.- An intuitionistic notion of hypothetical truth for which strong completeness intuitionistically holds.- Propositions and judgements in Martin-Löf.- Negationless Intuitionism.- Temporal and atemporal truth in intuitionistic mathematics.- Arbitrary reference in mathematical reasoning.- The priority of arithmetical truth over arithmetical provability.- The impredicativity of the intuitionistic meaning of logical constants.- The intuitionistic meaning of logical constants and fallible models.
| Erscheint lt. Verlag | 23.2.2018 |
|---|---|
| Reihe/Serie | Logic, Epistemology, and the Unity of Science |
| Zusatzinfo | XIII, 170 p. 1 illus. |
| Verlagsort | Cham |
| Sprache | englisch |
| Themenwelt | Geisteswissenschaften ► Philosophie ► Logik |
| Geisteswissenschaften ► Sprach- / Literaturwissenschaft ► Literaturwissenschaft | |
| Mathematik / Informatik ► Mathematik | |
| Schlagworte | Bar Theorem • Beth-Models • Brouwer Arend Heyting • Brouwer classical truth • Brouwer creative subject • Brouwer intuitionistic truth • Brouwer Michael Dummett • Brouwer Per Martin-Löf • Brouwer realistic truth • Brouwer Saul Kripke • Constructivism • Creative Subject • Fallible Models • impredicativity • Inductive Evidence • Informal Intuitionistic Proof • Intuitionistic Choice Sequences • Semantical Groundedness • Type Theory |
| ISBN-10 | 3-319-74357-0 / 3319743570 |
| ISBN-13 | 978-3-319-74357-8 / 9783319743578 |
| Haben Sie eine Frage zum Produkt? |
PDF (Wasserzeichen)Größe: 2,9 MB
DRM: Digitales Wasserzeichen
Dieses eBook enthält ein digitales Wasserzeichen und ist damit für Sie personalisiert. Bei einer missbräuchlichen Weitergabe des eBooks an Dritte ist eine Rückverfolgung an die Quelle möglich.
Dateiformat: PDF (Portable Document Format)
Mit einem festen Seitenlayout eignet sich die PDF besonders für Fachbücher mit Spalten, Tabellen und Abbildungen. Eine PDF kann auf fast allen Geräten angezeigt werden, ist aber für kleine Displays (Smartphone, eReader) nur eingeschränkt geeignet.
Systemvoraussetzungen:
PC/Mac: Mit einem PC oder Mac können Sie dieses eBook lesen. Sie benötigen dafür einen PDF-Viewer - z.B. den Adobe Reader oder Adobe Digital Editions.
eReader: Dieses eBook kann mit (fast) allen eBook-Readern gelesen werden. Mit dem amazon-Kindle ist es aber nicht kompatibel.
Smartphone/Tablet: Egal ob Apple oder Android, dieses eBook können Sie lesen. Sie benötigen dafür einen PDF-Viewer - z.B. die kostenlose Adobe Digital Editions-App.
Buying eBooks from abroad
For tax law reasons we can sell eBooks just within Germany and Switzerland. Regrettably we cannot fulfill eBook-orders from other countries.
aus dem Bereich
