Buch, Englisch, Band 327, 300 Seiten, Previously published in hardcover, Format (B × H): 160 mm x 240 mm, Gewicht: 520 g
Reihe: Synthese Library
Buch, Englisch, Band 327, 300 Seiten, Previously published in hardcover, Format (B × H): 160 mm x 240 mm, Gewicht: 520 g
Reihe: Synthese Library
ISBN: 978-90-481-6837-8
Verlag: Springer Netherlands
In the 20th century philosophy of mathematics has to a great extent been dominated by views developed during the so-called foundational crisis in the beginning of that century. These views have primarily focused on questions pertaining to the logical structure of mathematics and questions regarding the justi?cation and consistency of mathematics. Paradigmatic in this - spect is Hilbert’s program which inherits from Frege and Russell the project to formalize all areas of ordinary mathematics and then adds the requi- ment of a proof, by epistemically privileged means (?nitistic reasoning), of the consistency of such formalized theories. While interest in modi?ed v- sions of the original foundational programs is still thriving, in the second part of the twentieth century several philosophers and historians of mat- matics have questioned whether such foundational programs could exhaust the realm of important philosophical problems to be raised about the nature of mathematics. Some have done so in open confrontation (and hostility) to the logically based analysis of mathematics which characterized the cl- sical foundational programs, while others (and many of the contributors to this book belong to this tradition) have only called for an extension of the range of questions and problems that should be raised in connection with an understanding of mathematics. The focus has turned thus to a consideration of what mathematicians are actually doing when they produce mathematics. Questions concerning concept-formation, understanding, heuristics, changes instyle of reasoning, the role of analogies and diagrams etc.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik
- Interdisziplinäres Wissenschaften Wissenschaften: Allgemeines Wissenschaften: Theorie, Epistemologie, Methodik
- Geisteswissenschaften Philosophie Wissenschaftstheorie, Wissenschaftsphilosophie
- Mathematik | Informatik Mathematik Mathematik Allgemein Philosophie der Mathematik
- Geisteswissenschaften Philosophie Philosophie der Mathematik, Philosophie der Physik
Weitere Infos & Material
Mathematical Reasoning and Visualization.- Visualization in Logic and Mathematics.- From Symmetry Perception to Basic Geometry.- Naturalism, Pictures, and Platonic Intuitions.- Mathematical Activity.- Mathematical Explanation and Proof Styles.- Tertium Non Datur: On Reasoning Styles in Early Mathematics.- The Interplay Between Proof and Algorithm in 3rd Century China: The Operation as Prescription of Computation and the Operation as Argumento.- Proof Style and Understanding in Mathematics I: Visualization, Unification and Axiom Choice.- The Varieties of Mathematical Explanation.- The Aesthetics of Mathematics: A Study.
