Ebert, Philip A. (Editor)
Rossberg, Marcus (Editor)
Abstractionism, which is a development of Frege's original Logicism, is a recent and much debated position in the philosophy of mathematics. This volume contains 16 original papers by leading scholars on the philosophical and mathematical aspects of Abstractionism. After an extensive editors'introduction to the topic of abstractionism, five contributions deal with the semantics and meta-ontology of Abstractionism, as well as the so-called Caesar Problem. Four papers then discuss abstractionist epistemology, focusing on the idea of implicit definitions and non-evidential warrants(entitlements) to account for a priori mathematical knowledge. This is followed by four chapters concerning the mathematics of Abstractionism, in particular the issue of impredicativity, the Bad Company objection, and the question of abstractionist set theory. Finally, the last section of the bookcontains three contributions that discuss Frege's application constraint within an abstractionist setting.
...MoreReview Shay Allen Logan (2018) Review of "Abstractionism: Essays in Philosophy of Mathematics". Metascience: An International Review Journal for the History, Philosophy and Social Studies of Science (pp. 327-329).
Book
Oystein Linnebo;
(2018)
Thin Objects: An Abstractionist Account
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Book
Fine, Kit;
(2002)
The Limits of Abstraction
(/isis/citation/CBB000302227/)
Article
Lavers, Gregory;
(2013)
Frege, Carnap, and Explication: “Our Concern Here Is to Arrive at a Concept of Number Usable for the Purpose of Science”
(/isis/citation/CBB001212885/)
Book
Ricketts, Tom;
Potter, Michael D.;
(2010)
The Cambridge Companion to Frege
(/isis/citation/CBB001211647/)
Article
Reck, Erich H.;
(2013)
Frege, Dedekind, and the Origins of Logicism
(/isis/citation/CBB001212886/)
Article
Simon, Gérard;
(2007)
Le problème inverse de Lévi-Strauss
(/isis/citation/CBB000954363/)
Book
Woods, John;
(2003)
Paradox and Paraconsistency: Conflict Resolution in the Abstract Sciences
(/isis/citation/CBB000301990/)
Book
Künne, Wolfgang;
(2010)
Die Philosophische Logik Gottlob Freges: ein Kommentar; mit den Texten des Vorworts zu Grundgesetze der Arithmetik und der Logischen Untersuchungen I--IV
(/isis/citation/CBB001210615/)
Chapter
Beaney, Michael;
(2006)
Frege and the Role of Historical Elucidation: Methodology and the Foundations of Mathematics
(/isis/citation/CBB000800117/)
Article
Schirn, Matthias;
(2010)
On Translating Frege's Die Grundlagen der Arithmetik
(/isis/citation/CBB001210971/)
Article
John Woods;
(2021)
What did Frege take Russell to have proved?
(/isis/citation/CBB858610340/)
Chapter
Tappenden, Jamie;
(2006)
The Riemannian Background to Frege's Philosophy
(/isis/citation/CBB000800119/)
Article
Korhonen, Anssi;
(2012)
Logic as a Science and Logic as a Theory: Remarks on Frege, Russell and the Logocentric Predicament
(/isis/citation/CBB001214125/)
Book
Mario Castellana;
(2019)
Federigo Enriques e la “Nuova Epistemologia”
(/isis/citation/CBB605748137/)
Essay Review
Panza, Marco;
(2011)
Breathing Fresh Air into the Philosophy of Mathematics
(/isis/citation/CBB001566756/)
Book
Mancosu, Paolo;
(2008)
The Philosophy of Mathematical Practice
(/isis/citation/CBB000952048/)
Article
Domski, Mary;
(2013)
Kant and Newton on the a priori Necessity of Geometry
(/isis/citation/CBB001320266/)
Book
Andrea Pitasi;
(2023)
La matematica della società
(/isis/citation/CBB101212330/)
Thesis
Sepkoski, David Christopher;
(2002)
Numbers and Things: Nominalism and Constructivism in Seventeenth-Century Mathematical Philosophy
(/isis/citation/CBB001562503/)
Book
Karine Chemla;
Renaud Chorlay;
David Rabouin;
(2016)
The Oxford Handbook of Generality in Mathematics and the Sciences
(/isis/citation/CBB487165638/)
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