The aim of this article is to contribute to a better understanding of Frege’s views on semantics and metatheory by looking at his take on several themes in nineteenth century geometry that were significant for the development of modern model-theoretic semantics. I will focus on three issues in which a central semantic idea, the idea of reinterpreting non-logical terms, gradually came to play a substantial role: the introduction of elements at infinity in projective geometry; the study of transfer principles, especially the principle of duality; and the use of counterexamples in independence arguments. Based on a discussion of these issues and how nineteenth century geometers reflected about them, I will then look into Frege’s take on these matters. I conclude with a discussion of Frege’s views and what they entail for the debate about his stance towards semantics and metatheory more generally.
...MoreSimilar Citations
Chapter
Heck, Richard;
(2010)
Frege and Semantics
(/isis/citation/CBB001211655/)
Book
Ricketts, Tom;
Potter, Michael D.;
(2010)
The Cambridge Companion to Frege
(/isis/citation/CBB001211647/)
Chapter
Weiner, Joan;
(2010)
Understanding Frege's Project
(/isis/citation/CBB001211648/)
Book
Heijenoort, Jean van;
(2002)
From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931
(/isis/citation/CBB000201415/)
Article
Reck, Erich H.;
(2013)
Frege, Dedekind, and the Origins of Logicism
(/isis/citation/CBB001212886/)
Article
Mark Textor;
(2021)
Saying Something about a Concept: Frege on Statements of Number
(/isis/citation/CBB227044624/)
Chapter
Goldfarb, Warren;
(2010)
Frege's Conception of Logic
(/isis/citation/CBB001211649/)
Chapter
Wilson, Mark;
(2010)
Frege's Mathematical Setting
(/isis/citation/CBB001211656/)
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/)
Book
Frege, Gottlob;
(1999)
Idéographie
(/isis/citation/CBB000631020/)
Article
Schirn, Matthias;
(2010)
On Translating Frege's Die Grundlagen der Arithmetik
(/isis/citation/CBB001210971/)
Chapter
Thiel, Christian;
(2009)
Gottlob Frege and the Interplay between Logic and Mathematics
(/isis/citation/CBB001210345/)
Thesis
Rohloff, Waldemar;
(2007)
Kant and Frege on the a priori Applicability of Mathematics
(/isis/citation/CBB001561363/)
Chapter
Tappenden, Jamie;
(2006)
The Riemannian Background to Frege's Philosophy
(/isis/citation/CBB000800119/)
Article
Korte, Tapio;
(2010)
Frege's Begriffsschrift as a lingua characteristica
(/isis/citation/CBB001211456/)
Article
Belna, Jean Pierre;
(2002)
Frege et la géométrie projective: la Dissertation inaugurale de 1873
(/isis/citation/CBB000770938/)
Article
Belna, Jean-Pierre;
(2006)
Objectivité et principe de dualité: Le paragraphe 26 des Fondements de l'arithmétique de Frege
(/isis/citation/CBB000770988/)
Article
Günther Eder;
(2021)
Frege on intuition and objecthood in projective geometry
(/isis/citation/CBB221284966/)
Article
Boos, William;
(1985)
“The true” in Gottlob Frege's “Über die Grundlagen der Geometrie”
(/isis/citation/CBB000048186/)
Chapter
Hallett, Michael;
(2010)
Frege and Hilbert
(/isis/citation/CBB001211657/)
Be the first to comment!