Skolem and the löwenheim-skolem theorem: a case study of the philosophical significance of mathematical results
History and Philosophy of Logic 6 (1):75-89 (1985)
|Abstract||The dream of a community of philosophers engaged in inquiry with shared standards of evidence and justification has long been with us. It has led some thinkers puzzled by our mathematical experience to look to mathematics for adjudication between competing views. I am skeptical of this approach and consider Skolem's philosophical uses of the Löwenheim-Skolem Theorem to exemplify it. I argue that these uses invariably beg the questions at issue. I say ?uses?, because I claim further that Skolem shifted his position on the philosophical significance of the theorem as a result of a shift in his background beliefs. The nature of this shift and possible explanations for it are investigated. Ironically, Skolem's own case provides a historical example of the philosophical flexibility of his theorem. Our suspicion ought always to be aroused when a proof proves more than its means allow it. Something of this sort might be called ?a puffed-up proof?. Ludwig Wittgenstein, Remarks on the foundations of mathematics (revised edition), vol. 2, 21|
|Keywords||No keywords specified (fix it)|
|Through your library||Configure|
Similar books and articles
Rami Grossberg (1988). A Downward Löwenheim-Skolem Theorem for Infinitary Theories Which Have the Unsuperstability Property. Journal of Symbolic Logic 53 (1):231-242.
Virginia Klenk (1976). Intended Models and the Löwenheim-Skolem Theorem. Journal of Philosophical Logic 5 (4):475--89.
Thoralf Skolem (1941). Sur la Porté du Théorème Löwenheim-Skolem. In Thoralf Skolem (ed.), Selected Works in Logic. Universitetsforlaget.
Marek Zawadowski (1983). The Skolem-Löwenheim Theorem in Toposes. Studia Logica 42 (4):461 - 475.
Timothy Bays (2006). The Mathematics of Skolem's Paradox. In Dale Jacquette (ed.), Philosophy of Logic.
Timothy Bays (2009). Skolem's Paradox. In Edward N. Zalta (ed.), Stanford Encyclopedia of Philosophy.
Marek Zawadowski (1985). The Skolem-Löwenheim Theorem in Toposes. II. Studia Logica 44 (1):25 - 38.
George S. Boolos (1970). A Proof of the Löwenheim-Skolem Theorem. Notre Dame Journal of Formal Logic 11 (1):76-78.
Jan Von Plato (2007). In the Shadows of the Löwenheim-Skolem Theorem: Early Combinatorial Analyses of Mathematical Proofs. Bulletin of Symbolic Logic 13 (2):189-225.
Added to index2010-08-10
Total downloads15 ( #79,694 of 556,837 )
Recent downloads (6 months)1 ( #64,847 of 556,837 )
How can I increase my downloads?