Noûs 47 (3):467-481 (2013)
It is often alleged that, unlike typical axioms of mathematics, the Continuum Hypothesis (CH) is indeterminate. This position is normally defended on the ground that the CH is undecidable in a way that typical axioms are not. Call this kind of undecidability “absolute undecidability”. In this paper, I seek to understand what absolute undecidability could be such that one might hope to establish that (a) CH is absolutely undecidable, (b) typical axioms are not absolutely undecidable, and (c) if a mathematical hypothesis is absolutely undecidable, then it is indeterminate. I shall argue that on no understanding of absolute undecidability could one hope to establish all of (a)–(c). However, I will identify one understanding of absolute undecidability on which one might hope to establish both (a) and (c) to the exclusion of (b). This suggests that a new style of mathematical antirealism deserves attention—one that does not depend on familiar epistemological or ontological concerns. The key idea behind this view is that typical mathematical hypotheses are indeterminate because they are relevantly similar to CH.
|Keywords||Continuum Hypothesis Undecidability indeterminacy Disagreement|
|Categories||categorize this paper)|
References found in this work BETA
Philosophy of Mathematics: Structure and Ontology.Stewart Shapiro - 1997 - Oxford University Press.
Citations of this work BETA
Similar books and articles
Jacques Derrida and Alain Badiou: Is There a Relation Between Politics and Time?A. Calcagno - 2004 - Philosophy and Social Criticism 30 (7):799-815.
The Undecidability of the DA-Unification Problem.J. Siekmann & P. Szabó - 1989 - Journal of Symbolic Logic 54 (2):402 - 414.
Undecidability of the Real-Algebraic Structure of Models of Intuitionistic Elementary Analysis.Miklós Erdélyi-Szabó - 2000 - Journal of Symbolic Logic 65 (3):1014-1030.
Derrida and the Aporia of the Political, or the Theologico-Political Dimension of Deconstruction.Noah Horwitz - 2002 - Research in Phenomenology 32 (1):156-176.
The Undecidability of the Spatialized Prisoner's Dilemma.Patrick Grim - 1997 - Theory and Decision 42 (1):53-80.
On the Question of Absolute Undecidability.Peter Koellner - 2010 - In Kurt Gödel, Solomon Feferman, Charles Parsons & Stephen G. Simpson (eds.), Philosophia Mathematica. Association for Symbolic Logic. pp. 153-188.
Limited Ink : Interpreting and Misinterpreting GÜdel's Incompleteness Theorem in Legal Theory.Karen Crawley - unknown
Added to index2010-03-03
Total downloads595 ( #2,022 of 2,146,235 )
Recent downloads (6 months)22 ( #15,974 of 2,146,235 )
How can I increase my downloads?
There are no threads in this forum
Nothing in this forum yet.