What is Absolute Undecidability?†

Noûs 47 (3):467-481 (2013)
Abstract
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)
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
 
Download options
PhilPapers Archive Justin Clarke-Doane, What is Absolute Undecidability?†
External links
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA
George Boolos (1998). Must We Believe in Set Theory? In Richard Jeffrey (ed.), Logic, Logic, and Logic. Harvard University Press. 120-132.

View all 23 references

Citations of this work BETA
Similar books and articles
Analytics

Monthly downloads

Added to index

2010-03-03

Total downloads

156 ( #4,928 of 1,102,446 )

Recent downloads (6 months)

20 ( #8,615 of 1,102,446 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Start a new thread
Order:
There  are no threads in this forum
Nothing in this forum yet.