Induction and indefinite extensibility: The gödel sentence is true, but did someone change the subject?

Mind 107 (427):597-624 (1998)
Abstract
Over the last few decades Michael Dummett developed a rich program for assessing logic and the meaning of the terms of a language. He is also a major exponent of Frege's version of logicism in the philosophy of mathematics. Over the last decade, Neil Tennant developed an extensive version of logicism in Dummettian terms, and Dummett influences other contemporary logicists such as Crispin Wright and Bob Hale. The purpose of this paper is to explore the prospects for Fregean logicism within a broadly Dummettian framework. The conclusions are mostly negative: Dummett's views on analyticity and the logical/non-logical boundary leave little room for logicism. Dummett's considerations concerning manifestation and separability lead to a conservative extension requirement: if a sentence S is logically true, then there is a proof of S which uses only the introduction and elimination rules of the logical terms that occur in S. If basic arithmetic propositions are logically true - as the logicist contends - then there is tension between this conservation requirement and the ontological commitments of arithmetic. It follows from Dummett's manifestation requirements that if a sentence S is composed entirely of logical terminology, then there is a formal deductive system D such that S is analytic, or logically true, if and only if S is a theorem of D. There is a deep conflict between this result and the essential incompleteness, or as Dummett puts it, the indefinite extensibility, of arithmetic truth.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1093/mind/107.427.597
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
Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 28,756
Through your library
References found in this work BETA

No references found.

Add more references

Citations of this work BETA
Harmony and Autonomy in Classical Logic.Stephen Read - 2000 - Journal of Philosophical Logic 29 (2):123-154.
What Harmony Could and Could Not Be.Florian Steinberger - 2011 - Australasian Journal of Philosophy 89 (4):617 - 639.

Add more citations

Similar books and articles

Monthly downloads

Added to index

2009-01-28

Total downloads

75 ( #70,793 of 2,177,988 )

Recent downloads (6 months)

1 ( #317,698 of 2,177,988 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Order:
There  are no threads in this forum
Nothing in this forum yet.

Other forums