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

  title={Induction and indefinite extensibility: the G{\"o}del sentence is true, but did someone change the subject?},
  author={Stewart Shapiro},
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 influenced 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… 

Harmony and Autonomy in Classical Logic

  • S. Read
  • Philosophy
    J. Philos. Log.
  • 2000
It is argued that Dummett gives a mistaken elaboration of the notion of harmony, an idea stemming from a remark of Gerhard Gentzen, that the introduction-rules are autonomous if they are taken fully to specify the meaning of the logical constants, and the rules are harmonious if the elimination-rule draws its conclusion from just the grounds stated in the introduced-rule.

Intuitionism and logical revision.

The topic of this thesis is logical revision: should we revise the canons of classical reasoning in favour of a weaker logic, such as intuitionistic logic? In the first part of the thesis, I


There is an interesting connection between cardinality of language and the distinction of lingua characterica from calculus rationator. Calculus-type languages have only a countable number of

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School of Philosophical, Anthropological and Film Studies Doctor of Philosophy by Ole Thomassen Hjortland The model-theoretic analysis of the concept of logical consequence has come under heavy

How do We Know that the Gödel Sentence of a Consistent Theory Is True

Some earlier remarks Michael Dummett made on Godel’s theorem have recently inspired attempts to formulate an alternative to the standard demonstration of the truth of the Godel sentence. The idea

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There is a longstanding debate in the logico-philosophical community as to why the Godelian sentences of a consistent and sufficiently strong theory are true. The prevalent argument seems to be

Speaking with Shadows: A Study of Neo-Logicism

According to the species of neo-logicism advanced by Hale and Wright, mathematical knowledge is essentially logical knowledge. Their view is found to be best understood as a set of related though

Is Hume's Principle Analytic?

  • C. Wright
  • Philosophy
    Notre Dame J. Formal Log.
  • 1999
The present paper reviews five misgivings that developed in various of George Boolos’s writings and observes that each of them really concerns not ‘analyticity’ but either the truth of Hume's Principle or the authors' entitlement to accept it and reviews possible neologicist replies.

What Harmony Could and Could Not Be

The notion of harmony has played a pivotal role in a number of debates in the philosophy of logic. Yet there is little agreement as to how the requirement of harmony should be spelled out in detail

There May Be Many Arithmetical Gödel Sentences†

We argue that, under the usual assumptions for sufficiently strong arithmetical theories that are subject to Gödel’s First Incompleteness Theorem, one cannot, without impropriety, talk about the



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It is a very natural supposition that, for any particular consistent formal system of arithmetic, one of the pair consisting of the Godel sentence and its negation must be true. This was rejected by

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THIS work contains some thousands of propositions, each, with its proof, expressed in a shorthand so concise that if they were all expanded into ordinary language, the room taken up would be ten

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Foundations Without Foundationalism: A Case for Second-Order Logic.

Philosophy of Logic: Second Edition

Abstraction, 65, 69-70 Accent, 22, 58-59 Adverb, 31, 76-77 Alphabet, 37, 39-41 A1 ternation, 2 3-24 and quantification, 88, 91 ~ n a l o ~ u e , set-theoretic, 51-52, 67 Analyticity, 96 Arithmetized

Review: K. Jaakko Hintikka, Reductions in the Theory of Types