- Bob Hale “[Critical Notice of Kit Fine's] The Limits of Abstraction,” in: Philosophy and Phenomenological Research, vol. 72, no. 1, 2006
- Paolo Mancosu “The Russellian Influence on Hilbert and his School,” in: Synthese, vol. 137, no. 1-2, Special Issue: History of Logic, 2003
- Stanley Burris “The Algebra of Logic Tradition,” in: The Stanford Encyclopeida of Philosophy, March 2, 2009
以下、徒然なるままに書き記してみたいと思う。
を拾い読みしていると、tonk の話が出てくる。
それで Prior さんの tonk 論文と、Belnap さんの Tonk, Plonk and Plink 論文を読み直してみる。面白い。
Prior さんの tonk 論文は、短いし、興に任せて全文和訳してみたことがある。
ついでに、Belnap さんの論文も短いから、全文和訳しようかなと考えている。しかし、どうするかは、わからない。
- Alan Weir “Naïve Set Theory Is Innocent!,” in: Mind, vol. 107, no. 428, 1998
こちらを拾い読むと、2009年2月22日の日記の項目‘Professor Brady's Book Universal Logic’でも記した Brady さんの logic の話が出てくる。
もともとは Dummett さんの Indefinite Extensibility という概念について論じられているところから、この Weir 論文を入手したのですが、Brady さんの relevant logic も、からんでくるようでなかなか興味深い。
Weir さんの次の abstract も参考までに掲げておく*1。
- Alan Weir “In Defence of Naïve Set Theory”
In the first, negative part I argue that standard resolutions of the Russell paradox are self-refuting. Such solutions are explicitly or implicitly hierarchical and the general complaint is that in order to set up these hierarchies without falling into superparadox one must be outside the hierarchies, but there is no such vantage point; I look at a number of cases in a little more detail. The only alternative to embracing naïve set theory, I urge, is a highly unattractive theoretical nihilism.
In the second more positive part I analyse the antinomies as resulting from a combination of
i. intuitively sound logical operational rules,
ii. the intuitively correct naïve comprehension principles together with
iii. classical structural rules.
I advocate abandoning the latter. The positive proposal involves formalising a notion of indeterminacy and using it to place restrictions on generalised Cut (transitivity). The paradoxes then become proofs of the indeterminacy of the paradoxical sentences. It is argued, finally, that it is legitimate to lay down axiomatically that certain sentences are determinate, others are not, classical logic being legitimate for the determinate sub-sector of language. In this way we can achieve 'classical recapture' and generate all of standard mathematics.
この abstract では‘In the second more positive part’以下の記述が興味深い。
頭が痛いので寝ます。
おやすみなさい。
*1:One Hundred Years of Russell's Paradox: International Conference in Logic and Philosophy, University of Munich, Germany, June 2-5, 2001.
