Academic Journal
The Expressive Power of the N-Operator and the Decidability of Logic in Wittgenstein's Tractatus.
| العنوان: | The Expressive Power of the N-Operator and the Decidability of Logic in Wittgenstein's Tractatus. |
|---|---|
| المؤلفون: | Ferreira, Rodrigo Sabadin |
| المصدر: | History & Philosophy of Logic; Feb2023, Vol. 44 Issue 1, p33-53, 21p |
| مصطلحات موضوعية: | APHORISMS & apothegms, LOGIC diagrams, LOGIC, DECIDABILITY (Mathematical logic) |
| People: | WITTGENSTEIN, Ludwig, 1889-1951 |
| مستخلص: | The present text discusses whether there is a tension between aphorisms 6.1-6.13 of the Tractatus and the Church-Turing theorem about the decidability of predicate logic. We attempt to establish the following points: (i) Aphorisms 6.1-6.13 are not consistent with the Church-Turing theorem. (ii) The logical symbolism of the Tractatus, built from the N-operator, can (and should) be interpreted as expressively complete with respect to first-order formulas. (iii) Wittgenstein's reasons for believing that Logic is decidable were purely philosophical and the undecidability result shows that there are aspects of his criticisms of Frege and Russell that become unjustified in light of these results. [ABSTRACT FROM AUTHOR] |
| Copyright of History & Philosophy of Logic is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| قاعدة البيانات: | Complementary Index |
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