New essays on Tarski and philosophy.

*(English)*Zbl 1161.03002
Oxford: Oxford University Press (ISBN 978-0-19-929630-9/hbk). vi, 434 p. (2008).

This is a collection of commentaries on Tarski’s work on defining truth, logical notions, definition, and logical consequence. The fourteen contributions, which are surveyed in an introduction by the editor (pp. 1–20), are: (1) R. Murawski and J. Woleński, “Tarski and his Polish predecessors on truth” (pp. 21–43) and (2) A. Betti, “Polish axiomatics and its truth: On Tarski’s Leśniewskian background and the Ajdukiewicz connection” (pp. 44–71), in which the place of Tarski’s teachers Twardowski, Łukasiewicz, Kotarbiński, and Leśniewski is analysed, and the difference in philosophical positions of Tarski and his nominal doctoral advisor Leśniewski are found (in (2)) to be of a classical vs. modern nature, much like that between Frege and Hilbert; (3) S. Feferman, “Tarski’s conceptual analysis of semantical notions” (pp. 72–93), an analysis of the reasons why Tarski sought to define truth, given that most mathematical logicians were happy with the informal notion of truth in a structure; (4) W. Hodges, “Tarski’s theory of definition” (pp. 94–132), a critical survey of Tarski’s pronouncements on the theory of definitions, including Padoa’s method, between 1926 and 1938, which concludes that definitions appeared in Tarski’s work due to “his intense work in metatheory”, but that he “had no particular interest in definitions for their own sake”; (5) M. David, “Tarski’s convention T and the concept of truth” (pp. 133–156), (6) D. Patterson, “Tarski’s concept of meaning” (pp. 157–191) and (7) J. Azzouni, “Alternative logics and the role of truth in the interpretation of languages” (pp. 390–429), are in-depth commentaries of passages in Tarski’s [“Der Wahrheitsbegriff in den formalisierten Sprachen”, Studia Philos., Leopolis 1, 261–401 (1935; JFM 62.1051.05)], in particular on Tarski’s Convention T and the problems and limitations it raises; (8) P. Mancosu, “Tarski, Neurath, and Kokoszyńska on the semantic conception of truth” (pp. 192–224), is the result of an archival research containing exchanges from some forty-odd letters between Tarski and Neurath, triggered by the former’s presentation of the semantic concept of truth at the Paris Congress in 1935, as well as letters between Carnap, Neurath, Schlick, and Kokoszyńska; (9) G. Frost-Arnold, “Tarski’s nominalism” (pp. 225–246) and (10) P. Simons, “Truth on a tight budget: Tarski and nominalism” (pp. 369–389), offer different looks at the tension between Tarski’s nominalism and his semantic theory, relying on set theory, as well as compare Tarski’s variant of nominalism with other variants thereof; (11) P. Raatikainen, “Truth, meaning, and translation” (pp. 247–262), an in-depth look at the arguments of an early critic of Tarski’s theory of truth, H. Putnam, for whom it “fails as badly as it is possible for an account to fail”, and at Putnam’s modal objection; (12) J. Etchemendy, “Reflections on consequence” (pp. 263–299), presents a new version, in which he takes into account the various critiques leveled at his first attempt, [The concept of logical consequence. Cambridge, MA: Harvard University Press (1990; Zbl 0743.03002)], of his thesis that the “Tarskian analysis of logical consequence and logical truth is wrong”; (13) G. Sher, “Tarski’s thesis” (pp. 300–339), presenting the so-called Tarski-Sher thesis, which, inspired by the Kleinian definition of geometric notions in terms of invariance under a certain group of transformations, states that logical notions are those operators that are invariant under all isomorphisms of its argument-structures, together with Feferman’s criticism of the thesis as well as his counter-proposal (invariance under all epimorphisms of the argument-structure); (14) M. Gómez-Torrente, “Are there model-theoretic logical truths that are not logically true?” (pp. 340–368), which finds, much like (11), but with different arguments and examples, fault with Tarski’s theory of logical consequence and truth, but suggests a way to modify Tarski’s criterion to make it immune to the criticism that it fails to adequately capture modal and epistemic characteristics of the usual understanding of consequence.

Reviewer: Victor V. Pambuccian (Phoenix)

##### MSC:

03-03 | History of mathematical logic and foundations |

01A60 | History of mathematics in the 20th century |

03A05 | Philosophical and critical aspects of logic and foundations |

00B15 | Collections of articles of miscellaneous specific interest |

03-06 | Proceedings, conferences, collections, etc. pertaining to mathematical logic and foundations |