1994: Logical Truth: Comments on Etchemendy's Critique of Tarski Author (original) (raw)
1999: Tarski and Carnap on Logical Truth - or: what is Genuine Logic
1998
In (1936), Tarski presented for the first time, in Gemnan, his new semantic definition of logical consequence and logical truth. He starts to motivate his definition by cdtizicing traditional syntactic definitions. He gives two reasons why syntactic definitions are not satisfactory. First, the traditional calculus-based syntactic definitions (defined by a set of axioms and rules, and a recursive notion of proof) are too weak to capture the ordinary notion of logical consequence. Tat'ski gives the example of w-incomplete themies of Pea no arithmetics. Here it may be the case that P(n) is derivable (within the theory) for every natural number n, without having thatl.lxP(x) be dedvable, although the latter sentence intuitively follow (Tarski 1936, p. 41Of). Tarski continues that this is just one aspect of the incompleteness of first order arithmetics, which shows that calculus-based recursive definitions are 77 J. Wale,1ski and E. Kohler (eds.), Alfred Tarski and the Vienna Cire/e. 77~94.
Tarski's One and Only Concept of Truth
Synthese, 2014
In a recent article, Marian David (2008) distinguishes between two interpretations of Tarski's work on truth. The standard interpretation has it that Tarski gave us a definition of truth in-L within the meta-language; the non-standard interpretation, that Tarski did not give us a definition of true sentence in L, but rather a definition of truth, and Tarski does so for L within the meta-language. The difference is crucial: for on the standard view, there are different concepts of truth, while in the alternative interpretation there is just one concept. In this paper we will have a brief look at the distinction between these two interpretations and at the arguments David gives for each view. We will evaluate one of David's arguments for the alternative view by looking at Tarski's 'On the Concept of Truth in Formalized Languages', and his use of the term 'extension' therein, which, we shall find, yields no conclusive evidence for either position. Then we will look at how Tarski treats 'satisfaction', an essential concept for his definition of 'true sentence'. It will be argued that, in light of how Tarski talks about 'satisfaction' in §4 of 'On the Concept of Truth in Formalized Languages' and his claims in the Postscript, the alternative view is more likely than the standard one.
Tarski's Convention T and the Concept of Truth
New Essays on Tarski and Philosophy, 2008
In this paper, I want to discuss in some detail the original version of Tarski's condition of adequacy for a definition of truth, his Convention T. I will suggest that Tarski designed Convention T to serve two functions at once. I will then distinguish two possible interpretations of Tarski's work on truth: a standard interpretation and a non-standard, alternative interpretation. On the former, but not on the latter, the very title of Tarski's famous article about the concept of truth harbors a lie. Using the symbol 'Tr' to denote the class of all true sentences, the above postulate can be expressed in the following convention: CONVENTION T. A formally correct definition of the symbol 'Tr', formulated in the metalanguage, will be called an adequate definition of truth if it has the following consequences: (α) all sentences which are obtained from the expression 'x Tr if and only if p' by substituting for the symbol 'x' a structural-descriptive name of any sentence of the language in question and for the symbol 'p' the expression which forms the translation of this sentence into the metalanguage;
Dedicated to Professor Roberto Torretti, philosopher of science, historian of mathematics, teacher, friend, and collaborator—on his eightieth birthday. This paper discusses the history of the confusion and controversies over whether the definition of consequence presented in the 11-page 1936 Tarski consequence-definition paper is based on a monistic fixed-universe framework—like Begriffsschrift and Principia Mathematica. Monistic fixed-universe frameworks, common in pre-WWII logic, keep the range of the individual variables fixed as ‘the class of all individuals’. The contrary alternative is that the definition is predicated on a pluralistic multiple-universe framework—like the 1931 Gödel incompleteness paper. A pluralistic multiple-universe framework recognizes multiple universes of discourse serving as different ranges of the individual variables in different interpretations—as in post-WWII model theory. In the early 1960s, many logicians—mistakenly, as we show—held the ‘contrary alternative’ that Tarski 1936 had already adopted a Gödel-type, pluralistic, multiple-universe framework. We explain that Tarski had not yet shifted out of the monistic, Frege–Russell, fixed-universe paradigm. We further argue that between his Principia-influenced pre-WWII Warsaw period and his model-theoretic post-WWII Berkeley period, Tarski’s philosophy underwent many other radical changes.
Philosophies, 2024
Our standard model-theoretic definition of logical consequence is originally based on Alfred Tarski’s (1936) semantic definition, which, in turn, is based on Rudolf Carnap’s (1934) similar definition. In recent literature, Tarski’s definition is described as a conceptual analysis of the intuitive ‘everyday’ concept of consequence or as an explication of it, but the use of these terms is loose and largely unaccounted for. I argue that the definition is not an analysis but an explication, in the Carnapian sense: the replacement of the inexact everyday concept with an exact one. Some everyday intuitions were thus brought into a precise form, others were ignored and forgotten. How exactly did the concept of logical consequence change in this process? I suggest that we could find some of the forgotten intuitions in Bernard Bolzano’s (1837) definition of ‘deducibility’, which is traditionally viewed as the main precursor of Tarski’s definition from a time before formalized languages. It turns out that Bolzano’s definition is subject to just the kind of natural features—paradoxicality of everyday language, Platonism about propositions, and dependence on the external world—that Tarski sought to tame by constructing an artificial concept for the special needs of mathematical logic.
Tarski's Method of Truth Definition: Its Nature and Significance
Philosophica et Historica 2/2007, Miscellanea Logica (VIII), Foundations of Logic, 2010
In the classic work, 'Th e Concept of Truth in Formalized Languages' (CTFL), Alfred Tarski set out to examine thoroughly under what conditions and by what methods it is possible to construct a satisfactory defi nition of the notion of truth as predicated of sentences. 1 In the end, what he achieved was not a defi nition of the general notion of truth, not even of sentential truth, but a general method of defi ning a truth-predicate restricted to sentences of some given language L, where L belongs to a comprehensive group of formalized (or formalizable) languages of a certain sort. Tarski's method of truth defi nition and his approach to semantics in general has various logical, philosophical and mathematical aspects, owing to the fact that truth is a notion that plays a very special role in mathematical logic as well as in philosophy, in which disciplines Tarski had both interest and education. 2 However, its reception in these disciplines has been very diff erent. Logicians have concentrated mainly on 'formal' aspects of Tarski's method: the analysis and solution of semantic paradoxes, defi nability and indefi nability theorems, formal machinery of semantic defi nitions and the relations between (recursive) meta-mathematical and (explicit) set-theoretical defi nitions, etc. In their view, Tarski showed how to defi ne truth and related semantic notions by precise logico-mathematical methods, and they have been fairly widely agreed that his method of truth defi nition is a seminal contribution to their discipline. Philosophers, on the other hand, have focused more on 'material' aspects of the method: the adequacy criterion based on the so-called semantic conception of truth, the philosophical plausibility of the semantic conception of truth 2007 ACTA UNIVERSITATIS CAROLINAE PHILOSOPHICA ET HISTORICA 2 miscellanea logica (viii) PAG. 71-112 *
Chapter 7. Tarski's semantic conception of truth
Tarski suggests a characterization of truth as denotation of states of affairs in his paper "The Semantic Conception of Truth". After formulating what he calls "the classical Aristotelian conception of truth", encapsulated by the formula
Some reflections on the semantic approach, tarskian truth and structuralism
Perspectivas
In the present paper, we return to one of the main theses we already defended concerning the role of the tarskian truth notion within the semantic approach (CARNIER, 2022). As it was argued, this truth notion proves to be insufficient to be applied to scientific theories as they are conceived by this approach, i.e., as extralinguistic entities, because it is a property of sentences and because the tarskian truth of a sentence doesn't necessarily mean the world is as it describes, which results in the fact that other truth conceptions more appropriate need to be articulated within the several members of the semanticist family, in order to characterize the relationship between theory and phenomenon. Our argument in this regard was based in a case study applied to constructive empiricism and quasi-realism, but in this paper we extend our analysis to structuralism, assuming and endorsing the position according to which this proposal may be considered a member of the semantic approac...
Tarski's conceptual analysis of semantical notions
Tarski is famous for his widely accepted conceptual analysis (or, in his terms, "explication") of the notion of truth for formal languages and the allied notions of satisfaction, definability, and logical consequence.
Manuscrito, 2004
Abstract Guillermo Rosado-Haddock: In this paper on Oswaldo Chateaubriand's book Logical Forms I, I am mostly concerned with the critical task of indicating some shortcomings and stressing my disagreements with the distinguished scholar. The most important shortcoming of the book is Chateaubriand's unfamiliarity with Husserl's views on logic and semantics, some of which anticipate views propounded by the former--e.g., the distinction between logical law and logical necessity--, whereas others are more subtle than Chateaubriand's views--e.g. Husserl's views on the referent of statements. One of the most important contributions of Chateaubriand's book is his analysis and rejection of all forms of the so-called "slingshot argument". On the other hand, I disagree with Chateaubriand's rendering of some of Frege's views, though some of these are very common among Frege scholars. Finally, I assess Chateaubriand's criticisms of Kripke's views as well as those of Tarski. I tend to agree with his criticism of Kripke, but disagree with his assessment of Tarskian semantics. Abstract response: In §§1-2 I consider some issues that Guillermo raises in connection with Husserl, especially the distinction between the notion of state of affairs and the more general notion of situation of affairs conceived as a common substratum for different states of affairs. After a few remarks about Church’s slingshot argument in §3, I discuss several objections that Guillermo raises to my interpretation of Frege (§4), to Kripke’s notion of rigid designator (§5) and to my objections to Tarski’s semantic conception of truth (§6).
Quantificational Accounts of Logical Consequence II: In the Footsteps of Bolzano
Quantificational accounts of logical consequence account for it in terms of truth-preservation in all cases – be it admissible substitutional variants or interpretations with respect to non-logical terms. In this second of my three connected studies devoted to the quantificational tradition, I set out to reconstruct the seminal contributions of Russell, Carnap, Tarski and Quine and evaluate them vis-à-vis some of the most pressing objections. This study also prepares the ground for my discussion of the standard model-theoretic account of consequence to be found in the concluding study.
Tarski’s convention T: condition beta. South American Journal of Logic. 1, 3–32.
HISTORICAL NOTE: This paper is the culmination of a years-long joint effort by the two authors. A preliminary report appeared in 2013: Corcoran-Weber, Bulletin of Symbolic Logic, 19 (2013) 510–11. Their co-operative work was conducted by email dialogue in which each author’s work was developed and corrected by the other. Each section went through several iterations. The final version was the result of dozens of reciprocal exchanges; it is impossible to allocate credit. Each author learned from and taught the other. During this time they consulted several other scholars including the Tarski experts David Hitchcock, James Smith, and Albert Visser. The senior author expresses his deep gratitude to the junior author. Moreover the senior author acknowledges publicly what he has already said privately, viz. that without the junior author’s help and mastery of the relevant literature this paper would have been impossible. ABSTRACT: Tarski’s Convention T—presenting his notion of adequate definition of truth (sic)—contains two conditions: alpha and beta. Alpha requires that all instances of a certain T Schema be provable. Beta requires in effect the provability of ‘every truth is a sentence’. Beta formally recognizes the fact, repeatedly emphasized by Tarski, that sentences (devoid of free variable occurrences)—as opposed to pre-sentences (having free occurrences of variables)—exhaust the range of significance of is true. In Tarski’s preferred usage, it is part of the meaning of true that attribution of being true to a given thing presupposes the thing is a sentence. Beta’s importance is further highlighted by the fact that alpha can be satisfied using the recursively definable concept of being satisfied by every infinite sequence, which Tarski explicitly rejects. Moreover, in Definition 23, the famous truth-definition, Tarski supplements “being satisfied by every infinite sequence” by adding the condition “being a sentence”. Even where truth is undefinable and treated by Tarski axiomatically, he adds as an explicit axiom a sentence to the effect that every truth is a sentence. Surprisingly, the sentence just before the presentation of Convention T seems to imply that alpha alone might be sufficient. Even more surprising is the sentence just after Convention T saying beta “is not essential”. Why include a condition if it is not essential? Tarski says nothing about this dissonance. Considering the broader context, the Polish original, the German translation from which the English was derived, and other sources, we attempt to determine what Tarski might have intended by the two troubling sentences which, as they stand, are contrary to the spirit, if not the letter, of several other passages in Tarski’s corpus. Acknowledgements: William Abler, Otávio Bueno, Gabriela Fulugonio, David Hitchcock, Leon Horsten, Sriram Nambiar, Joaquin Miller, Frango Nabrasa, Jose Miguel Sagüillo, Matthias Schirn, James Smith, Albert Visser, Martin Walter, and others.
Ordinary Truth in Tarski and Næss
Poznań Studies in the Philosophy of the Sciences and Humanities, 2015
Tarski established two conditions that any theory of truth ought to satisfy: formal correctness and material adequacy. Though not widely noted, Tarski seems to indicate that a partial conception of truth, what has become known more widely as the T-schema, might be clarified by the application of empirical methods, specifically citing the experimental results of Arne Næss (1938a). The aim of this paper is to argue that Næss’ empirical work confirmed Tarski’s semantic conception of truth, among others. In the first part, I lay out the case for believing that Tarski’s T-schema, while not the formal and generalizable Convention-T, provides a partial account of truth and that partial account may be buttressed by an examination of ordinary person’s views of truth. Then, I will address a concern raised by Tarski’s contemporaries who saw Næss’ results as refuting Tarski’s semantic conception. Following that, I will summarize Næss’ results. Finally, I will contend with a few objections which suggest that a strict interpretation of Næss’ results might suggest an overturning of Tarski’s theory.
This book deals with the translational discrepancies between the most often read and quoted English version, the German translation which served as its basis, and the Polish original which was used for the German translation. Additionally to the translational issues, I will comment on certain, possibly most essential and perhaps, most controversial problems of Tarski's monograph. My commentary will not be exhaustive, a commentary rarely is. Tarski's writings, especially his monograph on truth, have been read, re-read and commented on multiple times. The scholars dealing with Tarski's work have much more experience and expertise in the subject matter than I do, and I shall not pretend otherwise just because Polish is my native language, instead I will suggest further literature to the reader. This monograph is meant to be read parallel to the English edition of Tarski's ``Concept of Truth in Formalized Languages'', as a kind of manual or a guide for better apprehension of the text. It is thought as auxiliary means for all scholars having the expertise in the subject but lacking the knowledge of Polish. It should also be helpful to philosophy students, of all levels, making the understanding of this very complex and groundbreaking text somewhat more reachable. The comprehension itself is left to the reader. The last chapter consists of a rare, and most valuable collection of the letters concerning the translation of Tarski's manuscript. Most of the presented letters were exchanged between Alfred Tarski and Kazimierz Twardowski, but there are also letters from Karl Popper. Additionally, there are a few letters not directly regarding the translation of Tarski's article, but interesting, nevertheless. The collection has never been published before, which makes it even more precious to include it in this publication.
Bulletin of Symbolic Logic, 1997
Tarski's 1936 paper, “On the concept of logical consequence”, is a rather philosophical, non-technical paper that leaves room for conflicting interpretations. My purpose is to review some important issues that explicitly or implicitly constitute its themes. My discussion contains four sections: (1) terminological and conceptual preliminaries, (2) Tarski's definition of the concept of logical consequence, (3) Tarski's discussion of omega-incomplete theories, and (4) concluding remarks concerning the kind of conception that Tarski's definition was intended to explicate. The third section involves subsidiary issues, such as Tarski's discussion concerning the distinction between material and formal consequence and the important question ofthe criterion for distinguishing between logical and non-logical terms.§1. Preliminaries. In this paper an argument is a two-part system composed of a set of propositions P (the premise-set) and a single proposition c (the conclusio...