Logical Truth and Tarskian Logical Truth

This paper examines the question of the extensional correctness of Tarskian definitions of logical truth and logical consequence. I identify a few different informal properties which are necessary for a sentence to be an informal logical truth and look at whether they are necessary properties of Tarskian logical truths. I examine arguments by John Etchemendy and Vann McGee to the effect that some of those properties are not necessary properties of some Tarskian logical truths, and find them unconvincing. I stress the point that since the hypothesis that Tarski's definitions are extensionally correct is deeply entrenched, the burden of proof is still on the shoulders of Tarski's critics, who have not lifted the burden. This revised version was published online in June 2006 with corrections to the Cover Date.     

More on Putnam and Tarski

Hilary Putnam's famous arguments criticizing Tarski's theory oftruth are evaluated. It is argued that they do not succeed to undermine Tarski's approach. One of the arguments is based on the problematic idea of a false instance of T-schema. The otherignores various issues essential for Tarski's setting such as language-relativity of truth definition.     

Wahrheit und Selbstrückbezüglichkeit

This paper is intended to discuss the problems occurring in the relation between the notion of truth and the question of self-reference. To do this, we shall review Tarski's (T) convention and its related terminology. We shall clarify the relation between truth and extension in order to lead into the question of semantic paradoxes appearing in the theoretical models concerned with truth. Subsequently, we shall review the logical system which develops in the reformulation of the modal proposal of the (T) convention. In closing, we shall critically examine Kripke's interpretation from the proposals made by Tarski.     

Events,Tropes, and Truthmaking

Nominalizations are expressions that are particularly challenging philosophically in that they help form singular terms that seem to refer to abstract or derived objects often considered controversial. The three standard views about the semantics of nominalizations are [1] that they map mere meanings onto objects, [2] that they refer to implicit arguments, and [3] that they introduce new objects, in virtue of their compositional semantics. In the second case, nominalizations do not add anything new but pick up objects that would be present anyway in the semantic structure of a corresponding sentence without a nominalization. In the first and third case, nominalizations in a sense ‘create’ new objects’, enriching the ontology on the basis of the meaning of expressions. I will argue that there is a fourth kind of nominalization which requires a quite different treatment. These are nominalizations that introduce ‘new’ objects, but only partially characterize them. Such nominalizations generally refer to events or tropes. I will explore an account according on which such nominalizations refer to truth makers.     

A UNIFIED THEORY OF QUOTATION

Abstract: This paper offers a theory of quotation by uniting two apparently disparate extant theories, Recanati's pragmatic theory and Washington's identity theory. Recanati draws a distinction between open and closed quotations, and contends that open quotations do not refer. Washington argues that closed quotations refer to various expression types, not just orthographic and/or phonetic types. By combining these views, this paper proposes a theory, according to which quotations, open or closed, may be tokens of semantico‐physical types (i.e., meaningful expressions), and while those types are mentioned (or referred to) by closed quotations, they are used in open quotations.     

Expressions of Evangelism in Latin America

The purpose of this article is to explore the expressions of evangelism that are emerging in Latin America within the Evangelical‐Pentecostal context of the continent. We will do this by approaching our subject from the perspective of change, religious mutation and transformational change: we will first refer to the shift in evangelism and mission perspective in Latin America. We will explore the shift in numerical growth, then will deal with the shift in the concept and praxis of evangelism. This will be followed by a discussion on the shift from Western forms in church liturgy, music and hymnology to more contextual and indigenous expressions. Finally, I will refer to the shift toward holistic practices in times of turmoil and violence.     

The Simplest Axiom System for Plane Hyperbolic Geometry

We provide a quantifier-free axiom system for plane hyperbolic geometry in a language containing only absolute geometrically meaningful ternary operations (in the sense that they have the same interpretation in Euclidean geometry as well). Each axiom contains at most 4 variables. It is known that there is no axiom system for plane hyperbolic consisting of only prenex 3-variable axioms. Changing one of the axioms, one obtains an axiom system for plane Euclidean geometry, expressed in the same language, all of whose axioms are also at most 4-variable universal sentences. We also provide an axiom system for plane hyperbolic geometry in Tarski's language L _B which might be the simplest possible one in that language.     

A Piagetian perspective on mathematical construction

In this paper, we offer a Piagetian perspective on the construction of the logico-mathematical schemas which embody our knowledge of logic and mathematics. Logico-mathematical entities are tied to the subject's activities, yet are so constructed by reflective abstraction that they result from sensorimotor experience only via the construction of intermediate schemas of increasing abstraction. The ‘axiom set’ does not exhaust the cognitive structure (schema network) which the mathematician thus acquires. We thus view ‘truth’ not as something to be defined within the closed ‘world’ of a formal system but rather in terms of the schema network within which the formal system is embedded. We differ from Piaget in that we see mathematical knowledge as based on social processes of mutual verification which provide an external drive to any ‘necessary dynamic’ of reflective abstraction within the individual. From this perspective, we argue that axiom schemas tied to a preferred interpretation may provide a necessary intermediate stage of reflective abstraction en route to acquisition of the ability to use formal systems in abstracto.     

塔斯基：语义性真理论与符合论

塔斯基语义性真理论是否为符合论是一个争论的热点。目前有两种观点认为它是符合论,其一是根据对象语言与元语言的区分,到目前为止此观点已受到激烈批评,其二是根据“满足”概念的递归定义,此观点到目前为止还没有被人详细地阐明。本文认为塔斯基的语义性真理论是符合论,为此将首先对第一种观点及其反对意见进行深入分析,并得出结论认为该观点不能成立,继而详细阐明第二种观点,表明它是塔斯基本人的意图。在讨论中本文将对一系列的逻辑哲学问题进行探讨。     

Truth as Translation – Part A

According to Tarski's Convention T, the adequacy of a truth definition is (implicitly) defined relatively to a translation mapping from the object language to the metalanguage; the translation mapping itself is left unspecified. This paper restates Convention T in a form in which the relativity to translation is made explicit. The notion of an interpreted language is introduced, and a corresponding notion of a translation between interpreted languages is defined. The latter definition is stated both in an algebraic version, and in an equivalent possible worlds version. It is a consequence of our definition that translation is indeterminate in certain cases. Finally, we give an application of our revised version of Convention T and show that interpreted languages exist, which allow for vicious self-reference but which nevertheless contain their own truth predicate. This is possible if only truth is based on a nonstandard translation mapping by which, e.g., the Liar sentence is translated to its own negation. In this part of the paper this existence result is proved only for languages without quantifiers; in Part B the result will be extended to first-order languages.     

Beyond Existence and Non-Existence

Abstract

When Husserl speaks of the so-called ‘transcendental reduction’ or ‘phenomenological epochē’ many believe that he is eschewing the question of truth or existence. Two reasons are given for this: First, Husserl explicitly states that when we perform the reduction, we should no longer naively ‘accept [the world] as it presents itself to me as factually existing’ (Id I §30, p. 53) and should suspend our judgement with regard to ‘the positing of its actual being’ (Id I §88, p. 182). Second, Husserl seems to have no problem in referring to an ‘object’ of thought even when we refer to non-existent, hallucinatory or indeed impossible objects. This seems to suggest that he is not interested in the question whether or not there is a corresponding ‘ordinary’ object. The paper seeks to question this and will show that his inquiry never loses sight of the questions of truth and existence but rather brings them into the foreground.     

Are natural languages universal?

Summary We began by distinguishing Tarskian and Fitchean notions of universality in such a way that the claim that no language is universal in the sense of Tarski is compatible with accepting Fitchean universality. Then we examined a proposal involving two truth concepts — one that fit the Fitchean notion and another that followed Tarski's views on truth — finding little advantage in such generosity. We attempted a reformulation of Herzberger's argument for the negative view — the view that no language is universal in Tarski's sense — but found it unsuccessful when the language of the argument's formulation was brought under consideration. A more persuasive argument for EI was found, free of the defect of the previous one. EI was then shown to have unsettling consequences, prompting us to inquire about avoiding it. We found this possible, noting that EI is itself a solution to the semantic paradoxes, to which there are alternatives that avoid the unwelcome aspects of EI. However, whether any such alternative is ultimately preferable to EI remains to be seen.Section 4 of this paper was presented at the 1973 Eastern Division Meeting of the American Philosophical Association, and I am particularly grateful to the paper's commentator, Stephen P. Stich, for his helpful comments. I have also profited from correspondence with Paul Teller, whose paper The Universality of Natural Languages and Paradoxes of Grounding in Semantics: A Response to Herzberger (1971, ditto) presents a position similar in certain respects to mine.     

Varieties of Objectivity: Reply to De Mesel

In a previous paper, I argued that the later Wittgenstein did not endorse a realist account of ethics, where a realist account is understood to involve a claim to truth as well as objectivity. In this paper, I respond to a number of critical questions that Benjamin De Mesel raises about that interpretation. I agree with him that just as there are uses for expressions such as “truth”, “fact” and “reality” in ethics, there are uses for expressions such as “objectivity” that do not involve a deeper realist commitment. But I uphold and reinforce my claim that objectivity in ethics as the realist conceives it is ruled out by Wittgenstein, who describes the correspondence between ethical expressions and reality in an entirely different way.     

Naming and Nonexistence

I defend a cluster of views about names from fiction and myth. The views are based on two claims: first, proper names refer directly to their bearers; and second, names from fiction and myth are genuinely empty, they simply do not refer. I argue that when such names are used in direct discourse, utterances containing them have truth values but do not express propositions. I also argue that it is a mistake to think that if an utterance of, for example, “Vulcan is a planet” fails to express a proposition, then an utterance of “Le Verrier believed that Vulcan is a planet” cannot express a proposition. The argument applies to claims about fiction, such as “Sherlock Holmes is strong,” and claims about the attitudes of authors and auditors. The upshot is a semantics for fictional statements that provides a satisfying way for direct reference theorists to avoid taking fictional entities to be abstract objects and to accept the commonsense view that what is true in a fiction is ultimately a matter of what is pretended to be the case.     

Radical quotation and real repetition

In this essay I argue for a constructivist account of the entities composing the object languages of Davidsonian truth theories and a quotational account of the reference from metalinguistic expressions to interpreted utterances. I claim that ‘radical quotation’ requires an ontology of repeatable events with strong similarities to Derrida's account of iterable events. In part one I summarise Davidson's account of interpretation and Olav Gjelsivk's arguments to the effect that the syntactic individuation of linguistic objects is only workable if interpreters make richer assumptions about semantic properties than Davidson can tolerate. In part two I show that the objectivist account of syntactic objects which Gjelsivk's arguments presuppose is incompatible with one corollary of Davidsonian semantic indeterminacy: namely, the relativity of language to interpretative scheme. In place of this an account of radical interpretation is presented in which a quotational theory of metalinguistic reference furnishes the requisite relativity. In part three I argue that this account requires that particular utterance events must be repeatable to be radically quotable and give reasons why particularity and repeatability are not incompatible.     

The semantics and acquisition of number words: integrating linguistic and developmental perspectives

This article brings together two independent lines of research on numerally quantified expressions, e.g. two girls. One stems from work in linguistic theory and asks what truth conditional contributions such expressions make to the utterances in which they are used--in other words, what do numerals mean? The other comes from the study of language development and asks when and how children learn the meaning of such expressions. My goal is to show that when integrated, these two perspectives can both constrain and enrich each other in ways hitherto not considered. Specifically, work in linguistic theory suggests that in addition to their 'exactly n' interpretation, numerally quantified NPs such as two hoops can also receive an 'at least n' and an 'at most n' interpretation, e.g. you need to put two hoops on the pole to win (i.e. at least two hoops) and you can miss two shots and still win (i.e. at most two shots). I demonstrate here through the results of three sets of experiments that by the age of 5 children have implicit knowledge of the fact that expressions like two N can be interpreted as 'at least two N' and 'at most two N' while they do not yet know the meaning of corresponding expressions such as at least/most two N which convey these senses explicitly. I show that these results have important implications for theories of the semantics of numerals and that they raise new questions for developmental accounts of the number vocabulary.     

Free Will,Determinism, and the Possibility of Doing Otherwise

I argue that free will and determinism are compatible, even when we take free will to require the ability to do otherwise and even when we interpret that ability modally, as the possibility of doing otherwise, and not just conditionally or dispositionally. My argument draws on a distinction between physical and agential possibility. Although in a deterministic world only one future sequence of events is physically possible for each state of the world, the more coarsely defined state of an agent and his or her environment can be consistent with more than one such sequence, and thus different actions can be “agentially possible”. The agential perspective is supported by our best theories of human behaviour, and so we should take it at face value when we refer to what an agent can and cannot do. On the picture I defend, free will is not a physical phenomenon, but a higher‐level one on a par with other higher‐level phenomena such as agency and intentionality.