Tarski hierarchies

The general notions of object- and metalanguage are discussed and as a special case of this relation an arbitrary first order language with an infinite model is expanded by a predicate symbol T₀ which is interpreted as truth predicate for . Then the expanded language is again augmented by a new truth predicate T₁ for the whole language plus T₀. This process is iterated into the transfinite to obtain the Tarskian hierarchy of languages. It is shown that there are natural points for stopping this process. The sets which become definable in suitable hierarchies are investigated, so that the relevance of the Tarskian hierarchy to some subjects of philosophy of mathematics are clarified.It should be noticed that these terms object language and meta language have only a relative sense. If, for instance, we become interested in the notion of truth applying to sentences, not of our original object-language, but of our meta-language, the latter becomes automatically the object-language of our discussion; and in order to define truth for this language, we have to go to a new meta-language — so to speak, to a meta-language of a higher level. In this way we arrive at a whole hierarchy of languages.(Tarski, 1986, p. 674f)     

Tarski On Logical Notions

We try to explain Tarski's conception of logical notions, as it emerges from alecture of his, delivered in 1966 and published posthumously in 1986 (Historyand Philosophy of Logic 7, 143–154), a conception based on the idea ofinvariance. The evaluation of Tarski's proposal leads us to consider an interesting(and neglected) reply to Skolem in which Tarski hints at his own point of view onthe foundations of set theory. Then, comparing the lecture of 1966 with Tarski'slast work and with an earlier paper written with Lindenbaum, it is shown thatTarski's conception of logical notions, with its essentially type-theoretic character,did not undergo any significant modifications throughout his life. A remark onTarski's prudential attitude on the topic in the famous paper on the concept oflogical consequence (and elsewhere) concludes our paper.     

The Trouble with Tarski

As a result of thinking ( pace Tarski, wrongly) that it is propositions, not sentences, that are true or false, it has been supposed (also wrongly) that propositions such as that 'Snow is white' is true if and only if snow is white are necessarily true. But changing the rules for the use of the words in a sentence has no effect on the truth of the proposition, only on what proposition it formulates. Many similar statements, e.g., that 'plus' does not mean plus, are only pragmatically contradictory: if this were true, it would be impossible to say so in these words. One should distinguish between sentences that express necessary truths, and sentences that necessarily express truths. It follows that many well known accounts of necessity are wrong, that the truth of an analytic proposition does not follow from the definitions of the words in the sentence that expresses it, that it is not helpful to define meaning in terms of truth, that truth is not relative to language, and that conventionalism is false. This paper is a move in the direction of establishing the eternity of truth.     

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.     

Tarski and the Metalinguistic Liar

I offer an interpretation of a familiar, but poorly understood portion of Tarskis work on truth – bringing to light a number of unnoticed aspects of Tarskis work. A serious misreading of this part of Tarski to be found in Scott Soames Understanding Truth is treated in detail. Soamesreading vies with the textual evidence, and would make Tarskis position inconsistent in an unsubtle way. I show that Soames does not finally have a coherent interpretation of Tarski. This is unfortunate, since Soames ultimately arrogates to himself a key position that he has denied to Tarski and which is rightfully Tarskis own.     

Unpublished draft paper on sexuality by Donald Meltzer

Editor's note : Albert Mason discovered an unpublished paper by Donald Meltzer dating from around 1968 and has made the text available to the IJP. He writes “my best guess is that Meltzer gave me the paper to read/approve about the time I was preparing to move to Los Angeles (1968–69) and that I hastily packed it away with other papers. It got buried, and only came to light recently, kind of like a lost score that turns up in someone's attic!” The patient Meltzer discusses in his paper is a patient who Dr Mason treated for approximately 11 years, and about whom Dr Mason consulted with Dr Meltzer early in the treatment. Dr Mason has also provided the original report he wrote about the patient in the 1960s. Following an introduction by Dr Abbot Bronstein, we have published extracts from Dr Mason's report, including the following: details about the case, the two dreams which Dr Mason believes were ‘turning point dreams’, and a third dream called the ‘hula hula dream’, as well as the clinical material leading up to it.     

张岱年先生的两个重要理论贡献——纪念张岱年先生逝世三周年

实践是检验真理的唯一标准,时间是对一个哲学家思想的真正考验。在纪念张岱年先生逝世三周年之际,当我们缅怀张先生在哲学理论、中国哲学史和文化研究三个方面做出的学术贡献时,有许多内容可以述说。本文谨略述张先生在哲学理论上的两个重要贡献,在我看来,这是经受了实践检验和时间考验的两个重要贡献。一道德之“变”与“常”1933年4月27日,张岱年先生在《大公报·世界思潮》发表《关于新唯物论》。他在此文中提出:“新唯物论或辩证的唯物论,实为现代最可注意之哲学。”“唯以新唯物论与现代他派哲学对较,然后乃可见新唯物论之为现代最可信…     

Logical consequence: A defense of Tarski

In his classic 1936 essay “On the Concept of Logical Consequence”, Alfred Tarski used the notion of satisfaction to give a semantic characterization of the logical properties. Tarski is generally credited with introducing the model-theoretic characterization of the logical properties familiar to us today. However, in his book, The Concept of Logical Consequence, Etchemendy argues that Tarski's account is inadequate for quite a number of reasons, and is actually incompatible with the standard model-theoretic account. Many of his criticisms are meant to apply to the model-theoretic account as well. In this paper, I discuss the following four critical charges that Etchemendy makes against Tarski and his account of the logical properties:

1. Tarski's account of logical consequence diverges from the standard model-theoretic account at points where the latter account gets it right.
2. Tarski's account cannot be brought into line with the model-theoretic account, because the two are fundamentally incompatible.
3. There are simple counterexamples (enumerated by Etchemendy) which show that Tarski's account is wrong.
4. Tarski committed a modal fallacy when arguing that his account captures our pre-theoretical concept of logical consequence, and so obscured an essential weakness of the account.
5. Tarski's account depends on there being a distinction between the “logical terms” and the “non-logical terms” of a language, but (according to Etchemendy) there are very simple (even first-order) languages for which no such distinction can be made. Etchemendy's critique raises historical and philosophical questions about important foundational work. However, Etchemendy is mistaken about each of these central criticisms. In the course of justifying that claim, I give a sustained explication and defense of Tarski's account. Moreover, since I will argue that Tarski's account and the model-theoretic account really do come to the same thing, my subsequent defense of Tarski's account against Etchemendy's other attacks doubles as a defense against criticisms that would apply equally to the familiar model-theoretic account of the logical properties.

     

Ray on Tarski on Logical Consequence

In Logical consequence: A defense of Tarski (Journal of Philosophical Logic, vol. 25, 1996, pp. 617–677), Greg Ray defends Tarski"s account of logical consequence against the criticisms of John Etchemendy. While Ray"s defense of Tarski is largely successful, his attempt to give a general proof that Tarskian consequence preserves truth fails. Analysis of this failure shows that de facto truth preservation is a very weak criterion of adequacy for a theory of logical consequence and should be replaced by a stronger absence-of-counterexamples criterion. It is argued that the latter criterion reflects the modal character of our intuitive concept of logical consequence, and it is shown that Tarskian consequence can be proved to satisfy this criterion for certain choices of logical constants. Finally, an apparent inconsistency in Ray"s interpretation of Tarski"s position on the modal status of the consequence relation is noted.     

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。     

Tarski on the Necessity Reading of Convention T

Tarski’s Convention T is often taken to claim that it is both sufficient and necessary for adequacy in a definition of truth that it imply instances of the T-schema where the embedded sentence translates the mentioned sentence. However, arguments against the necessity claim have recently appeared, and, furthermore, the necessity claim is actually not required for the indefinability results for which Tarski is justly famous; indeed, Tarski’s own presentation of the results in the later Undecidable Theories makes no mention of an assumption to the effect that the definition of truth implies the biconditionals. This raises a question: was Tarski in fact committed to the necessity claim in the important papers of the 1930s and 40s? I argue that he was not. The discussion of this apparently esoteric interpretive issue in fact gets to the heart of many important questions about truth, and in the final sections of the paper I discuss the importance of the T-biconditionals in the theory of meaning and the relation of deflationary and inflationary theories of truth to the semantic paradoxes.     

Pierre Janet and Auguste Forel: Two Historical Contributions

This paper discusses two 19th century French-speaking authors, Pierre Janet and Auguste Forel, who both employed hypnosis and in various ways were early influences on psychoanalysis. To acquaint the reader with the clinical works of these pioneers, a long case history by Janet, and a case history by Forel are presented. The connections between these two authors and modern developments are discussed. Both historical figures were contemporaries of Freud and their at times contentious relationships became part of their legacy.     

Superiority and Social Interest by Alfred Adler

This paper examines the advantages of a particular way of supervising psychotherapy, namely, in a group setting with a special focus on the supervisee's countertransference experience. Group supervision is conceptualized as much more than presenting a case and getting feedback. Rather, the group is used in all its interactive complexity as it resonates in a myriad of ways to aspects of the case being presented. Furthermore, because of the complexity of conscious and unconscious interactions and reverberations during this process, it is often helpful to have a focus in the supervision. One helpful possibility is to center on the supervisee's countertransference experience and use the group to reflect, amplify, and process that experience. This can be a highly valuable way of helping the therapists increase their understanding of the case and enhance the quality of therapeutic interventions.     

A note on three-valued logic and Tarski theorem on truth definitions

We introduce a notion of semantical closure for theories by formalizing Nepeivoda notion of truth. [10]. Tarski theorem on truth definitions is discussed in the light of Kleene's three valued logic (here treated with a formal reinterpretation of logical constants). Connections with Definability Theory are also established.A first version was prepared for sec. 5-Gnsaga-CNR and presented at the Logic Seminar, Institute of Philosophy, University of Firenze, in the academic year 1978–79. The author would like to thank the referee for his criticism and the Alexander von Humboldt-Stiftung for the support during the revision of the paper.