Alfred Tarski

Este texto é a tradução da introdução do livro Logical Forms feita por Guido Imaguire e revisada pelo próprio autor (que também fez algumas pequenas alterações no texto e é responsável por sua forma final). Muitas citações de textos originais nas notas de rodapé foram suprimidas na tradução.

Alfred Tarski’s semantic conception of truth is arguably the most influential – certainly, most discussed - modern conception of truth. It has provoked many different interpretations and reactions, some thinkers celebrating it for successfully explicating the notion of truth, whereas others have argued that it is no good as a philosophical account of truth. The aim of this work is to offer a systematic and critical investigation of its nature and significance, based on the thorough explanation of its conceptual, technical as well as historical underpinnings.

The methodological strategy adopted in the thesis reflects the author’s belief that in order to evaluate the import of Tarski’s conception we need to understand what logical, mathematical and philosophical aspects it has, what role they play in his project of theoretical semantics, which of them hang in together, and which should be kept separate. Chapter 2 therefore starts with a detailed exposition of the conceptual and historical background of Tarski’s semantic conception of truth and his method of truth definition for formalized languages, situating it within his project of theoretical semantics, and Chapter 3 explains the formal machinery of Tarski’s truth definitions for increasingly more complex languages. Chapters 4 - 7 form the core of the thesis, all being concerned with the problem of significance of Tarski’s conception. Chapter 4 explains its logico-mathematical import, connecting it to the related works of Gödel and Carnap. Having explained the seminal ideas of the model-theoretic approach to semantics, Chapter 5 tackles the question to what extent Tarski’s ‘The Concept of Truth in Formalized Languages’ (and related articles from the 1930s) anticipates this approach, and what elements might be missing from it. Chapter 6 then deals with the vexed question of its philosophical import and value as a theory of truth, reviewing a number of objections and arguments that purport to show that the method fails as an explanation (explication) of the ordinary notion of truth, and, in particular, that it is a confusion to think that Tarski’s truth definitions have semantic import. Finally, Chapter 7 is devoted to the question whether Tarski’s theory of truth is a robust or rather a deflationary theory of truth.

On the basis of a careful analysis, the thesis aims to substantiate the following view. [A] Tarski’s theory with its associated method of truth definition was primarily designed to serve logico-mathematical purposes. [B] It can be regarded a deflationary theory of a sort, since it completely abstracts from meta- semantical issues concerning the metaphysical or epistemological basis or status of semantic properties. Indeed, [C] this can be interpreted as its laudable feature, since by separating formal (or logico-mathematical) from meta-semantical (or foundational) aspects it usefully divides the theoretical labour to be done in the area of meaning and semantic properties in general. [D] In spite of the fact that Tarski’s conception of truth has this deflationary flavour, the formal structure of its method of truth-definition is quite neutral in that it can be interpreted and employed in several different ways, some of them deflationary, others more robust.

Susan Haack, “The Whole Truth and Nothing but the Truth.”

Abstract: “Much truth is spoken, that more may be concealed,” wrote Mr. Justice Darling in 1879. Opening with an articulation of the distinction between truth (the concept) and truths (particular true propositions), this paper is largely devoted to: developing an account of the dual meaning of “partially true” – “true-in-part” vs. “part of the truth”; and (ii) understanding the reasons for, and the dangers of, the very common tendency to tell only part of the relevant truth. 


Keywords: truth, truths, partial truth, Ramsey, laconicism, vagueness, deception

Susan Haack, “Justice, Truth, and Proof: Not So Simple, After All”

Background: This paper was written for a conference in Girona, Spain, on the work of Italian legal scholar Michele Taruffo—who is celebrated by the evidence group at the University of Girona for his defense of the so-called “rationalist conception of proof.” My paper is in part an attempt to disentangle the many elements that seem to be run together in that conception, and figure out which are defensible, and which not; and at the same time to suggest that his broad comparisons of common-law vs. civil-law evidentiary procedures require much closer attention to the details of how these work in practice. So it is a kind of conversation with Taruffo (and with other legal theorists in Spain, Colombia, Brazil, etc. who share these ideas).

Abstract: Preamble: Substantive justice requires factual truth. So if legal proof-procedures are to be more than judicial theater, they must be capable of arriving, often enough, at factually correct verdicts. 

§1. The very possibility of substantive justice requires:
• that there be such a thing as factual truth;
• which is objective (not a matter of what anyone, or everyone, believes;
• that it is often enough possible for us to figure out, at least fallibly, what the truth of a disputed factual matter in is;
• which in turn requires that there be objective standards of stronger and weaker evidence;
• and that the fact that evidence is, by these standards, good, be at least a fallible indication that it is likely true.

The truth of these presuppositions is defended by reference to the laconicist understanding of truth, and the foundherentist account of the structure and quality of evidence.

§2: It remains an open question, however, whether these or those evidentiary procedures are capable arriving, often enough, at true verdicts. 

POWERPOINTS TO ACCOMPANY THIS PAPER ARE AVAILABLE IN THE SECTION LABELED “SELECTED PRESENTATIONS” BELOW (UNDER “MORE”). A LINK TO A YOUTUBE VIDEO OF HAACK GIVING THIS PRESENTATION CAN BE FOUND UNDER “LINKS” IN THAT SECTION

Truth-preservation, implication-preservation, and cognition-preservation.

This is one in a series of presentations designed to alert the philosophical community that claims made for the importance of truth-preservation are often overblown, frequently false, and—even when strictly speaking true--misleading and counter-productive. Truth-preservation per se is not nearly as important as implication-preservation; implication-preservation per se is not nearly as important as, cognition-preservation

Tarski’s proof of the law of identity

  Tarski’s LEIBNIZ’S LAW [Introduction to Logic, Sect. 17] is the second-order sentence in variable-enhanced English:

For everything x, for everything y: x = y iff
x has every property y has and y has every property x has.

  The Law of Identity, Tarski’s LAW OF REFLEXIVITY FOR IDENTITY, is:

Everything is equal to itself. For everything x: x = x.

  Tarski says it can be “derived” from Leibniz’s Law. Indeed, the paragraph following its statement begins with the word “PROOF” and ends with the words “which was to be proved”. This paper analyzes Tarski’s argumentation. We found several errors, four noted below.

O tema da Linguagem ocupa um lugar central na Filosofia do século XX. Sob o influxo do giro linguís-tico, a Filosofia redefine não só a Ontologia como também a Epistemologia, a Ética, a Estética e a Lógica. Os estudos que compõem esta obra cons-tituem uma espécie de álbum de onde se pode vi-sualizar certas notas características do grande debate a respeito do tema. Reunindo pesquisadores de diferentes universidades o livro pretende ocupar um espaço que sirva de referência não somente para os que iniciam suas pesquisas como também para aqueles que pretendem ampliar o debate em Filosofia da Linguagem.

This is the second of a series of three lectures given at Peking University.

Haack explores correspondence theories, the semantic theory, and the Laconicist theory (also known as the "redundancy" theory).

After showing the [problems with the first two kinds of theory, Haack argues for the virtue of the last, but also looks at the several issues still in need of resolution.

Dois homens que se preocuparam com os caminhos da América (e do mundo) disseram frases com as palavras " verdade " e " liberdade " interconectadas. Seus nomes: Marcuse e Rorty. Marcuse disse certa vez que ter uma concepção errada de verdade levaria a uma concepção errada de liberdade. Rorty, por seu turno, diferentemente, afirmou que se deixarmos de investigar a verdade (não sabemos como definir) para cuidarmos da liberdade (que sabemos bem o que é quando a perdemos) estaremos fazendo algo melhor com nossas energias. A investigação que proponho aos que ficarem motivados a partir deste pequeno texto, não deverá contrariar marcusianos e rortianos. Os primeiros poderão investigar o que a filosofia diz atualmente sobre a verdade para, enfim, formularem suas concepções e, então, ver se isso realmente aperfeiçoa suas noções de liberdade. Os segundos, não estarão gastando energia à toa, uma vez que não estou propondo que se empenhem no tema acreditando que vão fundamentar a liberdade, mas apenas que vão entender, afinal, porque podemos, nos dias de hoje, falarmos meio que esquizofrenicamente. Esquizofrenia? Sim, porque assim agimos: em determinados momentos dizemos " eis aqui a verdade " e, então, quem nos escuta nos alerta " ei, você não é o dono da verdade " , e então, não raro, saltamos de lado e avisamos, " bem, tenho o modo meu de olhar as coisas, esta é a minha verdade ". Ora, mas afinal, quem assim age estava ou não querendo dizer a verdade? 1. O que é " discutir a verdade " em filosofia? Começo pelo episódio de Pedro. " E passada quase uma hora, um outro afirmava, dizendo: também este verdadeiramente estava com ele, pois também é galileu. E Pedro disse: homem, não sei o que dizes. E logo, estando ele ainda a falar, cantou o galo. E, virando-se o Senhor, olhou para Pedro, e Pedro lembrou-se das palavras do Senhor, como lhe havia dito: antes que o galo cante hoje, me negará três vezes ". Era então a terceira vez que Pedro, ao ser reconhecido como amigo de Jesus, mentia, afirmando que não conhecia seu mestre.

There are many different theories of truth, though the oldest and also the deepest analysed over the ages is surely the Clas- sical Theory of Truth. Although it is simply defined as “corre- spondence between thought and reality,” it has dozens of dif- ferent interpretations, depending on how “correspondence” is understood. Thus, some of them were named and separated from the Classical Theory, but it is still puzzling to clearly identify which theory is classical, correspondent or seman- tic. Analysis of the types of linkage between language and the world which have resulted in various theories deemed as classical will serve to illustrate the differences between these theories. The article will also provide an attempt to set a strict and clear division, which could help in better understanding these theories of truth.

This dissertation is a philosophical analysis of the concept of truth. It is a development and defense of
the “stratified” or “language-level” conception of truth, first advanced in Alfred Tarski’s 1933
monograph The Concept of Truth in Formalized Languages. Although Tarski’s paper had seminal
influence both in philosophy and in more technical disciplines, its central philosophical claim has not
been generally accepted. This work has two central goals: (a) to give a detailed and analytic presentation
of Tarski’s theory and the problems it faces; (b) to offer a solution to these problems and assess the
philosophical significance of this solution.
The essay is divided in two parts. Part One contains a detailed and analytic presentation and
interpretation of the stratified conception of truth. The analysis contains several steps: (a) Crucial basic
assumptions, such as the limitation to formalized languages and the requirement of explicit definitions,
are stated explicitly, motivated, and their philosophical significance discussed. (b) The main negative
result of the stratified conception, the impossibility of semantic closure and of a universal language, is
given in detail and interpreted. (c) Tarski’s criterion for adequate truth definitions, known as Convention
T, is stated and motivated. (d) The deep structure of Tarski-style truth definitions and the necessary
conditions for their availability are analyzed. In particular, the philosophical significance of Tarski’s
notion of “essential richness” is discussed. (e) Finally, several problems are raised for the stratified
conception, chief among them the unity objection, according to which the stratified conception is not a
viable analysis of the concept of truth, since (by (a) above) an analysis should take the form of a
definition, and on the stratified conception different languages have different definitions. There is
therefore no one analysis of the concept.
Part Two is a development of answers to the problems raised at the end of Part One. The crux of the
answer to the unity objection is that Convention T, the adequacy criterion, connects the many definitions
of truth into a single concept. However, in order to fulfill that role Convention T must apply universally,
and a universal language was shown to be impossible ((c) above). The task of Part Two is therefore to
develop a mode of expression that allows the universal applicability of Convention T without
commitment to a universal metalanguage. The procedure is as follows. (a) Convention T is formalized
in order to isolate the place in which universal applicability is required. (b) A new expressive resource
of “abstract generality” is developed. To this purpose a digression into the semantics of natural language
indexicals is undertaken. David Kaplan’s thesis of the direct reference of indexicals is analyzed and a
new formal system is proposed that embodies it. It is shown that this formal system expresses abstract
generality. (c) The notion of abstract generality is adapted to languages without indexicals and it isviii
shown that Convention T can be expressed without assuming a universal language. (d) A reconstrual of
the task of concept analysis is proposed, which is a generalization of the answer to the unity objection.
It is often complained against Tarski’s stratified conception of truth that it is of limited philosophical
significance. In this work I show that, on the contrary, the problems it faces and the solutions that can
be advanced to answer these problems have substantive philosophical consequences. The notion of
abstract generality gives rise to a distinction between two fundamentally different modes of discourse:
a universal but merely abstract methodological discourse on the one hand, and a concrete but inevitably
restricted theoretical discourse on the other. This distinction has many important implications for our
understanding of the concepts of truth, meaning and language.

Contemporary natural-language semantics began with the assumption that the meaning of a sentence could be modeled by a single truth-condition, or by an enti- ty with a truth-condition. But with the recent explosion of dynamic semantics and pragmatics and of work on non-truth-conditional dimensions of linguistic mean- ing, we’re now in the midst of a shift away from a truth-condition-centric view and toward the idea that a sentence’s meaning must be spelled out in terms of its vari- ous roles in conversation. This communicative turn in semantics raises a historical question: why was truth-conditional semantics dominant in the first place, and why were the phenomena now driving the communicative turn initially ignored or misunderstood by truth-conditional semanticists? I offer a historical answer to both questions. The history of natural language semantics—springing from the work of Donald Davidson and Richard Montague—began with a methodological toolkit that Frege, Tarski, Carnap, and others had created to better understand ar- tificial languages. For them, the study of linguistic meaning was subservient to other explanatory goals in logic, philosophy, and the foundations of mathematics, and this subservience was reflected in the fact that they idealized away from all aspects of meaning that get in the way of a one-to-one correspondence between sentences and truth-conditions. The truth-conditional beginnings of natural-lan- guage semantics are best explained by the fact that, upon turning their attention to the empirical study of natural language, Davidson and Montague adopted the methodological toolkit assembled by Frege, Tarski, and Carnap and, along with it, their idealization away from non-truth-conditional semantic phenomena. But this pivot in explanatory priorities toward natural language itself rendered the adop- tion of the truth-conditional idealization inappropriate. Lifting the truth-condi- tional idealization has forced semanticists to upend the conception of linguistic meaning that was originally embodied in their methodology.

In "Psychopower and Ordinary Madness" my ambition, as it relates to Bernard Stiegler's recent literature, was twofold: 1) critiquing Stiegler's work on exosomatization and artefactual posthumanism-or, more specifically, nonhumanism-to problematize approaches to media archaeology that rely upon technical exteriorization; 2) challenging how Stiegler engages with Giuseppe Longo and Francis Bailly's conception of negative entropy. These efforts were directed by a prevalent techno-cultural qualifier: the rise of Synthetic Intelligence (including neural nets, deep learning, predictive processing and Bayesian models of cognition). This paper continues this project but first directs a critical analytic lens at the Derridean practice of the ontologization of grammatization from which Stiegler emerges while also distinguishing how metalanguages operate in relation to object-oriented environmental interaction by way of inferentialism. Stalking continental (Kapp, Simondon, Leroi-Gourhan, etc.) and analytic traditions (e.g., Carnap, Chalmers, Clark, Sutton, Novaes, etc.), we move from artefacts to AI and Predictive Processing so as to link theories related to technicity with philosophy of mind. Simultaneously drawing forth Robert Brandom's conceptualization of the roles that commitments play in retrospectively reconstructing the social experiences that lead to our endorsement(s) of norms, we compliment this account with Reza Negarestani's deprivatized account of intelligence while analyzing the equipollent role between language and media (both digital and analog).

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.

Une introduction logique et philosophique au problème de la définition de la vérité. Le chapitre contient une présentation du travail de Tarski sur la vérité. Une présentation du travail de Kripke. Un aperçu sur quelques théories contemporaines plus récentes. Une présentation des débats philosophiques sur la nature de la vérité ouverts par le travail Tarski.

ARTÍCULOS

DIEGO TAJER
En defensa del argumento finitista

MAXIMILIANO ESCOBAR VIRE
La necesidad moral en Leibniz: su contenido alético y su significación específica

RAMIRO CASO
Una defensa de las aserciones suboracionales

LUIS MARIANO DE LA MAZA
Voluntad, razón práctica y reconocimiento en Hegel y Ricoeur


ESTUDIOS CRÍTICOS

RICARDO IBARLUCIA
La autonomía del arte en Benjamin y Heidegger: a propósito de la interpretación de Burkhardt Lindner


NOTAS

LEANDRO INDAVERA
Rousseau, Smith y las rudas selvas de la naturaleza


COMENTARIOS BIBLIOGRÁFICOS

LORENZINO DE’ MEDICI
Apología (F. Andrade Marambio)

LETICIA CABANAS y OSCAR M. ESQUISABEL (eds.)
Leibniz frente a Spinoza. Una interpretación panorámica (F. Raffo Quintana)

SERGIO SANCHEZ
La insensata fabrica de la vigilia. Nietzsche y el fenómeno del sueño (P. Hunziker)

MARIA CRISTINA DI GREGORI y FEDERICO E. LOPEZ (coords.)
Regreso a la experiencia: lecturas de Peirce, James, Dewey y Lewis (L. Mattarollo)

The Tarskian hierarchy of truth is formulated in the language of Peano arithmetic with truth predicates $T_\alpha$, where $\alpha$ ranges over some suitable initial segment of the ordinals. The main goal of this paper is to show (i) that the sets definable in the Tarskian truth-hierarchy with $\omega_1^{CK}$-many levels are exactly the hyperarithmetical sets and (ii) that the axioms for the Tarskian truth-hierarchy with $\epsilon_0$-many levels can be interpreted in any reasonable axiomatic theory of grounded truth. This is done in section 3 and 4, respectively. In sections 1-2 we survey some relevant background material on ordinal notations and recursion theory.

The Bounds of Logic presents a new philosophical theory of the scope and nature of logic based on critical analysis of the principles underlying modern Tarskian logic and inspired by mathematical and linguistic development. Extracting central philosophical ideas from Tarski’s early work in semantics, Sher questions whether these are fully realized by the standard first-order system. The answer lays the foundation for a new, broader conception of logic. By generally characterizing logical terms, Sher establishes a fundamental result in semantics. Her development of the notion of logicality for quantifiers and her work on branching are of great importance for linguistics. Sher outlines the boundaries of the new logic and points out some of the philosophical ramifications of the new view of logic for such issues as the logicist thesis, ontological commitment, the role of mathematics in logic, and the metaphysical underpinning of logic. She proposes a constructive definition of logical terms, reexamines and extends the notion of branching quantification, and discusses various linguistic issues and applications.

The concept of formal consequence is at the heart of logic today, and by extension, plays an important role in such diverse areas as mathematics, computing, philosophy, and linguistics.

In this dissertation, I trace the roots of this concept in medieval logic from Pseudo-Scotus and John Buridan back to the earliest treatises on consequences, and provide translations of the three earliest known treatises on consequences - two anonymous, a third by Walter Burley.

Chapter one introduces the reader to the dominant philosophical approaches to formal consequence from the turn of the twentieth century to today. After this, I introduce the account of formal consequence advanced by John Buridan, the medieval predecessor to the semantic account advocated by Tarski and his followers.

The second chapter provides a detailed contrast of Buridan's account of formal consequence with those of Tarski, on the one hand, and later classical logic, on the other.

Chapter three examines the account of formal consequence in Pseudo-Scotus. I show that Pseudo-Scotus' account is dependent on that of Buridan, and therefore most post-date it.

Chapter four examines the account of divided modal consequence in William of Ockham. I show that Ockham's divided modalities are not fully assimilable to narrow-scope propositions of classical modal logic; formalize Ockham's account in an extension of first-order modal logic with restricted quantification; and provide a complete account of relations between two-term divided modal propositions on Ockham's account.

Chapter five introduces Walter Burley's thinking about consequences, examining: Burley's division and enumeration of consequences; his distinction between principal and derivative rules licensing good consequences; the relation of the division of consequences into formal and material varieties to Burley's preferred division between natural and accidental consequences; the relation Burley's work bears to Buridan, to the Boethian reception of Aristotle's Topics, and to the earliest treatises on consequences.

The final chapter concludes: highlighting the characteristic marks of medieval and modern approaches to consequences relative to each other; summarizing the various developments that led to the adoption of the account of formal consequence epitomized in Buridan's work; and suggesting prospects for recovering the most promising aspects of the medieval treatments of the topic.

Theories of linguistic meaning have been a major influence in twentieth century philosophy.  This is due, in part, to the assumption that meaning is the crucial and interesting thing about language. To know the meaning of an expression is to understand it, and since understanding is central to philosophy in many different ways, it should be no surprise that the notion of meaning has often taken center stage. The aim of this paper is to briefly explore some influential views concerning linguistic meaning. The final objective will be to demonstrate some alternatives which are open to theory with respect to this notion--for there are those who have wanted to ban talk of meaning from serious scientific discourse.  The point is that many of the disadvantages of traditional notions of meaning are avoidable--in particular, they are avoidable along a path which starts from Frege and moves on via Tarski and Davidson.

The aim of this paper is to provide context for and historical exegesis of Carnap's alleged move from syntax to semantics. The Orthodox Received View states that there was a radical break, while the Unorthodox Received View holds that Carnap's syntactical period already had many significant semantical elements. I will argue that both of them are partly right, both of them contains a kernel of truth: it is true that Carnap's semantical period started after his Logical Syntax of Language – in one sense of semantics. But it is also true, that Carnap had semantical ideas already in LSL: though not (just) in the sense as URV maintained it. This latter sense of semantics is related to what is usually called inferentialism, and by getting a clearer picture of Carnap's original aims, context, and concept-usage, we might be in a better position to approach his alleged inferentialism.

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.

The paper surveys different notions of implicit definition. In particular , we offer an examination of a kind of definition commonly used in formal axiomatics, which in general terms is understood as providing a definition of the primitive terminology of an axiomatic theory. We argue that such "structural definitions" can be semantically understood in two different ways, namely (i) as specifications of the meaning of the primitive terms of a theory and (ii) as definitions of higher-order mathematical concepts or structures. We analyze these two conceptions of structural definition both in the history of modern axiomatics and in contemporary philosophical debates. Based on that, we give a systematic assessment of the underlying semantics of these two ways of understanding the definiens of such definitions, by considering alternative model-theoretic and inferential accounts of meaning.

Alethic functionalism, as propounded by Michael Lynch, is the view that there are different ways to be true, but that these differences nevertheless contain enough unity to forestall outright pluralism. This view has many virtues. Yet, since one could conceivably apply Lynch's "one and many" strategy to other debates, I try show to how his argumentative steps can be used to solve—not just the controversy pertaining to truth—but any controversy that surrounds a "What is X?" question.

JOHN CORCORAN’S JUNE 2015 ANNOTATIONS OF TARSKI’S 1994 INTRODUCTION TO LOGIC.
The immediate purpose of this posting is to provide information about Tarski’s use of ‘equals’, ‘is’, is identical to’, ‘=’, and the like to participants in the session on FORMALIZING EUCLID’S FIRST AXIOM Bulletin of Symbolic Logic. 20 (2014) 404–5. (Coauthor: Daniel Novotný).

Here is a tidbit from page 56.
In this book we consider the notion of equality among numbers always as a special case of the general concept of logical identity. One should add, however, that there have been (and perhaps still are) mathematicians who—as opposed to the standpoint adopted here—did not identify the symbol "=" occurring in arithmetic with the symbol of logical identity; they did not consider equal numbers to be necessarily identical, and therefore looked upon the notion of equality among numbers as a specifically arithmetical concept. 1994/61

This book is alleged to be a comprehensive but largely elementary description of mathematical logic including its historical development, its most important achievements and its implications for philosophy. Although the intended audience includes both mathematicians
and philosophers, 'the book presupposes no knowledge of logic and only high school mathematics". The author avows an aim "to stimulate long-lived interest by communicating some of the excitement and beauty of the subject". Details and techniques are eschewed in favor of emphasis on the development of an overview.
The book is also intended by the author to serve as an introduction to logic. His opinion of the shortcomings of most introductions to logic is perceptive and insightful.

El libro Verdad. Controversias abiertas analiza la discusión habida desde un punto de vista histórico y sistemático del concepto “verdad” desde sus origines hasta la actualidad. En nuestro uso cotidiano, el término “verdad” hace referencia a que lo que expresamos está de acuerdo con los hechos o la realidad. También nos referimos a que algo es auténtico o fiel. Muchas actividades humanas dependen de dicho concepto por lo que se asume su naturaleza como concepto. Por ello, “verdad” es abordado en la amplia mayoría de las ciencias, el Derecho o nuestra la vida cotidiana. Para Parménides, la esencia de la verdad se enlaza al desenmascaramiento o la revelación. Así pues, el término está estrechamente emparentado al hallazgo de lo que antes estaba oculto como revela el uso del término griego de aletheia. Consecuentemente, el concepto de verdad se considera esencial por lo que no puede ser descripto en términos que sean más sencillos de entender que el concepto de verdad mismo. En dicho contexto, la verdad se enmarca en una correspondencia entre el lenguaje del pensamiento con una realidad independiente.
Requerimos más de dos mil años para transformar este enfoque analizando el enigma en un marco más adecuado, dilucidando su estructura lógica y semántica con el fin de descubrir sus límites y posibilidades. Verdad se opone a falsedad que asume asimismo un significado formal. Con ello, el lenguaje y las palabras dejan de ser un medio utilizado para determinar lo que es una “verdad” y se transforma en el centro de examen. Se estudia la estructura del lenguaje en el que aparece el predicado “verdad” y el modo como viene adscrito así como las funciones que asume. Esta investigación desplaza las viejas cuestiones acerca de las indagaciones sobre qué cosas son verdaderas o falsas; o, cómo definir, identificar y distinguir la verdad; o, si la verdad es subjetiva u objetiva, relativa o absoluta.
Gracias a la indagación formal se han conseguido seleccionar ciertos patrones racionales que pueden ayudarnos a decidir si una proposición es verdadera o falsa. En dicho sentido “verdad” se estudia en el marco de un lenguaje específico mediante una interpretación específica, considerando un sistema lógico afín y los presupuestos empíricos en los que se desenvuelve. Por esta razón, cualquier enunciado no es meramente considerado como una afirmación contingente sobre algún hecho aislado sino que ha de ser detallado en todas las interpretaciones posibles. Hemos puesto especial atención en desarrollar la teoría semántica de la verdad en la que se analizan los lenguajes abiertos. Según este punto de vista, ningún lenguaje puede contener su propio predicado de verdad por lo que la expresión “es verdadero” sólo se aplica a los enunciados del lenguaje objeto desde el metalenguaje. La razón de esta restricción se debe a que los lenguajes que contienen su propio predicado de verdad son propensos a generar enunciados paradójicos. Una consecuencia inmediata de esta condición es que la propuesta semántica no se puede aplicar a los lenguajes naturales ya que admiten sus propios predicados de verdad.
Por el contrario, se ha propuesto como modelo alternativo escrutar el predicado “verdad” introduciendo una restricción de los lenguajes naturales por lo que se puede probar que pueden contener su propio predicado de verdad sin dar lugar a la contradicción. El libro muestra el procedimiento seguido en la interpretación en los que intervienen lenguajes cerrados. Desde un punto de vista formal dicha propuesta implica que algunas oraciones no son ni verdaderas ni falsas. Esto contradice el principio de la bivalencia según el cual todo enunciado es, o bien, verdadero, o bien, falso. Este principio es una premisa clave para derivar la paradoja del mentiroso que también es abordado en estas páginas. En el capítulo en el que se estudia la distinción entre verdad y demostración se señala que la autorreferencia no puede evitarse ingenuamente, ya que las proposiciones sobre objetos aparentemente no relacionados pueden tener un significado autorreferencial informal. Gödel y Tarski descubrieron que el predicado “verdad” no puede ser definido de manera consistente. Por todo ello, el sistema cerrado acarrea una contradicción ya que el predicado de verdad que se construye es meramente parcial. Considera que ciertas proposiciones como las construidas en la prueba de Tarski con verdaderas pero a su vez inconsistentes. Se sigue pues discutiendo si la prueba de Tarski puede aplicarse a cualquier sistema de verdad parcial ya que hasta la fecha ninguno ha sido consistente con métodos aceptables usados en la lógica matemática.
El libro concluye con el estudio sistemático de algunas consideraciones acerca de los presupuestos empíricos que se presuponen en el uso del predicado verdadero en los modelos estudiados.

This chapter retraces the way in which the Austrian philosopher Sir Karl Popper came to accept a Correspondence Theory of Truth from the work of the Polish logician and mathematician Alfred Tarski. It is argued that Popper's use of Tarski's semantic theory of truth reveals crucial insights into the fundamental characteristics of Popper's social philosophy. Quite deceptively, arguments based upon Tarski's theory of truth appear implicitly throughout the text of The Open Society and Its Enemies (1945). It is then demonstrated how Popper integrated a correspondence theory of truth into a theory of the functions of communicative language that he received from Karl Bühler.

Farklı kategorilerin birbiriyle karıştırılması çağdaş felsefede “kategori hataları” (category mistakes) adıyla bilinir. Söz konusu hatanın bu isimle olmasa da felsefe tarihi boyunca çeşitli bağlamlarda tartışıldığı ve birtakım problemlerin kökeninde yer aldığını biliyoruz. Ancak kategori hatalarının dil, mantık ve matematikle ilişkili olarak daha dikkatlice incelenmesinin 20. yüzyılda başladığını söyleyebiliriz. 20. yüzyıl Batı felsefesindeki iki ana eğilimi oluşturan Kıta felsefesi ve analitik felsefe geleneklerinin kökeninde yer alan iki önemli filozofun da bu hataya dikkat çektiğini görmekteyiz. Bu filozoflar, analitik geleneğin ortaya çıkışında önemli bir rol oynayan Bertrand Russell ve özelde fenomenoloji geleneğinin kurucusu olup Kıta felsefesinin şekillenmesini derinden etkilemiş Edmund Husserl’dir. Adı geçen iki filozofun kategori hatalarını ele aldıkları bağlamlar ve savundukları yaklaşımların muhtemel tarihsel etkileri bu yazının konusunu oluşturuyor.

Tarski characterized logical notions as invariant under permutations of the domain. The outcome, according to Tarski, is that our logic, which is commonly said to be a logic of extension rather than intension, is not even a logic of extension—it is a logic of cardinality (or, more accurately, of “isomorphism type”). In this paper, I make this idea precise. We look at a scale inspired by Ruth Barcan Marcus of various levels of meaning: extensions, intensions and hyperintensions. On this scale, the lower the level of meaning, the more coarse-grained and less “intensional” it is. I propose to extend this scale to accommodate a level of meaning appropriate for logic. Thus, below the level of extension, we will have a more coarse-grained level of form. I employ a semantic conception of form, adopted from Sher, where forms are features of things “in the world”. Each expression in the language embodies a form, and by the definition we give, forms will be invariant under permutations and thus Tarskian logical notions. I then define the logical terms of a language as those terms whose extension can be determined by their form. Logicality will be shown to be a lower level analogue of rigidity. Using Barcan Marcus’s principles of explicit and implicit extensionality, we are able to characterize purely logical languages as “sub-extensional”, namely, as concerned only with form, and we thus obtain a wider perspective on both logicality and extensionality.

This paper is more a series of notes than a scholarly treatise. It focuses on certain achievements
of Aristotle, Boole and Tarski. The notes presented here using concepts introduced or formalized
by Tarski contribute toward two main goals: comparing Aristotle’s system with one Boole constructed
intending to broaden and to justify Aristotle’s, and giving a modern perspective to both logics. Choice
of these three logicians has other advantages. In history of logic, Aristotle is the best representative
of the earliest period, Boole the best of the transitional period, and Tarski the best of the most recent
period. In philosophy of logic, all three were amazingly successful in having their ideas incorporated
into mainstream logical theory. This last fact makes them hard to describe to a modern logician who
must be continually reminded that many of the concepts, principles, and methods that are taken to be
“natural” or “intuitive” today were all at one time discoveries.
Keywords: Counterargument, countermodel, formal epistemology, formal ontology, many‑sorted,
metalogic, one‑sorted, proof, range‑indicator, reinterpretation.

Mark Wilson argues that the standard categorizations of "Theory T thinking"— logic-centered conceptions of scientific organization (canonized via logical empiricists in the mid-twentieth century)—dampens the understanding and appreciation of those strategic subtleties working within science. By "Theory T thinking," we mean to describe the simplistic methodology in which mathematical science allegedly supplies ‘processes’ that parallel nature's own in a tidily isomorphic fashion, wherein "Theory T’s" feigned rigor and methodological dogmas advance inadequate discrimination that fails to distinguish between explanatory structures that are architecturally distinct. One of Wilson's main goals is to reverse such premature exclusions and, thus, early on Wilson returns to John Locke's original physical concerns regarding material science and the congeries of descriptive concern insofar as capturing varied phenomena (i.e., cohesion, elasticity, fracture, and the transmission of coherent work) encountered amongst ordinary solids like wood and steel are concerned. Of course, Wilson methodologically updates such a purview by appealing to multiscalar techniques of modern computing, drawing from Robert Batterman's work on the greediness of scales and Jim Woodward's insights on causation.

Reviewed: Bulletin of Symbolic Logic. 14 (2008) 271–2; History and Philosophy of Logic 30 (2009), 397–401; and Mathematical Reviews MR2402502 (2009e:03003).

This paper focuses on certain achievements of Aristotle, Boole and Tarski. The notes presented here using concepts introduced or formalized by Tarski contribute toward two main goals: comparing Aristotle’s system with one Boole constructed intending to broaden and to justify Aristotle’s, and giving a modern perspective to both logics. Choice
of these three logicians has other advantages. In history of logic, Aristotle is the best representative of the earliest period, Boole the best of the transitional period, and Tarski the best of the most recent period. All three were amazingly successful in having their ideas incorporated into mainstream logical theory. This last fact makes their ideas hard to describe to a modern logician who must be continually reminded that many of the concepts, principles, and methods that are taken to be “natural” or “intuitive” today were all at one time unknowns waiting to become discoveries.
Keywords: Counterargument, countermodel, formal epistemology, formal ontology, many sorted, metalogic, one sorted, proof, range indicator, reinterpretation.