Logic has pride of place in mathematics and its 20th century offshoot, computer science. Modern symbolic logic was developed, in part, as a way to provide a formal framework for mathematics: Frege, Peano, Whitehead and Russell, as well as Hilbert developed systems of logic to formalize mathematics. These systems were meant to serve either as themselves foundational, or at least as formal analogs of mathematical reasoning amenable to mathematical study, e.g., in Hilbert’s consistency program. Similar efforts continue, but have been (...) expanded by the development of sophisticated methods to study the properties of such systems using proof and model theory. In parallel with this evolution of logical formalisms as tools for articulating mathematical theories (broadly speaking), much progress has been made in the quest for a mechanization of logical inference and the investigation of its theoretical limits, culminating recently in the development of new foundational frameworks for mathematics with sophisticated computer-assisted proof systems. In addition, logical formalisms developed by logicians in mathematical and philosophical contexts have proved immensely useful in describing theories and systems of interest to computer scientists, and to some degree, vice versa. Three examples of the influence of logic in computer science are automated reasoning, computer verification, and type systems for programming languages. (shrink)

Este trabajo abordará cuestiones esenciales sobre el imaginario colectivo y sus relaciones con la realidad y la verdad. Primero, debemos abordar este tema dentro de un marco conceptual, seguido del correspondiente análisis fáctico de realidades conductuales demostrables. Adoptaremos no solo la metodología, sino sobre todo los principios y proposiciones de la filosofía analítica, que seguramente quedarán patentes a lo largo del estudio y podrán identificarse por las características descritas por Pérez. : Rabossi (1975) sostiene que la filosofía analítica puede identificarse (...) considerando ciertos parecidos familiares. Sugiere los siguientes rasgos familiares: una actitud positiva hacia el conocimiento científico; un enfoque cauteloso de la metafísica; una concepción de la filosofía como tarea conceptual, que toma como método el análisis conceptual; una estrecha relación entre lengua y Filosofía; una preocupación por buscar respuestas argumentativas a problemas filosóficos; la búsqueda de claridad conceptual. -/- Estos conceptos originales implican contenidos culturales, sociales, religiosos, científicos, filosóficos, morales y políticos propios de cada existencia colectiva. En este estudio no debatiremos ni demostraremos. Nuestro objetivo no es establecer sistemáticamente un método, criticar o aportar pruebas. Este trabajo se basa en la reflexión analítica. Especularemos lo más completa y profundamente posible y expresaremos los resultados de nuestros pensamientos. Sin perjuicio del carácter multidisciplinar del tema y de la apertura metodológica para aceptar aportaciones de cualquier campo científico, este trabajo pertenece a la psicología y la ontología o, en otras palabras, a la psicología social y ontológica. La metodología libre que orienta estas reflexiones abarca y considera todo lo que se acerca a la coherencia con la epistemología filosófica y psicológica. Esta metodología no busca evidencia, sino que busca la interrelación entre evidencia existente de cualquier naturaleza y magnitud, infiriendo significado consistente a partir de cosas reales. Muchos grandes pensadores en ningún momento han buscado demostraciones, teorizaciones o sistematizaciones. Estos pensadores pensaron, meditaron y pudieron acercarse a la verdad con la iluminación de su humildad. Ellos serán nuestra referencia y el ejemplo a seguir. De hecho, no encontraremos la verdad. Sin embargo, de una cosa podemos estar seguros: muchas veces nos acercaremos a la verdad y en todo momento nos alejaremos de la mentira. El objetivo principal de este estudio es observar cómo funcionan algunos de los atributos evolutivos esenciales de la humanidad. Al igual que la creatividad, la imaginación y la asociación pueden convertirse en una enfermedad peligrosa, al abrigo de las brumosas sombras de la inteligencia. -/- . (shrink)

Unger’s Problem of the Many seems to show that the familiar macroscopic world is much stranger than it appears. From plausible theses about the boundaries of or- dinary objects, Unger drew the conclusion that wherever there seems to be just one cat, cloud, table, human, or thinker, really there are many millions; and likewise for any other familiar kind of individual. In Lewis’s hands, this puzzle was subtly altered by an appeal to vagueness or indeterminacy about the the boundaries of (...) ordinary objects. This thesis examines the relation between these puzzles, and also to the phenomenon of vagueness. Chapter 1 begins by distinguishing Unger’s puzzle of too many candidates from Lewis’s puzzle of borderline, or vague, candidates. We show that, contra Unger, the question of whether this is a genuine, as opposed to merely apparent, distinction cannot be settled without investigation into the nature of vagueness. Chapter 2 begins this investigation by developing a broadly supervaluationist account of vague- ness that is immune to the standard objections. This account is applied to Unger’s and Lewis’s puzzles in chapters 3 and 4. Chapter 3 shows that, despite its popularity, Lewis’s own approach to the puzzles is unsatisfactory: it does not so much solve the puzzle, as prevent us from expressing them; it cannot be extended to objects that self-refer; it is committed to objectionable theses about temporal and modal metaphysics and semantics. Chapter 4 develops a conception of ordinary objects that emphasises the role of identity conditions and change, and uses it to resolve both Problems of the Many. This allows us to diagnose the source of the puzzles: an overemphasis on mereology in contemporary material ontology. (shrink)

According to the interpretational theory of logical validity (IR), logical validity is preservation of truth in all interpretations compatible with the intended meaning of logical expressions. IR suffers from a seemingly defeating objection, the so-called cardinality problem: any instance of the statement ‘There are n things’ is true under all interpretations, since it can be written down using only logical expressions that are not to be reinterpreted; yet ‘There are n things’ is not logically true. I argue that the cardinality (...) problem is indeed a serious problem for IR, when understood in terms of ‘asymmetry of information’. I then argue that IR can be rehabilitated by making quantifiers context-sensitive: what we do not reinterpret is the Kaplanian character of a quantifier, rather than its content. ‘There are n things’ is false in a context where fewer than n things are relevant, so it is not logically true in IR. I finally discuss some objections and ramifications of my account: I discuss how to make space for the possibility of an explicitly absolutely general quantifier in my framework, how terms can be logical even though context-sensitive, and how to recapture classical logic within my framework. (shrink)

В данной работе рассматриваются важнейшие вопросы о коллективном воображаемом и его отношениях с реальностью и истиной. Сначала мы рассмотрим эту тему в концептуальных рамках, а затем проведем соответствующий фактологический анализ наглядных поведенческих реалий. Мы будем опираться не только на методологию, но и, главным образом, на постулаты и положения аналитической философии, которые, безусловно, будут проявляться на протяжении всего исследования и могут быть идентифицированы по признакам, описанным Пересом : Рабосси (1975) отстаивает идею, что аналитическая философия может быть идентифицирована путем рассмотрения некоторых семейных (...) сходств. Он предлагает следующие семейные черты: позитивное отношение к научному знанию; осторожное отношение к метафизике; представление о философии как о концептуальной задаче, в которой в качестве метода используется концептуальный анализ; тесная связь между языком и философией; стремление к аргументированным ответам на философские проблемы; поиск концептуальной ясности. Эти базовые понятия включают в себя культурное, социальное, религиозное, научное, философское, моральное и политическое содержание, принадлежащее каждому и коллективному существованию. В данной статье мы не будем дискутировать и доказывать. Наша цель — не систематическая методология, не критика и не доказательство. Настоящая работа основана на аналитической рефлексии. Мы будем рассуждать как можно более полно и глубоко и излагать результаты своих размышлений. Несмотря на междисциплинарный характер темы и методологическую открытость к принятию вклада из любой области науки, данная работа относится к психологии и онтологии, или, другими словами, к социальной и онтологической психологии. Свободная методология, направляющая такие размышления, охватывает и рассматривает все, что приближается к согласованности с философской и психологической эпистемологией. Эта методология не гонится за доказательствами, а ищет взаимосвязь между существующими доказательствами любой природы и величины, выводя когерентный смысл реальных вещей. (shrink)

Diese Arbeit wird wesentliche Fragen über das kollektive Imaginär und seine Beziehungen zur Realität und Wahrheit ansprechen. Zunächst sollten wir dieses Thema in einem konzeptionellen Rahmen ansprechen, gefolgt von der entsprechenden Tatsachenanalyse demonstrierbarer Verhaltensrealitäten. Wir werden nicht nur die Methodik, sondern vor allem die Prinzipien und Sätze der analytischen Philosophie annehmen. Die vorliegende Arbeit beruht analytischer Reflexion. Wir werden so umfassend und tief wie möglich spekulieren und die Ergebnisse unserer Gedanken ausdrücken. Trotz des multidisziplinären Charakters des Themas und der methodischen (...) Offenheit für die Annahme. Beiträge aus jedem Bereich der Wissenschaft, diese Arbeit gehört zu Psychologie und Ontologie oder, mit anderen Worten, soziale und ontologische Psychologie. Die freie Methodik, die solche Reflexionen leitet, umfasst und betrachtet alles, was sich der Kohärenz mit der philosophischen und psychologischen Epistemologie nähert. Diese Methodik verfolgt keine Beweise, sondern sucht nach der Wechselbeziehung zwischen bestehenden Beweisen jeglicher Art und Größe, die eine kohärente Bedeutung zu den realen Dingen ableiten. Der Hauptbereich dieses Titels besteht darin, zu beobachten, wie einige der wesentlichen evolutionären Attribute der Menschheit, wie Kreativität, Fantasie und Assoziation, zu einer gefährlichen Krankheit werden können, die in den Nebelschatten der Intelligenz versteckt ist. (shrink)

The purpose of this introduction is to give a rough overview of the discussion of the formalization of arguments, focusing on deductive arguments. The discussion is structured around four important junctions: i) the notion of support, which captures the relation between the conclusion and premises of an argument, ii) the choice of a formal language into which the argument is translated in order to make it amenable to evaluation via formal methods, iii) the question of quality criteria for such formalizations, (...) and finally iv) the choice of the underlying logic. This introductory discussion is supplemented by a brief description of the genesis of the special issue, acknowledgements, and summaries of each article. (shrink)

There is a common demand that moral theory be 'practical', voiced both in- and outside of philosophy. Neo-Humeans, Kantian constitutivists and Aristotelian naturalists have all advocated the idea that my knowledge that I ought to do something must lead me to actually do it—an idea sometimes called the “practicality requirement” for moral theory. Some university administrators apply this idea in practice, when they force students who violate the code of conduct to complete classes in moral theory, hoping that the knowledge (...) obtained there would lead the student not to reoffend. I argue that the practicality requirement rests on a false understanding of the relation both between knowledge and motivation, focusing my critique on recent Aristotelian proposals. (shrink)

The aim of this paper is twofold: first, I provide a cluster of theories of truth in classical logic that is (internally) consistent with global reflection principles: the theories of positive truth (and falsity). After that, I analyse the _epistemic value_ of such theories. I do so employing the framework of cognitive projects introduced by Wright (Proc Aristot Soc 78:167–245, 2004), and employed—in the context of theories of truth—by Fischer et al. (Noûs 2019. https://doi.org/10.1111/nous.12292 ). In particular, I will argue (...) that theories of positive truth are _trustworthy_, analogously to the theories of full disquotational truth. Moreover, I argue that, for a given cognitive project, _if_ the acceptance of trustworthy theories is taken to be an _epistemic norm_ of cognitive project, then one has good reasons to accept theories of positive truth over other rival theories of truth in classical logic. On the other hand, the latter theories are deemed epistemically unacceptable. (shrink)

Does the materiality of a three-dimensional model have an effect on how this model operates in an exploratory way, how it prompts discovery of new mathematical results? Material mathematical models were produced and used during the second half of the nineteenth century, visualizing mathematical objects, such as curves and surfaces—and these were produced from a variety of materials: paper, cardboard, plaster, strings, wood. However, the question, whether their materiality influenced the status of these models—considered as exploratory, technical, or representational—was hardly (...) touched upon. This article aims to approach this question by investigating two case studies: Beltrami’s paper models vs. Dyck’s plaster ones of the hyperbolic plane; and Chisini’s string models of braids vs. Artin’s and Moishezon’s algebraization of these braids. These two case studies indicate that materiality might have a decisive role in how the model was taken into account mathematically: either as an exploratory or rather as a technical or pedagogical object. (shrink)

This is the book of abstracts of the 19th Brazilian Logic Conferences. The Brazilian Logic Conferences (EBL) is one of the most traditional logic conferences in South America. Organized by the Brazilian Logic Society (SBL), its main goal is to promote the dissemination of research in logic in a broad sense. It has been occurring since 1979, congregating logicians of different fields — mostly philosophy, mathematics and computer science — and with different backgrounds — from undergraduate students to senior researchers. (...) The meeting is an important moment for the Brazilian and South American logical community to join together and discuss recent developments of the field. The areas of logic covered in the conference spread over foundations and philosophy of science, analytic philosophy, philosophy and history of logic, mathematics, computer science, informatics, linguistics and artificial intelligence. Previous editions of the EBL have been a great success, attracting researchers from all over Latin America and elsewhere. -/- The 19th edition of EBL takes place from May 6-10, 2019, in the beautiful city of João Pessoa, at the northeast coast of Brazil. It is conjointly organized by Federal University of Paraíba (UFPB), whose main campus is located in João Pessoa, Federal University of Campina Grande (UFCG), whose main campus is located in the nearby city of Campina Grande (the second-largest city in Paraíba state) and SBL. It is sponsored by UFPB, UFCG, the Brazilian Council for Scientific and Technological Development (CNPq) and the State Ministry of Education, Science and Technology of Paraíba. It takes place at Hotel Luxxor Nord Tambaú, privileged located right in front Tambaú beach, one of João Pessoa’s most famous beaches. (shrink)

Three metascientific concepts that have been object of philosophical analysis are the concepts oflaw, model and theory. The aim ofthis article is to present the explication of these concepts, and of their relationships, made within the framework of Sneedean or Metatheoretical Structuralism (Balzer et al. 1987), and of their application to a case from the realm of biology: Population Dynamics. The analysis carried out will make it possible to support, contrary to what some philosophers of science in general and of (...) biology in particular hold, the following claims: a) there are "laws" in biological sciences, b) many of the heterogeneous and different "models" of biology can be accommodated under some "theory", and c) this is exactly what confers great unifying power to biological theories. (shrink)

No presente trabalho, vamos abordar algumas das questões essenciais sobre o imaginário coletivo e suas relações com a realidade e a verdade. Devemos encarar esse assunto em uma estrutura conceptual, seguida pela análise factual correspondente às realidades comportamentais demonstráveis. Adotaremos não apenas a metodologia, mas principalmente os princípios e proposições da filosofia analítica, que com certeza serão evidentes ao longo do estudo e podem ser identificados pelos recursos descritos por Perez[1] : Rabossi (1975) defende a ideia de que a filosofia (...) analítica pode ser identificada considerando-se certas semelhanças familiares. Ele sugere os seguintes traços familiares: uma atitude positiva em relação ao conhecimento científico; uma atitude cautelosa em relação à metafísica; uma concepção da filosofia como uma tarefa conceptual, que toma a análise conteudo como um método; uma estreita relação entre linguagem e filosofia; uma preocupação em buscar respostas argumentativas para problemas filosóficos, e procura de clareza conceptual. Esses conceitos centrais envolvem conteúdos culturais, sociais, religiosos, científicos, filosóficos, morais e políticos, pertencentes à existência individual e coletiva de cada um de nós. Neste artigo, não discutiremos nem demonstraremos. Nosso objetivo não é o de sistematicamente criticar ou evidenciar qualquer coisa, de qualquer maneira. O presente trabalho se baseia na reflexão analítica. Apenas especularemos da maneira mais abrangente e profunda que pudermos e expressaremos os resultados de nossos pensamentos. Não obstante a natureza multidisciplinar do assunto e a abertura metodológica para aceitar contribuições de qualquer campo da ciência, este trabalho pertence ao objetivo da psicologia e ontologia ou, em outros termos, da psicologia social e ontológica. A metodologia livre que norteia tais reflexões abrange e leva em consideração tudo o que se aproxima da coerência com a epistemologia filosófica e psicológica. Essa metodologia não busca alcançar evidências, mas apenas procura a inter-relação entre evidências já existentes, de qualquer natureza e magnitude, inferindo um significado coerente para as coisas reais. Muitos dos grandes pensadores, a qualquer momento, nunca procuraram demonstrações, teorizações ou sistematizações. Esses pensadores apenas pensavam, meditavam e com a iluminação de sua humildade podiam se aproximar da verdade. Eles serão nossa referência e o exemplo a ser seguido. Com certeza, não encontraremos a verdade, mas podemos ter certeza de alguma coisa: em muitos momentos, chegaremos perto da verdade e, em todos os momentos, estaremos nos afastando da inverdade e da mentira. O escopo principal deste estudo é observar como alguns dos atributos evolutivos essenciais da humanidade, como criatividade, imaginação e associação, podem se tornar uma doença perigosa, abrigada nas sombras enevoadas da inteligência. (shrink)

This paper proposes substitutional definitions of logical truth and consequence in terms of relative interpretations that are extensionally equivalent to the model-theoretic definitions for any relational first-order language. Our philosophical motivation to consider substitutional definitions is based on the hope to simplify the meta-theory of logical consequence. We discuss to what extent our definitions can contribute to that.

In this work, we will approach some essential questions about the collective imaginary and their relations with reality and truth. We should face this subject in a conceptual framework, followed by the corresponding factual analysis of demonstrable behavioral realities. We will adopt not only the methodology, but mostly the tenets and propositions of the analytic philosophy, which certainly will be apparent throughout the study, and may be identified by the features described by Perez : -/- Rabossi (1975) defends the idea (...) that analytic philosophy can be identified by considering certain family resemblances. He suggests the following family traits: a positive attitude toward scientific knowledge; a cautious attitude toward metaphysics; a conception of philosophy as a conceptual task, which takes conceptual analysis as a method; a close relationship between language and philosophy; a concern with seeking argumentative answers to philosophical problems; search for conceptual clarity Perez, Diana Ines, "Analytic Philosophy in Latin America”, The Stanford Encyclopedia of Philosophy ). These core concepts involve cultural, social, religious, scientific, philosophic, moral, and political contents, belonging to the individual and collective existence of each one of us. The present work grounds itself on analytical reflection. We will speculate the most comprehensive and profound way we can and express the results of our thoughts. Notwithstanding the multidisciplinary nature of the subject and the methodological openness for accepting contributions from any field of science, this work belongs to the aim of psychology and ontology or, in other terms, social and ontological psychology. The main scope of this paper is to observe how some essential evolutionary attributes of humankind, like creativity, imagination, and association, can become a hazardous sickness, sheltered in the misty shadows of the intelligence. (shrink)

Logical pluralism is the view that there is more than one correct logic. This very general characterization gives rise to a whole family of positions. I argue that not all of them are stable. The main argument in the paper is inspired by considerations known as the “collapse problem”, and it aims at the most popular form of logical pluralism advocated by JC Beall and Greg Restall. I argue that there is a more general argument available that challenges all variants (...) of logical pluralism that meet the following three conditions: that there are at least two correct logical systems characterized in terms of different consequence relations, that there is some sort of rivalry among the correct logics, and that logical consequence is normative. The hypothesis I argue for amounts to conditional claim: If a position satisfies all these conditions, then that position is unstable in the sense that it collapses into competing positions. (shrink)

Work on the nature and scope of formal logic has focused unduly on the distinction between logical and extra-logical vocabulary; which argument forms a logical theory countenances depends not only on its stock of logical terms, but also on its range of grammatical categories and modes of composition. Furthermore, there is a sense in which logical terms are unnecessary. Alexandra Zinke has recently pointed out that propositional logic can be done without logical terms. By defining a logical-term-free language with the (...) full expressive power of first-order logic with identity, I show that this is true of logic more generally. Furthermore, having, in a logical theory, non-trivial valid forms that do not involve logical terms is not merely a technical possibility. As the case of adverbs shows, issues about the range of argument forms logic should countenance can quite naturally arise in such a way that they do not turn on whether we countenance certain terms as logical. (shrink)

Logical pluralism is the view that there is more than one correct logic. Most logical pluralists think that logic is normative in the sense that you make a mistake if you accept the premisses of a valid argument but reject its conclusion. Some authors have argued that this combination is self-undermining: Suppose that L1 and L2 are correct logics that coincide except for the argument from Γ to φ, which is valid in L1 but invalid in L2. If you accept (...) all sentences in Γ, then, by normativity, you make a mistake if you reject φ. In order to avoid mistakes, you should accept φ or suspend judgment about φ. Both options are problematic for pluralism. Can pluralists avoid this worry by rejecting the normativity of logic? I argue that they cannot. All else being equal, the argument goes through even if logic is not normative. (shrink)

Se examinan las motivaciones teóricas, los lineamientos generales y las principales variantes de dos modos complementarios de entender la naturaleza de la lógica. El primero centrado en logros técnicos alcanzados desde fines del siglo XIX, y el segundo vinculado con la reflexión clásica sobre la naturaleza de los principios de la actividad de la razón. Se pone énfasis en la importancia del vínculo constitutivo entre las reglas y leyes lógicas y la estructura del lenguaje, en particular de aquél que subyace (...) cuando el habla se orienta por pretensiones cognoscitivas. (shrink)

It is often argued that by assuming the existence of a universal language, one prohibits oneself from conducting semantical investigations. It could thus be thought that Tarski’s stance towards a universal language in his fruitful Wahrheitsbegriff differs essentially from Carnap’s in the latter’s less successful Untersuchungen zur allgemeinen Axiomatik. Yet this is not the case. Rather, these two works differ in whether or not the studied fragments of the universal language are languages themselves, i.e., whether or not they are closed (...) under derivation rules. In Carnap’s case, axiom systems are not closed under derivation rules, which enables him to adopt a substitutional concept of models. His approach is directly rooted in the tradition of formal axiomatics, we argue, and in this contrary to Tarski’s. In comparing these works by Carnap and Tarski, our aim will be to qualify the connection between Tarski’s approach and the tradition of formal axiomatics, which has been overemphasized in the literature. (shrink)

This paper concerns Carnap’s early contributions to formal semantics in his work on general axiomatics between 1928 and 1936. Its main focus is on whether he held a variable domain conception of models. I argue that interpreting Carnap’s account in terms of a fixed domain approach fails to describe his premodern understanding of formal models. By drawing attention to the second part of Carnap’s unpublished manuscript Untersuchungen zur allgemeinen Axiomatik, an alternative interpretation of the notions ‘model’, ‘model extension’ and ‘submodel’ (...) in his theory of axiomatics is presented. Specifically, it is shown that Carnap’s early model theory is based on a convention to simulate domain variation that is not identical but logically comparable to the modern account. (shrink)

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. (shrink)

We provide for the first time an exact translation into English of the Polish version of Alfred Tarski's classic 1936 paper, whose title we translate as ?On the Concept of Following Logically?. We also provide in footnotes an exact translation of all respects in which the German version, used as the basis of the previously published and rather inexact English translation, differs from the Polish. Although the two versions are basically identical, to an extent that is even uncanny, we note (...) more than 400 differences. Several dozen of these are substantive differences due to revisions by Tarski to the Polish version which he did not incorporate in the German version. With respect to these revisions the Polish version should be regarded as more authoritative than the German. Hence scholars limited to an English translation should use ours. (shrink)

The period from 1900 to 1935 was particularly fruitful and important for the development of logic and logical metatheory. This survey is organized along eight "itineraries" concentrating on historically and conceptually linked strands in this development. Itinerary I deals with the evolution of conceptions of axiomatics. Itinerary II centers on the logical work of Bertrand Russell. Itinerary III presents the development of set theory from Zermelo onward. Itinerary IV discusses the contributions of the algebra of logic tradition, in particular, Löwenheim (...) and Skolem. Itinerary V surveys the work in logic connected to the Hilbert school, and itinerary V deals specifically with consistency proofs and metamathematics, including the incompleteness theorems. Itinerary VII traces the development of intuitionistic and many-valued logics. Itinerary VIII surveys the development of semantical notions from the early work on axiomatics up to Tarski's work on truth. (shrink)

A formula is (materially) valid iff all its instances are true sentences; and an axiomatic system is called (materially) sound and complete iff it proves all and only valid formulas. These are 'natural' concepts of validity and completeness, which were, however, in the course of the history of modern logic, stealthily replaced by their formal descendants: formal validity and completeness. A formula is formally valid iff it is true under all interpretations in all universes; and an axiomatic system is called (...) formally sound and complete iff it proves all and only formulas valid in this sense. Though the step from material to formal validity and completeness may seem to be merely an unproblematic case of explication, I argue that it is not; and that mistaking the latter concepts for the former ones may lead to serious conceptual confusions. (shrink)

In the early 20th century, scepticism was common among philosophers about the very meaningfulness of the notion of truth – and of the related notions of denotation, definition etc. (i.e., what Tarski called semantical concepts). Awareness was growing of the various logical paradoxes and anomalies arising from these concepts. In addition, more philosophical reasons were being given for this aversion.1 The atmosphere changed dramatically with Alfred Tarski’s path-breaking contribution. What Tarski did was to show that, assuming that the syntax of (...) the object language is specified exactly enough, and that the metatheory has a certain amount of set theoretic power,2 one can explicitly define truth in the object language. And what can be explicitly defined can be eliminated. It follows that the defined concept cannot give rise to any inconsistencies (that is, paradoxes). This gave new respectability to the concept of truth and related notions. Nevertheless, philosophers’ judgements on the nature and philosophical relevance of Tarski’s work have varied. It is my aim here to review and evaluate some threads in this debate. (shrink)

In a recent series of articles, Beall has developed the view that FDE is the formal system most deserving of the honorific “Logic”. The Simple Argument for this view is a cost-benefit analysis: the view that FDE is Logic has no drawbacks and it has some benefits when compared with any of its rivals. In this paper, I argue that both premises of the Simple Argument are mistaken. I use this as an opportunity to further reflect on how such arguments (...) can be bolstered to provide more substantial and productive support for revisionary theses about Logic. (shrink)

What we call first‐order logic over fixed domain was initiated, in a certain guise, by Peirce around 1885 and championed, albeit in idiosyncratic form, by Zermelo in papers from the 1930s. We characterise such logics model‐ and proof‐theoretically and argue that they constitute exploration of a clearly circumscribed conception of domain‐dependent generality. Whereas a logic, or family of such, can be of interest for any of a variety of reasons, we suggest that one of those reasons might be that said (...) logic fosters some clarification regarding just what qualifies as a logical concept, a logical operation, or a logical law. (shrink)

The book provides a historical and systematic exposition of the semantic theory of truth formulated by Alfred Tarski in the 1930s. This theory became famous very soon and inspired logicians and philosophers. It has two different, but interconnected aspects: formal-logical and philosophical. The book deals with both, but it is intended mostly as a philosophical monograph. It explains Tarski’s motivation and presents discussions about his ideas as well as points out various applications of the semantic theory of truth to philosophical (...) problems. (shrink)

In Untersuchungen zur allgemeinen Axiomatik and Abriss der Logistik, Carnap attempted to formulate the metatheory of axiomatic theories within a single, fully interpreted type-theoretic framework and to investigate a number of meta-logical notions in it, such as those of model, consequence, consistency, completeness, and decidability. These attempts were largely unsuccessful, also in his own considered judgment. A detailed assessment of Carnap’s attempt shows, nevertheless, that his approach is much less confused and hopeless than it has often been made out to (...) be. By providing such a reassessment, the paper contributes to a reevaluation of Carnap’s contributions to the development of modern logic. (shrink)

In Untersuchungen zur allgemeinen Axiomatik and Abriss der Logistik, Carnap attempted to formulate the metatheory of axiomatic theories within a single, fully interpreted type-theoretic framework and to investigate a number of meta-logical notions in it, such as those of model, consequence, consistency, completeness, and decidability. These attempts were largely unsuccessful, also in his own considered judgment. A detailed assessment of Carnap’s attempt shows, nevertheless, that his approach is much less confused and hopeless than it has often been made out to (...) be. By providing such a reassessment, the paper contributes to a reevaluation of Carnap’s contributions to the development of modern logic. (shrink)

Theory and Reality is about the connection between true theories and the world. A mathematical framefork for such connections is given, and it is shown how that framework can be used to infer facts about the structure of reality from facts about the structure of true theories, The book starts with an overview of various approaches to metaphysics. Beginning with Quine's programmatic "On what there is", the first chapter then discusses the perils involved in going from language to metaphysics. It (...) criticises contemporary intuition-driven metaphysics, comments on naturalistic approaches, and then presents the main proposition put forward in the thesis: we should base metaphysics on model theory. In chapters 2 to 5, mathematical treatments are given of concepts that we need: theories, metaphysics, necessitation and semantics. These are used in chapters 6 and 7 to prove that, seen from a certain informative view point, any true theory will give rise to an isomorphism between that theory and the world. This conclusion is similar to Wittgenstein's in the Tractatus, but differs in that it places the structural relationship on the level of whole theories, rather than single propositions. (shrink)

Many papers have been devoted to the semantic turn Carnap took in the late 1930s after Tarski had explained to him his method for defining truth and his work on the establishment of scientific semantics. Commentators have often argued that the major turn in Carnap’s approach to languages had already been taken in the Logical Syntax of Language, but they have usually assumed that Carnap was happy to subsequently follow Tarski and adopt Tarskian semantics. In this paper, it is argued (...) that this assumption needs to be qualified and that Carnap was actually far from following Tarski when he decided to complement his syntactic method with a semantic one. Carnap and Tarski had different goals, divergent programs, and dissenting views on truth and semantics. After exploring several possible methods for the explication of logical concepts such as L-truth and L-implication, Carnap opted for definitions based on concepts he had found in Wittgenstein’s Tractatus and Waismann’s work on a logical interpretation of probability. Carnap’s reasons for taking a semantic turn are to be understood in the context of his principle of tolerance. He first hoped he could use Tarski’s technique to recover in the semantic setting the completeness result he had tried to establish in the Logical Syntax. His eventual adoption of non-Tarskian semantics can be accounted for by his program of a logical analysis of science—including empirical science—and his ambition to elaborate a unified logical framework for deductive, inductive, and modal logic, and for explicating analyticity. (shrink)

Inference versus consequence , an invited lecture at the LOGICA 1997 conference at Castle Liblice, was part of a series of articles for which I did research during a Stockholm sabbatical in the autumn of 1995. The article seems to have been fairly effective in getting its point across and addresses a topic highly germane to the Uppsala workshop. Owing to its appearance in the LOGICA Yearbook 1997 , Filosofia Publishers, Prague, 1998, it has been rather inaccessible. Accordingly it is (...) republished here with only bibliographical changes and an afterword. (shrink)

In this paper the informativeness account of assertion (Pagin in Assertion. Oxford University Press, Oxford, 2011) is extended to account for inference. I characterize the conclusion of an inference as asserted conditionally on the assertion of the premises. This gives a notion of conditional assertion (distinct from the standard notion related to the affirmation of conditionals). Validity and logical validity of an inference is characterized in terms of the application of method that preserves informativeness, and contrasted with consequence and logical (...) consequence, that is defined in terms of truth preservation. The proposed account is compared with that of Prawitz (Logica yearbook 2008, pp. 175-192. College Publications, London, 2009). (shrink)

Tarskian model theory is almost universally understood as a formal counterpart of the preformal notion of semantics, of the “linkage between words and things”. The wide-spread opinion is that to account for the semantics of natural language is to furnish its settheoretic interpretation in a suitable model structure; as exemplified by Montague 1974.

Structural realism has been proposed as an epistemological position interpolating between realism and sceptical anti-realism about scientific theories. The structural realist who accepts a scientific theory thinks that is empirically correct, and furthermore is a realist about the ‘structural content’ of . But what exactly is ‘structural content’? One proposal is that the ‘structural content’ of a scientific theory may be associated with its Ramsey sentence (). However, Demopoulos and Friedman have argued, using ideas drawn from Newman's earlier criticism of (...) Russell's structuralism, that this move fails to achieve an interesting intermediate position between realism and anti-realism. Rather, () adds little content beyond the instrumentalistically acceptable claim that the theory is empirically adequate. Here, I formulate carefully the crucial claim of Demopoulos and Friedman, and show that the Ramsey sentence () is true just in case possesses a full model which is empirically correct and satisfies a certain cardinality condition on its theoretical domain. This suggests that structural realism is not a position significantly different from the anti-realism it attempts to distinguish itself from. Introduction Technical framework Ramsification Empirical adequacy Ramsification empirical adequacy + cardinality constraint Conclusion. (shrink)

Tarski and Mautner proposed to characterize the "logical" operations on a given domain as those invariant under arbitrary permutations. These operations are the ones that can be obtained as combinations of the operations on the following list: identity; substitution of variables; negation; finite or infinite disjunction; and existential quantification with respect to a finite or infinite block of variables. Inasmuch as every operation on this list is intuitively "logical", this lends support to the Tarski-Mautner proposal.

Když jsem v roce 1992 začínal na filosofické fakultě UK přednášet teorii sémantiky, cítil jsem intenzivní potřebu poskytnout studentům nějaký učební text. O překotném vývoji tohoto interdisciplinárního oboru, který odstartovalo v sedmdesátých letech úspěšné “zkřížení logiky s lingvistikou” Richardem Montaguem a dalšími a který se nezpomalil dodnes, totiž v češtině neexistovaly prakticky žádné zprávy (s čestnou výjimkou přístupu tzv. transparentní intenzionální logiky, který byl dílem českého emigranta Pavla Tichého a o kterém u nás psal Pavel Materna). Přehledové publikace, jaké jsou (...) potřeba pro někoho, kdo se chce v dané problematice zorientovat, se ovšem v té době i po světě teprve začínaly objevovat: v roce 1990 vyšla kniha An Introduction to Semantics Gennara Chierchii a Sally McConell-Ginnetové a v roce 1991 vydala skupina holandských logiků pod kolektivním pseudonymem L.T.F. Gamut dvousvazkovou knihu Language and Meaning. Za této situace jsem se pokusil co nejrychleji sepsat učební text, který by moji studenti i jiní zájemci o sémantiku mohli použít; a protože o jeho vydání paradoxně projevila větší zájem filosofická fakulta Masarykovy univerzity v Brně (kde jsem já osobně nikdy neučil; ale zájem o sémantiku tam neúnavně podněcoval a vydání mého textu tam zprostředkoval kolega Materna) než filosofická fakulta mojí domovské Karlovy univerzity, vyšel tento text v Brně, a to pod názvem Úvod do teoretické sémantiky. (shrink)

The entire development of modern logic is characterized by various forms of confrontation of what has come to be called proof theory with what has earned the label of model theory. For a long time the widely accepted view was that while model theory captures directly what logical formalisms are about, proof theory is merely our technical means of getting some incomplete grip on this; but in recent decades the situation has altered. Not only did proof theory expand into new (...) realms, generalizing the concept of proof in various directions; many philosophers also realized that meaning may be seen as primarily consisting in certain rules rather than in language-world links. However, the possibility of construing meaning as an inferential role is often seen as essentially compromised by the limits of prooftheoretical means. The aim of this paper is to sort out the cluster of problems besetting logical inferentialism by disentangling and clarifying one of them, namely determining the power of various inferential frameworks as measured by that of explicitly semantic ones. (shrink)

Following Hartry Field in distinguishing disquotational truth from a conception that grounds truth conditions in a community's usage, it is argued that the notions are materially inequivalent (since the latter allows truth-value gaps) and that both are needed. In addition to allowing blanket endorsements ("Everything the Pope says is true"), disquotational truth facilitates mathematical discovery, as when we establish the Gödel sentence by noting that the theorems are all disquotationally true and the disquotational truths are consistent. We require a more (...) substantial notion, however, if we intend to use truth values and truth conditions in explaining communication by language. (shrink)

Logical consequence in first-order predicate logic is defined substitutionally in set theory augmented with a primitive satisfaction predicate: an argument is defined to be logically valid if and only if there is no substitution instance with true premises and a false conclusion. Substitution instances are permitted to contain parameters. Variants of this definition of logical consequence are given: logical validity can be defined with or without identity as a logical constant, and quantifiers can be relativized in substitution instances or not. (...) It is shown that the resulting notions of logical consequence are extensionally equivalent to versions of first-order provability and model-theoretic consequence. Every model-theoretic interpretation has a substitutional counterpart, but not vice versa. In particular, in contrast to the model-theoretic account, there is a trivial intended interpretation on the substitutional account, namely, the homophonic interpretation that does not substitute anything. Applications to free logic, and theories and languages other than set theory are sketched. (shrink)

The problem of logical constants consists in finding a principled way to draw the line between those expressions of a language that are logical and those that are not. The criterion of invariance under permutation, attributed to Tarski, is probably the most common answer to this problem, at least within the semantic tradition. However, as the received view on the matter, it has recently come under heavy attack. Does this mean that the criterion should be amended, or maybe even that (...) it should be abandoned? I shall review the different types of objections that have been made against invariance as a logicality criterion and distinguish between three kinds of objections, skeptical worries against the very relevance of such a demarcation, intensional warnings against the level at which the criterion operates, and extensional quarrels against the results that are obtained. I shall argue that the first two kinds of objections are at least partly misguided and that the third kind of objection calls for amendment rather than abandonment. (shrink)