Why should moral philosophers, moral psychologists, and machine ethicists care about computational complexity? Debates on whether artificial intelligence (AI) can or should be used to solve problems in ethical domains have mainly been driven by what AI can or cannot do in terms of human capacities. In this paper, we tackle the problem from the other end by exploring what kind of moral machines are possible based on what computational systems can or cannot do. To do so, we analyze normative (...) ethics through the lens of computational complexity. First, we introduce computational complexity for the uninitiated reader and discuss how the complexity of ethical problems can be framed within Marr’s three levels of analysis. We then study a range of ethical problems based on consequentialism, deontology, and virtue ethics, with the aim of elucidating the complexity associated with the problems themselves (e.g., due to combinatorics, uncertainty, strategic dynamics), the computational methods employed (e.g., probability, logic, learning), and the available resources (e.g., time, knowledge, learning). The results indicate that most problems the normative frameworks pose lead to tractability issues in every category analyzed. Our investigation also provides several insights about the computational nature of normative ethics, including the differences between rule- and outcome-based moral strategies, and the implementation-variance with regard to moral resources. We then discuss the consequences complexity results have for the prospect of moral machines in virtue of the trade-off between optimality and efficiency. Finally, we elucidate how computational complexity can be used to inform both philosophical and cognitive-psychological research on human morality by advancing the moral tractability thesis. (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)

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)

Words change meaning, usually in unpredictable ways. But some words’ meanings are revised intentionally. Revisionary projects are normally put forward in the service of some purpose – some serve specific goals of inquiry, and others serve ethical, political or social aims. Revisionist projects can ameliorate meanings, but they can also pervert. In this paper, I want to draw attention to the dangers of meaning perversions, and argue that the self-declared goodness of a revisionist project doesn’t suffice to avoid meaning perversions. (...) The road to Hell, or to horrors on Earth, is paved with good intentions. Finally and more importantly, I want to demarcate what meaning perversions are. This, I hope, can help us assess the moral and political legitimacy of revisionary projects. (shrink)

In §2-4, I survey three extant ways of making sense of indeterminate truth and find each of them wanting. All the later sections of the paper are concerned with showing that the most promising way of making sense of indeterminate truth is via either a theory of truthmaker gaps or via a theory of truthmaking gaps. The first intimations of a truthmaker–truthmaking gap theory of indeterminacy are to be found in Quine (1981). In §5, we see how Quine proposes to (...) solve Unger’s problem of the many via positing the possibility of groundless truth. In §6, I elaborate the truthmaker gap model of indeterminacy first sketched by Sorensen (2001, ch.11) and use it to give a reductive analysis of indeterminate truth. In §7, I briefly assess what kind of formal framework can best express the possibility of truthmaker gaps. In §8, I contrast what I dub ‘the ordinary conception of worldly indeterminacy’ with Williamson’s conception of worldly indeterminacy. In §9, I show how one can distinguish linguistic from worldly indeterminacy on a truthmaker gap conception. In §10, I briefly sketch the relationship between truthmaker gaps and ignorance. In §11, I assess whether a truthmaker gap conception of vagueness is really just a form of epistemicism. In §12, I propose that truthmaker gaps can yield a plausible model of (semantic) presupposition failure. In §13, in response to the worry that a truthmaker gap conception of indeterminacy is both parochial and controversial—since it commits us to an implausibly strong theory of truthmaking—I set forth a truthmaking gap conception of indeterminacy. In §14, I answer the worry that groundless truths, of whatever species, are just unacceptably queer. A key part of this answer is that a truthmaker–truthmaking gap model of indeterminacy turns out to be considerably less queer than any model of indeterminacy which gives up on Tarski’s T-schema for truth (and cognate schemas). (shrink)

Contributors: Steven Barbone, Laurent Bove, Edwin Curley, Valérie Debuiche, Michael Della Rocca, Simon B. Duffy, Daniel Garber, Pascale Gillot, Céline Hervet, Jonathan Israel, Chantal Jaquet, Mogens Lærke, Jacqueline Lagrée, Martin Lin, Yitzhak Y. Melamed, Pierre-François Moreau, Steven Nadler, Knox Peden, Alison Peterman, Charles Ramond, Michael A. Rosenthal, Pascal Sévérac, Hasana Sharp, Jack Stetter, Ariel Suhamy, Lorenzo Vinciguerra.

The paper presents an alternative substitutional semantics for first-order modal logic which, in contrast to traditional substitutional (or truth-value) semantics, allows for a fine-grained explanation of the semantical behavior of the terms from which atomic formulae are composed. In contrast to denotational semantics, which is inherently reference-guided, this semantics supports a non-referential conception of modal truth and does not give rise to the problems which pertain to the philosophical interpretation of objectual domains (concerning, e.g., possibilia or trans-world identity). The paper (...) also proposes the notion of modality de nomine as an alternative to the denotational notion of modality de re. (shrink)

A. J. Ayer’s Language, Truth, and Logic had been responsible for introducing the Vienna Circle’s ideas, developed within a Germanophone framework, to an Anglophone readership. Inevitably, this migration from one context to another resulted in the alteration of some of the concepts being transmitted. Such alterations have served to facilitate a number of false impressions of Logical Empiricism from which recent scholarship still tries to recover. In this paper, I will attempt to point to the ways in which LTL has (...) helped to foster the various mistaken stereotypes about Logical Empiricism which were combined into the received view. I will begin by examining Ayer’s all too brief presentation of an Anglocentric lineage for his ideas. This lineage, as we shall see, simply omits the major 19th century Germanophone influences on the rise of analytic philosophy. The Germanophone ideas he presents are selectively introduced into an Anglophone context, and directed towards various concerns that arose within that context. I will focus on the differences between Carnap’s version of the overcoming of metaphysics, and Ayer’s reconfiguration into what he calls the elimination of metaphysics. Having discussed the above, I will very briefly outline the consequences that Ayer’s radicalisation of the Vienna Circle’s doctrines had on the subsequent Anglophone reception of Logical Empiricism. (shrink)

One well known problem regarding quantifiers, in particular the 1storder quantifiers, is connected with their syntactic categories and denotations. The unsatisfactory efforts to establish the syntactic and ontological categories of quantifiers in formalized first-order languages can be solved by means of the so called principle of categorial compatibility formulated by Roman Suszko, referring to some innovative ideas of Gottlob Frege and visible in syntactic and semantic compatibility of language expressions. In the paper the principle is introduced for categorial languages generated (...) by the Ajdukiewicz’s classical categorial grammar. The 1st-order quantifiers are typically ambiguous. Every 1st-order quantifier of the type k > 0 is treated as a two-argument functorfunction defined on the variable standing at this quantifier and its scope (the sentential function with exactly k free variables, including the variable bound by this quantifier); a binary function defined on denotations of its two arguments is its denotation. Denotations of sentential functions, and hence also quantifiers, are defined separately in Fregean and in situational semantics. They belong to the ontological categories that correspond to the syntactic categories of these sentential functions and the considered quantifiers. The main result of the paper is a solution of the problem of categories of the 1st-order quantifiers based on the principle of categorial compatibility. (shrink)

Kotarbiński is one of the leading figures in the Lvov-Warsaw school of Polish philosophy. We summarize the development of Kotarbiński’s thought from his early nominalism and ‘pansomatistic reism’ to the later doctrine of ‘temporal phases’. We show that the surface clarity and simplicity of Kotarbiński’s writings mask a number of profound philosophical difficulties, connected above all with the problem of giving an adequate account of the truth of contingent (tensed) predications. The paper will examine in particular the attempts to resolve (...) these difficulties on the part of Leśniewski. It will continue with an account of the relations of Kotarbińskian reism to the ontology of things or entia realia defended by the later Brentano. Kotarbiński’s identification of Brentano as a precursor of reism is, it will be suggested, at least questionable, and the paper will conclude with a more careful attempt to situate the Brentanian and Kotarbińskian ontologies within the spectrum of competing ontological views. (shrink)

Alfred Tarski seems to endorse a partial conception of truth, the T-schema, which he believes might be clarified by the application of empirical methods, specifically citing the experimental results of Arne Næss (1938a). The aim of this paper is to argue that Næss’ empirical work confirmed Tarski’s semantic conception of truth, among others. In the first part, I lay out the case for believing that Tarski’s T-schema, while not the formal and generalizable Convention-T, provides a partial account of truth that (...) may be buttressed by an examination of the ordinary person’s views of truth. Then, I address a concern raised by Tarski’s contemporaries who saw Næss’ results as refuting Tarski’s semantic conception. Following that, I summarize Næss’ results. Finally, I will contend with a few objections that suggest a strict interpretation of Næss’ results might recommend an overturning of Tarski’s theory. (shrink)

This volume examines the limitations of mathematical logic and proposes a new approach to logic intended to overcome them. To this end, the book compares mathematical logic with earlier views of logic, both in the ancient and in the modern age, including those of Plato, Aristotle, Bacon, Descartes, Leibniz, and Kant. From the comparison it is apparent that a basic limitation of mathematical logic is that it narrows down the scope of logic confining it to the study of deduction, without (...) providing tools for discovering anything new. As a result, mathematical logic has had little impact on scientific practice. Therefore, this volume proposes a view of logic according to which logic is intended, first of all, to provide rules of discovery, that is, non-deductive rules for finding hypotheses to solve problems. This is essential if logic is to play any relevant role in mathematics, science and even philosophy. To comply with this view of logic, this volume formulates several rules of discovery, such as induction, analogy, generalization, specialization, metaphor, metonymy, definition, and diagrams. A logic based on such rules is basically a logic of discovery, and involves a new view of the relation of logic to evolution, language, reason, method and knowledge, particularly mathematical knowledge. It also involves a new view of the relation of philosophy to knowledge. This book puts forward such new views, trying to open again many doors that the founding fathers of mathematical logic had closed historically. (shrink)

Quantum computer is considered as a generalization of Turing machine. The bits are substituted by qubits. In turn, a "qubit" is the generalization of "bit" referring to infinite sets or series. It extends the consept of calculation from finite processes and algorithms to infinite ones, impossible as to any Turing machines (such as our computers). However, the concept of quantum computer mets all paradoxes of infinity such as Gödel's incompletness theorems (1931), etc. A philosophical reflection on how quantum computer might (...) implement the idea of "infinite calculation" is the main subject. (shrink)

The book is devoted to the contemporary stage of quantum mechanics – quantum information, and especially to its philosophical interpretation and comprehension: the first one of a series monographs about the philosophy of quantum information. The second will consider Be l l ’ s inequalities, their modified variants and similar to them relations. The beginning of quantum information was in the thirties of the last century. Its speed development has started over the last two decades. The main phenomenon is entanglement. (...) The subareas are quantum computer, quantum communication (and teleportation), and quantum cryptography. The book offers the following main conceptions, theses and hypotheses: – dualistic Phythagoreanism as a new kind among the interpretations of quantum mechanics and information: arithmetical, logical, and metamathematical one; – Gödel ’ s first incompleteness theorem is an undecidable proposition, and consequently the second one,too. – a partial rehabilitation of Hilbert ’ s program for the self-foundation of mathematics; – the dual-foundation of mathematics; – Skolemian relativity between: Cantor ’s kinds of infinity, finiteness and infinity, discreteness and continuity, completeness and incompleteness, etc.; – information is a physical quantity representing the non-reducibility of a system to its parts, particularly nonaddtivity; – there exist pure relations «by itself», which cannot be reduced to predications; – energy conservation can and should be generalized; – Einstein’ s «general covariance» or «principle of relativity» can and should be generalized to cover discrete morphisms where the notion of velocity does not make sense. (shrink)

This book provides a detailed commentary on the classic monograph by Alfred Tarski, and offers a reinterpretation and retranslation of the work using the original Polish text and the English and German translations. In the original work, Tarski presents a method for constructing definitions of truth for classical, quantificational formal languages. Furthermore, using the defined notion of truth, he demonstrates that it is possible to provide intuitively adequate definitions of the semantic notions of definability and denotation and that the notion (...) in a structure can be defined in a way that is analogous to that used to define truth. Tarski’s piece is considered to be one of the major contributions to logic, semantics, and epistemology in the 20th century. However, the author points out that some mistakes were introduced into the text when it was translated into German in 1935. As the 1956 English version of the work was translated from the German text, those discrepancies were carried over in addition to new mistakes. The author has painstakingly compared the three texts, sentence-by-sentence, highlighting the inaccurate translations, offering explanations as to how they came about, and commenting on how they have influenced the content and suggesting a correct interpretation of certain passages. Furthermore, the author thoroughly examines Tarski’s article, offering interpretations and comments on the work. (shrink)

ABSTRACTIn this paper, I develop a truthmaker semantics for essence and use the semantics to investigate the explanatory role of essence.

Pogląd standardowy jest taki, że semantyka formalna stosuje się do języka naturalnego tylko w bardzo ograniczonym stopniu. Powodem tego stanu rzeczy jest nieunikniona nieokreśloność mowy potocznej polegająca m. in. na wieloznaczno- ściach, nieostrości czy tolerancji składniowej, a także obecności kontekstów intensjonalnych, co skutkuje limitacjami zasady kompozycjonalności. Ponadto konwersacja potoczna korzysta z rozmaitych reguł, np. reguł Grice’a, które wykraczają poza formalizm logiczny. W konsekwencji język naturalny nie podlega pełnej formalizacji. Z drugiej strony, jeśli L jest językiem formalnym, to metajęzyk ML, w (...) którym ten pierwszy jest opisywany, musi być częściowo nieformalny – zawiera np. terminy zwykłej matematyki, w szczególności teorii mnogości. Nawet jeśli, np. dzięki technice arytmetyzacji, ML daje się przedstawić w L, tego rodzaju reprezentacja jest tylko lokalna. W gruncie rzeczy pogląd taki można wyprowadzić z pewnych uwag Tarskiego o roli języka naturalnego. Zwykle przyjmuje się, że tzw. uniwersalność języka potocznego jest źródłem kłopotów związanych z antynomiami. Tak jest oczywiście i okoliczność ta wymaga pewnej „sanacji”, np. postaci odróżnienia stopni języka. Jednakże nawet usunięcie antynomii w taki lub inny sposób nie zmienia faktu, że to, co nieformalne ma priorytet wobec tego, co formalne. W konsekwencji także semantyka formalna ma także swoje ograniczenia w odniesieniu do języków sformalizowanych. (shrink)

Alfred Tarski frequently declared that his semantic definition of truth was inspired by Aristotle’s views. The present paper discusses this issue in the context of Marian Wesoły’s criticism of the thesis that there is an affinity between Tarski’s views and those of Aristotle. The article concludes with an inquiry into whether Aristotle’s definition of truthfulness can be identified with the correspondence theory of truth.

This paper was written with two aims in mind. A large part of it is just an exposition of Tarski's theory of truth. Philosophers do not agree on how Tarski's theory is related to their investigations. Some of them doubt whether that theory has any relevance to philosophical issues and in particular whether it can be applied in dealing with the problems of philosophy (theory) of science.In this paper I argue that Tarski's chief concern was the following question. Suppose a (...) language L belongs to the class of languages for which, in full accordance with some formal conditions set in advance, we are able to define the class of all the semantic interpretations the language may acquire. Every interpretation of L can be viewed as a certain structure to which the expressions of the language may refer. Suppose that a specific interpretation of the language L was singled out as the intended one. Suppose, moreover, that the intended interpretation can be characterized in a metalanguage L +. If the above assumptions are satisfied, can the notion of truth for L be defined in the metalanguage L + and, if it can, how can this be done? (shrink)

We discuss four distinct semantic consequence relations which are based on Strong Kleene theories of truth and which generalize the notion of classical consequence to 3-valued logics. Then we set up a uniform signed tableau calculus, which we show to be sound and complete with respect to each of the four semantic consequence relations. The signs employed by our calculus are,, and, which indicate a strict assertion, strict denial, tolerant assertion and tolerant denial respectively. Recently, Ripley applied the strict–tolerant account (...) of assertion and denial to develop a new approach to truth and alethic paradox, which we call the Strict–Tolerant Conceptionof Truth. The paper aims to contribute to our understanding of STCT in at least three ways. First, by developing the strict–tolerant calculus.Second, by developing a semantic version of the strict–tolerant calculus, which informs us about the assertoric possibilities relative to a fixed ground model. Third, by showing that the strict–tolerant calculus and assertoric semantics jointly suggest that STCT's claim that the strict and tolerant can be understood in terms of one another has to be reconsidered. (shrink)

Infinite regress arguments show up in many philosophical debates. But what actually is a regress argument? This article reviews two theories: the Paradox Theory and the Failure Theory. According to the Paradox Theory, regress arguments can be used to refute an existentially or universally quantified statement (e.g. to refute the statement that at least one discussion is settled, or the statement that discussions are settled only if there is an agreed-upon criterion to settle them). According to the Failure Theory, regress (...) arguments can be used to demonstrate that a certain solution fails to solve an existentially or universally quantified problem (e.g. to demonstrate that a certain solution fails to settle all discussions, or that it fails to settle even one discussion). In the literature, the Paradox Theory is fairly well-developed, and this article shows that the Failure Theory can be supplied with similar tools. (shrink)

This book on infinite regress arguments provides (i) an up-to-date overview of the literature on the topic, (ii) ready-to-use insights for all domains of philosophy, and (iii) two case studies to illustrate these insights in some detail. Infinite regress arguments play an important role in all domains of philosophy. There are infinite regresses of reasons, obligations, rules, and disputes, and all are supposed to have their own moral. Yet most of them are involved in controversy. Hence the question is: what (...) exactly is an infinite regress argument, and when is such an argument a good one? (shrink)

I shall elaborate more on the idea of anti-irrationalism proposed by the Polish analytic philosopher Kazimierz Ajdukiewicz, a prominent member of the Lvov-Warsaw School of philosophy and logic. In my reading, anti-irrationalism stands in opposition not only to overt irrationalism, which is made clear by the term itself, but also to all forms of rationalism that tip toward something like worship of reason. Having characterized anti-irrationalism as it originally appeared in Ajdukiewicz’s works, I shall propose a certain reformulation of it, (...) so as to capture a broader philosophical legacy in Poland, primarily, yet not exclusively the Lvov-Warsaw School. (shrink)

An investigation into what kind of knowledge is necessary for interpretation is an important research project for the two fields of the theory of meaning and epistemology, through which they are combined. By examining the two basic requirements for a theory on the interpretation of language drafted by Donald Davidson, this paper analyzes several kinds of knowledge which are necessary for interpretation. The goal is to explore the knowledge of radical interpretation and the distinctions and connections between this knowledge and (...) radical translation and Convention-T, thus revealing its characteristics and possibility to interpretation. (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)

The 2-c debate between the Greek Apologists and the pagan Graeco-Roman tradition is multifaceted and complex. Common ground can be found in the mutual commitment to reason as a reflection of the Logos: Reason, or the rationality embedded in things. Logos, in this picture, is participated in through a performance of reasoning whose reliability is presupposed in the discourses of both debating parties—contextualized here as the presupposition that the deliverances and activity of reason are reliable for uncovering reality. Presuppositions are (...) starting points and driving principles of inquiry, here designated as first principles. One presuppositional conflict between 2-c Greek Apologists, taking the apologetic works of Justin, Theophilus, Athenagoras, and the author of the Epistle to Diognetus as a sample, and the pagan tradition, taking Celsus as its 2-c culmination, is over how to justify the commitment to reason’s reliability in the above sense. My claim in this paper is twofold: first, that the pagan position is unable in principle to demonstrate the reliability of its own reasoning and that all such inquiry is circular: it is always a further question for the pagan why reasoning reveals reality. I propose that what would count as an answer to this challenge is a metaphysical ‘fit’ between human embodiment and reality. And second, that the Apologists avoid this unhappy conclusion by committing themselves to the embodiment of Reason in Jesus—that the embodied act of human reasoning reveals reality because Reason itself is embodied in the same way. The upshot is that unless the pagan abandons his position, he is trapped in a circular epistemology and cannot encounter the Christian witness on its own terms. (shrink)

Thomas Scanlon and Derek Parfit have recently defended a meta-ethical view that is supposed to satisfy realistic intuitions about morality, without the metaphysical implications that many find hard to accept in other realist views. Both philosophers argue that truths in the normative domain do not have ontological implications, while truths in the scientific domain presuppose a metaphysical reality. What distinguishes Scanlon and Parfit’s approach from other realistic meta-ethical theories is that they maintain that normative entities exist in a way that (...) is different from (some) non-normative entities. Moreover, they think that this view about the way normative entities exist helps to answer the metaphysical worries that are often thought to plague non-naturalism. To make sense of this idea, I develop their view as a version of alethic pluralism: the position that there is more than one truth property. I argue, however, that when their view is developed in this way it fails to satisfy realistic intuitions about morality. This shows that on a plausible and initially promising reading of what it takes for a normative entity to exist in a way that is different from non-normative entities, Parfit’s and Scanlon’s non-metaphysical moral realism fails to be more realistic than contemporary versions of anti-realism. (shrink)

Bayesianism and likelihoodism are two of the most important frameworks philosophers of science use to analyse scientific methodology. However, both frameworks face a serious objection: much scientific inquiry takes place in highly idealized frameworks where all the hypotheses are known to be false. Yet, both Bayesianism and likelihoodism seem to be based on the assumption that the goal of scientific inquiry is always truth rather than closeness to the truth. Here, I argue in favour of a verisimilitude framework for inductive (...) inference. In the verisimilitude framework, scientific inquiry is conceived of, in part, as a process where inference methods ought to be calibrated to appropriate measures of closeness to the truth. To illustrate the verisimilitude framework, I offer a reconstruction of parsimony evaluations of scientific theories, and I give a reconstruction and extended analysis of the use of parsimony inference in phylogenetics. By recasting phylogenetic inference in the verisimilitude framework, it becomes possible to both raise and address objections to phylogenetic methods that rely on parsimony. 1Introduction2Problems with the Law of Likelihood3Introducing Verisimilitude-Based Inference4Examples of Verisimilitude-Based Inference Procedures4.1Parsimony inference over theories4.2Parsimony inference in phylogenetics5Conclusion. (shrink)

The liar paradox is a famous and ancient paradox related to logic and philosophy. It shows it is perfectly possible to construct sentences that are correct grammatically and semantically but that cannot be true or false in the traditional sense. In this paper the authors show four approaches to interpreting paradoxes that illustrate the influence of: the levels of language, their belonging to indeterminate compatible propositions or indeterminate propositions, being based on universal antinomy and the theory of dialetheism.

In this paper, we introduce Speedith which is an interactive diagrammatic theorem prover for the well-known language of spider diagrams. Speedith provides a way to input spider diagrams, transform them via the diagrammatic inference rules, and prove diagrammatic theorems. Speedith’s inference rules are sound and complete, extending previous research by including all the classical logic connectives. In addition to being a stand-alone proof system, Speedith is also designed as a program that plugs into existing general purpose theorem provers. This allows (...) for other systems to access diagrammatic reasoning via Speedith, as well as a formal verification of diagrammatic proof steps within standard sentential proof assistants. We describe the general structure of Speedith, the diagrammatic language, the automatic mechanism that draws the diagrams when inference rules are applied on them, and how formal diagrammatic proofs are constructed. (shrink)

Alfred Tarski’s refinement of an account of truth into a formal system that turns on the acceptance of Convention-T has had a lasting impact on philosophical logic, especially work concerning truth, meaning, and other semantic notions. In a series of studies completed from the 1930s to the 1960s, Arne Næss collected and analysed intuitive responses from non-philosophers to questions concerning truth, synonymy, certainty, and probability. Among the formulations of truth studied by Næss were practical variants of expressions of the form (...) “p’ is true if and only if p’. This paper calls attention to a series of experimental results Næss overlooked in his original study. These data collectively suggest that acceptance of expressions of the form “p’ is true if and only if p’ varies according to what kind of statement p is. (shrink)

This is a companion article to the translation of ‘Zasada sprzeczności a logika symboliczna’, the appendix on symbolic logic of Jan Łukasiewicz's 1910 book O zasadzie sprzeczności u Arytotelesa (On the Principle of Contradiction in Aristotle). While the appendix closely follows Couturat's 1905 book L'algebra de la logique (The Algebra of Logic), footnotes show that Łukasiewicz was aware of the work of Peirce, Huntington and Russell (before Principia Mathematica). This appendix was influential in the development of the Polish school of (...) logic, directly inspiring Stanisław Leśniewski and Leon Chwistek and more widely by serving as a text of the new symbolic logic. This appendix was an important source of the dominant algebraic logic in Poland, but also indicates that Łukasiewicz appreciated Russell's axiomatic approach to logic. (shrink)

In a recent paper on Truth, Knowability and Neutrality Timothy Kenyon sets out to defend the coherence of a putative anti-realist truth-predicate, superassertibility, due to Wright (1992, 1999), against a number of Wright’s critics. By his own admission, the success of Kenyon’s defensive strategies turns out to hinge upon a realist conception of absolute warrant which conflicts with the anti-realist character of the original proposal, based, as it was, on a notion of defeasible warrant. Kenyon’s potential success in resisting Wright’s (...) critics brings a pyrrhic victory: either way, realism wins. Here I argue that the link between superassertibility and defeasible warrant can be restored in a way which clarifies the consistency of the pair, provided that the notion of inference to superassertibility is properly understood in logical terms. As one might expect, the requisite notion is not classical in character. As one might not expect, the notion cannot be properly construed in intuitionist terms either. Hence, I propose an alternative logical framework which, I believe, is at least formally adequate to the representation of superassertibility on the basis of defeasible warrant. The price to be paid for rejecting the ‘third way’ proposed here in favour of either of the two more traditional logical options is precisely that indicated by Kenyon’s discussion. (shrink)

The present-day traditional view of language has an essentially pedagogical background inherited from antiquity. Certain features of this heritage have passed through the centuries, reached our days and continue to be a sort of implicit postulates penetrating almost into every scientific conception of language. This causes specific divergences between the scientific view of language and its introspective view, i.e., the way it is actually conceived by an individual during ordinary communication. Studying those divergences is important for a better grasping the (...) nature of natural language and for a more adequate approaching to certain problems. (shrink)

The starting point of this paper is a claim defended most famously by Graham Priest: that given certain observed similarities between the set-theoretic and the semantic paradoxes, we should be looking for a ‘uniform solution’ to the members of both families. Despite its indisputable surface attractiveness, I argue that this claim hinges on a problematic reasoning move. This is seen most clearly, I suggest, when the claim and its underlying assumptions are examined by the lights of a novel, quite general (...) and, I contend, promising take on inter-theoretic analogy. The ensuing discussion is intended to serve as both a possible case study and a first step towards the broader aim of the paper: namely, to initiate a wider conversation on the methodology of paradox-solving on the one hand, and the use of inter-theoretic analogies on the other. (shrink)

Many take the lesson of the paradoxes to be that we ought to impose some form of logical revision. It is argued here that this kind of move should not be taken lightly.

Compared to the extensive amount of literature on various themes of W.V.O. Quine’s philosophy, his immanent concept of truth remains a relatively unexplored topic. This relative lack of research contributes to a persistent confusion on the deflationary and inflationary details of Quine’s truth. According to a popular reading, Quine’s disquotational definition of the truth predicate exhausts the content of truth, thus amounting to a deflationary view. Others promote opposing interpretations. I argue that by relying on Tarski’s semantic conception of truth, (...) Quine’s disquotational account inherits a commitment to classical correspondence intuitions. Based on this, Quine posits a firm constitution for truth as an intermediary between language and the world. From this constitution claim follows that the disquotational account proves incompatible with both the general deflationary thesis and, more specifically, the minimalist account, which deny any constitution for truth past what is given by the preferred deflationary schema. This reading is significant for refuting the widespread misrepresentations of Quine as a prominent deflationist. (shrink)

According to methodological anti-exceptionalism, logic follows a scientific methodology. There has been some discussion about which methodology logic has. Authors such as Priest, Hjortland and Williamson have argued that logic can be characterized by an abductive methodology. We choose the logical theory that behaves better under a set of epistemic criteria. In this paper, I analyze some important discussions in the philosophy of logic, and I show that they presuppose different methodologies, involving different notions of evidence and different epistemic values. (...) I argue that, rather than having a specific methodology such as abductivism, logic can be characterized by methodological pluralism. This position can also be seen as the application of scientific pluralism to the realm of logic. (shrink)

Scientific Realism (SR) has three crucial aspects: 1) the centrality of the concept of truth, 2) the idea that success is a reliable indicator of truth, and 3) the idea that the Inference to the Best Explanation is a reliable inference rule. It will be outlined how some realists try to overcome the difficulties which arise in justifying such crucial aspects relying on an adaptationist view of evolutionism, and why such attempts are inadequate. Finally, we will briefly sketch some of (...) the main difficulties the realist has to face in defending those crucial aspects, and how such difficulties are deeply related: they derive from the inability of SR to satisfyingly avoid the sceptical challenge of the criterion of truth. Indeed, SR seems not to be able to fill the so-called ‘epistemic gap’ (Sankey 2008). In fact, the epistemic gap cannot be filled in no way other than obtaining a criterion of truth, but such a criterion cannot be obtained if the epistemic gap obtains. (shrink)