The third part, Cognition, concerns abstract questions about knowledge and truth as well as more concrete questions about the usefulness and tractability of various graphic representations of information. The book would be of special interest to Research Institutes in Computer Science, Researchers in Philosophical Logic, Deontic Logic, Applied Logic, Artificial Intelligence, and Cognitive Science.

The period in the foundations of mathematics that started in 1879 with the publication of Frege's Begriffsschrift and ended in 1931 with Gödel's Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I can reasonably be called the classical period. It saw the development of three major foundational programmes: the logicism of Frege, Russell and Whitehead, the intuitionism of Brouwer, and Hilbert's formalist and proof-theoretic programme. In this period, there were also lively exchanges between the various schools culminating in (...) the famous Hilbert-Brouwer controversy in the 1920s. -/- The purpose of this anthology is to review the programmes in the foundations of mathematics from the classical period and to assess their possible relevance for contemporary philosophy of mathematics. What can we say, in retrospect, about the various foundational programmes of the classical period and the disputes that took place between them? To what extent do the classical programmes of logicism, intuitionism and formalism represent options that are still alive today? These questions are addressed in this volume by leading mathematical logicians and philosophers of mathematics. (shrink)

This book brings together philosophers, mathematicians and logicians to penetrate important problems in the philosophy and foundations of mathematics. In philosophy, one has been concerned with the opposition between constructivism and classical mathematics and the different ontological and epistemological views that are reflected in this opposition. The dominant foundational framework for current mathematics is classical logic and set theory with the axiom of choice. This framework is, however, laden with philosophical difficulties. One important alternative foundational programme that is actively pursued (...) today is predicativistic constructivism based on Martin-Löf type theory. Associated philosophical foundations are meaning theories in the tradition of Wittgenstein, Dummett, Prawitz and Martin-Löf. What is the relation between proof-theoretical semantics in the tradition of Gentzen, Prawitz, and Martin-Löf and Wittgensteinian or other accounts of meaning-as-use? What can proof-theoretical analyses tell us about the scope and limits of constructive and predicative mathematics? (shrink)

Machine generated contents note: -- Preface -- Acknowledgements -- Notes on Contributors -- PART I: COMPLEXITY IN ANIMAL MINDS -- Introduction: M.McGonigle-Chalmers -- Relational and Absolute Discrimination Learning by Squirrel Monkeys: Establishing a Common Ground with Human Cognition; B.T.Jones -- Serial List Retention by Non-Human Primates: Complexity and Cognitive Continuity; F.R.Treichler -- The Use of Spatial Structure in Working Memory: A Comparative Standpoint; C.De Lillo -- The Emergence of Linear Sequencing in Children: A Continuity Account and a Formal Model; M.McGonigle-Chalmers&I.Kusel (...) -- Sensitivity to Quantity: What Counts Across Species?; S.T.Boysen&A.M.Yocom -- PART II: COMPLEXITY IN ROBOTS -- Editorial Introduction; D.McFarland -- Towards Cognitive Robotics: Robotics, Biology and Developmental Psychology; M.Lee, U.Nehmzow&M.Rodriguez -- Structuring Intelligence: The Role of Hierarchy, Modularity and Learning in Generating Intelligent Behaviour; J.J.Bryson -- Epistemology, Access, and Computational Models; G.Luger -- Reasoning About Representations in Autonomous Systems: What P´Olya and Lakatos Have To Say; A.Bundy -- PART III: LANGUAGE, EVOLUTION AND THE COMPLEX MIND -- Editorial Introduction; K.Stenning -- How to Qualify for a Cognitive Upgrade: Executive Control, Glass Ceilings, and the Limits of Simian Success; A.Clark -- Private Codes and Public Structures; C.Allen -- The Emergence of Complex Language; W.Hinzen -- Language Evolution: Enlarging the Picture; K.Stenning&M.Van Lambalgen -- Epilogue: Reminiscences of Brendan McGonigle -- Index. (shrink)

In 1981 I published an article called Early Supposition Theory. Then as now, the magisterial work on the subject was L.M. de Rijk’s Logica Modernorum and then as now any discussion of the topic would have to rely to a great extent on the texts published there. This means that many of the problems that existed then still remain, but a couple of important new studies and several new texts have been published in the meantime, so it may be time (...) to try to take stock of the situation. I will first look at the origin of the term suppositio and then at the chronology of our source texts. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Abaelards Logik by Wolfgang LenzenSten EbbesenWolfgang Lenzen. Abaelards Logik. Paderborn: Brill | mentis, 2021. Pp. 206. Hardback, €59.00.According to its author, this book aims at reconstructing key parts of Abelard's logic while denying him a role as a hero of connexive logic or more generally as one of history's greatest logicians. At the end of the preface, we are told that "Abaelard hat die Logik seiner Zeit nicht (...) revolutioniert; er hat keine Kalküle konstruiert; und er hat auch nicht die Logik seiner Zeit auf ein höheres Niveau gehoben" (xiv).The book is divided into twenty-three chapters with titles such as "'Destruierende' versus 'separierende' Negation," "Vollkommene und unvollkommne Folgerungen," and "'Leere' Begriffe." As the titles show, it ranges over a large field. The results of Lenzen's analyses of Abelard's argumentation are presented in modern logical notation. There are many fine analyses, and despite Lenzen's refusal to see Abelard as a genius, he, too, seems to have been quite impressed by the old logician. However, at the end of the day, I am not sure that I have become any wiser about Abelard's contribution to the history of logic.Lenzen is a newcomer to the study of twelfth-century logic, and the book is marked by this in several ways. Thus, he informs the reader that "Spätestens seit Prantls Publikation der 'Geschichte der Logik im Abendlande' steht fest, dass Abaelards Traktat 'De Sillogismis Ypoteticis' sich stark an das Werk 'De syllogismo hypothetico' von Boethius (470–524) anlehnt" (165). This is quite true, but anything else would have been very remarkable, so the reference to Prantl serves no purpose.Unsurprisingly, the main source texts used are Abelard's Dialectica and his Glosae super Peri hermeneias, a part of the series of commentaries on the Ars vetus that go under the common name of Logica ingredientibus. Lenzen displays a cavalier attitude to philology. He quotes the Dialectica from De Rijk's second edition (1970), but in the bibliography he mentions that there are two editions without stating explicitly which one he quotes. In the case of the Glosae, he uses the obsolete editio princeps by Bernhard Geyer from 1927, and he does not even mention its replacement, Klaus Jacobi and Christian Strub's much superior 2010 edition in the series Corpus Christianorum, Continuatio Mediaevalis. This is inexplicable, for in his preface Lenzen describes his book as the child of a research project he began several years after the publication of the new edition. Now, fortunately, the use of Geyer does not have disastrous consequences for Lenzen's interpretation of Abelard, but had he used Jacobi and Strub's edition, he would not have had to propose a textual emendation in one place (88n17), nor would he have needed to quote, in another place, a Latin text (which he does not translate) with a nonsensical significantem instead of figurative (94n1o).Lenzen sometimes proposes textual emendations, but not always in a perspicuous way, and they are not all felicitous. For example, a quotation of L. M. de Rijk's edition of Introductiones Montane Minores in Logica Modernorum (LM) II.2 (1967) contains the phrase aliquod opposit[or]um (127n2). An unsuspecting reader would think this means De Rijk had conjecturally emended oppositorum into oppositum, for this is what opposit[or]um would mean in LM II.2. In fact, De Rijk just prints oppositum, so Lenzen's opposit[or]um must mean that he wants to correct De Rijk's text by inserting 'or,' but he forgets to tell us that he does not [End Page 520] faithfully reproduce the text quoted and that his square brackets mean something different from what they do in De Rijk's edition. This issue aside, his conjecture is superfluous, as proven by a parallel passage in LM II.2: 118. Similarly, he quotes Abelard as saying "alterum istorum [est]: vel nox vel dies" (152). The "[est]" is Lenzen's own, again superfluous, contribution to the text. By contrast, elsewhere he proposes to insert a non at LM II.2: 64.2. This time, he explains what he is doing, and I think his conjecture... (shrink)

This is a reproduction of a book published before 1923. This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections (...) in the preservation process, and hope you enjoy this valuable book. (shrink)

A series of four lectures given in Athens during the author's tenure of a Fulbright Fellowship. The intention is to introduce Athenian public to three classical American philosophers, as well as to contemporary trends. The author sees interesting parallels between Emerson and the Byzantine Mystics and predicts that the interest of Americans in Ancient Greek philosophy will lead to closer studies of Byzantine philosophy. The chief defect of the book is its willingness to sacrifice content for coverage. Presentation is cursory (...) and often by terms which are misleading in themselves and particularly unfortunate when rendered into modern Greek.--. (shrink)

A series of four lectures given in Athens during the author's tenure of a Fulbright Fellowship. The intention is to introduce Athenian public to three classical American philosophers, as well as to contemporary trends. The author sees interesting parallels between Emerson and the Byzantine Mystics and predicts that the interest of Americans in Ancient Greek philosophy will lead to closer studies of Byzantine philosophy. The chief defect of the book is its willingness to sacrifice content for coverage. Presentation is cursory (...) and often by terms which are misleading in themselves and particularly unfortunate when rendered into modern Greek.--. (shrink)

pt. 1. Introduction and indices -- pt. 2. Catalogue.

This study described the relationships between academic class and student moral sensitivity and reasoning and between curriculum design components for ethics education and student moral sensitivity and reasoning. The data were collected from freshman (n = 506) and senior students (n = 440) in eight baccalaureate nursing programs in South Korea by survey; the survey consisted of the Korean Moral Sensitivity Questionnaire and the Korean Defining Issues Test. The results showed that moral sensitivity scores in patient-oriented care and conflict were (...) higher in senior students than in freshman students. Furthermore, more hours of ethics content were associated with higher principled thinking scores of senior students. Nursing education in South Korea may have an impact on developing student moral sensitivity. Planned ethics content in nursing curricula is necessary to improve moral sensitivity and moral reasoning of students. (shrink)

When governments introduce controversial policies or face a risk of policy failure, officeholders try to avoid blame and justify their decisions by using various legitimation strategies. This paper focuses on the ways in which legitimations are expressed in government social media communication, using the Twitter posts of the British government’s Brexit department as an example. We show how governments may seek legitimacy by appealing to (1) the personal authority of individual policymakers, (2) the collective authority of (political) organisations, (3) the (...) impersonal authority of rules or documents, (4) the goals or effects of government policy, (5) ‘the will of the people’, and (6) time pressure. The results suggest that official legitimations in social media posts tend to rely more on references to authority and shared values rather than presentation of evidence and sound arguments. (shrink)

Artificiell intelligens (AI) är ett ungt forskningsområde där många av de grundläggande problemen förefaller att vara av filosofisk art.1 Ämnet har sina filosofiska rötter dels i traditionen från Leibniz, Frege, Russell och Hilbert, som strävar efter att formalisera principerna för exakt tänkande, dels i den klassiska mekanismen: idén att människan är en maskin och att det mänskliga tänkandet är en mekanisk process. Som en första approximation kan vi säga att AI är det vetenskapliga studiet av hur man konstruerar och bygger (...) maskiner (datorer) som är intelligenta (eller uppvisar intelligent beteende). Det är lätt att se att denna forskning aktualiserar frågor av filosofiskt slag. Hit hör problem som rör tänkandets natur samt förhållandet mellan medvetandet och kroppen. Inom AI ses ofta datorns arbetssätt som en modell för människans kognitiva processer och man föreställer sig kanske att hjärnan är ett slags dator. Eftersom hjärnan liknas vid en dator och en dator tänks arbeta rent mekaniskt i enlighet med ett givet program (en given algoritm), så föreställer man sig att samma sak bör gälla för hjärnan. Analogin hjärna-dator leder till föreställningen att tänkande inte är något annat än en dators mekaniska manipulerande av symboler i enlighet med givna formella regler. Denna uppfattning om tänkandets natur förefaller samtidigt problematisk: mekanisk manipulation av symboler förutsätter ingen förståelse av symbolernas innebörd; genuint tänkande, å andra sidan, tycks förutsätta sådan förståelse. Ibland verkar också analogin hjärna-dator i den motsatta riktningen. Eftersom hjärnan liknas vid en dator och hjärnan har en mental dimension, så föreställer man sig kanske att samma sak måste gälla för vissa datorer: synen på hjärnan som en dator leder till tanken att det borde vara möjligt att konstruera datorer som bokstavligen tänker, känner och förnimmer. Man föreställer sig kanske att man skall kunna konstruera ett artificiellt medvetande. Vi är alla förtrogna med datorer som (i en viss mening) kan lösa förelagda uppgifter på ett intelligent sätt, men följer det därav att dessa datorer kan tänka? Inte tänker väl en schackspelande dator på schack? Hur intelligent dagens datorer än beter sig, så verkar det ändå inte rimligt att säga att de har tankar, känslor eller upplevelser. Men kan man utesluta att vi någon gång i framtiden kommer att kunna konstruera datorer som verkligen förstår, är medvetna, och tänker? Dessa frågor rymmer många begreppsliga oklarheter. Vad är intelligens, tänkande, förståelse, medvetande? Hur förhåller sig intelligens och tänkande till medvetandets fenomenella sida: upplevelser och känslor? Om vad slags ting är det meningsfullt att säga att de har intelligens, medvetande, mentala tillstånd, etc.? Är det meningsfullt att säga detta om en hjärna, en maskin, en dator? Vad menas med en maskin (dator)? Hur kan vi veta (avgöra) om ett ting har intelligens, tankar, känslor eller upplevelser? I denna uppsats avser vi att närmare belysa sambandet mellan filosofi och AI samt kritiskt granska några av AI-forskningens förutsättningar inom filosofi och logik. (shrink)

Is there any argument for scepticism? The epistemic problem of the possibility of error. Arguments for scepticism rest on the assumption that knowledge claims are fallible. For this reason the concept of knowledge appears to be questionable. Since it is necessary to distinguish doubts from possible doubts, the arguments for scepticism appear to be unconvincing. If we take it into account that we know something that is immune to doubt, we should draw the conclusion that, contrary to scepticism, knowledge claims (...) have to be compatible with being fallible. Thus any knowledge claim is capable of being doubted. (shrink)

In the late summer of 1998, the authors, a cognitive scientist and a logician, started talking about the relevance of modern mathematical logic to the study of human reasoning, and we have been talking ever since. This book is an interim report of that conversation. It argues that results such as those on the Wason selection task, purportedly showing the irrelevance of formal logic to actual human reasoning, have been widely misinterpreted, mainly because the picture of logic current in psychology (...) and cognitive science is completely mistaken. We aim to give the reader a more accurate picture of mathematical logic and, in doing so, hope to show that logic, properly conceived, is still a very helpful tool in cognitive science. The main thrust of the book is therefore constructive. We give a number of examples in which logical theorizing helps in understanding and modeling observed behavior in reasoning tasks, deviations of that behavior in a psychiatric disorder (autism), and even the roots of that behavior in the evolution of the brain. (shrink)

We discuss external and internal graphical and linguistic representational systems. We argue that a cognitive theory of peoples' reasoning performance must account for (a) the logical equivalence of inferences expressed in graphical and linguistic form; and (b) the implementational differences that affect facility of inference. Our theory proposes that graphical representations limit abstraction and thereby aid processibility. We discuss the ideas of specificity and abstraction, and their cognitive relevance. Empirical support comes from tasks (i) involving and (ii) not involving the (...) manipulation of external graphics. For (i), we take Euler's Circles, provide a novel computational reconstruction, show how it captures abstractions, and contrast it with earlier construals, and with Mental Models' representations. We demonstrate equivalence of the graphical Euler system, and the non-graphical Mental Models system. For (ii), we discuss text comprehension, and the mental performance of syllogisms. By positing an internal system with the same specificity as Euler's Circles we cover the Mental Models data, and generate new empirical predictions. Finally, we consider how the architecture of working memory explains why such specific representations are relatively easy to store. (shrink)

The objective of our article is to show how “quality of evidence” and “imprecision,” as they are defined in Grading of Recommendations Assessment, Development, and Evaluation articles, may lead to confusion. We focus only on the context of systematic reviews.

In medical research, it is not unusual that risks are ruled out without any specification the exact risk that was ruled out. This makes it difficult to balance expected health benefits and risk of harm when choosing between alternative treatment options. International guidelines for reporting medical research results are sufficiently specific when it comes to establishing health benefits. However, there is a lack of standards for reporting on ruling out risks. We argue that transparency is needed, as in the case (...) of non-inferiority trials. The Consolidated Standards of Reporting Trials and the Preferred Reporting Items for Systematic Reviews and Meta-Analyses statements should be revised accordingly. (shrink)

We discuss external and internal graphical and linguistic representational systems. We argue that a cognitive theory of peoples' reasoning performance must account for (a) the logical equivalence of inferences expressed in graphical and linguistic form, and (b) the implementational differences that affect facility of inference. Our theory proposes that graphical representation limit abstraction and thereby aid “processibility”. We discuss the ideas of specificity and abstraction, and their cognitive relevance. Empirical support both comes from tasks which involve the manipulation of external (...) graphics and tasks that do not. For the former, we take Euler's (1772) circles, provide a novel computational reconstruction, show how it captures abstractions, and contrast it with earlier construals and with Johnson‐Laird's (1983) mental models representations. We demonstrate equivalence of the graphical Euler system, and the nongraphical mental models system. For tasks not involving manipulation of external graphics, we discuss text comprehension, and the mental performance of syllogisms. By positing an internal system with the same specificity as Euler's circles, we cover the mental models data, and generate new empirical predictions. Finally, we consider how the architecture of working memory explains why such specific representations are relatively easy to store. (shrink)

Theoria, Volume 88, Issue 3, Page 494-528, June 2022.

In earlier papers (Lindström & Rabinowicz, 1989. 1990), we proposed a generalization of the AGM approach to belief revision. Our proposal was to view belief revision as a relation rather thanas a function on theories (or belief sets). The idea was to allow for there being several equally reasonable revisions of a theory with a given proposition. In the present paper, we show that the relational approach is the natural result of generalizing in a certain way an approach to belief (...) revision due to Adam Grove. In his (1988) paper, Grove presents two closely related modelings of functional belief revision, one in terms of a family of "spheres" around the agent's theory G and the other in terms of an epistemic entrenchment ordering of propositions. The "sphere"-terminology is natural when one looks upon theories and propositions as being represented by sets of possible worlds. Grove's spheres may be thought of as possible "fallback" theories relative to the agent's original theory: theories that he may reach by deleting propositions that are not "sufficiently" entrenched (according to standards of sufficient entrenchment of varying stringency). To put it differently, fallbacks are theories that are closed upwards under entrenchment The entrenchment ordering can be recovered from the family of fallbacks by the definition: A is at least as entrenched as B iff A belongs to every fallback to which B belongs. To revise a theory T with a proposition A, we go to the smallest sphere that contain A-worlds and intersect it with A. The relational notion of belief revision that we are interested in, results from weakening epistemic entrenchment by not assuming it to be connected. I.e., we want to allow that some propositions may be incomparable with respect to epistemic entrenchment. As a result, the family of fallbacks around a given theory will no longer have to be nested. This change opens up the possibility for several different ways of revising a theory with a given proposition. (shrink)

The theories of belief change developed within the AGM-tradition are not logics in the proper sense, but rather informal axiomatic theories of belief change. Instead of characterizing the models of belief and belief change in a formalized object language, the AGM-approach uses a natural language — ordinary mathematical English — to characterize the mathematical structures that are under study. Recently, however, various authors such as Johan van Benthem and Maarten de Rijke have suggested representing doxastic change within a formal logical (...) language: a dynamic modal logic. Inspired by these suggestions Krister Segerberg has developed a very general logical framework for reasoning about doxastic change: dynamic doxastic logic (DDL). This framework may be seen as an extension of standard Hintikka-style doxastic logic with dynamic operators representing various kinds of transformations of the agent's doxastic state. Basic DDL describes an agent that has opinions about the external world and an ability to change these opinions in the light of new information. Such an agent is non-introspective in the sense that he lacks opinions about his own belief states. Here we are going to discuss various possibilities for developing a dynamic doxastic logic for introspective agents: full DDL or DDL unlimited. The project of constructing such a logic is faced with difficulties due to the fact that the agent’s own doxastic state now becomes a part of the reality that he is trying to explore: when an introspective agent learns more about the world, then the reality he holds beliefs about undergoes a change. But then his introspective (higher-order) beliefs have to be adjusted accordingly. In the paper we shall consider various ways of solving this problem. (shrink)

Modal logic is one of philosophy’s many children. As a mature adult it has moved out of the parental home and is nowadays straying far from its parent. But the ties are still there: philosophy is important to modal logic, modal logic is important for philosophy. Or, at least, this is a thesis we try to defend in this chapter. Limitations of space have ruled out any attempt at writing a survey of all the work going on in our field—a (...) book would be needed for that. Instead, we have tried to select material that is of interest in its own right or exemplifies noteworthy features in interesting ways. Here are some themes that have guided us throughout the writing: • The back-and-forth between philosophy and modal logic. There has been a good deal of give-and-take in the past. Carnap tried to use his modal logic to throw light on old philosophical questions, thereby inspiring others to continue his work and still others to criticise it. He certainly provoked Quine, who in his turn provided—and continues to provide—a healthy challenge to modal logicians. And Kripke’s and David Lewis’s philosophies are connected, in interesting ways, with their modal logic. Analytic philosophy would have been a lot different without modal logic! • The interpretation problem. The problem of providing a certain modal logic with an intuitive interpretation should not be conflated with the problem of providing a formal system with a model-theoretic semantics. An intuitively appealing model-theoretic semantics may be an important step towards solving the interpretation problem, but only a step. One may compare this situation with that in probability theory, where definitions of concepts like ‘outcome space’ and ‘random variable’ are orthogonal to questions about “interpretations” of the concept of probability. • The value of formalisation. Modal logic sets standards of precision, which are a challenge to—and sometimes a model for—philosophy. Classical philosophical questions can be sharpened and seen from a new perspective when formulated in a framework of modal logic. On the other hand, representing old questions in a formal garb has its dangers, such as simplification and distortion. • Why modal logic rather than classical (first or higher order) logic? The idioms of modal logic—today there are many!—seem better to correspond to human ways of thinking than ordinary extensional logic. (Cf. Chomsky’s conjecture that the NP + VP pattern is wired into the human brain.) In his An Essay in Modal Logic (1951) von Wright distinguished between four kinds of modalities: alethic (modes of truth: necessity, possibility and impossibility), epistemic (modes of being known: known to be true, known to be false, undecided), deontic (modes of obligation: obligatory, permitted, forbidden) and existential (modes of existence: universality, existence, emptiness). The existential modalities are not usually counted as modalities, but the other three categories are exemplified in three sections into which this chapter is divided. Section 1 is devoted to alethic modal logic and reviews some main themes at the heart of philosophical modal logic. Sections 2 and 3 deal with topics in epistemic logic and deontic logic, respectively, and are meant to illustrate two different uses that modal logic or indeed any logic can have: it may be applied to already existing (non-logical) theory, or it can be used to develop new theory. (shrink)