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)

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)

Epistemic conditionals have often been thought to satisfy the Ramsey test : If A, then B is acceptable in a belief state G if and only if B should be accepted upon revising G with A. But as Peter Gärdenfors has shown, RT conflicts with the intuitively plausible condition of Preservation on belief revision. We investigate what happens if RT is retained while Preservation is weakened, or vice versa. We also generalize Gärdenfors' approach by treating belief revision as a relation (...) rather than as a function.In our semantic approach, the same relation is used to model belief revision and to give truth-conditions for conditionals. The approach validates a weak version of the Ramsey Test — essentially, a restriction of RT to maximally consistent belief states. (shrink)

According to the ‘fact-plus-value’ model of pathology propounded by K. W. M. Fulford, ‘disease’ is a value term that ought to reflect a ‘balance of values’ stemming from patients and doctors and other ‘stakeholders’ in medical nosology. In the present article I take issue with his linguistic-analytical arguments for why pathological status must be relative to such a kind of medico-ethical normativity. Fulford is right to point out that Boorse and other naturalists are compelled to utilize evaluative terminology when they (...) characterize the nature of diseases and biological dysfunctions. But the relevant ‘biofunctional judgements’ are no less factual and empirical for that. While it is indeed evaluative to say that biological dysfunctions involve failures to execute naturally selected functions, such judgments are not bound to entail anything about what is good or bad for us, and what should be treated or not. In the last part of the paper I ruminate briefly on the relationship between ‘biological evaluationism’, on my construal, and descriptions of ‘causal biology’. As I note in my conclusion, a strict bioevaluative concept of disease can be valid for every species on earth, and thus be of particular usefulness in general biological contexts. (shrink)

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

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

Gerhard von Rad was both a professor and a preacher. He understood and taught the Old Testament as a text to be preached and closely connected with the New Testament to form a theological basis for Christian faith.

I develop a notion of nonlinear stochastic integrals for hyperfinite Lévy processes and use it to find exact formulas for expressions which are intuitively of the form $\sum_{s=0}^t\phi(\omega,dl_{s},s)$ and $\prod_{s=0}^t\psi(\omega,dl_{s},s)$ , where l is a Lévy process. These formulas are then applied to geometric Lévy processes, infinitesimal transformations of hyperfinite Lévy processes, and to minimal martingale measures. Some of the central concepts and results are closely related to those found in S. Cohen’s work on stochastic calculus for processes with jumps (...) on manifolds, and the paper may be regarded as a reworking of his ideas in a different setting and with totally different techniques. (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)

The Greek under the Latin and the Latin under the Greek -- Greek-Latin philosophical interaction -- The odyssey of semantics from the Stoa to Buridan -- The Chimera's diary -- Where were the stoics in the late Middle Ages? -- Theories of language in the Hellenistic age and in the twelfth and thirteenth centuries -- Late-ancient ancestors of medieval philosophical commentaries -- Boethius on Aristotle -- Boethius on the metaphysics of words -- Western and Byzantine approaches to logic -- Greek (...) and Latin medieval logic -- Philoponus, Alexander, and the origins of medieval logic -- Analyzing syllogisms or anonymus Aurelianensis III, the (presumably) earliest extant Latin commentary on the prior analytics, and its Greek model -- Fragments of Alexander's commentaries on Analytica posteriora and Sophistici elenchi. (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)

Interpretation is the process whereby a hearer reasons to an interpretation of a speaker's discourse. The hearer normally adopts a credulous attitude to the discourse, at least for the purposes of interpreting it. That is to say the hearer tries to accommodate the truth of all the speaker's utterances in deriving an intended model. We present a nonmonotonic logical model of this process which defines unique minimal preferred models and efficiently simulates a kind of closed-world reasoning of particular interest for (...) human cognition. Byrne's “suppression” data (Byrne, 1989) are used to illustrate how variants on this logic can capture and motivate subtly different interpretative stances which different subjects adopt, thus indicating where more fine-grained empirical data are required to understand what subjects are doing in this task. We then show that this logical competence model can be implemented in spreading activation network models. A one pass process interprets the textual input by constructing a network which then computes minimal preferred models for (3-valued) valuations of the set of propositions of the text. The neural implementation distinguishes easy forward reasoning from more complex backward reasoning in a way that may be useful in explaining directionality in human reasoning. (shrink)

Interpretation is the process whereby a hearer reasons to an interpretation of a speaker's discourse. The hearer normally adopts a credulous attitude to the discourse, at least for the purposes of interpreting it. That is to say the hearer tries to accommodate the truth of all the speaker's utterances in deriving an intended model. We present a nonmonotonic logical model of this process which defines unique minimal preferred models and efficiently simulates a kind of closed‐world reasoning of particular interest for (...) human cognition. Byrne's “suppression” data (Byrne, 1989) are used to illustrate how variants on this logic can capture and motivate subtly different interpretative stances which different subjects adopt, thus indicating where more fine‐grained empirical data are required to understand what subjects are doing in this task. We then show that this logical competence model can be implemented in spreading activation network models. A one pass process interprets the textual input by constructing a network which then computes minimal preferred models for (3‐valued) valuations of the set of propositions of the text. The neural implementation distinguishes easy forward reasoning from more complex backward reasoning in a way that may be useful in explaining directionality in human reasoning. (shrink)

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)

As emphasized by Alonzo Church and David Kaplan (Church 1974, Kaplan 1975), the philosophies of language of Frege and Russell incorporate quite different methods of semantic analysis with different basic concepts and different ontologies. Accordingly we distinguish between a Fregean and a Russellian tradition in intensional semantics. The purpose of this paper is to pursue the Russellian alternative and to provide a language of intensional logic with a model-theoretic semantics. We also discuss the so-called Russell-Myhill paradox that threatens simple Russellian (...) type theory if propositions satisfies very strict principles of individuation. One way of avoiding the paradox is to adopt a ramified rather than a simple theory of types. (shrink)

Several of Beller, Bender, and Medin’s (2012) issues are as relevant within cognitive science as between it and anthropology. Knowledge-rich human mental processes impose hermeneutic tasks, both on subjects and researchers. Psychology's current philosophy of science is ill suited to analyzing these: Its demand for ‘‘stimulus control’’ needs to give way to ‘‘negotiation of mutual interpretation.’’ Cognitive science has ways to address these issues, as does anthropology. An example from my own work is about how defeasible logics are mathematical models (...) of some aspects of simple hermeneutic processes. They explain processing relative to databases of knowledge and belief—that is, content. A specific example is syllogistic reasoning, which raises issues of experimenters’ interpretations of subjects’ reasoning. Science, especially since the advent of understandings of computation, does not have to be reductive. How does this approach transfer onto anthropological topics? Recent cognitive science approaches to anthropological topics have taken a reductive stance in terms of modules. We end with some speculations about a different cognitive approach to, for example, religion. (shrink)

Modern logic provides accounts of both interpretation and derivation which work together to provide abstract frameworks for modelling the sensitivity of human reasoning to task, context and content. Cognitive theories have underplayed the importance of interpretative processes. We illustrate, using Wason's [Q. J. Exp. Psychol. 20 (1968) 273] selection task, how better empirical cognitive investigations and theories can be built directly on logical accounts when this imbalance is redressed. Subjects quite reasonably experience great difficulty in assigning logical form to descriptively (...) interpreted rules in this task and materials, though not to deontically interpreted ones. The main empirical contrasts in reasoning performance are precisely between these interpretations, so better semantic theory can explain the main empirical effects. However, a more adequate notion of logical form than that typically employed in the psychology of reasoning is required, and we offer a richer alternative. Prima facie evidence that subjects do in fact experience the predicted difficulties in interpreting descriptive materials is provided by analyses of socratic tutoring dialogues. Experimental verification that these difficulties do in fact affect subjects' performance in the standard task is provided by six novel experimental conditions each designed to test different aspects of the semantic predictions. The results bear out the predictions. The semantic distinction between descriptive and deontic rules interacts with the task specifics to provide powerful generalisations about reasoning which surface in detailed explanations of many disparate observations. We conclude that semantic analyses have more direct benefits for psychological investigation than is usually credited, and conversely, that the extraordinary pragmatic circumstances of psychological experiments yield much thought provoking data for semantic analysis. © 2004 Cognitive Science Society, Inc. All rights reserved.Subjects quite reasonably experience great difficulty in assigning logical form to descriptively interpreted rules in this task and materials, though not to deontically interpreted ones. The main empirical contracts in reasoning performance are precisely between these interpretatins, so better semantic theory can explain the main empirical effects. Howevers, a more adequate nation of logical from than that typically employed in the psychology of reasoning in required, and we offer a richer alternative.Prima facie evidence that subjects do in fact experience the predicted difficulties in interpreting descriptive materials is provided by analyses of socratic tutoring dialogues. Experimental verification that these difficulties do in fact affect subjects' performance in the standard task is provided by six novel experimental conditions each designed to test different aspects of the semantic predications.The resluts bear out the predictions. The semantic distinction between descriptive and deontic rules interacts with the task specifics to provide powerful generalisations about reasoning which surface in detailed explanations of many disparate observations. We conclude that semantic analyses have more direct benefits for psychological investigation than is usually credited, and conversely, that the extraordinary pragmatic circumstances of psychological experiments yield much thought provoking data for semantic analysis. (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)

Si les penseurs anciens s’accordaient pour dire que les mots reçoivent leur signification d’une institution, leurs vues divergeaient, en revanche, quant à la question de savoir jusqu’à quel point leurs instituteurs étaient libres de choisir tels ou tels sons pour désigner telle ou telle chose. Il ne fait pas de doute que, pour les Stoïciens, ceux qui ont imposés les noms visaient d’ordinaire à créer des expressions linguistiques capables d’évoquer d’une certaine manière les choses signifiées. L’article rejette cependant l’idée que (...) les Stoïciens présupposaient une situation initiale où l’ensemble des termes d’une langue donnée étaient parfaitement adaptés à leur fonction, les aberrations ou anomalies du langage ordinaire étant liées à une dégradation progressive de conditions de départ idéales. Ils pensaient, au contraire, que l’imposition des mots est un processus continu, que les locuteurs ordinaires entretiennent pour des raisons essentiellement utilitaires ; processus qui n’est que partiellement réglé par leur rationalité commune. Ce qui explique pourquoi le Grec qu’ils se trouvaient parler présentait à leurs yeux un défaut de systématicité que les Stoïciens se sont dès lors appliqués à corriger par le biais d’une nomenclature qui se voulait rigoureuse et cohérente. (shrink)

Critics of attention-deficit/hyperactivity disorder (ADHD) have repeatedly argued that there is no proof for the condition being symptomatic of an organic brain disease and that the current "ADHD epidemic" is an expression of medicalization. To this, the supporters of ADHD can retort that the condition is only defined as a mental disorder and not a physical disease. As such, ADHD needs only be a harmful mental dysfunction, which, like other genuine disorders, can have a complex and obscure etiology. This article (...) argues that such a line of argument fails to save ADHD as a valid diagnostic category. Given the general diagnostic logic of the DSM-IV and how ADHD has been defined in terms of everyday (male) child behaviors, there are compelling grounds to disbelieve that ADHD can be a true medical syndrome united by some type of harmful dysfunction. Indeed, strong logical and empirical reasons will be adduced to show that people may qualify for ADHD diagnosis without suffering from any type of underlying pathology. (shrink)

Learning with different kinds of ICT-based tools is an important issue in today's society. In this article we focus on how design of technology rich environments based on state of the art learning principles can give us new insights about how learning occur, and how we can develop new types of learning environments. Medical education constitutes the subject domain. There has been a considerable effort to develop 3D technologies in this field, and the article provides a careful review of how (...) these technologies are applied. There is, however, a substantial gap between these advances and the use of technologies in medical education. Related work proposes individualistic assumptions or metaphors that do not focus explicitly on learning and technology mediation. Based on theoretical analysis of previous literature in the field we argue that there is a need for a new unit of analysis that includes the relationship between individual and collective activity and the role of technology herein. The socio-cultural and especially activity theory is taken as the perspective which gives the possibility to develop the argumentation about the unit of analysis. The unit of analysis also has implications for design of 3D environments. The design principles are elaborated upon and examples are given in relation to an application called Matador (Medical Advanced Training in an Artificial Distributed Environment). Matador is aimed at developing a simulation environment for training in emergency medicine. (shrink)