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

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 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)

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)

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)

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)

Festschrift for Michiel van Lambalgen on the occasion of his retirement as professor of logic and cognitive science at the University of Amsterdam.

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)

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)

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 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)

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)

v. 1. The Greek tradition -- v. 2. Greek texts and fragments of the Latin translation of "Alexander's" commentary -- v. 3. Appendices, Danish summary, indices.

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)

We advance a theoretical framework which combines recent insights of research in logic, psychology, and formal semantics, on the nature of diagrammatic representation and reasoning. In particular, we wish to explain the varied efficacy of reasoning and representing with diagrams. In general we consider diagrammatic representations to be restricted in expressive power, and we wish to explain efficacy of reasoning with diagrams via the semantical and computational properties of such restricted `languages'. Connecting these foundational insights (from semantics and complexity theory) (...) to the psychology of reasoning with diagrams requires us to develop the notion of the {\it availability} (to an agent) of {\it constraints} operating within representation systems, as a consequence of their direct semantic interpretation. Thus we offer a number of fundamental definitions as well as a research programme which aligns current efforts in the logical and psychological analysis of diagrammatic representation systems. (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 this paper we distinguish between various kinds of doxastic theories. One distinction is between informal and formal doxastic theories. AGM-type theories of belief change are of the former kind, while Hintikka’s logic of knowledge and belief is of the latter. Then we distinguish between static theories that study the unchanging beliefs of a certain agent and dynamic theories that investigate not only the constraints that can reasonably be imposed on the doxastic states of a rational agent but also rationality (...) constraints on the changes of doxastic state that may occur in such agents. An additional distinction is that between non-introspective theories and introspective ones. Non-introspective theories investigate agents that have opinions about the external world but no higher-order opinions about their own doxasticnstates. Standard AGM-type theories as well as the currently existing versions of Segerberg’s dynamic doxastic logic (DDL) are non-introspective. Hintikka-style doxastic logic is of course introspective but it is a static theory. Thus, the challenge remains to devise doxastic theories that are both dynamic and introspective. We outline the semantics for truly introspective dynamic doxastic logic, i.e., a dynamic doxastic logic that allows us to describe agents who have both the ability to form higher-order beliefs and to reflect upon and change their minds about their own (higher-order) beliefs. This extension of DDL demands that we give up the Preservation condition on revision. We make some suggestions as to how such a non-preservative revision operation can be constructed. We also consider extending DDL with conditionals satisfying the Ramsey test and show that Gärdenfors’ well-known impossibility result applies to such a framework. Also in this case, Preservation has to be given up. (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)

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)

. In what follows, I review the modern theory of the origin of the universe as astronomers and physicists are coming to understand it during the last decades of the twentieth century. An unexpected discovery of this study is that the story of “cosmogenesis” cannot be completely told unless we understand the fundamental nature of matter, space, and time. In the context of modern cosmology space has become not only the bedrock of our physical existence, it may yield a fuller (...) understanding of the universe itself. (shrink)

Executive function has become an important concept in explanations of psychiatric disorders, but we currently lack comprehensive models of normal executive function and of its malfunctions. Here we illustrate how defeasible logical analysis can aid progress in this area. We illustrate using autism and attention deficit hyperactivity disorder (ADHD) as example disorders, and show how logical analysis reveals commonalities between linguistic and non-linguistic behaviours within each disorder, and how contrasting sub-components of executive function are involved across disorders. This analysis reveals (...) how logical analysis is as applicable to fast, automatic and unconscious reasoning as it is to slow deliberate cogitation. (shrink)

The catalogue contains lists of questions found in Latin commentaries on Aristotle’s De sensu, De memoria and De somno et vigilia composed between 1260 and 1320, approximately, plus a selection of commentaries by notable later medieval authors. Most of the texts included are inedita. The catalogue provides information about the title of each question and its location in the relevant manuscript.

Executive function has become an important concept in explanations of psychiatric disorders, but we currently lack comprehensive models of normal executive function and of its malfunctions. Here we illustrate how defeasible logical analysis can aid progress in this area. We illustrate using autism and attention deficit hyperactivity disorder (ADHD) as example disorders, and show how logical analysis reveals commonalities between linguistic and non-linguistic behaviours within each disorder, and how contrasting sub-components of executive function are involved across disorders. This analysis reveals (...) how logical analysis is as applicable to fast, automatic and unconscious reasoning as it is to slow deliberate cogitation. (shrink)

This reply to Oaksford and Chater’s ’s critical discussion of our use of logic programming to model and predict patterns of conditional reasoning will frame the dispute in terms of the semantics of the conditional. We begin by outlining some common features of LP and probabilistic conditionals in knowledge-rich reasoning over long-term memory knowledge bases. For both, context determines causal strength; there are inferences from the absence of certain evidence; and both have analogues of the Ramsey test. Some current work (...) shows how a combination of counting defeaters and statistics from network monitoring can provide the information for graded responses from LP reasoning. With this much introduction, we then respond to O&C’s specific criticisms and misunderstandings. (shrink)