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5214Human reasoning and cognitive scienceMIT Press. 2008.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 psycholo…Read more
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3051A formalization of kant’s transcendental logicReview of Symbolic Logic 4 (2): 254-289. 2011.Although Kant (1998) envisaged a prominent role for logic in the argumentative structure of his Critique of Pure Reason, logicians and philosophers have generally judged Kantgeneralformaltranscendental logics is a logic in the strict formal sense, albeit with a semantics and a definition of validity that are vastly more complex than that of first-order logic. The main technical application of the formalism developed here is a formal proof that Kants logic is after all a distinguished subsystem o…Read more
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753In this article we provide a mathematical model of Kant?s temporal continuum that satisfies the (not obviously consistent) synthetic a priori principles for time that Kant lists in the Critique of pure Reason (CPR), the Metaphysical Foundations of Natural Science (MFNS), the Opus Postumum and the notes and frag- ments published after his death. The continuum so obtained has some affinities with the Brouwerian continuum, but it also has ‘infinitesimal intervals’ consisting of nilpotent infinitesi…Read more
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260Independence, randomness and the axiom of choiceJournal of Symbolic Logic 57 (4): 1274-1304. 1992.We investigate various ways of introducing axioms for randomness in set theory. The results show that these axioms, when added to ZF, imply the failure of AC. But the axiom of extensionality plays an essential role in the derivation, and a deeper analysis may ultimately show that randomness is incompatible with extensionality
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240Naturalising Mathematics? A Wittgensteinian PerspectivePhilosophies 7 (4): 85. 2022.There is a noticeable gap between results of cognitive neuroscientific research into basic mathematical abilities and philosophical and empirical investigations of mathematics as a distinct intellectual activity. The paper explores the relevance of a Wittgensteinian framework for dealing with this discrepancy.
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224What Cost Naturalism?In Wiebke Petersen & Kata Balogh (eds.), BRIDGE 2014 Proceedings, University of Duesselfors Press. forthcoming.The paper traces some of the assumptions that have informed conservative naturalism in linguistic theory, critically examines their justification, and proposes a more liberal alternative.
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156Semantics as a foundation for psychology: A case study of Wason's selection task (review)Journal of Logic, Language and Information 10 (3): 273-317. 2001.We review the various explanations that have been offered toaccount for subjects'' behaviour in Wason ''s famous selection task. Weargue that one element that is lacking is a good understanding ofsubjects'' semantics for the key expressions involved, and anunderstanding of how this semantics is affected by the demands the taskputs upon the subject''s cognitive system. We make novel proposals inthese terms for explaining the major content effects of deonticmaterials. Throughout we illustrate with…Read more
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155Abstracte begrippen en concrete werkelijkheid - Twee vragen voor Hans RadderAlgemeen Nederlands Tijdschrift voor Wijsbegeerte 106 (1): 69-74. 2014.Amsterdam University Press is a leading publisher of academic books, journals and textbooks in the Humanities and Social Sciences. Our aim is to make current research available to scholars, students, innovators, and the general public. AUP stands for scholarly excellence, global presence, and engagement with the international academic community.
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106Algorithmic information theoryJournal of Symbolic Logic 54 (4): 1389-1400. 1989.We present a critical discussion of the claim (most forcefully propounded by Chaitin) that algorithmic information theory sheds new light on Godel's first incompleteness theorem
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102Logic in the study of psychiatric disorders: Executive function and rule-followingTopoi 26 (1): 97-114. 2007.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 …Read more
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81Von Mises' definition of random sequences reconsideredJournal of Symbolic Logic 52 (3): 725-755. 1987.We review briefly the attempts to define random sequences. These attempts suggest two theorems: one concerning the number of subsequence selection procedures that transform a random sequence into a random sequence; the other concerning the relationship between definitions of randomness based on subsequence selection and those based on statistical tests.
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80Language, linguistics and cognitionIn Ruth M. Kempson, Tim Fernando & Nicholas Asher (eds.), Philosophy of Linguistics, North Holland. 2012.
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77“Nonmonotonic” does not mean “probabilistic”Behavioral and Brain Sciences 32 (1): 102-103. 2009.Oaksford & Chater (O&C) advocate Bayesian probability as a way to deal formally with the pervasive nonmonotonicity of common sense reasoning. We show that some forms of nonmonotonicity cannot be treated by Bayesian methods
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67Logic as Marr's Computational Level: Four Case StudiesTopics in Cognitive Science 7 (2): 287-298. 2015.We sketch four applications of Marr's levels-of-analysis methodology to the relations between logic and experimental data in the cognitive neuroscience of language and reasoning. The first part of the paper illustrates the explanatory power of computational level theories based on logic. We show that a Bayesian treatment of the suppression task in reasoning with conditionals is ruled out by EEG data, supporting instead an analysis based on defeasible logic. Further, we describe how results from …Read more
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58The Processing Consequences of the Imperfective Paradox: ArticlesJournal of Semantics 24 (4): 307-330. 2007.In this paper we present a semantic analysis of the imperfective paradox based on the Event Calculus, a planning formalism characterizing a class of models which can be computed by connectionist networks. We report the results of a questionnaire that support the semantic theory and suggest that different aspectual classes of VPs in the progressive give rise to different entailment patterns. Further, a processing model is outlined, combining the semantic analysis with the psycholinguistic princip…Read more
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54The axiomatization of randomnessJournal of Symbolic Logic 55 (3): 1143-1167. 1990.We present a faithful axiomatization of von Mises' notion of a random sequence, using an abstract independence relation. A byproduct is a quantifier elimination theorem for Friedman's "almost all" quantifier in terms of this independence relation
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53Discourse processing in attention-deficit hyperactivity disorder (adhd)Journal of Logic, Language and Information 17 (4): 467-487. 2008.ADHD is a psychiatric disorder characterised by persistent and developmentally inappropriate levels of inattention, impulsivity and hyperactivity. It is known that children with ADHD tend to produce incoherent discourses, e.g. by narrating events out of sequence. Here the aetiology of ADHD becomes of interest. One prominent theory is that ADHD is an executive function disorder, showing deficiencies of planning. Given the close link between planning, verb tense and discourse coherence postulated …Read more
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52A logic of visionLinguistics and Philosophy 23 (1): 1-92. 2000.This essay attempts to develop a psychologically informed semantics of perception reports, whose predictions match with the linguistic data. As suggested by the quotation from Miller and Johnson-Laird, we take a hallmark of perception to be its fallible nature; the resulting semantics thus necessarily differs from situation semantics. On the psychological side, our main inspiration is Marr's (1982) theory of vision, which can easily accomodate fallible perception. In Marr's theory, vision is a m…Read more
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48Abstracties en idealisaties: de constructie van de moderne taalkundeTijdschrift Voor Filosofie 72 (4): 749-776. 2010.The paper addresses the way in which modern linguistics, − in particular, but not exclusively, the generative tradition − , has constructed its core concepts. It argues that a particular form of construction, reminiscent of, but crucially different from, abstrac- tion, which is dubbed ‘idealisation’, plays a central role here. The resemblances and differences between abstractions and idealisations are investigated, and consequences of the reliance on idealisations are reviewed.
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47A little logic goes a long way: basing experiment on semantic theory in the cognitive science of conditional reasoningCognitive Science 28 (4): 481-529. 2004.
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44The processing consequences of compositionalityIn Markus Werning, Wolfram Hinzen & Edouard Machery (eds.), The Oxford Handbook of Compositionality, Oxford University Press. 2012.Compositionality remains effective as an explanation of cases in which processing complexity increases due to syntactic factors only. It falls short of accounting for situations in which complexity arises from interactions with the sentence or discourse context, perceptual cues, and stored knowledge. The idea of compositionality as a methodological principle is appealing, but imputing the complexity to one component of the grammar or another, instead of enriching the notion of composition, is no…Read more
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43Sieg has proposed axioms for computability whose models can be reduced to Turing machines. This lecture will investigate to what extent these axioms hold for reasoning. In particular we focus on the requirement that the configurations that a computing agent (whether human or machine) operates on must be ’immediately recognisable’. If one thinks of reasoning as derivation in a calculus, this requirement is satisfied; but even in contexts which are only slightly less formal, the requirement cannot…Read more
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41The representation of Takeuti's *20c ||_ -operatorStudia Logica 42 (4). 1983.Gaisi Takeuti has recently proposed a new operation on orthomodular lattices L, ⫫: $\scr{P}(L)\rightarrow L$ . The properties of ⫫ suggest that the value of ⫫ $(A)(A\subseteq L)$ corresponds to the degree in which the elements of A behave classically. To make this idea precise, we investigate the connection between structural properties of orthomodular lattices L and the existence of two-valued homomorphisms on L
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39Reasoning in Non-probabilistic Uncertainty: Logic Programming and Neural-Symbolic Computing as ExamplesMinds and Machines 27 (1): 37-77. 2017.This article aims to achieve two goals: to show that probability is not the only way of dealing with uncertainty ; and to provide evidence that logic-based methods can well support reasoning with uncertainty. For the latter claim, two paradigmatic examples are presented: logic programming with Kleene semantics for modelling reasoning from information in a discourse, to an interpretation of the state of affairs of the intended model, and a neural-symbolic implementation of input/output logic for …Read more
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39A Logic of VisionLinguistics and Philosophy 23 (1). 2000.This essay attempts to develop a psychologically informed semantics of perception reports, whose predictions match with the linguistic data. As suggested by the quotation from Miller and Johnson-Laird, we take a hallmark of perception to be its fallible nature; the resulting semantics thus necessarily differs from situation semantics. On the psychological side, our main inspiration is Marr's (1982) theory of vision, which can easily accomodate fallible perception. In Marr's theory, vision is a m…Read more
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36Logic as Marr's Computational Level: Four Case StudiesTopics in Cognitive Science 7 (2): 287-298. 2015.We sketch four applications of Marr's levels‐of‐analysis methodology to the relations between logic and experimental data in the cognitive neuroscience of language and reasoning. The first part of the paper illustrates the explanatory power of computational level theories based on logic. We show that a Bayesian treatment of the suppression task in reasoning with conditionals is ruled out by EEG data, supporting instead an analysis based on defeasible logic. Further, we describe how results from …Read more
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36Semantic Interpretation as Computation in Nonmonotonic Logic: The Real Meaning of the Suppression TaskCognitive Science 29 (6): 919-960. 2005.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 pa…Read more
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36Logic programming, probability, and two-system accounts of reasoning: a rejoinder to Oaksford and ChaterThinking and Reasoning 22 (3): 355-368. 2016.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 Ra…Read more
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