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32A 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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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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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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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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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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16Explaining intersubjectivity. A comment on Arie Verhagen, Constructions of IntersubjectivityCognitive Linguistics 19 (1). 2008.
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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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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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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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23Interpretation, representation, and deductive reasoningIn Jonathan Eric Adler & Lance J. Rips (eds.), Reasoning: Studies of Human Inference and its Foundations, Cambridge University Press. pp. 223-248. 2008.
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17The Representation of Takeuti's ⫫-OperatorStudia Logica 42 (4): 407-415. 1983.Gaisi Takeuti has recently proposed a new operation on orthomodular lattices L, ⫫: $\scr{P}\rightarrow L$ . The properties of ⫫ suggest that the value of ⫫ $$ 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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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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22Editorial: An invitation to cognitive science (review)Journal of Logic, Language and Information 10 (2): 145-146. 2001.
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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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29On a Spector Ultrapower for the Solovay ModelMathematical Logic Quarterly 43 (3): 389-395. 1997.We prove that a Spector‐like ultrapower extension ???? of a countable Solovay model ???? (where all sets of reals are Lebesgue measurable) is equal to the set of all sets constructible from reals in a generic extension ????[a], where a is a random real over ????. The proof involves the Solovay almost everywhere uniformization technique.
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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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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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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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10Language Evolution: Enlarging the PictureIn David McFarland, Keith Stenning & Maggie McGonigle (eds.), The Complex Mind, Palgrave-macmillan. pp. 264-282. 2012.
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26The representation of Takeuti's $$\begin{array}{*{20}c} \parallel \\ \_ \\ \end{array} $$ -operatorStudia Logica 42 (4): 407-415. 1983.Gaisi Takeuti has recently proposed a new operation on orthomodular latticesL, $\begin{array}{*{20}c} \parallel \\ \_ \\ \end{array} $ :P(L)»L. The properties of $\begin{array}{*{20}c} \parallel \\ \_ \\ \end{array} $ suggest that the value of $\begin{array}{*{20}c} \parallel \\ \_ \\ \end{array} $ (A) (A) $ \subseteq $ L) corresponds to the degree in which the elements ofA behave classically. To make this idea precise, we investigate the connection between structural properties of orthomodular …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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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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