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On the cognitive link between space and number: A meta-analysis of the SNARC effectPsychology Science Quarterly 50 (4). 2008.
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40Another Look at ReflectionErkenntnis 88 (2): 479-509. 2021.Reflection principles are of central interest in the development of axiomatic theories. Whereas they are independent statements they appear to have a specific epistemological status. Our trust in those principles is as warranted as our trust in the axioms of the system itself. This paper is an attempt in clarifying this special epistemic status. We provide a motivation for the adoption of uniform reflection principles by their analogy to a form of the constructive \(\omega \) -rule. Additionally…Read more
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21Cross-Disciplinary Research on Learning and Instruction – Coming to TermsFrontiers in Psychology 11. 2021.no abstract for opinion paper.
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9Cognitive Foundations of Human Number Representations and Mental ArithmeticIn Roi Cohen Kadosh & Ann Dowker (eds.), The Oxford Handbook of Numerical Cognition, Oxford University Press Uk. 2015.The chapters in this section of the volume reveal the striking variety of human numerical cognition. The section comprises four chapters that focus on different aspects of the representation of numerical knowledge, as well as three chapters that examine the several cognitive processes involved in the manipulation of numbers during simple mental arithmetic. They show how chronometric analyses, in combination with clever experimental designs, can reveal the cognitive processes and representations …Read more
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36Iterated reflection over full disquotational truthJournal of Logic and Computation 27 (8): 2631-2651. 2017.Iterated reflection principles have been employed extensively to unfold epistemic commitments that are incurred by accepting a mathematical theory. Recently this has been applied to theories of truth. The idea is to start with a collection of Tarski-biconditionals and arrive by iterated reflection at strong compositional truth theories. In the context of classical logic, it is incoherent to adopt an initial truth theory in which A and ‘A is truen’ are inter-derivable. In this article, we show ho…Read more
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33Definite totalities and determinate truth in conceptual structuralismSynthese 203 (1): 1-22. 2024.This article investigates the connection and dependence between the definiteness of the totalities involved in mathematical structures and the determinateness of statements about that structure. From a logical perspective, we investigate whether logical principles expressing the definiteness of totalities license the use of classical logic. From a philosophical perspective, this article provides a reconstruction of Solomon Feferman’s claim that the definiteness of the natural number conception i…Read more
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53Nonclassical Truth with Classical Strength. A Proof-Theoretic Analysis of Compositional Truth Over HypeReview of Symbolic Logic 16 (2): 425-448. 2023.Questions concerning the proof-theoretic strength of classical versus nonclassical theories of truth have received some attention recently. A particularly convenient case study concerns classical and nonclassical axiomatizations of fixed-point semantics. It is known that nonclassical axiomatizations in four- or three-valued logics are substantially weaker than their classical counterparts. In this paper we consider the addition of a suitable conditional to First-Degree Entailment—a logic recentl…Read more
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209Hypatia's silenceNoûs 55 (1): 62-85. 2021.Hartry Field distinguished two concepts of type‐free truth: scientific truth and disquotational truth. We argue that scientific type‐free truth cannot do justificatory work in the foundations of mathematics. We also present an argument, based on Crispin Wright's theory of cognitive projects and entitlement, that disquotational truth can do justificatory work in the foundations of mathematics. The price to pay for this is that the concept of disquotational truth requires non‐classical logical tre…Read more
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83Internal Categoricity, Truth and DeterminacyJournal of Philosophical Logic 52 (5): 1295-1325. 2023.This paper focuses on the categoricity of arithmetic and determinacy of arithmetical truth. Several ‘internal’ categoricity results have been discussed in the recent literature. Against the background of the philosophical position called internalism, we propose and investigate truth-theoretic versions of internal categoricity based on a primitive truth predicate. We argue for the compatibility of a primitive truth predicate with internalism and provide a novel argument for (and proof of) a truth…Read more
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11Theologische Männerforschung?: Zur Frage der Relevanz von Männerforschung in der TheologieZeitschrift Für Evangelische Ethik 50 (1): 138-144. 2006.
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72The Expressive Power of TruthReview of Symbolic Logic 8 (2): 345-369. 2015.There are two perspectives from which formal theories can be viewed. On the one hand, one can take a theory to be about some privileged models. On the other hand, one can take all models of a theory to be on a par. In contrast with what is usually done in philosophical debates, we adopt the latter viewpoint. Suppose that from this perspective we want to add an adequate truth predicate to a background theory. Then on the one hand the truth theory ought to be semantically conservative over the bac…Read more
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158Axiomatizing semantic theories of truth?Review of Symbolic Logic 8 (2): 257-278. 2015.We discuss the interplay between the axiomatic and the semantic approach to truth. Often, semantic constructions have guided the development of axiomatic theories and certain axiomatic theories have been claimed to capture a semantic construction. We ask under which conditions an axiomatic theory captures a semantic construction. After discussing some potential criteria, we focus on the criterion of ℕ-categoricity and discuss its usefulness and limits
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62Paradoxes of Interaction?Journal of Philosophical Logic 44 (3): 287-308. 2015.Since Montague’s work it is well known that treating a single modality as a predicate may lead to paradox. In their paper “No Future”, Horsten and Leitgeb show that if the two temporal modalities are treated as predicates paradox might arise as well. In our paper we investigate whether paradoxes of multiple modalities, such as the No Future paradox, are genuinely new paradoxes or whether they “reduce” to the paradoxes of single modalities. In order to address this question we develop a notion of…Read more
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36More is Better: English Language Statistics are Biased Toward AdditionCognitive Science 47 (4). 2023.We have evolved to become who we are, at least in part, due to our general drive to create new things and ideas. When seeking to improve our creations, ideas, or situations, we systematically overlook opportunities to perform subtractive changes. For example, when tasked with giving feedback on an academic paper, reviewers will tend to suggest additional explanations and analyses rather than delete existing ones. Here, we show that this addition bias is systematically reflected in English langua…Read more
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15Truth, Partial Logic and Infinitary Proof SystemsStudia Logica 106 (3): 515-540. 2018.In this paper we apply proof theoretic methods used for classical systems in order to obtain upper bounds for systems in partial logic. We focus on a truth predicate interpreted in a Kripke style way via strong Kleene; whereas the aim is to connect harmoniously the partial version of Kripke–Feferman with its intended semantics. The method we apply is based on infinitary proof systems containing an ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \use…Read more
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19Sequent Calculi for the Propositional Logic of HYPEStudia Logica 110 (3): 643-677. 2021.In this paper we discuss sequent calculi for the propositional fragment of the logic of HYPE. The logic of HYPE was recently suggested by Leitgeb as a logic for hyperintensional contexts. On the one hand we introduce a simple \-system employing rules of contraposition. On the other hand we present a \-system with an admissible rule of contraposition. Both systems are equivalent as well as sound and complete proof-system of HYPE. In order to provide a cut-elimination procedure, we expand the calc…Read more
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47Is the HYPE about strength warranted?Synthese 200 (3): 1-25. 2022.In comparing classical and non-classical solutions to the semantic paradoxes arguments relying on strength have been influential. In this paper I argue that non-classical solutions should preserve the proof-theoretic strength of classical solutions. Leitgeb’s logic of HYPE is then presented as an interesting possibility to strengthen FDE with a suitable conditional. It is shown that HYPE allows for a non-classical Kripkean theory of truth, called KFL, that is strong enough for the relevant purpo…Read more
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17Separation/connection procedures: From cleansing behavior to numerical cognitionBehavioral and Brain Sciences 44. 2021.Lee and Schwarz suggest that separation is the grounded procedure underlying cleansing effects in different psychological domains. Here, we interpret L&S's account from a hierarchical view of cognition that considers the influence of physical properties and sensorimotor constraints on mental representations. This approach allows theoretical integration and generalization of L&S's account to the domain of formal quantitative reasoning.
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32The Force of Numbers: Investigating Manual Signatures of Embodied Number ProcessingFrontiers in Human Neuroscience 14. 2021.The study has two objectives: to introduce grip force recording as a new technique for studying embodied numerical processing; and to demonstrate how three competing accounts of numerical magnitude representation can be tested by using this new technique: the Mental Number Line, A Theory of Magnitude and Embodied Cognition account. While 26 healthy adults processed visually presented single digits in a go/no-go n-back paradigm, their passive holding forces for two small sensors were recorded in …Read more
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18Diagnostic Activities and Diagnostic Practices in Medical Education and Teacher Education: An Interdisciplinary ComparisonFrontiers in Psychology 11. 2020.
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60Commentary: A mental number line in human newbornsFrontiers in Human Neuroscience 14 511395. 2020.
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24The Tarskian Turn: deflationism and axiomatic truthBulletin of Symbolic Logic 18 (3): 403-405. 2012.
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43The Use of Social Robots and the Uncanny Valley PhenomenonIn Yuefang Zhou & Martin H. Fischer (eds.), Ai Love You : Developments in Human-Robot Intimate Relationships, Springer Verlag. 2019.Social robots are increasingly used in different areas of society such as public health, elderly care, education, and commerce. They have also been successfully employed in autism spectrum disorders therapy with children. Humans strive to find in them not only assistants but also friends. Although forms and functionalities of such robots vary, there is a strong tendency to anthropomorphize artificial agents, making them look and behave as human as possible and imputing human attributes to them. …Read more
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37Intimate Relationships with Humanoid Robots: Exploring Human Sexuality in the Twenty-First CenturyIn Yuefang Zhou & Martin H. Fischer (eds.), Ai Love You : Developments in Human-Robot Intimate Relationships, Springer Verlag. 2019.Sex robots are humanoid robots with artificial intelligence, designed to interact sexually with humans. They have received much attention in recent discussions about technology, human relationships and the future of human sexuality. Based on available evidence so far, this outlook aims to give tentative answers to two fundamental questions surrounding the topic of human–robot intimate relationships. First, whether intelligent humanoid robots are technologically ready to be our intimate partners.…Read more
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24Cross-Representational Interactions: Interface and Overlap MechanismsFrontiers in Psychology 7. 2017.