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Logic, Methodology and Philosophy of Science - Proceedings of the 15th International Congress, 2015 (edited book)College Publications. 2017.
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259Vindicating the verifiability criterionPhilosophical Studies 181 (1): 223-245. 2024.The aim of this paper is to argue for a revised and precisified version of the infamous Verifiability Criterion for the meaningfulness of declarative sentences. The argument is based on independently plausible premises concerning probabilistic confirmation and meaning as context-change potential, it is shown to be logically valid, and its ramifications for potential applications of the criterion are being discussed. Although the paper is not historical but systematic, the criterion thus vindicat…Read more
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63When betting odds and credences come apart : more worries for Dutch book argumentsAnalysis 66 (2). 2011.If an agent believes that the probability of E being true is 1/2, should she accept a bet on E at even odds or better? Yes, but only given certain conditions. This paper is about what those conditions are. In particular, we think that there is a condition that has been overlooked so far in the literature. We discovered it in response to a paper by Hitchcock (2004) in which he argues for the 1/3 answer to the Sleeping Beauty problem. Hitchcock argues that this credence follows from calculating he…Read more
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76Reduction, Abstraction, Analysis (edited book)Ontos. 2009.This volume collects contributions comprising all these topics, including articles by Alexander Bird, Jaakko Hintikka, James Ladyman, Rohit Parikh, Gerhard ...
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6Metaphysical Modalities in Scientific Language: A Roadmap of (Im-)PossibilitiesIn Hans Rott & Vitezslav Horak (eds.), Possibility and Reality, Walter De Gruyter. pp. 187-220. 2003.
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How Similarities ComposeIn Markus Werning, Edouard Machery & Gerhard Schurz (eds.), The Compositionality of Meaning and Content. Volume I - Foundational Issues,, De Gruyter. pp. 147-168. 2005.
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9How Abstraction WorksIn Alexander Hieke & Hannes Leitgeb (eds.), Reduction, abstraction, analysis: proceedings of the 31th International Ludwig Wittgenstein-Symposium in Kirchberg, 2008, De Gruyter. pp. 217-226. 2009.
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64Reduction: Between the Mind and the Brain (edited book)Ontos Verlag. 2009.This volume collects contributions that comprise each view point, and incorporates articles by William Bechtel, Jerry Fodor, Jaegwon Kim, Joėlle Proust, and ...
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23Neural Network Models of ConditionalsIn Sven Ove Hansson & Vincent F. Hendricks (eds.), Introduction to Formal Philosophy, Springer. pp. 147-176. 2012.This chapter explains how artificial neural networks may be used as models for reasoning, conditionals, and conditional logic. It starts with the historical overlap between neural network research and logic, it discusses connectionism as a paradigm in cognitive science that opposes the traditional paradigm of symbolic computationalism, it mentions some recent accounts of how logic and neural networks may be combined, and it ends with a couple of open questions concerning the future of this area …Read more
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53Circular languagesJournal of Logic, Language and Information 13 (3): 341-371. 2004.In this paper we investigate two purely syntactical notions ofcircularity, which we call ``self-application'''' and ``self-inclusion.'''' Alanguage containing self-application allows linguistic items to beapplied to themselves. In a language allowing for self-inclusion thereare expressions which include themselves as a proper part. We introduceaxiomatic systems of syntax which include identity criteria andexistence axioms for such expressions. The consistency of these axiomsystems will be shown …Read more
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117Revision RevisitedReview of Symbolic Logic 5 (4): 642-664. 2012.This article explores ways in which the Revision Theory of Truth can be expressed in the object language. In particular, we investigate the extent to which semantic deficiency, stable truth, and nearly stable truth can be so expressed, and we study different axiomatic systems for the Revision Theory of Truth.
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88No futureJournal of Philosophical Logic 30 (3): 259-265. 2001.The difficulties with formalizing the intensional notions necessity, knowability and omniscience, and rational belief are well-known. If these notions are formalized as predicates applying to (codes of) sentences, then from apparently weak and uncontroversial logical principles governing these notions, outright contradictions can be derived. Tense logic is one of the best understood and most extensively developed branches of intensional logic. In tense logic, the temporal notions future and past…Read more
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72Probability for the Revision Theory of TruthJournal of Philosophical Logic 48 (1): 87-112. 2019.We investigate how to assign probabilities to sentences that contain a type-free truth predicate. These probability values track how often a sentence is satisfied in transfinite revision sequences, following Gupta and Belnap’s revision theory of truth. This answers an open problem by Leitgeb which asks how one might describe transfinite stages of the revision sequence using such probability functions. We offer a general construction, and explore additional constraints that lead to desirable prop…Read more
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221. Not a Sure Thing: Fitness, Probability, and Causation Not a Sure Thing: Fitness, Probability, and Causation (pp. 147-171) (review)Philosophy of Science 77 (2): 172-200. 2010.Hierarchical Bayesian models provide an account of Bayesian inference in a hierarchically structured hypothesis space. Scientific theories are plausibly regarded as organized into hierarchies in many cases, with higher levels sometimes called ‘paradigms’ and lower levels encoding more specific or concrete hypotheses. Therefore, HBMs provide a useful model for scientific theory change, showing how higher-level theory change may be driven by the impact of evidence on lower levels. HBMs capture fea…Read more
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16Reduction, abstraction, analysis: proceedings of the 31th International Ludwig Wittgenstein-Symposium in Kirchberg, 2008 (edited book)de Gruyter. 2009.Philosophers often have tried to either reduce "disagreeable" objects or concepts to (more) acceptable objects or concepts. Reduction is regarded attractive by those who subscribe to an ideal of ontological parsimony. But the topic is not just restricted to traditional metaphysics or ontology. In the philosophy of mathematics, abstraction principles, such as Hume's principle, have been suggested to support a reconstruction of mathematics by logical means only. In the philosophy of language and t…Read more
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46Axioms for Type-Free Subjective ProbabilityReview of Symbolic Logic 17 (2): 493-508. 2024.We formulate and explore two basic axiomatic systems of type-free subjective probability. One of them explicates a notion of finitely additive probability. The other explicates a concept of infinitely additive probability. It is argued that the first of these systems is a suitable background theory for formally investigating controversial principles about type-free subjective probability.
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2A class of n-valued statement calculi: Many universes statement calculusKriterion - Journal of Philosophy 1 (11): 3-15. 1997.
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76Ramsification and Semantic IndeterminacyReview of Symbolic Logic 16 (3): 900-950. 2022.Is it possible to maintain classical logic, stay close to classical semantics, and yet accept that language might be semantically indeterminate? The article gives an affirmative answer by Ramsifying classical semantics, which yields a new semantic theory that remains much closer to classical semantics than supervaluationism but which at the same time avoids the problematic classical presupposition of semantic determinacy. The resulting Ramsey semantics is developed in detail, it is shown to supp…Read more
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91A Structural Justification of Probabilism: From Partition Invariance to Subjective ProbabilityPhilosophy of Science 88 (2): 341-365. 2021.A new justification of probabilism is developed that pays close attention to the structure of the underlying space of possibilities. Its central assumption is that rational numerical degrees of bel...
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10Nonmonotonic reasoning by inhibition nets☆☆This paper has been supported by the Austrian Research Fund FWF (SFB F012)Artificial Intelligence 128 (1-2): 161-201. 2001.
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99On Non-Eliminative Structuralism. Unlabeled Graphs as a Case Study, Part A†Philosophia Mathematica 28 (3): 317-346. 2020.This is Part A of an article that defends non-eliminative structuralism about mathematics by means of a concrete case study: a theory of unlabeled graphs. Part A summarizes the general attractions of non-eliminative structuralism. Afterwards, it motivates an understanding of unlabeled graphs as structures sui generis and develops a corresponding axiomatic theory of unlabeled graphs. As the theory demonstrates, graph theory can be developed consistently without eliminating unlabeled graphs in fav…Read more
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65On Non-Eliminative Structuralism. Unlabeled Graphs as a Case Study, Part B†Philosophia Mathematica 29 (1): 64-87. 2021.This is Part B of an article that defends non-eliminative structuralism about mathematics by means of a concrete case study: a theory of unlabeled graphs. Part A motivated an understanding of unlabeled graphs as structures sui generis and developed a corresponding axiomatic theory of unlabeled graphs. Part B turns to the philosophical interpretation and assessment of the theory: it points out how the theory avoids well-known problems concerning identity, objecthood, and reference that have been …Read more
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Reduction and Elimination in Philosophy and the Sciences. Papers of the 31st International Wittgenstein Symposium (edited book)Austrian Ludwig Wittgenstein Society. 2008.
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35Correction to: HYPE: A System of Hyperintensional LogicJournal of Philosophical Logic 48 (2): 407-407. 2019.The original version of the article unfortunately contained a mistake. The author missed to mention the support by a EU-funded research network that he is involved in. See below. This work was supported by the Marie-Sklodowska-Curie Innovative Training Network DIAPHORA.
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138Why pure mathematical truths are metaphysically necessary: a set-theoretic explanationSynthese 197 (7): 3113-3120. 2020.Pure mathematical truths are commonly thought to be metaphysically necessary. Assuming the truth of pure mathematics as currently pursued, and presupposing that set theory serves as a foundation of pure mathematics, this article aims to provide a metaphysical explanation of why pure mathematics is metaphysically necessary.
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283HYPE: A System of Hyperintensional LogicJournal of Philosophical Logic 48 (2): 305-405. 2019.This article introduces, studies, and applies a new system of logic which is called ‘HYPE’. In HYPE, formulas are evaluated at states that may exhibit truth value gaps and truth value gluts. Simple and natural semantic rules for negation and the conditional operator are formulated based on an incompatibility relation and a partial fusion operation on states. The semantics is worked out in formal and philosophical detail, and a sound and complete axiomatization is provided both for the propositio…Read more
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97Imaging all the peopleEpisteme 14 (4): 463-479. 2017.It is well known that aggregating the degree-of-belief functions of different subjects by linear pooling or averaging is subject to a commutativity dilemma: other than in trivial cases, conditionalizing the individual degree-of-belief functions on a piece of evidence E followed by linearly aggregating them does not yield the same result as rst aggregating them linearly and then conditionalizing the resulting social degree- of-belief function on E. In the present paper we suggest a novel way out…Read more
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Inference on the Low Level: An Investigation into Deduction, Nonmonotonic Reasoning, and the Philosophy of CognitionJournal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 38 (2): 393-395. 2007.