
46A Structural Justification of Probabilism: From Partition Invariance to Subjective ProbabilityPhilosophy of Science 88 (2): 341365. 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...

Nonmonotonic reasoning by inhibition nets☆☆This paper has been supported by the Austrian Research Fund FWF (SFB F012)Artificial Intelligence 128 (12): 161201. 2001.

38On NonEliminative Structuralism. Unlabeled Graphs as a Case Study, Part A†Philosophia Mathematica 28 (3): 317346. 2020.This is Part A of an article that defends noneliminative structuralism about mathematics by means of a concrete case study: a theory of unlabeled graphs. Part A summarizes the general attractions of noneliminative 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

21On NonEliminative Structuralism. Unlabeled Graphs as a Case Study, Part BPhilosophia Mathematica. forthcoming.This is Part B of an article that defends noneliminative 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 wellknown problems concerning identity, objecthood, and reference that have been …Read more

Reduction and Elimination in Philosophy and the Sciences. Papers of the 31st International Wittgenstein Symposium (edited book)Austrian Ludwig Wittgenstein Society. 2008.

26Correction to: HYPE: A System of Hyperintensional LogicJournal of Philosophical Logic 48 (2): 407407. 2019.The original version of the article unfortunately contained a mistake. The author missed to mention the support by a EUfunded research network that he is involved in. See below. This work was supported by the MarieSklodowskaCurie Innovative Training Network DIAPHORA.

78Why pure mathematical truths are metaphysically necessary: a settheoretic explanationSynthese 197 (7): 31133120. 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.

131HYPE: A System of Hyperintensional LogicJournal of Philosophical Logic 48 (2): 305405. 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

30Imaging all the peopleEpisteme 14 (4): 463479. 2017.It is well known that aggregating the degreeofbelief functions of different subjects by linear pooling or averaging is subject to a commutativity dilemma: other than in trivial cases, conditionalizing the individual degreeofbelief 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 ofbelief function on E. In the present paper we suggest a novel way out…Read more

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): 393395. 2007.

269Criteria of identity and structuralist ontologyPhilosophia Mathematica 16 (3): 388396. 2008.In discussions about whether the Principle of the Identity of Indiscernibles is compatible with structuralist ontologies of mathematics, it is usually assumed that individual objects are subject to criteria of identity which somehow account for the identity of the individuals. Much of this debate concerns structures that admit of nontrivial automorphisms. We consider cases from graph theory that violate even weak formulations of PII. We argue that (i) the identity or difference of places in a s…Read more

86Timothy Williamson, knowledge and its limits. Oxford: Oxford university press, 2000Grazer Philosophische Studien 65 (1): 195205. 2002.

80A New Analysis of QuasianalysisJournal of Philosophical Logic 36 (2): 181226. 2007.We investigate the conditions under which quasianalysis, i.e., Carnap's method of abstraction in his Aufbau, yields adequate results. In particular, we state both necessary and sufficient conditions for the socalled faithfulness and fullness of quasianalysis, and analyze adequacy as the conjunction of faithfulness and fullness. It is shown that there is no method of (re)constructing properties from similarity that delivers adequate results in all possible cases, if the same set of individuals …Read more

13Towards a logic 0f typefree modality and truthIn Costas Dimitracopoulos (ed.), Logic Colloquium 2005: Proceedings of the Annual European Summer Meeting of the Association for Symbolic Logic, Held in Athens, Greece, July 28August 3, 2005, Cambridge University Press. pp. 2868. 2008.

40Truth and the Liar in De MorganValued ModelsNotre Dame Journal of Formal Logic 40 (4): 496514. 1999.The aim of this paper is to give a certain algebraic account of truth: we want to define what we mean by De Morganvalued truth models and show their existence even in the case of semantical closure: that is, languages may contain their own truth predicate if they are interpreted by De Morganvalued models. Before we can prove this result, we have to repeat some basic facts concerning De Morganvalued models in general, and we will introduce a notion of truth both on the object and on the metal…Read more

97Logic in general philosophy of science: old things and new thingsSynthese 179 (2). 2011.This is a personal, incomplete, and very informal take on the role of logic in general philosophy of science, which is aimed at a broader audience. We defend and advertise the application of logical methods in philosophy of science, starting with the beginnings in the Vienna Circle and ending with some more recent logical developments

893When betting odds and credences come apart: more worries for Dutch book argumentsAnalysis 66 (2): 119127. 2006.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

44Hodges’ Theorem Does not Account for Determinacy of Translation. A Reply to WerningErkenntnis 62 (3): 411425. 2005.Werning applies a theorem by Hodges in order to put forward an argument against Quine's thesis of the indeterminacy of translation and in favour of what Werning calls 'semantic realism'. We show that the argument rests on two critical premises both of which are false. The reasons for these failures are explained and the actual place of this application of Hodges' theorem within Quine's philosophy of language is outlined.

167What Truth Depends onJournal of Philosophical Logic 34 (2): 155192. 2005.What kinds of sentences with truth predicate may be inserted plausibly and consistently into the Tscheme? We state an answer in terms of dependence: those sentences which depend directly or indirectly on nonsemantic states of affairs (only). In order to make this precise we introduce a theory of dependence according to which a sentence φ is said to depend on a set Φ of sentences iff the truth value of φ supervenes on the presence or absence of the sentences of Φ in/from the extension of the tr…Read more

120A Probabilistic Semantics for Counterfactuals. Part BReview of Symbolic Logic 5 (1): 85121. 2012.This is part B of a paper in which we defend a semantics for counterfactuals which is probabilistic in the sense that the truth condition for counterfactuals refers to a probability measure. Because of its probabilistic nature, it allows a counterfactual to be true even in the presence of relevant worlds, as long such exceptions are not too widely spread. The semantics is made precise and studied in different versions which are related to each other by representation theorems. Despite its proba…Read more

79The Review Paradox: On The Diachronic Costs of Not Closing Rational Belief Under ConjunctionNoûs 48 (4): 781793. 2014.We argue that giving up on the closure of rational belief under conjunction comes with a substantial price. Either rational belief is closed under conjunction, or else the epistemology of belief has a serious diachronic deficit over and above the synchronic failures of conjunctive closure. The argument for this, which can be viewed as a sequel to the preface paradox, is called the ‘review paradox'; it is presented in four distinct, but closely related versions

41A class of nvalued statement calculi: Many universes statement calculusKriterion  Journal of Philosophy 11 (1): 315. 1997.

On the metatheory of Field's `Solving the paradoxes, escaping revenge'In J. C. Beall (ed.), Revenge of the Liar: New Essays on the Paradox, Oxford University Press. 2007.

14College, 124 Raymond avenue, poughkeepsie, ny 12604, usa. In a review, a reference “jsl xliii 148,” for example, refers either to the publication reviewed on page 148 of volume 43 of the journal, or to the review itself (which contains full bibliographical information for the reviewed publication). Analogously, a reference “bsl VII 376” refers to the review beginning on page 376 in volume 7 of this bulletin, or (review)Bulletin of Symbolic Logic 17 (1). 2011.

68Inference on the Low Level: An Investigation Into Deduction, Nonmonotonic Reasoning, and the Philosophy of CognitionKluwer Academic Publishers. 2004.This monograph provides a new account of justified inference as a cognitive process. In contrast to the prevailing tradition in epistemology, the focus is on lowlevel inferences, i.e., those inferences that we are usually not consciously aware of and that we share with the cat nearby which infers that the bird which she sees picking grains from the dirt, is able to fly. Presumably, such inferences are not generated by explicit logical reasoning, but logical methods can be used to describe and a…Read more

538Finitistic and Frequentistic Approximation of Probability Measures with or without σAdditivityStudia Logica 89 (2): 257283. 2008.In this paper a theory of finitistic and frequentistic approximations — in short: fapproximations — of probability measures P over a countably infinite outcome space N is developed. The family of subsets of N for which fapproximations converge to a frequency limit forms a preDynkin system $D \subseteq \wp $. The limiting probability measure over D can always be extended to a probability measure over $\wp $, but this measure is not always σadditive. We conclude that probability measures can b…Read more

175Criteria of Identity: Strong and WrongBritish Journal for the Philosophy of Science 64 (1): 6168. 2013.We show that finitely axiomatized firstorder theories that involve some criterion of identity for entities of a category C can be reformulated as conjunctions of a nontriviality statement and a criterion of identity for entities of category C again. From this, we draw two conclusions: First, criteria of identity can be very strong deductively. Second, although the criteria of identity that are constructed in the proof of the theorem are not good ones intuitively, it is difficult to say what ex…Read more