•  46
    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...
  •  38
    On 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
  •  21
    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
  •  26
    Correction to: HYPE: A System of Hyperintensional Logic
    Journal 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.
  •  78
    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.
  •  131
    HYPE: A System of Hyperintensional Logic
    Journal 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
  •  30
    Imaging all the people
    Episteme 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
  • Inference on the Low Level: An Investigation into Deduction, Nonmonotonic Reasoning, and the Philosophy of Cognition
    Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 38 (2): 393-395. 2007.
  •  269
    Criteria of identity and structuralist ontology
    Philosophia Mathematica 16 (3): 388-396. 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 non-trivial 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
  •  86
    Timothy Williamson, knowledge and its limits. Oxford: Oxford university press, 2000
    Grazer Philosophische Studien 65 (1): 195-205. 2002.
  •  80
    A New Analysis of Quasianalysis
    Journal of Philosophical Logic 36 (2): 181-226. 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 so-called 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
  •  40
    Truth and the Liar in De Morgan-Valued Models
    Notre Dame Journal of Formal Logic 40 (4): 496-514. 1999.
    The aim of this paper is to give a certain algebraic account of truth: we want to define what we mean by De Morgan-valued 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 Morgan-valued models. Before we can prove this result, we have to repeat some basic facts concerning De Morgan-valued models in general, and we will introduce a notion of truth both on the object- and on the metal…Read more
  •  31
    Paradox by definition
    Analysis 65 (4): 275-278. 2005.
  •  97
    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
  •  893
    When betting odds and credences come apart: more worries for Dutch book arguments
    with Darren Bradley
    Analysis 66 (2): 119-127. 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
  •  44
    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.
  •  167
    What Truth Depends on
    Journal of Philosophical Logic 34 (2): 155-192. 2005.
    What kinds of sentences with truth predicate may be inserted plausibly and consistently into the T-scheme? We state an answer in terms of dependence: those sentences which depend directly or indirectly on non-semantic 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
  •  120
    A Probabilistic Semantics for Counterfactuals. Part B
    Review of Symbolic Logic 5 (1): 85-121. 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
  •  79
    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
  •  68
    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 low-level 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
  •  538
    In this paper a theory of finitistic and frequentistic approximations — in short: f-approximations — of probability measures P over a countably infinite outcome space N is developed. The family of subsets of N for which f-approximations converge to a frequency limit forms a pre-Dynkin 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 σ-additive. We conclude that probability measures can b…Read more
  •  175
    Criteria of Identity: Strong and Wrong
    British Journal for the Philosophy of Science 64 (1): 61-68. 2013.
    We show that finitely axiomatized first-order theories that involve some criterion of identity for entities of a category C can be reformulated as conjunctions of a non-triviality 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