•  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
  •  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
  •  388
    An Objective Justification of Bayesianism I: Measuring Inaccuracy
    Philosophy of Science 77 (2): 201-235. 2010.
    One of the fundamental problems of epistemology is to say when the evidence in an agent’s possession justifies the beliefs she holds. In this paper and its sequel, we defend the Bayesian solution to this problem by appealing to the following fundamental norm: Accuracy An epistemic agent ought to minimize the inaccuracy of her partial beliefs. In this paper, we make this norm mathematically precise in various ways. We describe three epistemic dilemmas that an agent might face if she attempts to f…Read more
  •  330
    New Life for Carnap’s Aufbau?
    Synthese 180 (2): 265-299. 2011.
    Rudolf Carnap's Der logische Aufbau der Welt (The Logical Structure of the World) is generally conceived of as being the failed manifesto of logical positivism. In this paper we will consider the following question: How much of the Aufbau can actually be saved? We will argue that there is an adaptation of the old system which satisfies many of the demands of the original programme. In order to defend this thesis, we have to show how a new 'Aufbau-like' programme may solve or circumvent the probl…Read more
  •  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
  •  261
    Beliefs in conditionals vs. conditional beliefs
    Topoi 26 (1): 115-132. 2007.
    On the basis of impossibility results on probability, belief revision, and conditionals, it is argued that conditional beliefs differ from beliefs in conditionals qua mental states. Once this is established, it will be pointed out in what sense conditional beliefs are still conditional, even though they may lack conditional contents, and why it is permissible to still regard them as beliefs, although they are not beliefs in conditionals. Along the way, the main logical, dispositional, representa…Read more
  •  244
    One of the fundamental problems of epistemology is to say when the evidence in an agent’s possession justifies the beliefs she holds. In this paper and its prequel, we defend the Bayesian solution to this problem by appealing to the following fundamental norm: Accuracy An epistemic agent ought to minimize the inaccuracy of her partial beliefs. In the prequel, we made this norm mathematically precise; in this paper, we derive its consequences. We show that the two core tenets of Bayesianism follo…Read more
  •  233
    The Stability Theory of Belief
    Philosophical Review 123 (2): 131-171. 2014.
    This essay develops a joint theory of rational (all-or-nothing) belief and degrees of belief. The theory is based on three assumptions: the logical closure of rational belief; the axioms of probability for rational degrees of belief; and the so-called Lockean thesis, in which the concepts of rational belief and rational degree of belief figure simultaneously. In spite of what is commonly believed, this essay will show that this combination of principles is satisfiable (and indeed nontrivially so…Read more
  •  204
    Sleeping beauty and eternal recurrence
    Analysis 70 (2): 203-205. 2010.
    (No abstract is available for this citation)
  •  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
  •  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
  •  149
    Dynamic doxastic logic: why, how, and where to?
    Synthese 155 (2): 167-190. 2007.
    We investigate the research programme of dynamic doxastic logic (DDL) and analyze its underlying methodology. The Ramsey test for conditionals is used to characterize the logical and philosophical differences between two paradigmatic systems, AGM and KGM, which we develop and compare axiomatically and semantically. The importance of Gärdenfors’s impossibility result on the Ramsey test is highlighted by a comparison with Arrow’s impossibility result on social choice. We end with an outlook on the…Read more
  •  137
    Scientific Philosophy, Mathematical Philosophy, and All That
    Metaphilosophy 44 (3): 267-275. 2013.
    This article suggests that scientific philosophy, especially mathematical philosophy, might be one important way of doing philosophy in the future. Along the way, the article distinguishes between different types of scientific philosophy; it mentions some of the scientific methods that can serve philosophers; it aims to undermine some worries about mathematical philosophy; and it tries to make clear why in certain cases the application of mathematical methods is necessary for philosophical progr…Read more
  •  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
  •  128
    The so-called Paradox of Serious Possibility is usually regarded as showing that the standard axioms of belief revision do not apply to belief sets that are introspectively closed. In this article we argue to the contrary: we suggest a way of dissolving the Paradox of Serious Possibility so that introspective statements are taken to express propositions in the standard sense, which may thus be proper members of belief sets, and accordingly the normal axioms of belief revision apply to them. Inst…Read more
  •  126
    Possible-worlds semantics for modal notions conceived as predicates
    with Volker Halbach and Philip Welch
    Journal of Philosophical Logic 32 (2): 179-223. 2003.
    If □ is conceived as an operator, i.e., an expression that gives applied to a formula another formula, the expressive power of the language is severely restricted when compared to a language where □ is conceived as a predicate, i.e., an expression that yields a formula if it is applied to a term. This consideration favours the predicate approach. The predicate view, however, is threatened mainly by two problems: Some obvious predicate systems are inconsistent, and possible-worlds semantics for p…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
  •  109
    On the Ramsey Test without Triviality
    Notre Dame Journal of Formal Logic 51 (1): 21-54. 2010.
    We present a way of classifying the logically possible ways out of Gärdenfors' inconsistency or triviality result on belief revision with conditionals. For one of these ways—conditionals which are not descriptive but which only have an inferential role as being given by the Ramsey test—we determine which of the assumptions in three different versions of Gärdenfors' theorem turn out to be false. This is done by constructing ranked models in which such Ramsey-test conditionals are evaluated and wh…Read more
  •  103
    On the probabilistic convention T
    Review of Symbolic Logic 1 (2): 218-224. 2008.
    We introduce an epistemic theory of truth according to which the same rational degree of belief is assigned to Tr(. It is shown that if epistemic probability measures are only demanded to be finitely additive (but not necessarily σ-additive), then such a theory is consistent even for object languages that contain their own truth predicate. As the proof of this result indicates, the theory can also be interpreted as deriving from a quantitative version of the Revision Theory of Truth
  •  101
    A way out of the preface paradox?
    Analysis 74 (1). 2014.
    The thesis defended in this article is that by uttering or publishing a great many declarative sentences in assertoric mode, one does not actually assert that their conjunction is true – one rather asserts that the vast majority of these sentences are true. Accordingly, the belief that is expressed thereby is the belief that the vast majority of these sentences are true. In the article, we make this proposal precise, we explain the context-dependency of belief that corresponds to it, we point ou…Read more
  •  97
    Truth as translation – part a
    Journal of Philosophical Logic 30 (4): 281-307. 2001.
    This is the second part of a paper dealing with truth and translation. In Part A a revised version of Tarski's Convention T has been presented, which explicitly refers to a translation mapping from the object language to the metalanguage; the vague notion of a translation has been replaced by a precise definition. At the end of Part A it has been shown that interpreted languages exist, which allow for vicious self-reference but which nevertheless contain their own truth predicate - this is possi…Read more
  •  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
  •  93
    Reducing belief simpliciter to degrees of belief
    Annals of Pure and Applied Logic 164 (12): 1338-1389. 2013.
    Is it possible to give an explicit definition of belief in terms of subjective probability, such that believed propositions are guaranteed to have a sufficiently high probability, and yet it is neither the case that belief is stripped of any of its usual logical properties, nor is it the case that believed propositions are bound to have probability 1? We prove the answer is ‘yes’, and that given some plausible logical postulates on belief that involve a contextual “cautiousness” threshold, there…Read more
  •  90
    An impossibility result on semantic resemblance
    Dialectica 62 (3): 293-306. 2008.
    We show that a set of prima facie plausible assumptions on the relation of meaning resemblance – one of which is a compositionality postulate – is inconsistent. On this basis we argue that either there is no theoretically useful notion of semantic resemblance at all, or the traditional conception of the compositionality of meaning has to be adapted. In the former case, arguments put forward by Nelson Goodman and Paul Churchland in favor of the concept of meaning resemblance are defeated. In the …Read more
  •  86
    Timothy Williamson, knowledge and its limits. Oxford: Oxford university press, 2000
    Grazer Philosophische Studien 65 (1): 195-205. 2002.
  •  83
    A Lottery Paradox for Counterfactuals Without Agglomeration
    Philosophy and Phenomenological Research 89 (3): 605-636. 2014.
    We will present a new lottery-style paradox on counterfactuals and chance. The upshot will be: combining natural assumptions on the truth values of ordinary counterfactuals, the conditional chances of possible but non-actual events, the manner in which and relate to each other, and a fragment of the logic of counterfactuals leads to disaster. In contrast with the usual lottery-style paradoxes, logical closure under conjunction—that is, in this case, the rule of Agglomeration of counterfactuals—w…Read more
  •  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