Hannes Leitgeb

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 out why our everyday oral practice of single assertions is not affected by it, and we argue that the proposal leads to a way out of the Paradox of the Preface

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) and that the principles are jointly satisfied if and only if rational belief is equivalent to the assignment of a stably high rational degree of belief. Although the logical closure of belief and the Lockean thesis are attractive postulates in themselves, initially this may seem like a formal “curiosity”; however, as will be argued in the rest of the essay, a very reasonable theory of rational belief can be built around these principles that is not ad hoc and that has various philosophical features that are plausible independently. In particular, this essay shows that the theory allows for a solution to the Lottery Paradox, and it has nice applications to formal epistemology. The price that is to be paid for this theory is a strong dependency of belief on the context, where a context involves both the agent's degree of belief function and the partitioning or individuation of the underlying possibilities. But as this essay argues, that price seems to be affordable.

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 other case, it must be possible to account for 'degrees of compositionality' or for other refinements of compositionality that are compatible with meaning resemblance.

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 progress

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. Instead the paradox is avoided by making explicit, for any occurrence of an introspective modality in the object language, the belief state to which this occurrence refers; this will make it impossible for any doxastic modality to refer to two distinct belief sets within one and the same context of doxastic appraisal. By this move the standard derivation of a contradiction from the theory of belief revision in the presence of introspectively closed belief sets does not go through any more, and indeed the premisses of the Paradox of Serious Possibility become jointly consistent once they are reformulated with our amended introspective modalities only. Additionally, we present a probabilistic version of the Paradox of Serious Possibility which can be avoided in a perfectly analogous manner

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 which are subject to natural postulates on belief revision and acceptability sets for conditionals. Along the way we show that in contrast with what Gärdenfors himself proposed, there is no dichotomy of the form: either the Ramsey test has to be given up or the Preservation condition. Instead, both of them follow from our postulates