Hannes Leitgeb

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 metalanguage level appropriate for such models. The definitions and the existence theorem are extensions of Kripke's, Woodruff's, and Visser's concepts and results concerning three- and four-valued truth models

This paper suggests a bridge principle for all-or-nothing belief and degrees of belief to the effect that belief corresponds to stably high degree of belief. Different ways of making this Humean thesis on belief precise are discussed, and one of them is shown to stand out by unifying the others. The resulting version of the thesis proves to be fruitful in entailing the logical closure of belief, the Lockean thesis on belief, and coherence between decision-making based on all-or-nothing beliefs and on degrees of belief.

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 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refers to a translation mapping from the object language to the metalanguage; the vague notion of a translation has been replaced by a precise definition.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 possible if truth is based on a nonstandard translation mapping. However, this result has only been proved for languages without quantifiers. In Part B we now extend the result to first-order languages, and we show that this can be done in three different ways. In each case, the addition of a truth predicate to an interpreted language with a high degree of expressiveness leads to changes in the ontology of the language

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.

In this chapter we will deal with “mechanizing” induction, i.e. with ways in which theoretical computer science approaches inductive generalization. In the field of Machine Learning, algorithms for induction are developed. Depending on the form of the available data, the nature of these algorithms may be very different. Some of them combine geometric and statistical ideas, while others use classical reasoning based on logical formalism. However, we are not so much interested in the algorithms themselves, but more on the philosophical and theoretical foundations they share. Thus in the first of two parts, we will examine different approaches and inductive assumptions in two particular learning settings. While many machine learning algorithms work well on a lot of tasks, the interpretation of the learned hypothesis is often difficult. Thus, while e.g. an algorithm surprisingly is able to determine the gender of the author of a given text with about 80 percent accuracy [Argamon and Shimoni, 2003], for a human it takes some extra effort to understand on the basis of which criteria the algorithm is able to do so. With that respect the advantage of approaches using logic are obvious: If the output hypothesis is a formula of predicate logic, it is easy to interpret. However, if decision trees or algorithms from the area of inductive logic programming are based purely on classical logic, they suffer from the fact that most universal statements do not hold for exceptional cases, and classical logic does not offer any convenient way of representing statements which are meant to hold in the “normal case”. Thus, in the second part we will focus on approaches for Nonmonotonic Reasoning that try to handle this problem. Both Machine Learning and Nonmonotonic Reasoning have been anticipated partially by work in philosophy of science and philosophical logic. At the same time, recent developments in theoretical computer science are expected to trig- ger further progress in philosophical theories of inference, confirmation, theory revision, learning, and the semantic and pragmatics of conditionals. We hope this survey will contribute to this kind of progress by building bridges between computational, logical, and philosophical accounts of induction.

Famously, Frank P. Ramsey suggested a test for the acceptability of conditionals. Recently, David Chalmers and Alan Hájek (2007) have criticized a qualitative variant of the Ramsey test for indicative conditionals. In this paper we argue for the following three claims: (i) Chalmers and Hájek are right that the variant of the Ramsey test that they attack is not the correct way of spelling out an acceptability test for indicative conditionals. But there is a suppositional variant of the Ramsey test which is still stated in purely qualitative terms, which avoids the problems, and which looks correct. (ii) While the variant of the Ramsey test that Chalmers and Hájek criticize is not correct, it is still a good approximation of a correct formulation of the Ramsey test which may be usefully employed in various contexts. (iii) The variant of the Ramsey test that Chalmers and Hájek suggest as a substitute for the deficient version of the Ramsey test is itself subject to worries similar to those raised by Chalmers and Hájek, if it is given a non-suppositional interpretation

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 follow Accuracy, and we show that the only inaccuracy measures that do not give rise to such dilemmas are the quadratic inaccuracy measures. In the sequel, we derive the main tenets of Bayesianism from the relevant mathematical versions of Accuracy to which this characterization of the legitimate inaccuracy measures gives rise, but we also show that Jeffrey conditionalization has to be replaced by a different method of update in order for Accuracy to be satisfied.