Truth approximation,belief merging,and peer disagreement

In this paper, we investigate the problem of truth approximation via belief merging, i.e., we ask whether, and under what conditions, a group of inquirers merging together their beliefs makes progress toward the truth about the underlying domain. We answer this question by proving some formal results on how belief merging operators perform with respect to the task of truth approximation, construed as increasing verisimilitude or truthlikeness. Our results shed new light on the issue of how rational (dis)agreement affects the inquirers’ quest for truth. In particular, they vindicate the intuition that scientific inquiry, and rational discussion in general, benefits from some heterogeneity in opinion and interaction among different viewpoints. The links between our approach and related analyses of truth tracking, judgment aggregation, and opinion dynamics, are also highlighted.     

Approximation,Idealization, and Laws of Nature

Traditional theories construe approximate truth or truthlikeness as a measure of closeness to facts, singular facts, and idealization as an act of either assuming zero of otherwise very small differences from facts or imagining ideal conditions under which scientific laws are either approximately true or will be so when the conditions are relaxed. I first explain the serious but not insurmountable difficulties for the theories of approximation, and then argue that more serious and perhaps insurmountable difficulties for the theory of idealization force us to sever its close tie to approximation. This leads to an appreciation of lawlikeness as a measure of closeness to laws, which I argue is the real measure of idealization whose main purpose is to carve nature at its joints. This revised version was published online in June 2006 with corrections to the Cover Date.     

Probability,Approximate Truth,and Truthlikeness: More Ways out of the Preface Paradox

The so-called Preface Paradox seems to show that one can rationally believe two logically incompatible propositions. We address this puzzle, relying on the notions of truthlikeness and approximate truth as studied within the post-Popperian research programme on verisimilitude. In particular, we show that adequately combining probability, approximate truth, and truthlikeness leads to an explanation of how rational belief is possible in the face of the Preface Paradox. We argue that our account is superior to other solutions of the paradox, including a recent one advanced by Hannes Leitgeb (Analysis 74.1).     

Naive and refined truth approximation

The naive structuralist definition of truthlikeness is an idealization in the sense that it assumes that all mistaken models of a theory are equally bad. The natural concretization is a refined definition based on an underlying notion of structurelikeness.In Section 1 the naive definition of truthlikeness of theories is presented, using a new conceptual justification, in terms of instantial and explanatory mistakes.In Section 2 general constraints are formulated for the notions of structurelikeness and truthlikeness of structures.In Section 3 a refined definition of truthlikeness of theories is presented, based on the notion of structurelikeness, using a sophisticated version of the conceptual justification for the naive definition.In Section 4 it is shown that idealization and concretization is a special kind of potentially refined truth approximation.I would like to acknowledge that van Benthem (1987) played in several respects a crucial role in the research for a new refined definition. Moreover, I like to thank David Miller, Ilkka Niiniluoto, and two referees for their comments on an earlier version. One of the referees notes that the Miller version of the naive approach (in model-theoretic terms, and identifying the truth with the truth about the actual world) has been criticised on several occasions for its failure to accommodate likeness between structures by Oddie (notably Oddie, 1986). The idea that likeness between structures should be a guiding idea behind truthlikeness is said to be a constant theme of Oddie's work. All this may well be true, but I should add however that Oddie's publications did not play any role in my research. The local references to Oddie are based on the suggestions by the referee.     

Verisimilitude and Belief Revision. With a Focus on the Relevant Element Account

The expansion or revision of false theories by true evidence does not always increase their verisimilitude. After a comparison of different notions of verisimilitude the relation between verisimilitude and belief expansion or revision is investigated within the framework of the relevant element account. We are able to find certain interesting conditions under which both the expansion and the revision of theories by true evidence is guaranteed to increase their verisimilitude.     

Truly Justified Belief

I defend the view that justified belief is preferable to plain belief only because the former enhances the likelihood that the belief is true: call that sort of justification truth-linked. A collection of philosophical theories either state outright that this is not so, imply it via other doctrines, or adopt a notion of truth that renders the link innocuous. The discussion proceeds as follows. Issues and various positions are outlined, and needed qualifications are entered (parts I-III). We then note general shortcomings of all views rejecting the truth-link, and critically examine a powerful thought experiment underlying the rejection (part IV). In the final sections we explore two other challenges to the truth-link. First (part V), we consider forms of idealized justification theory that would imply the independence of justification from the relevant sort of truth conduciveness; next (part VI) we investigate a view, Pragmatism, which maintains that epistemic justification is sanctioned by ends other than a tendency towards truth.     

The Dangers of Pragmatic Virtue

Many people want to hold that some theoretical virtues—simplicity, elegance, familiarity or others—are only pragmatic virtues. That is, these features do not give us any more reason to think a theory is true, or close to true, but they justify choosing one theoretical option over another because they are desirable for some other, practical purpose. Using pragmatic virtues in theory choice apparently brings with it a dilemma: if we are deciding what to accept on the basis of considerations that are not truth-conducive, it looks like we should either refrain from believing what we accept, and adopt some sort of instrumentalist attitude to the theories we cherish; or alternatively, we stand charged with engaging in theoretical irrationality in our belief formation. This paper discusses the appropriate response to this dilemma.     

How Truth Behaves When There’s No Vicious Reference

In The Revision Theory of Truth (MIT Press), Gupta and Belnap (1993) claim as an advantage of their approach to truth “its consequence that truth behaves like an ordinary classical concept under certain conditions—conditions that can roughly be characterized as those in which there is no vicious reference in the language.” To clarify this remark, they define Thomason models, nonpathological models in which truth behaves like a classical concept, and investigate conditions under which a model is Thomason: they argue that a model is Thomason when there is no vicious reference in it. We extend their investigation, considering notions of nonpathologicality and senses of “no vicious reference” generated both by revision theories of truth and by fixed-point theories of truth. We show that some of the fixed-point theories have an advantage analogous to that which Gupta and Belnap claim for their approach, and that at least one revision theory does not. This calls into question the claim that the revision theories have a distinctive advantage in this regard.     

A Critique of the Constitutive Role of Truthlikeness in the Similarity Approach

The similarity approach stands as a significant attempt to defend scientific realism from the attack of the pessimistic meta-induction. The strategy behind the similarity approach is to shift from an absolute notion of truth to the more flexible one of truthlikeness. Nonetheless, some authors are not satisfied with this attempt to defend realism and find that the notion of truthlikeness is not fully convincing. The aim of this paper is to analyze and understand the reasons of this dissatisfaction. Our thesis is that the dissatisfaction with the notion of truthlikeness concerns the double role that this notion plays within the similarity approach: This notion plays both a regulative role in the conception of theories and a constitutive one in their selection.     

Coherence and Conservatism in the Dynamics of Belief

In this paper I discuss the foundations of a formal theory of coherent and conservative belief change that is (a) suitable to be used as a method for constructing iterated changes of belief, (b) sensitive to the history of earlier belief changes, and (c) independent of any form of dispositional coherence. I review various ways to conceive the relationship between the beliefs actually held by an agent and her belief change strategies (that also deal with potential belief sets), show the problems they suffer from, and suggest that belief states should be represented by unary revision functions that take sequences of inputs. Three concepts of coherence implicit in current theories of belief change are distinguished: synchronic, diachronic and dispositional coherence. Diachronic coherence is essentially identified with what is known as conservatism in epistemology. The present paper elaborates on the philosophical motivation of the general framework; formal details and results are provided in a companion paper.     

Truth in the Tractatus

My paper takes issue both with the standard view that the Tractatus contains a correspondence theory and with recent suggestions that it features a deflationary or semantic theory. Standard correspondence interpretations are mistaken, because they treat the isomorphism between a sentence and what it depicts as a sufficient condition of truth rather than of sense. The semantic/deflationary interpretation ignores passages that suggest some kind of correspondence theory. The official theory of truth in the Tractatus is an obtainment theory – a sentence is true iff the state of affairs it depicts obtains. This theory differs from deflationary theories in that it involves an ontology of states of affairs/facts; and it can be transformed into a type of correspondence theory: a sentence is true iff it corresponds to, i.e. depicts an obtaining state of affairs (fact). Admittedly, unlike correspondence theories as commonly portrayed, this account does not involve a genuinely truth-making relation. It features a relation of correspondence, yet it is that of depicting, between a meaningful sentence and its sense – a possible state of affairs. What makes for truth is not that relation, but the obtaining of the depicted state of affairs. This does not disqualify the Tractatus from holding a correspondence theory, however, since the correspondence theories of Moore and Russell are committed to a similar position. Alternatively, the obtainment theory can be seen as a synthesis of correspondence, semantic and deflationary approaches. It does justice to the idea that what is true depends solely on what is the case, and it combines a semantic explanation of the relation between a sentence and what it says with a deflationary account of the agreement between what the sentence says and what obtains or is the case if it is true     

Editorial Introduction

I survey some important semantical and axiomatic theories of self-referential truth. Kripke's fixed-point theory, the revision theory of truth and appraoches involving fuzzy logic are the main examples of semantical theories. I look at axiomatic theories devised by Cantini, Feferman, Freidman and Sheard. Finally some applications of the theory of self-referential truth are considered.     

On the aim of the theory of verisimilitude

J. P. Z. Bonilla's methodological approach to truthlikeness is evaluated critically. On a more general level, various senses in which the theory of truthlikeness could be seen as a theory concerned with methodology are distinguished, and it is argued that providing speical sciences with methodological tools is unrealistic as an aim of the theory of verisimilitude. Rather, when developing this theory, one should rest contnet with the more modest aim of conceptual analysis, or of providing explications for the relational concept of being closer to the truth. In addition, some remarks will be made on the difficulties which the similarity approach to truthlikeness has in realizing this aim and which are caused by the important role that Hintikka's constituents have in it.     

Truth-conditions,truth-bearers and the new B-theory of time

In this paper I consider two strategies for providing tenseless truth-conditions for tensed sentences: the token-reflexive theory and the date theory. Both theories have faced a number of objections by prominent A-theorists such as Quentin Smith and William Lane Craig. Traditionally, these two theories have been viewed as rival methods for providing truth-conditions for tensed sentences. I argue that the debate over whether the token-reflexive theory or the date theory is true has arisen from a failure to distinguish between conditions for the truth of tensed tokens and conditions for the truth of propositions expressed by tensed tokens. I demonstrate that there is a true formulation of the token-reflexive theory that provides necessary and sufficient conditions for the truth of tensed tokens, and there is a true formulation of the date theory that provides necessary and sufficient conditions for the truth of propositions expressed by tensed tokens. I argue that once the views are properly formulated, the A-theorist’s objections fail to make their mark. However, I conclude by claiming that even though there is a true formulation of the token-reflexive theory and a true formulation of the date theory, the New B-theory nonetheless fails to provide a complete account of the truth and falsity of tensed sentences.

Taking aim at the truth

One prominent feature of belief is that a belief cannot be formed at will. This paper argues that the best explanation of this fact is that belief formation is a process that takes aim at the truth. Taking aim at the truth is to be understood as causal responsiveness of the processes constituting belief formation to what facilitates achieving true beliefs. The requirement for this responsiveness precludes the possibility of belief formation responding to intentions in a way that would count as forming a belief at will.     

Truthlikeness,Rationality And Scientific Method

I. A. Kieseppä's criticism of the methodological use of the theory of verisimilitude, and D. B. Resnik's arguments against the explanation of scientific method by appeal to scientific aims are critically considered. Since the notion of verisimilitude was introduced as an attempt to show that science can be seen as a rational enterprise in the pursuit of truth, defenders of the verisimilitude programme need to show that scientific norms can be interpreted (at least in principle) as rules that try to increase the degree of truthlikeness of scientific theories. This possibility is explored for several approaches to the problem of verisimilitude.     

Australasian Journal of Philosophy Contents of Volume 88

Veritism says that the fundamental source of epistemic value for a doxastic state is the extent to which it represents the world correctly: that is, its fundamental epistemic value is determined entirely by its truth or falsity. The Swamping Problem says that Veritism is incompatible with two pre-theoretic beliefs about epistemic value: (I) a true justified belief is more (epistemically) valuable than a true unjustified belief; (II) a false justified belief is more (epistemically) valuable than a false unjustified belief. In this paper, I consider the Swamping Problem from the vantage-point of decision theory. I note that the central premise in the argument is what Stefánsson and Bradley call Chance Neutrality in Richard Jeffrey’s decision-theoretic framework. And I describe their argument that it should be rejected. Using this insight, I respond to the Swamping Problem on behalf of the veritist.     

Convergence to the Truth Without Countable Additivity

Must probabilities be countably additive? On the one hand, arguably, requiring countable additivity is too restrictive. As de Finetti pointed out, there are situations in which it is reasonable to use merely finitely additive probabilities. On the other hand, countable additivity is fruitful. It can be used to prove deep mathematical theorems that do not follow from finite additivity alone. One of the most philosophically important examples of such a result is the Bayesian convergence to the truth theorem, which says that conditional probabilities converge to 1 for true hypotheses and to 0 for false hypotheses. In view of the long-standing debate about countable additivity, it is natural to ask in what circumstances finitely additive theories deliver the same results as the countably additive theory. This paper addresses that question and initiates a systematic study of convergence to the truth in a finitely additive setting. There is also some discussion of how the formal results can be applied to ongoing debates in epistemology and the philosophy of science.

     

Belief Revision and Verisimilitude Based on Preference and Truth Orderings

In this rather technical paper we establish a useful combination of belief revision and verisimilitude according to which better theories provide better predictions, and revising with more verisimilar data results in theories that are closer to the truth. Moreover, this paper presents two alternative definitions of refined verisimilitude, which are more perspicuous than the algebraic version used in previous publications.