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.     

Verisimilitude based on concept analysis

In the paper ordering relations for comparison of verisimilitude of theories are introduced and discussed. The relations refer to semantic analysis of the results of theories, in particular to analysis of concepts the theories deal with.     

Zwart and Franssen’s impossibility theorem holds for possible-world-accounts but not for consequence-accounts to verisimilitude

Zwart and Franssen’s impossibility theorem reveals a conflict between the possible-world-based content-definition and the possible-world-based likeness-definition of verisimilitude. In Sect. 2 we show that the possible-world-based content-definition violates four basic intuitions of Popper’s consequence-based content-account to verisimilitude, and therefore cannot be said to be in the spirit of Popper’s account, although this is the opinion of some prominent authors. In Sect. 3 we argue that in consequence-accounts, content-aspects and likeness-aspects of verisimilitude are not in conflict with each other, but in agreement. We explain this fact by pointing towards the deep difference between possible-world- and the consequence-accounts, which does not lie in the difference between syntactic (object-language) versus semantic (meta-language) formulations, but in the difference between ‘disjunction-of-possible-worlds’ versus ‘conjunction-of-parts’ representations of theories. Drawing on earlier work, we explain in Sect. 4 how the shortcomings of Popper’s original definition can be repaired by what we call the relevant element approach. We propose a quantitative likeness-definition of verisimilitude based on relevant elements which provably agrees with the qualitative relevant content-definition of verisimilitude on all pairs of comparable theories. We conclude the paper with a plea for consequence-accounts and a brief analysis of the problem of language-dependence (Sect. 6).     

Approximative truth of fact-statements,laws, and theories

Summary The paper is a sketch of a conception of approximative truth (or verisimilitude). The concepts of relative error, and degree of inadequacy are introduced. By means of them the concept of truth-content of quantitative facts-statements, laws and theories is defined. Laws and theories accepted in science have a high truth-content, i.e. they are approximately true.     

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.     

Point-Free Geometry and Verisimilitude of Theories

A metric approach to Popper’s verisimilitude question is proposed which is related to point-free geometry. Indeed, we define the theory of approximate metric spaces whose primitive notions are regions, inclusion relation, minimum distance, and maximum distance between regions. Then, we show that the class of possible scientific theories has the structure of an approximate metric space. So, we can define the verisimilitude of a theory as a function of its (approximate) distance from the truth. This avoids some of the difficulties arising from the known definitions of verisimilitude.     

Truth and beauty in scientific reason

A rationalist and realist model of scientific revolutions will be constructed by reference to two categories of criteria of theory-evaluation, denominated indicators of truth and of beauty. Whereas indicators of truth are formulateda priori and thus unite science in the pursuit of verisimilitude, aesthetic criteria are inductive constructs which lag behind the progression of theories in truthlikeness. Revolutions occur when the evaluative divergence between the two categories of criteria proves too wide to be recomposed or overlooked. This model of revolutions depends upon a substantial new treatment of aesthetic criteria in science with which much of the paper will therefore be occupied.     

Verisimilitude and Belief Change for Conjunctive Theories

Theory change is a central concern in contemporary epistemology and philosophy of science. In this paper, we investigate the relationships between two ongoing research programs providing formal treatments of theory change: the (post-Popperian) approach to verisimilitude and the AGM theory of belief change. We show that appropriately construed accounts emerging from those two lines of epistemological research do yield convergences relative to a specified kind of theories, here labeled “conjunctive”. In this domain, a set of plausible conditions are identified which demonstrably capture the verisimilitudinarian effectiveness of AGM belief change, i.e., its effectiveness in tracking truth approximation. We conclude by indicating some further developments and open issues arising from our results.     

The Problem of Verisimilitude and Counting Partially Identical Properties

In this paper I propose a solution to the qualitative version of David Miller's verisimilitude reversal argument. Miller (1974) shows that verisimilitude rankings are relative to language choice and hence, are not objective. My solution stems from a reply to an earlier solution proposed by Eric Barnes (1991). Barnes argues that the verisimilitude reversal problem can be solved by revealing an epistemic dimension. I show that Miller's problem cannot be solved by side-stepping foundational metaphysical claims as his epistemic solution suggests. Rather, a substantive metaphysical basis grounds identity relations among properties. The problem of verisimilitude cannot be solved without embracing the fundamental metaphysical distinctions between basic and composite properties that ground the relationship of partial identity among properties.     

An impossibility theorem for verisimilitude

In this paper, we show that Arrow’s well-known impossibility theorem is instrumental in bringing the ongoing discussion about verisimilitude to a more general level of abstraction. After some preparatory technical steps, we show that Arrow’s requirements for voting procedures in social choice are also natural desiderata for a general verisimilitude definition that places content and likeness considerations on the same footing. Our main result states that no qualitative unifying procedure of a functional form can simultaneously satisfy the requirements of Unanimity, Independence of irrelevant alternatives and Non-dictatorship at the level of sentence variables. By giving a formal account of the incompatibility of the considerations of content and likeness, our impossibility result makes it possible to systematize the discussion about verisimilitude, and to understand it in more general terms.     

Decision-theoretic epistemology

In this paper, I examine the possibility of accounting for the rationality of belief-formation by utilising decision-theoretic considerations. I consider the utilities to be used by such an approach, propose to employ verisimilitude as a measure of cognitive utility, and suggest a natural way of generalising any measure of verisimilitude defined on propositions to partial belief-systems, a generalisation which may enable us to incorporate Popper's insightful notion of verisimilitude within a Bayesian framework. I examine a dilemma generated by the decision-theoretic procedure and consider an adequacy condition (immodesty) designed to ameliorate one of its horns. Finally, I argue in a sceptical vein that no adequate verisimilitude measure can be used decision-theoretically.I am grateful to Philip Percival for his very useful comments and criticism on earlier drafts. This paper was written with the support of a Scheuer fellowship, for which I am most thankful.     

Cliometric metatheory: II. Criteria scientists use in theory appraisal and why it is rational to do so

Definitive tests of theories are often impossible in the life sciences because auxiliary assumptions are problematic. In the appraisal of competing theories, history of science shows that scientists use various theory characteristics such as aspects of parsimony, the number, qualitative diversity, novelty, and numerical precision of facts derived, number of misderived facts, and reducibility relations to other accepted theories. Statistical arguments are offered to show why, given minimal assumptions about the world and the mind, many of these attributes are expectable correlates of verisimilitude. A statistical composite of these attributes could provide an actuarial basis for theory appraisal (cliometric metatheory).     

The path analysis controversy: a new statistical approach to strong appraisal of verisimilitude

A new approach for using path analysis to appraise the verisimilitude of theories is described. Rather than trying to test a model's truth (correctness), this method corroborates a class of path diagrams by determining how well they predict intradata relations in comparison with other diagrams. The observed correlation matrix is partitioned into disjoint sets. One set is used to estimate the model parameters, and a nonoverlapping set is used to assess the model's verisimilitude. Computer code was written to generate competing models and to test the conjectured model's superiority (relative to the generated set) using diagram combinatorics and is available on the Web (http://www.vanderbilt.edu/quantmetheval/downloads.htm).     

Verisimilitude: a causal approach

I present a new definition of verisimilitude, framed in terms of causes. Roughly speaking, according to it a scientific model is approximately true if it captures accurately the strengths of the causes present in any given situation. Against much of the literature, I argue that any satisfactory account of verisimilitude must inevitably restrict its judgments to context-specific models rather than general theories. We may still endorse—and only need—a relativized notion of scientific progress, understood now not as global advance but rather as the mastering of particular problems. This also sheds new light on longstanding difficulties surrounding language-dependence and models committed to false ontologies.     

A note on verisimilitude and relativization to problems

This note aims at critically assessing a little-noticed proposal made by Popper in the second edition ofObjective Knowledge to the effect that verisimilitude of scientific theories should be made relative to the problems they deal with. Using a simple propositional calculus formalism, it is shown that the relativized definition fails for the very same reason why Popper's original concept of verisimilitude collapsed-only if one of two theories is true can they be compared in terms of the suggested definition of versimilitude.This note was written when the author was visiting the Groupe de Recherche en Épistémologie Comparative (Université du Québec à Montréal).     

Verisimilitude and Content

Popper’s original definition of verisimilitude in terms of comparisons of truth content and falsity content has known counter-examples. More complicated approaches have met with mixed success. This paper uses a new account of logical content to develop a definition of verisimilitude that is close to Popper’s original account. It is claimed that Popper’s mistake was to couch his account of truth and falsity content in terms of true and false consequences. Comparison to a similar approach by Schurz and Wiengartner show certain advantages of this new approach.     

On comparison of theories by their contents

Popper's definition of verisimilitude was criticized for its paradoxical consequences in the case of false theories. The aim of this paper is to show that paradoxes disappear if the falsity content of a theory is defined with help of dCn or Cn ^–1.To the memory of Jerzy SupeckiI am grateful to David Pearce, Gerhard Schurz, Peter Simons, Maciej Spasowski and Jan Zygmunt for their helpful discussions on issues analysed in this paper. Particularly, Zygmunt's and Spasowski's comments enabled me to correct several mistakes of the earlier drafts.     

Truthlikeness without truth: A methodological approach

In this paper, an attempt is made to solve various problems posed to current theories of verisimilitude: (1) the (Miller's) problem of linguistic variance; (2) the problem of which are the best scientific methods for getting the most verisimilar theories; and (3) the question of the ontological commitment in scientific theories. As a result of my solution ot these problems, and with the help of other considerations of epistemological character, I conclude that the notion of Tarskian truth is dispensable in a rational (and realist) interpretation of the scientific enterprise. As a logical result, however, falsificationism will be vindicated.

... and in brief, a speaker must always aim at verisimilitude, and send the truth packing.

Plato,Phaedrus, 272 EI want to express my gratitude to Professors García-Bermejo, Niiniluoto, and Zofío for interesting comments and critiques of several of the ideas in this paper, and to Miss Karen Firnich for correcting my English. I am also thankful to an anonymous referee who indicated several dark points on a previous version of my article.     

Accuracy,Verisimilitude, and Scoring Rules

Suppose that beliefs come in degrees. How should we then measure the accuracy of these degrees of belief? Scoring rules are usually thought to be the mathematical tool appropriate for this job. But there are many scoring rules, which lead to different ordinal accuracy rankings. Recently, Fallis and Lewis [2016] have given an argument that, if sound, rules out many popular scoring rules, including the Brier score, as genuine measures of accuracy. I respond to this argument, in part by noting that the argument fails to account for verisimilitude—that certain false hypotheses might be closer to the truth than other false hypotheses are. Oddie [forthcoming], however, has argued that no member of a very wide class of scoring rules (the so-called proper scores) can appropriately handle verisimilitude. I explain how to respond to Oddie's argument, and I recommend a class of weighted scoring rules that, I argue, genuinely measure accuracy while escaping the arguments of Fallis and Lewis as well as Oddie.     

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.