In this paper, we address the problem of truth approximation through theory change, asking whether revising our theories by newly acquired data leads us closer to the truth about a given domain. More particularly, we focus on “nomic conjunctive theories”, i.e., theories expressed as conjunctions of logically independent statements concerning the physical or, more generally, nomic possibilities and impossibilities of the domain under inquiry. We define both a comparative and a quantitative notion of the verisimilitude of such theories, and identify (...) suitable conditions concerning the (partial) correctness of acquired data, under which revising our theories by data leads us closer to “the nomic truth”, construed as the target of scientific inquiry. We conclude by indicating some further developments, generalizations, and open issues arising from our results. (shrink)

In this paper we provide a compact presentation of the verisimilitudinarian approach to scientific progress (VS, for short) and defend it against the sustained attack recently mounted by Alexander Bird (2007). Advocated by such authors as Ilkka Niiniluoto and Theo Kuipers, VS is the view that progress can be explained in terms of the increasing verisimilitude (or, equivalently, truthlikeness, or approximation to the truth) of scientific theories. According to Bird, VS overlooks the central issue of the appropriate grounding of scientific (...) beliefs in the evidence, and it is therefore unable (a) to reconstruct in a satisfactory way some hypothetical cases of scientific progress, and (b) to provide an explanation of the aversion to falsity that characterizes scientific practice. We rebut both of these criticisms and argue that they reveal a misunderstanding of some key concepts underlying VS. (shrink)

Theories of truthlikeness (or verisimilitude) are currently being classified according to two independent distinctions: that between ‘content’ and ‘likeness’ accounts, and that between ‘conjunctive’ and ‘disjunctive’ ones. In this article, I present and discuss a new definition of truthlikeness, which employs Carnap’s notion of the content elements entailed by a theory or proposition, and is then labelled ‘Carnapian’. After studying in detail the properties and shortcomings of this definition, I argue that it occupies a unique position in the landscape of (...) different approaches to truthlikeness. More precisely, I show that it provides the only explication of truthlikeness which is both ‘conjunctive’ and ‘content-based’ in a suitably defined sense. (shrink)

Popper’s original definition of truthlikeness relied on a central insight: that truthlikeness combines truth and information, in the sense that a proposition is closer to the truth the more true consequences and the less false consequences it entails. As intuitively compelling as this definition may be, it is untenable, as proved long ago; still, one can arguably rely on Popper’s intuition to provide an adequate account of truthlikeness. To this aim, we mobilize some classical work on partial entailment in defining (...) a new measure of truthlikeness which satisfies a number of desiderata. The resulting account has some interesting and surprising connections with other accounts on the market, thus shedding new light on current attempts of systematizing different approaches to verisimilitude. (shrink)

I argue that scientific progress is precisely the accumulation of scientific knowledge.

Belief revision (BR) and truthlikeness (TL) emerged independently as two research programmes in formal methodology in the 1970s. A natural way of connecting BR and TL is to ask under what conditions the revision of a belief system by new input information leads the system towards the truth. It turns out that, for the AGM model of belief revision, the only safe case is the expansion of true beliefs by true input, but this is not very interesting or realistic as (...) a model of theory change in science. The new accounts of non-prioritized belief revision do not seem more promising in this respect, and the alternative BR account of updating by imaging leads to other problems. Still, positive results about increasing truthlikeness by belief revision may be sought by restricting attention to special kinds of theories. Another approach is to link truthlikeness to epistemic matters by an estimation function which calculates expected degrees of truthlikeness relative to evidence. Then we can study how the expected truthlikeness of a theory changes when probabilities are revised by conditionalization or imaging. Again, we can ask under what conditions such changes lead our best theories towards the truth. (shrink)

The subject of the present inquiry is the approach-to-the-truth research, which started with the publication of Sir Karl Popper's Conjectures and Refutations. In the decade before this publication, Popper fiercely attacked the ideas of Rudolf Carnap about confirmation and induction; and ten years later, in the famous tenth chapter of Conjectures he introduced his own ideas about scientific progress and verisimilitude. Abhorring inductivism for its apprecia tion of logical weakness rather than strength, Popper tried to show that fallibilism could serve (...) the purpose of approach to the truth. To substantiate this idea he formalized the common sense intuition about preferences, that is: B is to be preferred to A if B has more advantages andfewer drawbacks than A. In 1974, however, David Millerand Pavel Tichy proved that Popper's formal explication could not be used to compare false theories. Subsequently, many researchers proposed alternatives or tried to improve Popper's original definition. (shrink)

This collection brings together several essays which have been written between the years 197 5 and 1983. During that period I have been occupied with the attempt to find a satisfactory explicate for the notion of tnithlike ness or verisimilitude. The technical results of this search have partly appeared elsewhere, and I am also working on a systematic presentation of them in a companion volume to this book: Truthlikeness. The essays collected in this book are less formal and more philos (...) ophical: they all explore various aspects of the idea that progress in science is associated with an increase in the truthlikeness of its results. Even though they do not exhaust the problem area of scientific change, together they constitute a step in the direction which I find most promising in the defence of critical scientific realism. * Chapter 1 appeared originally in Finnish as the opening article of a new journal Tiede 2000 - a Finnish counterpart to journals such as Science and Scientific American. This explains its programmatic character. It tries to give a compact answer to the question 'What is science?', and serves therefore as an introduction to the problem area of the later chapters. Chapter 2 is a revised translation of my inaugural lecture for the chair of Theoretical Philosophy in the University of Helsinki on April 8, 1981. It appeared in Finnish inParnasso 31, pp. (shrink)

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. (shrink)

Measures of theory-Distance are defined for theories formalizable within first-Order predicate logic by using distributive normal forms. The account is applied to give measures of verisimilitude.

Of two false theories, One can be, Intuitively, Closer to the truth than the other. The purpose of the article is to propose a rigorous explication of this intuitive notion.

2 Popper's Logical Definition of Verisimilitude. 3 Popper's Probabilistic Definition of Verisimilitude. 4 Conclusion.

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). (shrink)

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 versus semantic 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. (shrink)

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.

What does it take for one proposition to be closer to the truth than another. In this, the first published monograph on the topic, Oddie develops a comprehensive theory that takes the likeness in truthlikeness seriously.

Theories of verisimilitude have routinely been classified into two rival camps—the content approach and the likeness approach—and these appear to be motivated by very different sets of data and principles. The question thus naturally arises as to whether these approaches can be fruitfully combined. Recently Zwart and Franssen (Synthese 158(1):75–92, 2007) have offered precise analyses of the content and likeness approaches, and shown that given these analyses any attempt to meld content and likeness orderings violates some basic desiderata. Unfortunately their (...) characterizations of the approaches do not embrace the paradigm examples of those approaches. I offer somewhat different characterizations of these two approaches, as well as of the consequence approach (Schurz and Weingartner (Synthese 172(3):415–436, 2010) which happily embrace their respective paradigms. Finally I prove that the three approaches are indeed compatible, but only just, and that the cost of combining them is too high. Any account which combines the strictures of what I call the strong likeness approach with the demands of either the content or the consequence approach suffers from precisely the same defect as Popper’s—namely, it entails the trivialization of truthlikeness. The downside of eschewing the strong likeness constraints and embracing the content constraints alone is the underdetermination of the concept of truthlikeness. (shrink)

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. (shrink)

The modern history of verisimilitude can be divided into three periods. The first began in 1960, when Karl Popper proposed his qualitative definition of what it is for one theory to be more truthlike than another theory, and lasted until 1974, when David Miller and Pavel Trich published their refutation of Popper's definition. The second period started immediately with the attempt to explicate truthlikeness by means of relations of similarity or resemblance between states of affairs (or their linguistic representations); the (...) work within this similarity approach was summarized in the books of Graham Oddie [1986] and Ilkka Niiniluoto [1987]. During the subsequent third period, studies in verisimilitude have been actively continued, and interesting results and applications have been achieved, but not many dramatic novelties. While it is now obsolete to claim that truthlikeness with reasonable properties cannot be defined at all, there is still a lot of controversy about the best and least arbitrary approach to doing this. (shrink)

The modern history of verisimilitude can be divided into three periods. The first began in 1960, when Karl Popper proposed his qualitative definition of what it is for one theory to be more truthlike than another theory, and lasted until 1974, when David Miller and Pavel Trichý published their refutation of Popper's definition. The second period started immediately with the attempt to explicate truthlikeness by means of relations of similarity or resemblance between states of affairs (or their linguistic representations); the (...) work within this similarity approach was summarized in the books of Graham Oddie [1986] and Ilkka Niiniluoto [1987]. During the subsequent third period, studies in verisimilitude have been actively continued, and interesting results and applications have been achieved, but not many dramatic novelties. While it is now obsolete to claim that truthlikeness with reasonable properties cannot be defined at all, there is still a lot of controversy about the best and least arbitrary approach to doing this. (shrink)

According to the foundationalist picture, shared by many rationalists and positivist empiricists, science makes cognitive progress by accumulating justified truths. Fallibilists, who point out that complete certainty cannot be achieved in empirical science, can still argue that even successions of false theories may progress toward the truth. This proposal was supported by Karl Popper with his notion of truthlikeness or verisimilitude. Popper’s own technical definition failed, but the idea that scientific progress means increasing truthlikeness can be expressed by defining degrees (...) of truthlikeness in terms of similarities between states of affairs. This paper defends the verisimilitude approach against Alexander Bird who argues that the “semantic” definition is not sufficient to define progress, but the “epistemic” definition referring to justification and knowledge is more adequate. Here Bird ignores the crucial distinction between real progress and estimated progress, explicated by the difference between absolute degrees of truthlikeness and their evidence-relative expected values. Further, it is argued that Bird’s idea of returning to the cumulative model of growth requires an implausible trick of transforming past false theories into true ones. (shrink)

This paper utilizes Scott domains (continuous lattices) to provide a mathematical model for the use of idealized and approximately true data in the testing of scientific theories. Key episodes from the history of science can be understood in terms of this model as attempts to demonstrate that theories are monotonic, that is, yield better predictions when fed better or more realistic data. However, as we show, monotonicity and truth of theories are independent notions. A formal description is given of the (...) pragmatic virtues of theories which are monotonic. We also introduce the stronger concept of continuity and show how it relates to the finite nature of scientific computations. Finally, we show that the space of theories also has the structure of a Scott domain. This result provides an analysis of how one theory can be said to approximate another. (shrink)

In my From Instrumentalism to Constructive Realism I have shown how an instrumentalist account of empirical progress can be related to nomic truth approximation. However, it was assumed that a strong notion of nomic theories was needed for that analysis. In this paper it is shown, in terms of truth and falsity content, that the analysis already applies when, in line with scientific common sense, nomic theories are merely assumed to exclude certain conceptual possibilities as nomic possibilities.

Surprisingly, modified versions of the confirmation theory (Carnap and Hempel) and truth approximation theory (Popper) turn out to be smoothly sythesizable. The glue between the two appears to be the instrumentalist methodology, rather than that of the falsificationalist. The instrumentalist methodology, used in the separate, comparative evaluation of theories in terms of their successes and problems (hence, even if already falsified), provides in theory and practice the straight road to short-term empirical progress in science ( à la Laudan). It is (...) also argued that such progress is also functional for all kinds of truth approximation: observational, referential, and theoretical. This sheds new light on the long-term dynamics of science and hence on the relation between the main epistemological positions, viz., instrumentalism (Toulmin, Laudan), constructive empiricism (Van Fraassen), referential realism (Hacking, Cartwright), and theory realism of a non-essentialist nature (constructive realism à la Popper). Readership: Open minded philosophers and scientists. The book explains and justifies the scientist's intuition that the debate among philosophers about instrumentalism and realism has almost no practical consequences. (shrink)

In this article I give a naturalistic-cum-formal analysis of the relation between beauty, empirical success, and truth. The analysis is based on the one hand on a hypothetical variant of the so-called 'mere-exposure effect' which has been more or less established in experimental psychology regarding exposure-affect relationships in general and aesthetic appreciation in particular (Zajonc 1968; Temme 1983; Bornstein 1989; (Ye 2000). On the other hand it is based on the formal theory of truthlikeness and truth approximation as presented in (...) my From Instrumentalism to Constructive Realism (2000). The analysis supports the findings of James McAllister in his beautiful Beauty and Revolutiorl in Science (1996), by explaining and justifying them. First, scientists are essentially right in regarding aesthetic criteria useful for empirical progress and even for truth approximation, provided they conceive of them as less hard than empirical criteria. Second, the aesthetic criteria of the time, the 'aesthetic canon', may well be based on 'aesthetic induction' regarding nonempirical features of paradigms of successful theories which scientists have come to appreciate as beautiful. Third, aesthetic criteria can play a crucial, schismatic role in scientific revolutions. Since they may well be wrong, they may, in the hands of aesthetic conservatives, retard empirical progress and hence truth approximation, but this does not happen in the hands of aesthetically flexible, 'revolutionary' scientists. (shrink)

This book is concerned with the problem of applying the theory of verisimilitude to cognitive problems of a quantitative nature. Attention is mostly focused on hypotheses concerned with (physical or other) systems whose state can be represented with an element of a multidimensional state space, but hypotheses concerned with quantitative laws are also considered. The book provides a systematic introduction to the main contemporary forms of the theory of verisimilitude, including both proposed definitions of quantitative degrees of verisimilitude and proposed (...) definitions of the relation `closer to the truth than'. It shows why the quantitative measures that have been proposed earlier produce unacceptable results in the multidimensional case and, using the tools of geometric measure theory, works out alternatives for them in detail. In addition, the standard structuralist theory of science and the way in which the problems of approximation are dealt with in it are presented and evaluated critically. (shrink)

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. (shrink)

Popper’s original definition of truthlikeness relied on a central insight: that truthlikeness combines truth and information, in the sense that a proposition is closer to the truth the more true consequences and the less false consequences it entails. As intuitively compelling as this definition may be, it is untenable, as proved long ago; still, one can arguably rely on Popper’s intuition to provide an adequate account of truthlikeness. To this aim, we mobilize some classical work on partial entailment in defining (...) a new measure of truthlikeness which satisfies a number of desiderata. The resulting account has some interesting and surprising connections with other accounts on the market, thus shedding new light on current attempts of systematizing different approaches to verisimilitude. (shrink)

Popper formulates and explains his non-justificationist theory of knowledge. Science--empirical science--aims at true explanatory theories, yet it can never prove, finally establish, or justify any of its theories as true, not even if it is in fact a true theory. Science must continue to question and criticize all its theories, even those which happen to be true.