The present article shows that there are consistent and decidable manyvalued systems of propositional logic which satisfy two or all the three criteria for non-trivial inconsistent theories by da Costa . The weaker one of these paraconsistent system is also able to avoid a series of paradoxes which come up when classical logic is applied to empirical sciences. These paraconsistent systems are based on a 6-valued system of propositional logic for avoiding difficulties in several domains of empirical science ).

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. (shrink)

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. (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)

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). (shrink)

Knowledge representation is a central issue in a number of areas, but few attempts are usually made to bridge different approaches accross different fields. As a contribution in this direction, in this paper I focus on one such approach, the theory of conceptual spaces developed within cognitive science, and explore its potential applications in the fields of philosophy of science and formal epistemology. My case-study is provided by the theory of truthlikeness, construed as closeness to “the whole truth” about a (...) given domain, as described in the underlying language. I show how modeling propositions and their relations within a conceptual space has interesting implications for two issues in truthlikeness theory: the so called problem of language dependence, and that of measure sensitivity. I conclude by pointing at some open issues arising from the application of conceptual spaces to the analysis of philosophical problems. (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)

This paper aims at elucidating the connection between explanatory considerations and epistemic justification stipulated by explanationism which take epistemic justification to be definable in terms of best explanations. By relying on the notion of truthlikeness, this paper argues that it is rational for a subject to expect the best explanation she has for her evidence to be more truthlike than any of the other potential explanations available to her by virtue of containing a class of propositions that, given her evidence, (...) she is justified in believing. Based on this elucidation of the connection between explanatory considerations and epistemic justification, an explanationist account of the evidential support relation is then offered. (shrink)

This undergraduate textbook introduces some fundamental issues in philosophy of science for students of philosophy and science students. The book is divided into two parts. Part 1 deals with knowledge and values. Chap. 1 presents the classical conception of knowledge as initiated by the ancient Greeks and elaborated during the development of science, introducing the central concepts of truth, belief and justification. Aspects of the quest for objectivity are taken up in the following two chapters. Moral issues are broached in (...) Chap. 4, which discusses some aspects of the use and abuse of science, taking up the responsibilities of scientists in properly conducting their business and decision-makers in their concerns with the import of science for society. Part 2 contrasts the view of scientific progress as the rejecting of old hypotheses and theories and replacing them with new ones, represented by Karl Popper, with the conception of progress as accumulating knowledge, saving as much as possible from older theories, represented by Pierre Duhem. A concluding chapter defends the natural attitude of taking the theories of modern science to be literally true, i.e. realism, in the face of arguments drawn partly from the history of scientific progress in criticism of this stance. (shrink)

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.

The paper discusses problems which arise in attempts to axiomatize parts of religion or religious belief systems. Besides those problems already investigated by Bochenski, like that of the propositional content or the meaning of religious discourse there are several further ones. This paper deals with the question whether full Classical Logic is suitable, whether one universe of discourse is sufficient, how to use definitions and analogous concepts and whether justifications satisfy credibility criteria.

The paper offers a matrix-based logic (relevant matrix quantum physics) for propositions which seems suitable as an underlying logic for empirical sciences and especially for quantum physics. This logic is motivated by two criteria which serve to clean derivations of classical logic from superfluous redundancies and uninformative complexities. It distinguishes those valid derivations (inferences) of classical logic which contain superfluous redundancies and complexities and are in this sense from those which are or in the sense of allowing only the most (...) informative consequences in the derivations. The latter derivations are strictly valid in RMQ, whereas the former are only materially valid. RMQ is a decidable matrix calculus which possesses a semantics and has the finite model property. It is shown in the paper how RMQ by its strictly valid derivations can avoid the difficulties with commensurability, distributivity, and Bell's inequalities when it is applied to quantum physics. (shrink)

The purpose of this paper is to discuss conditions of rationality for scientific research (SR) where "conditions" are understood as "necessary conditions". This will be done in the following way: First, I shall deal with the aim of SR since conditions of rationality (for SR) are to be understood as necessary means for reaching the aim (goal) of SR. Subsequently, the following necessary conditions will be discussed: Rational Communication, Methodological Rules, Ideals of Rationality and its Realistic Aspects, Methodological and Ontological (...) Conditions (Universality, Rules for Experiments, Causality), and Metaphysical Presuppositions and Extrapolations. (shrink)

This article proposes a basic logic for application in physics dispensing with the Principle of Excluded Middle. It is based on the article “Matrix Based Logics for Application in Physics (RMQ) which appeared 2009. In his article with Stachow on the Principle of Excluded Middle in Quantum Logic (QL), Peter Mittelstaedt showed that for some suitable QLs, including their own, the Principle of Excluded Middle can be added without any harm for QL; where ‘without any harm for QL’ means that (...) the basic desiderata and the basic results (theorems) of those QLs remain satised in the sense that they avoid the well known difficulties with commensurability and distributivity.In the following article I want to show that the basic desiderata and results (theorems) of RMQ (of avoiding the well-known difficulties with commensurability, distributivity, fusion and Bell’s inequalities) remain satised if by introducing a strong negation (or strong negation and disjunction) the resulting weak intuitionist system RMQI dispenses with the Principle of Excluded Middle; it becomes either invalid or not strictly valid. (shrink)

In this paper, we take a fresh look at three Popperian concepts: riskiness, falsifiability, and truthlikeness of scientific hypotheses or theories. First, we make explicit the dimensions that underlie the notion of riskiness. Secondly, we examine if and how degrees of falsifiability can be defined, and how they are related to various dimensions of the concept of riskiness as well as the experimental context. Thirdly, we consider the relation of riskiness to truthlikeness. Throughout, we pay special attention to probabilistic theories (...) and we offer a tentative, quantitative account of verisimilitude for probabilistic theories. (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 (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.

In “What price coherence?”, Klein and Warfield put forward a simple argument that triggered an extensive debate on the epistemic virtues of coherence. As is well-known, this debate yielded far-reaching impossibility results to the effect that coherence is not conducive to truth, even if construed in a ceteris paribus sense. A large part of the present paper is devoted to a re-evaluation of these results. As is argued, all explications of truth-conduciveness leave out an important aspect: while it might not (...) be the case that coherence is truth-conducive, it might be conducive to verisimilitude or epistemic utility. Unfortunately, it is shown that the answer for both these issues must be in the negative, again. Furthermore, we shift the focus from sets of beliefs to particular beliefs: as is shown, neither is any of the extant probabilistic measures of coherence truth-conducive on the level of particular beliefs, nor does weakening these measures to quasi-orderings establish the link between coherence and truth for an important amount of measures. All in all, the results in this paper cast a serious doubt on the approach of establishing a link between coherence and truth. Finally, recent arguments that shift the focus from the relationship between coherence and truth to the one between coherence and confirmation are assessed. (shrink)

This is a response to the papers in the special issue Logical Perspectives on Science and Cognition—The Philosophy of Gerhard Schurz.

This paper describes the development of theories of scientific explanation since Hempel's earliest models in the 1940ies. It focuses on deductive and probabilistic whyexplanations and their main problems: lawlikeness, explanation-prediction asymmetries, causality, deductive and probabilistic relevance, maximal specifity and homogenity, the height of the probability value. For all of these topic the paper explains the most important approaches as well as their criticism, including the author's own accounts. Three main theses of this paper are: (1) Both deductive and probabilistic explanations (...) are important in science, not reducible to each other. (2) One must distinguish between (cause giving) explanations and (reason giving) justifications and predictions. (3) The adequacy of deductive as well as probabilistic explanations is relative to a pragmatically given background knowledge-which does not exclude, however, the possibility of purely semantic models. (shrink)

The paper starts with the distinction between conjunction-of-parts accounts and disjunction-of-possibilities accounts to truthlikeness. In Sect. 3, three distinctions between kinds of truthlikeness measures are introduced: comparative versus numeric t-measures, t-measures for qualitative versus quantitative theories, and t-measures for deterministic versus probabilistic truth. These three kinds of truthlikeness are explicated and developed within a version of conjunctive part accounts based on content elements. The focus lies on measures of probabilistic truthlikeness, that are divided into t-measures for statistical probabilities and single (...) case probabilities. The logical notion of probabilistic truthlikeness can be treated as a subcase of deterministic truthlikeness for quantitative theories. In contrast, the epistemic notion of probabilistic truthlikeness creates genuinely new problems, especially for hypotheses about single case probabilities that are evaluated not by comparison to observed frequencies, but by comparison to the truth values of single event statements. By the method of meta-induction, competing theories about single case probabilities can be aggregated into a combined theory with optimal predictive success and epistemic truthlikeness. (shrink)

It is shown that the criteria of T-theoreticity proposed by Balzer and Gähde lead to strongly counterintuitive and in this sense paradoxical results: most of the obviously empirical or at least nontheoretical terms come out as theoretical. This is demonstrated for a lot of theories in different areas. On the way, some improved and some new structuralist theory-reconstructions are given. The conclusion is drawn that the T-theoreticity of a term cannot possibly be proved on the basis of the mathematical structure (...) of theory T alone (as Gähde and Balzer suggest). Rather, an independent notion of pre-T-theoreticity and-more importantly-of empiricity is needed; i.e., not empirical and not pre-T-theoretical are independent, necessary but not sufficient conditions for T-theoretical (this is also a necessary complement of Sneed's original criterion). Finally it is asked whether the structuralist criterion of T-theoreticity complemented by such independent conditions would be a satisfactory answer to Putnam's challenge, and the answer again is negative: the criterion is not able to distinguish between empirically contentful and completely contentless (superfluous) theoretical terms. (shrink)

The basic theory of scientific understanding presented in Sections 1–2 exploits three main ideas.First, that to understand a phenomenonP (for a given agent) is to be able to fitP into the cognitive background corpusC (of the agent).Second, that to fitP intoC is to connectP with parts ofC (via arguments in a very broad sense) such that the unification ofC increases.Third, that the cognitive changes involved in unification can be treated as sequences of shifts of phenomena inC. How the theory fits (...) typical examples of understanding and how it excludes spurious unifications is explained in detail. Section 3 gives a formal description of the structure of cognitive corpuses which contain descriptive as well as inferential components. The theory of unification is then refined in the light of so called puzzling phenomena, to enable important distinctions, such as that between consonant and dissonant understanding. In Section 4, the refined theory is applied to several examples, among them a case study of the development of the atomic model. The final part contains a classification of kinds of understanding and a discussion of the relation between understanding and explanation. (shrink)

Criteria of approximate scientific success are defined within a formal paradigm of empirical inquiry. One consequence of aiming for less than perfect truth is examined.

A criterion of adequacy is proposed for theories of relevant consequence. According to the criterion, scientists whose deductive reasoning is limited to some proposed subset of the standard consequence relation must not thereby suffer a reduction in scientific competence. A simple theory of relevant consequence is introduced and shown to satisfy the criterion with respect to a formally defined paradigm of empirical inquiry.

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)

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)

The notion of truthlikeness or verisimilitude has been a topic of intensive discussion ever since the definition proposed by Karl Popper was refuted in 1974. This paper gives an analysis of old and new debates about this notion. There is a fairly large agreement about the truthlikeness ordering of conjunctive theories, but the main rival approaches differ especially about false disjunctive theories. Continuing the debate between Niiniluoto’s min-sum measure and Schurz’s relevant consequence measure, the paper also gives a critical assessment (...) of Oddie’s new defense of the average measure and Kuipers’ refined definition of truth approximation. (shrink)

The notion of truthlikeness or verisimilitude has been a topic of intensive discussion ever since the definition proposed by Karl Popper was refuted in 1974. This paper gives an analysis of old and new debates about this notion. There is a fairly large agreement about the truthlikeness ordering of conjunctive theories, but the main rival approaches differ especially about false disjunctive theories. Continuing the debate between Niiniluoto’s min-sum measure and Schurz’s relevant consequence measure, the paper also gives a critical assessment (...) of Oddie’s new defense of the average measure and Kuipers’ refined definition of truth approximation. (shrink)

After Karl Popper’s original work, several approaches were developed to provide a sound explication of the notion of verisimilitude. With few exceptions, these contributions have assumed that the truth to be approximated is deterministic. This collection of ten papers addresses the more general problem of approaching probabilistic truths. They include attempts to find appropriate measures for the closeness to probabilistic truth and to evaluate claims about such distances on the basis of empirical evidence. The papers employ multiple analytical approaches, and (...) connect the research to related issues in the philosophy of science. (shrink)

The concept of approximate truth plays a prominent role in most versions of scientific realism. However, adequately conceptualizing ?approximate truth? has proved challenging. This article argues that the goal of articulating the concept of approximate truth can be advanced by first investigating the processes by which science accords theories the status of accepted or rejected. Accordingly, this article uses a path diagram model as a visual heuristic for the purpose of showing the processes in science that are involved in determining (...) a theory's status. This ?inductive realist? model of theory status then serves as a starting point for explicating an inductive realist view of approximate truth that, it is argued, can explain instances of the success of science, but does not (1) require science's theories to be strictly true in any world or (2) require a metric for measuring how close an approximately true theory is to some strictly true theory. To show the advantages of the inductive realist approach to approximate truth, an example of a major success story of science, the successful eradication of smallpox, is reviewed and then explained. (shrink)

This paper develops a semantical model - theoretic account of (logical) content complementing the syntactically specified account of content developed in "A New Theory of Content I", JPL 23: 596-620, 1994. Proofs of Completeness are given for both propositional and quantificational languages (without identity). Means for handling a quantificational language with identity are also explored. Finally, this new notion of content is compared, in respect of both logical properties and philosophical applications, to alternative partitions of the standard consequence class relation (...) proposed by Stelzner, Schurz and Wiengartner. (shrink)

I provide and defend a hyper-intensional account of verisimilitude within the truthmaker framework.

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)

The Linda paradox is a key topic in current debates on the rationality of human reasoning and its limitations. We present a novel analysis of this paradox, based on the notion of verisimilitude as studied in the philosophy of science. The comparison with an alternative analysis based on probabilistic confirmation suggests how to overcome some problems of our account by introducing an adequately defined notion of verisimilitudinarian confirmation.

In robustness analysis, hypotheses are supported to the extent that a result proves robust, and a result is robust to the extent that we detect it in diverse ways. But what precise sense of diversity is at work here? In this paper, I show that the formal explications of evidential diversity most often appealed to in work on robustness – which all draw in one way or another on probabilistic independence – fail to shed light on the notion of diversity (...) relevant to robustness analysis. I close by briefly outlining a promising alternative approach inspired by Horwich’s (1982) eliminative account of evidential diversity. (shrink)