The Twentieth Century has seen a dramatic rise in the use of probability and statistics in almost all fields of research. This has stimulated many new philosophical ideas on probability. _Philosophical Theories of Probability_ is the first book to present a clear, comprehensive and systematic account of these various theories and to explain how they relate to one another. Gillies also offers a distinctive version of the propensity theory of probability, and the intersubjective interpretation, which develops the subjective theory.

Philosophy of Science: A Unified Approach combines a general introduction to philosophy of science with an integrated survey of all its important subfields. As the book’s subtitle suggests, this excellent overview is guided methodologically by "a unified approach" to philosophy of science: behind the diversity of scientific fields one can recognize a methodological unity of the sciences. This unity is worked out in this book, revealing all the while important differences between subject areas. Structurally, this comprehensive book offers a two-part (...) approach, which makes it an excellent introduction for students new to the field and a useful resource for more advanced students. Each chapter is divided into two sections. The first section assumes no foreknowledge of the subject introduced, and the second section builds upon the first by bringing into the conversation more advanced, complementary topics. Definitions, key propositions, examples and figures overview all of the core material. At the end of every chapter there are selected readings and exercises . The book also includes a comprehensive bibliography and an index. (shrink)

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 most elaborate recent accounts of truthlikeness (verisimilitude) apply this notion primarily to generalizations in first-order languages with qualitative predicates. This paper outlines a new approach to the definition of truthlikeness for quantitative statements, including singular statements (point estimation), interval statements (interval estimation), and quantitative laws. In the case of laws, the basic issue is reduced to the topological problem of measuring the distance between two real-valued functions. The solution of this problem makes it possible to define also the notion (...) of approximate truth for quantitative laws. (shrink)

The philosophical theory of scientific explanation proposed here involves a radically new treatment of causality that accords with the pervasively statistical character of contemporary science. Wesley C. Salmon describes three fundamental conceptions of scientific explanation--the epistemic, modal, and ontic. He argues that the prevailing view is untenable and that the modal conception is scientifically out-dated. Significantly revising aspects of his earlier work, he defends a causal/mechanical theory that is a version of the ontic conception. Professor Salmon's theory furnishes a robust (...) argument for scientific realism akin to the argument that convinced twentieth-century physical scientists of the existence of atoms and molecules. To do justice to such notions as irreducibly statistical laws and statistical explanation, he offers a novel account of physical randomness. The transition from the "reviewed view" of scientific explanation to the causal/mechanical model requires fundamental rethinking of basic explanatory concepts. (shrink)

Scientific reasoning is—and ought to be—conducted in accordance with the axioms of probability. This Bayesian view—so called because of the central role it accords to a theorem first proved by Thomas Bayes in the late eighteenth ...

In this paper it is shown that, in spite of their intuitive starting points, Kuipers' accounts lead to counterintuitive consequences. The counterintuitive results of Kuipers' account of H-D confirmation stem from the fact that Kuipers explicates a concept of partial (as opposed to full) confirmation. It is shown that Schurz-Weingartner's relevant-element approach as well as Gemes' content-part approach provide an account of full confirmation that does not lead to these counterintuitive results. One of the unwelcome results of Kuipers' account of (...) nomic truthlikeness is the consequence that a theory Y, in order to be more truthlike than a theory X (where Y and X are incompatible), must imply the entire nomic truth. It is shown how the relevant-element approach to truthlikeness avoids this result. (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)

Several different Bayesian models of epistemic utilities (see, e. g., [37], [24], [40], [46]) have been used to explain why it is rational for scientists to perform experiments. In this paper, I argue that a model-suggested independently by Patrick Maher [40] and Graham Oddie [46]-that assigns epistemic utility to degrees of belief in hypotheses provides the most comprehensive explanation. This is because this proper scoring rule (PSR) model captures a wider range of scientifically acceptable attitudes toward epistemic risk than the (...) other Bayesian models that have been proposed. I also argue, however, that even the PSR model places unreasonably tight restrictions on a scientist's attitude toward epistemic risk. As a result, such Bayesian models of epistemic utilities fail as normative accounts-not just as descriptive accounts (see, e. g., [31], [14])-of scientific inquiry. (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 article is a reappraisal of the requirement of maximal specificity (RMS) proposed by the author as a means of avoiding "ambiguity" in probabilistic explanation. The author argues that RMS is not, as he had held in one earlier publication, a rough substitute for the requirement of total evidence, but is independent of it and has quite a different rationale. A group of recent objections to RMS is answered by stressing that the statistical generalizations invoked in probabilistic explanations must be (...) lawlike, and by arguing that predicates fit for occurrence in lawlike statistical probability statements must meet two conditions, at least one of which is violated in each of the counterexamples adduced in the objections. These considerations suggest the conception that probabilistic-statistical laws concern the long-run frequency of some characteristic within a reference class as characterized by some particular "description" or predicate expression, and that replacement of such a description by a coextensive one may turn a statement that is lawlike into another that is not. Finally, to repair a defect noted by Grandy, the author's earlier formulation of RMS is replaced by a modified version. (shrink)

A new approach to Hume's problem of induction that justifies the optimality of induction at the level of meta-induction. Hume's problem of justifying induction has been among epistemology's greatest challenges for centuries. In this book, Gerhard Schurz proposes a new approach to Hume's problem. Acknowledging the force of Hume's arguments against the possibility of a noncircular justification of the reliability of induction, Schurz demonstrates instead the possibility of a noncircular justification of the optimality of induction, or, more precisely, of meta-induction (...) (the application of induction to competing prediction models). Drawing on discoveries in computational learning theory, Schurz demonstrates that a regret-based learning strategy, attractivity-weighted meta-induction, is predictively optimal in all possible worlds among all prediction methods accessible to the epistemic agent. Moreover, the a priori justification of meta-induction generates a noncircular a posteriori justification of object induction. Taken together, these two results provide a noncircular solution to Hume's problem. Schurz discusses the philosophical debate on the problem of induction, addressing all major attempts at a solution to Hume's problem and describing their shortcomings; presents a series of theorems, accompanied by a description of computer simulations illustrating the content of these theorems (with proofs presented in a mathematical appendix); and defends, refines, and applies core insights regarding the optimality of meta-induction, explaining applications in neighboring disciplines including forecasting sciences, cognitive science, social epistemology, and generalized evolution theory. Finally, Schurz generalizes the method of optimality-based justification to a new strategy of justification in epistemology, arguing that optimality justifications can avoid the problems of justificatory circularity and regress. (shrink)

This monograph presents new ideas in nomic truth approximation. It features original and revised papers from a philosopher of science who has studied the concept for more than 35 years. Over the course of time, the author's initial ideas evolved. He discovered a way to generalize his first theory of nomic truth approximation, viz. by dropping an unnecessarily strong assumption. In particular, he first believed to have to assume that theories were maximally specific in the sense that they did not (...) only exclude certain conceptual possibilities, but also that all non-excluded possibilities were in fact claimed to be nomically possible. Now, he argues that the exclusion claim alone, or for that matter the inclusion claim alone, is sufficient to motivate the formal definition of being closer to the nomic truth. The papers collected here detail this generalized view of nomic truthlikeness or verisimilitude. Besides this, the book presents, in adapted form, the relation with several other topics, such as, domain revision, aesthetic progress, abduction, inference to the best explanation, pragmatic aspects, probabilistic methods, belief revision and epistemological positions, notably constructive realism. Overall, the volume presents profound insight into nomic truth approximation. This idea seeks to determine how one theory can be closer to, or more similar to, the truth about what is nomically, e.g. physically, chemically, biologically, possible than another theory. As a result, it represents the ultimate goal of theory oriented empirical science. Theo Kuipers is the author of Studies in Inductive Probability and Rational Expectation, From Instrumentalism to Constructive Realism and Structures in Science. He is the volume-editor of the Handbook on General Philosophy of Science. In 2005 there appeared two volumes of Essays in Debate with Theo Kuipers, entitled Confirmation, Empirical Progress, and Truth Approximation and Cognitive Structures in Scientific Inquiry. (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)

The concepts of coherence and confirmation are closely intertwined: according to a prominent proposal coherence is nothing but mutual confirmation. Accordingly, it should come as no surprise that both are confronted with similar problems. As regards Bayesian confirmation measures these are illustrated by the problem of tacking by conjunction. On the other hand, Bayesian coherence measures face the problem of belief individuation. In this paper we want to outline the benefit of an approach to coherence and confirmation based on content (...) elements. It will be shown that the resulting concepts, called genuine coherence and genuine confirmation, can be used in order to solve the two mentioned problems. In a final section we present some results on degrees of genuine coherence and genuine confirmation. (shrink)

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

This paper describes a theory of accuracy or approximate truth and applies it to problems in the realist interpretation of scientific theories. It argues not only that realism requires approximate truth, but that an adequate theory of approximation also presupposes some elements of a realist interpretation of theories. The paper distinguishes approximate truth from vagueness, probability and verisimilitude, and applies it to problems of confirmation and deduction from inaccurate premises. Basic results are cited, but details appear elsewhere. Objections are surveyed, (...) including arguments by Miller, Laymon, and Laudan. Comparison is made with Niiniluoto's theory of verisimilitude, and the utility of his theory for realism assessed. (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)

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.

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. (shrink)

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

We must restrict to mere probability not only statements of comparatively great uncertainty, like predictions about the weather, where we would cautiously ...

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)

It is undeniable that inductive reasoning has brought us much good. At least since Hume, however, philosophers have wondered how to justify our reliance on induction. In important recent work, Schurz points out that philosophers have been wrongly assuming that justifying induction is tantamount to showing induction to be reliable. According to him, to justify our reliance on induction, it is enough to show that induction is optimal. His optimality approach consists of two steps: an analytic argument for meta-induction (that (...) is, induction over inductive methods) and an application of meta-induction to empirical findings concerning the predictive accuracy of our actual inductive practices as compared to various non-inductive methods. The present article agrees with Schurz’s general conclusion but also argues that it leaves an important aspect of our inductive practices unaccounted for, to wit, that these practices have so far been highly successful; to satisfy the optimality requirement, induction only needs to be as successful as random guessing. To explain the success of induction, I turn to insights from social epistemology, also highlighted in Schurz’s work, and make these formally explicit in a framework that combines the Hegselmann–Krause model for opinion dynamics and Carnap’s system of λ rules. Within this framework, I use a standard evolutionary algorithm to show how communities of interacting agents may, through variation and selection, come to consist of highly successful inductive reasoners. (shrink)

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)

This paper presents an outline of a new theory of relevant deduction which arose from the purpose of solving paradoxes in various fields of analytic philosophy. In distinction to relevance logics, this approach does not replace classical logic by a new one, but distinguishes between relevance and validity. It is argued that irrelevant arguments are, although formally valid, nonsensical and even harmful in practical applications. The basic idea is this: a valid deduction is relevant iff no subformula of the conclusion (...) is replaceable on some of its occurrences by any other formula salva validitate of the deduction. The paper first motivates the approach by showing that four paradoxes seemingly very distant from each other have a common source. Then the exact definition of relevant deduction is given and its logical properties are investigated. An extension to relevance of premises is discussed. Finally the paper presents an overview of its applications in philosophy of science, ethics, cognitive psychology and artificial intelligence. (shrink)

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)

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)

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)

Philosophers of science as divergent as the inductivist Carnap and the deductivist Popper share the notion that the (logical) content of a proposition is given by its consequence class. I claim that this notion of content is (a) unintuitive and (b) inappropriate for many of the formal needs of philosophers of science. The basic problem is that given this notion of content, for any arbitrary p and q, [(p ∨ q)] will count as part of the content of both p (...) and q. In other words, any arbitrary p and q share some common content. This notion of content has disastrous effects on, for instance, Carnap's attempts to explicate the notion of confirmation in terms of probabilistic favorable relevance, and Popper's attempts to define verisimilitude. After briefly reviewing some of the problems of the traditional notion of content I present an alternative notion of (basic) content which (a) better fits our intuitions about content and (b) better serves the formal needs of philosophers of science. (shrink)