Theo Kuipers

Assuming that the target of theory oriented empirical science in general and of nomic truth approximation in particular is to characterize the boundary or demarcation between nomic possibilities and nomic impossibilities, I have presented in Chap. 4 (“Models, postulates, and generalized nomic truth approximation”) the ‘basic’ version of generalized nomic truth approximation, starting from ‘two-sided’ theories. Its main claim is that nomic truth approximation can perfectly be achieved by combining two prima facie opposing views on theories: (1) the traditional (Popperian) view: theories are (sets of models of) postulates that exclude certain possibilities from being realizable, enabling explanation and prediction and (2) the model view: theories are sets of models that claim to (approximately) represent certain realizable possibilities. Nomic truth approximation, i.e., increasing truth-content and decreasing falsity-content, becomes in this way revising theories by revising their models and/or their postulates in the face of increasing evidence.The basic version of generalized nomic truth approximation is in many respects as simple as possible. Among other things, it is qualitative in the sense that it is purely based on set-theoretic relations. The present chapter presents the straightforward quantitative concretization of it. According to the ‘expected success theorem’, based on some probabilistic experimental conditions, greater truthlikeness, or verisimilitude, leads to greater expected empirical success. This enables tentative nomic truth approximation conclusions by abductive reasoning.

Assuming that the target of theory oriented empirical science in general and of nomic truth approximation in particular is to characterize the boundary or demarcation between nomic possibilities and nomic impossibilities, I have presented in Chap. 4 (“Models, postulates, and generalized nomic truth approximation”) the ‘basic’ version of generalized nomic truth approximation, starting from ‘two-sided’ theories. Its main claim is that nomic truth approximation can perfectly be achieved by combining two prima facie opposing views on theories: (1) the traditional (Popperian) view: theories are (sets of models of) postulates that exclude certain possibilities from being realizable, enabling explanation and prediction and (2) the model view: theories are sets of models that claim to (approximately) represent certain realizable possibilities. Nomic truth approximation, i.e., increasing truth-content and decreasing falsity-content, becomes in this way revising theories by revising their models and/or their postulates in the face of increasing evidence.The basic version of generalized nomic truth approximation is in many respects as simple as possible. Among other things, it does not take into account that one conceptual possibility may be more similar (or closer) to another than a third one (is to that other). However, for example, one theory may include a possibility that is more similar to a wrongly not included possibility than another theory can offer. Similarly, for wrongly not excluded possibilities. In this chapter it will be shown that such ‘refined’ considerations can be taken into account by adapted clauses based on a ternary similarity relation between possibilities (structures). This allows again abductive conclusions about refined truth approximation if a theory is persistently more successful in the refined sense than another.It will also be indicated and illustrated that this refined approach enables a specification to the effect that refined truth approximation can be obtained by the method of idealization and subsequent concretization. Finally, the basic and the refined approach will be evaluated with regard to some general principles and objections that have been discussed in the literature.

Assuming that the target of theory oriented empirical science in general and of nomic truth approximation in particular is to characterize the boundary or demarcation between nomic possibilities and nomic impossibilities, I have presented in Chap. 4 (“Models, postulates, and generalized nomic truth approximation”) the ‘basic’ version of generalized nomic truth approximation, starting from ‘two-sided’ theories. Its main claim is that nomic truth approximation can perfectly be achieved by combining two prima facie opposing views on theories: (1) the traditional (Popperian) view: theories are (sets of models of) postulates that exclude certain possibilities from being realizable, enabling explanation and prediction and (2) the model view: theories are sets of models that claim to (approximately) represent certain realizable possibilities. Nomic truth approximation, i.e., increasing truth-content and decreasing falsity-content, becomes in this way revising theories by revising their models and/or their postulates in the face of increasing evidence.The basic version of generalized nomic truth approximation is in many respects as simple as possible. Among other things, the basic version does not make a (theory-relative) distinction between an observational and a theoretical level. This raises the question to what extent in a stratified set-up (nomic) truth approximation on a theoretical level entails truth approximation on the observational level. In other words, the question whether ‘closer to the truth’ can be projected from the theoretical to the observational level. Of course, ‘empirical success’ is now explicated in observational terms, and ‘closer to the observational truth’ and ‘more successfulness’ are now related in the same way as in the unstratified case.The chapter closes with quantitative and refined versions of stratified nomic truth approximation in line with Chaps. 5 and 6, respectively. (Referential truth approximation is dealt with in Chap. 11 )

In this chapter I will draw a very general picture of an overall pragmatic theory of justification from the viewpoint of truth approximation. Crucial is the comparative definition of success according to which a theory P* is more successful than a theory P if and only if (1) P* shares all general successes of P, that is all empirically confirmed general implications, and has some extra ones, and (2) P shares all empirical counter-examples of P*. The rule of success says that if so far P* has been more successful than P, then – for the time being – accept P* as the better one and eliminate P. It is further argued that according to the pragmatic-instrumentalist view of scientific theories, theory elimination should exclusively be guided by the rule of success rather than by Popper’s rule of falsification – for it is pragmatically reasonable to accept the most successful theory available, even if this theory is known to be false. In the last part of the chapter, it is argued that the connection between pragmatic theory-success and truth approximation is otherwise rather close to Popper: at least ‘almost’ always, a theory which is closer to the truth will also turn out to be the pragmatically more successful theory. However, in the upshot, ‘being false’ and hence ‘being falsified’ are not very important for truth approximation.

Three related intuitions are explicated in this chapter. The first is the idea that there must be some kind of probabilistic version of the HD-method, a ‘Hypothetico-Probabilistic (HP-) method’, in terms of something like probabilistic consequences, instead of deductive consequences. According to the second intuition, the comparative application of this method should also be functional for some probabilistic kind of empirical progress, and according to the third intuition this should be functional for something like probabilistic truth approximation. In all three cases, the guiding idea is to explicate these intuitions by explicating the crucial notions as appropriate ‘concretizations’ of their basic or deductive analogues, being ‘idealizations’.It turns out that the comparative version of the proposed HP-method amounts to a sophisticated likelihood ratio success (SLRS-) method applied to the cumulated evidence. This method turns out to be not only functional for probabilistic empirical progress but also for probabilistic truth approximation. The latter is based on a probabilistic threshold theorem constituting for this reason the analogue of the deductive success theorem.This chapter is in fact a supplement to Chap. 5. Despite some terminological deviation, there is substantial partial overlap to enable independent reading.

This chapter primarily deals with the conceptual prospects for generalizing the aim of abduction from the standard one of explaining surprising or anomalous observations to that of empirical progress or even truth approximation. It turns out that the main abduction task then becomes the instrumentalist task of theory revision aiming at an empirically more successful theory, relative to the available data, but not necessarily compatible with them. The rest, that is, genuine empirical progress as well as observational, referential and theoretical truth approximation, is a matter of evaluation and selection, and possibly new generation tasks for further improvement. The chapter concludes with a survey of possible points of departure, in AI and logic, for computational treatment of the instrumentalist task guided by the ‘comparative evaluation matrix’.

An interesting consequence of the theory of nomic truth approximation, as developed in my From Instrumentalism to Constructive Realism (Kuipers T, From instrumentalism to constructive realism. On some relations between confirmation, empirical progress, and truth approximation. Synthese Library 287. Kluwer Academic Publishers, Dordrecht, 2000), and enriched in this book, concerns so-called ‘inference to the best explanation’ (IBE). It can be argued that this popular rule among scientific realists can better be replaced by, various kinds of, ‘inference to the best theory’ (IBT). This chapter provides a survey of observational, theoretical, and referential kinds of IBT and discusses when and in what sense they may be seen as cases of ‘abduction’, that is, arguments for which an ‘abductive’ formulation and, hence, justification can be given in the minimal sense of Peirce.Whereas it is difficult to imagine an abductive justification for IBE, especially due to its asymmetric character, it appears that abductive justifications can be given for IBT as the closest to the relevant truth, where ‘the (relevant) truth’ is defined as the strongest true claim that can be made with the relevant vocabulary about the relevant domain.The relation of IBT with the instrumentalist or evaluative use of the hypothetico-deductive (HD-)method is also indicated. In particular, it is argued that the theoretical kind of IBT may well be seen as the proper realist extension of the instrumentalist rule of success, prescribing to choose the most successful theory, whether already falsified or not.The chapter also introduces weak and strong forms of observational, theoretical, and referential induction. The weak forms merely conclude that a theory is true in the relevant sense and the strong forms can be seen as extreme special cases of the corresponding kinds of IBT, viz. ‘inference to the best theory as the relevant truth’. Finally, it is argued that the most benevolent and defensible reading of IBE combines IBT with the corresponding weak kind of induction.

Arguments for and against scientific realism usually presuppose as the main epistemic claim about theories that we may have good reasons to conclude that they are true, or at least approximately true. The antirealist charges against this claim are not easy to counter. In this chapter it is argued that the defense of realism is much easier if we relativize its epistemic claim in the light of (theories of) truth approximation. From this comparative realist perspective the main epistemic claim becomes that we may have good reasons to conclude that successor theories are closer to the truth than their predecessors. For example, although Einstein’s theory of general relativity may still be false, and not even approximately true, we have good reasons to assume that it is closer to the truth than Newton’s theory of gravitation. A similar relativization of claims that theoretical terms refer to things in the world is argued for in terms of ‘being closer to the referential truth’. For both purposes it is also plausible to relativize ‘being empirically successful’ to the comparative notion of ‘being (persistently) empirically more successful’.Comparative realism hence is realism guided by the comparative perspective on success and on truth approximation, that is, the notions of ‘more successful’ and ‘closer to the (observational, referential, and theoretical) truth’, and their mutual relations. This approach is defended against the antirealist charges and compared with the main other realist responses. The main positive claim of comparative realism is that (theoretical) truth approximation provides the (stratified) default explanation and prediction of empirical progress between non-empirically equivalent theories and of ‘aesthetic progress’ between empirically equivalent theories. Here ‘aesthetic progress’ is based on the comparative notion of ‘aesthetically more successful’ and specified in terms of the prevailing ‘aesthetic canon’ in the relevant field and period, that is, the prevailing non-empirical virtues of theories.

Gustavo Cevolani et al. (Erkenntnis 75(2):183–202, 2011) have shown that their account of verisimilitude of ‘conjunctive theories’ of a finite propositional language can be nicely linked to a variant of AGM belief set revision, viz. belief base revision, in the sense that the latter kind of revision is functional for truth approximation according to the conjunctive account. In the present chapter I offer a generalization of these ideas to the case of approaching any divide of a (finite or infinite) universe, allowing several interpretations, besides true (false) atomic propositions, notably nomic states (not) in equilibrium, nomic (im-)possibilities, (non-)instantiated ‘Q-predicates’ of a monadic language. It shows how and why approximation of ‘the true boundary’ takes place by belief base revision guided by evidence.In the nomic (im-)possibilities interpretation this chapter essentially deals with a belief base revision perspective on basic and quantitative nomic truth approximation of two-sided theories in the sense of Chaps. 4 and 5. The previous chapter dealt with a belief set revision (i.e., AGM-) perspective on basic and refined nomic truth approximation of (one-sided) exclusion theories. This chapter will leave the challenge open of a belief base revision perspective on refined nomic truth approximation of two-sided theories, and, more generally, a belief base perspective on refined approximation of ‘the true boundary’ belonging to whatever interpretation.

Straightforward theory revision, taking into account as effectively as possible the established nomic possibilities and, on their basis induced empirical laws, is conducive for nomic truth approximation. The question this paper asks is: is it possible to reconstruct the relevant theory revision steps, on the basis of incoming evidence, in the terms of so-called belief revision and, more specifically, in the terms of belief set revision, also called the AGM-approach? Assumin g exclusion theories, a positive answer will be given in two rounds, first for the case in which the initial theory is compatible with the established empirical laws, then for the case in which it is incompatible with at least one such a law.

Nomic truth approximation and its relation to confirmation and empirical progress were the leading themes of my book From instrumentalism to constructive realism of 2000. The present book offers again a synthesis of articles. It concerns in the first place six chapters ( 2, 3, 4, 5, 6, and 7 ) dealing with a very broad generalization of the theory of nomic truth approximation, discovered in 2012. Moreover it presents adapted and otherwise revised versions of nine previously published articles (8–16) about extensions, related kinds of reasoning, including belief revision, and the resulting epistemological position. This introductory chapter starts with a global description of this background. Then it presents the main conclusions of From instrumentalism to constructive realism, which roughly remain valid. This is followed by an overview of all chapters and next a list with references to the origin of them. It concludes with some indications for new research in order to compare the presented approach with other approaches.

In my From Instrumentalism to Constructive Realism (2000) 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 chapter 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. The resulting generalized and thereby simplified approach to nomic truth approximation was strongly stimulated by the related work on conjunctive theories of Gustavo Cevolani, Vincenzo Crupi and Roberto Festa (Erkenntnis, 2011), in particular their systematic way of defining the truth- and falsity-content of a theory. It will be shown that explicating ‘(nomic) truth approximation’ and ‘empirical progress’ in these terms does justice to some basic instrumentalist/empiricist and realist conditions of adequacy.

The account of nomic truth approximation by empirical progress presented in Chap. 2 is based on the exclusion claim of theories. It is a simplified and generalized version of the one presented in my book From Instrumentalism to Constructive Realism of 2000. However, its core itself, called the basic account, is based on several idealizations. In this chapter I will sketch a number of possible concretizations, to begin with a two-sided, otherwise also basic, version, based on an exclusion and inclusion claim, followed by quantification, refinement and stratification of this two-sided version. They will be elaborated in Chaps. 4, 5, 6, and 7.Chapter 2 also illustrated straightforwardly how a theory of truth approximation in relation to empirical progress can be set up. The general tenet and the common elements will be summarized in this chapter. It will lead to a general outline of theories of nomic truth approximation by empirical progress. This will guide, explicitly or implicitly, the elaborating Chaps. 4, 5, 6, and 7.Moreover, the common core of such theories of nomic truth approximation will also be summarized: the Nomic Principle, postulating a unique divide between nomic possibilities and impossibilities, the formal structure of nomic evidence, in terms of realized (nomic) possibilities and induced generalizations, and the hypothetico-deductive background of nomic evidence.

The qualitative theory of nomic truth approximation, presented in Kuipers (From instrumentalism to constructive realism. On some relations between confirmation, empirical progress, and truth approximation. Synthese library, vol. 287. Kluwer Academic Publishers, Dordrecht, 2000), in which ‘the truth’ concerns the distinction between nomic, e.g. physical, possibilities and impossibilities, rests on a very restrictive assumption viz. that theories always claim to characterize the boundary between nomic possibilities and impossibilities. In Chap. 2 we have already shown that truth approximation is possible by ascribing, in Popperian spirit, theories only an excluding function. By fully recognizing two different functions of theories, viz. excluding and representing (including), this chapter drops the restrictive assumption by conceiving theories in development as tuples of postulates and models, where the postulates claim to exclude nomic impossibilities and the (not-excluded) models claim to represent nomic possibilities.Revising such ‘two-sided’ theories becomes then a matter of adding or revising models and/or postulates in the light of increasing evidence, now captured by a special kind of theories, viz. ‘data-theories’. Under the assumption that the data-theory is true, achieving empirical progress on its basis provides good reasons for the abductive conclusion that truth approximation has been achieved as well. As in Chap. 2, the notions of truth approximation and empirical progress are formally direct generalizations of the earlier ones. However, truth approximation is now explicitly defined in two-sided terms of increasing truth-content and decreasing falsity-content of theories, whereas empirical progress is defined in terms of lasting increased accepted-content and decreased rejected-content in the light of increasing evidence. As already noted in Chap. 2, these definitions are strongly inspired by a paper of Gustavo Cevolani, Vincenzo Crupi and Roberto Festa, viz., “Verisimilitude and belief change for conjunctive theories” (Erkenntnis, 2011).

The theory of nomic truth approximation essentially deals primarily with truth approximation by theory revision for a fixed domain. However, variable domains and a fixed theory can also be taken into account, where the main changes concern domain extensions and restrictions. In this chapter I will present a coherent set of definitions of ‘more truthlikeness’, ‘empirical progress’ and ‘truth approximation’ due to a revision of the ‘domain of intended applications’. This set of definitions seems to be the natural counterpart of the basic definitions of similar notions as far as theory revision is concerned.The resulting formal aspects of theory and domain revision strongly suggest an analogy between truth approximation and design research, for example, drug research: a new drug (theory) may be better for a certain disease (domain) than an old one. However, it also occurs that a certain drug may be better for another disease than for the original target disease, a phenomenon which was nicely captured by the title of a study by Rein Vos (1991): Drugs Looking for Diseases. Similarly, truth approximation may not only take the shape of theory revision but also of domain revision, naturally suggesting the phenomenon of ‘Theories looking for domains’. However, whereas Vos documented his title with a number of examples, so far, apart from plausible cases of ‘truth accumulation by domain extension’ and the conjecture that cases of so-called Kuhn-loss can be reconstructed as cases of ‘truth approximation by domain restriction’, I did not find clear-cut but more complex empirical instantiations of the analogy, only some very interesting, non-empirical examples.

In this chapter 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. It was initiated by Robert Zajonc (Attitudinal effects of mere exposure. J Pers Soc Psychol Monogr Suppl 9:1–27, 1968). 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 revolution 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 non-empirical 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.

The qualitative theory of nomic truth approximation, presented in Kuipers in his (from instrumentalism to constructive realism, 2000), in which ‘the truth’ concerns the distinction between nomic, e.g. physical, possibilities and impossibilities, rests on a very restrictive assumption, viz. that theories always claim to characterize the boundary between nomic possibilities and impossibilities. Fully recognizing two different functions of theories, viz. excluding and representing, this paper drops this assumption by conceiving theories in development as tuples of postulates and models, where the postulates claim to exclude nomic impossibilities and the (not-excluded) models claim to represent nomic possibilities. Revising theories becomes then a matter of adding or revising models and/or postulates in the light of increasing evidence, captured by a special kind of theories, viz. ‘data-theories’. Under the assumption that the data-theory is true, achieving empirical progress in this way provides good reasons for the abductive conclusion that truth approximation has been achieved as well. Here, the notions of truth approximation and empirical progress are formally direct generalizations of the earlier ones. However, truth approximation is now explicitly defined in terms of increasing truth-content and decreasing falsity-content of theories, whereas empirical progress is defined in terms of lasting increased accepted and decreased rejected content in the light of increasing evidence. These definitions are strongly inspired by a paper of Gustavo Cevolani, Vincenzo Crupi and Roberto Festa, viz., “Verisimilitude and belief change for conjunctive theories” (Cevolani et al. in Erkenntnis 75(2):183–222, 2011).

Carnap’s The continuum of inductive methods (University of Chicago Press, 1952) is frequently mentioned as an historical milestone in inductive logic, but seldom used in age old problem situations. In this paper it will be shown that the application of Carnapian distributions may be very plausible in certain cases, in particular in coproduction with the Bayesian way of dealing with problems. This will be illustrated in perhaps the simplest possible way, viz. in the context where the question whether a (i.i.d.) device is fair is at stake.

This collection of 17 articles offers an overview of the philosophical activities of a group of philosophers (who have been) working at the Groningen University. The meta-methodological assumption which unifies the research of this group, holds that there is a way to do philosophy which is a middle course between abstract normative philosophy of science and descriptive social studies of science. On the one hand it is argued with social studies of science that philosophy should take notice of what scientists actually do. On the other hand, however, it is claimed that philosophy can and should aim to reveal cognitive patterns in the processes and products of scientific and common sense knowledge. Since it is thought that those patterns can function as guidelines in new research and/or in research in other disciplines, philosophy can nevertheless hold on to the normative aim which is characteristic of 'classical' philosophy of science. Compared to this common assumption, there is a diversity of subjects. Some papers deal with general problems of science, knowledge, cognition and argumentation, others with topics relating to foundational problems of particular sciences. Therefore this volume is of interest to philosophers of science, to philosophers of knowledge and argumentation in general, to philosophers of mind, as well as for scientists working in the physical and applied sciences, biology, psychology and economy who are interested in the foundations of their disciplines. After a foreword by Leszek Nowak and a general introduction by the editors, the book is divided into four parts, with special introductions. - I: Conceptual Analysis in Service of Various Research Programmes (Henk Zandvoort, Rein Vos, Rick Looijen, Gerben Stavenga, Renée Dalitz); - II: The Logic of the Evaluation of Arguments, Hypotheses, Default Rules, and Interesting Theorems (Erik Krabbe, Theo Kuipers, Alfons Keupink, Maarten Janssen/Yao-Hua Tan, Bert Hamminga); - III: Three Challenges to the Truth Approximation Programme (Sjoerd Zwart, Hinne Hettema/Theo Kuipers, Roberto Festa); - IV: Explicating Psychological Intuitions (Anne-Ruth Mackor, Jeanne Peijnenburg, Lex Guichard, Michel ter Hark). The Groningen research group was recently qualified, by an official international assessment committee, as one of the best philosophy research groups in the Netherlands.

Examples of hypotheses about the number of planets are frequently used to introduce the topic of (actual) truthlikeness but never analyzed in detail. In this paper we first deal with the truthlikeness of singular quantity hypotheses, with reference to several ‘the number of planets’ examples, such as ‘The number of planets is 10 _versus_ 10 billion (instead of 8).’ For the relevant ratio scale of quantities we will propose two, strongly related, normalized metrics, the proportional metric and the (simplest and hence favorite) fractional metric, to express e.g. the distance from a hypothetical number to the true number of planets, i.e. the distance between quantities. We argue that they are, in view of the examples and plausible conditions of adequacy, much more appropriate, than the standardly suggested, normalized absolute difference, metric. Next we deal with disjunctive hypotheses, such as ‘The number of planets is between 7 and 10 inclusive is much more truthlike than between 1 and 10 billion inclusive.’ We compare three (clusters of) general ways of dealing with such hypotheses, one from Ilkka Niiniluoto, one from Pavel Tichý and Graham Oddie, and a trio of ways from Theo Kuipers. Using primarily the fractional metric, we conclude that all five measures can be used for expressing the distance of disjunctive hypotheses from the actual truth, that all of them have their strong and weak points, but that (the combined) one of the trio is, in view of principle and practical considerations, the most plausible measure.