Suppose that scientific realists believe that a successful theory is approximately true, and that constructive empiricists believe that it is empirically adequate. Whose belief is more likely to be false? The problem of underdetermination does not yield an answer to this question one way or the other, but the pessimistic induction does. The pessimistic induction, if correct, indicates that successful theories, both past and current, are empirically inadequate. It is arguable, however, that they are approximately true. Therefore, scientific realists overall (...) take less epistemic risk than constructive empiricists. (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)

The main question addressed in this paper is whether some false sentences can constitute evidence for the truth of other propositions. In this paper it is argued that there are good reasons to suspect that at least some false propositions can constitute evidence for the truth of certain other contingent propositions. The paper also introduces a novel condition concerning propositions that constitute evidence that explains a ubiquitous evidential practice and it contains a defense of a particular condition concerning (...) the possession of evidence. The core position adopted here then is that false propositions that are approximately true reports of measurements can constitute evidence for the truth of other propositions. So, it will be argued that evidence is only quasi-factive in this very specific sense. (shrink)

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)

There is good reason to suppose that our best physical theories, quantum mechanics and special relativity, are false if taken together and literally. If they are in fact false, then how should they count as providing knowledge of the physical world? One might imagine that, while strictly false, our best physical theories are nevertheless in some sense probably approximately true. This paper presents a notion of local probable approximate truth in terms of descriptive nesting relations between current and (...) subsequent theories. This notion helps explain how false physical theories might nevertheless provide physical knowledge of a variety that is particularly salient to diachronic empirical inquiry. (shrink)

Arguably, there is no substantial, general answer to the question of what makes for the approximate truth of theories. But in one class of cases, the issue seems simply resolved. A wide class of applied dynamical theories can be treated as two-component theories—one component specifying a certain kind of abstract geometrical structure, the other giving empirical application to this structure by claiming that it replicates, subject to arbitrary scaling for units etc., the geometric structure to be found in (...) some real-world dynamical phenomenon. In such a case, a theory is approximately true just if the one geometric structure approximately replicates the other (and if problems remain here, they are problems in geometry, of specifying suitable metric approximation relations, not conceptual problems). This article amplifies and defends this simple approach to approximate truth for dynamical theories. (shrink)

The technical results presented here on continuity and approximate implication are obviously incomplete. In particular, a syntactic characterization of approximate implication is highly desirable. Nevertheless, I believe the results above do show that the theory has considerable promise for application to the areas mentioned at the top of the paper.Formulation and defense of realist interpretations of science, for example, require approximate truth because we hardly ever have evidence that a particular scientific theory corresponds perfectly with a (...) portion of the real world. Realists need to assert, then, that evidence for a theory is evidence for its approximate truth, not its truth (see [3] and [18]). Approximate truth is, however, a vague notion, and specification of quantity terms and of a sense of approximation are needed to make precise applications of it. Suitability of both vocabulary and sense of approximation depend on the subject matter, and their selection is a partly empirical matter that raises complex issues. In light of the number of common inferences which are not continuous, realists also need to be concerned about indiscriminate use of deductive logic to derive consequences from approximately true theories. These issues will be considered further in a future paper.Approximate truth also has potential application in areas of artificial intelligence that require inference from inaccurate data. In the ‘qualitative’ physical theories of de Kleer and Brown [6], for example, ‘qualitative’ values are derived by partitioning the real numbers into regions. Inferences leading from inside to outside a region must be identified and avoided, and approximate implication and continuity may prove useful in doing this. More generally, growing use of predicate logic as a programming language invites application of the theory of approximate truth as a symbolic substitute for numerical evaluation of computation errors. This too will be the subject of a future paper. (shrink)

Approximation involves representing things in ways that might be close to the truth but are nevertheless false. Given the widespread reliance on approximations in science and everyday life, here we ask whether it is conceptually possible for false approximations to qualify as knowledge. According to the factivity account, it is impossible to know false approximations, because knowledge requires truth. According to the representational adequacy account, it is possible to know false approximations, if they are close enough to the (...) truth for present purposes. In this paper, we adopt an experimental methodology to begin testing these two theories. When an agent provides a false and practically inadequate answer, both theories predict that people will deny knowledge. But the theories disagree about an agent who provides a false but practically adequate answer: the factivity hypothesis again predicts knowledge denial, whereas the representational adequacy hypothesis predicts knowledge attribution. Across two experiments, our principal finding was that people tended to attribute knowledge for false but practically adequate answers, which supports the representational adequacy account. We propose an interpretation of existing findings that preserves a conceptual link between knowledge and truth. According to this proposal, truth is not necessary for knowledge, but it is a feature of prototypical knowledge. (shrink)

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

In this paper I show that Goodman's theory of projectibility, although partly successful, is inadequate since it fails to take into consideration the "approximate" nature of certain scientific hypotheses.

Scientific Realists argue that it would be a miracle if scientific theories were getting more predictive without getting closer to the truth; so they must be getting closer to the truth. Van Fraassen, Laudan et al. argue that owing to the underdetermination of theory by data (UDT) for all we know, it is a miracle, a fluke. So we should not believe in even the approximate truth of theories. I argue that there is a test for (...) who is right: suppose we are at the limit of inquiry. Suppose that we then have all the logically possible theories that are adequate to all the actual data. If they all resembled in their theoretical claims, since one of them must be true, all of them would then resemble it, whichever it is. We would thus be justified in saying they all approximated the truth in the degree to which they co-resembled. If they don't all co-resemble, the SRs are wrong; more predictive theories are not necessarily closer to the theoretical truth. Prior to the limit, if, in spite of our best efforts to the contrary, all the theories we can make adequate to current data tend to co-resemble, we have inductive warrant for thinking more predictive theories are closer to the truth. If they don't resemble, we have inductive warrant for thinking that more predictive theories are not necessarily closer to the truth. (shrink)

Most commonly, the scientific realism debate is seen as dividing those who do and do not think that the striking empirical and practical successes of at least our best scientific theories indicate with high probability that those theories are ‘approximately true’. But I want to suggest that this characterization of the debate has far outlived its usefulness. Not only does it obscure the central differences between two profoundly different types of contemporary scientific realist, but even more importantly it serves to (...) disguise the most substantial points of actual disagreement between these two kinds of realists and those who instead think the historical record of scientific inquiry itself reveals that such realism is untenable in either form. (shrink)

I examine the role that approximate truth plays in arguments for convergent realism and diagnose some difficulties that face attempts to defend realism by employing this slippery concept. Approximate truth plays two important roles in convergent realism : it functions as a truth surrogate and it helps explain the success of science. I argue that approximate truth cannot perform both of these roles. If it adequately fulfills its role as a truth surrogate, (...) then it cannot explain the success of science. If it adequately explains the success of science, then it cannot function as a truth surrogate. (shrink)

Scientists and Bayesian statisticians often study hypotheses that they know to be false. This creates an interpretive problem because the Bayesian probability of a hypothesis is supposed to represent the probability that the hypothesis is true. I investigate whether Bayesianism can accommodate the idea that false hypotheses are sometimes approximately true or that some hypotheses or models can be closer to the truth than others. I argue that the idea that some hypotheses are approximately true in an absolute sense (...) is hard to square with Bayesianism, but that the notion that some hypotheses are comparatively closer to the truth than others can be made compatible with Bayesianism, and that this provides an adequate and potentially useful solution to the interpretive problem. Finally, I compare my ``verisimilitude'' solution to the interpretive problem with a ``counterfactual'' solution recently proposed by Jan Sprenger. (shrink)

The example can be generalized. Suppose that ϕ and ψ are suffi- ciently different functions of an independent variable t. We may show that whenever X’s predictions for ϕ and ψ lie (weakly) between Z’s predictions and T’s predictions (the true values), then there are other quantities, interdefinable with ϕ and ψ, that reverse the ordering.

This paper highlights some connections between work on truth approximation and work in social epistemology, in particular work on peer disagreement. In some of the literature on truth approximation, questions have been addressed concerning the efficiency of research strategies for approximating the truth. So far, social aspects of research strategies have not received any attention in this context. Recent findings in the field of opinion dynamics suggest that this is a mistake. How scientists exchange and take into (...) account information about each others’ beliefs may greatly influence the accuracy and speed with which the scientific community as a whole approximates the truth. On the other hand, social epistemologists concerned with peer disagreement have so far neglected the question of how practices of responding to disagreements with peers fare with respect to the goal of approximating the truth. Again, work on opinion dynamics shows that this may be a mistake, and that how we ought to respond to disagreements with our peers may depend on the specific purposes of our investigations. (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 argues against a particular version of the inference from the success of a scientific theory to the claim that the theory must be approximately true to some extent. The kind of success at issue is comparative, where one theory is more empirically successful than its rival if that theory predicts phenomena that are inexplicable or anomalous according to its rival. A theory that exhibits this kind of comparative success can be seen as thereby achieving empirical progress over its (...) rival. David Harker has developed a form of selective scientific realism based on the idea that this kind of success is evidence for the approximate truth of the parts of theories responsible for such success. Counterexamples to Harker’s position are cases in which a theory is more successful than its rival in virtue of containing parts that are not even approximately true. In order to identify some counterexamples to Harker’s position, this paper considers four historical cases that Greg Frost-Arnold has recently used to motivate a novel historical challenge to realism called the Problem of Misleading Evidence. This paper argues that these four cases are counterexamples to Harker’s position, and that they provide a strong reason to doubt his position and the kind of success-to-truth inference that he defends. (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)

We investigate the logical and conceptual connections between abductive reasoning construed as a process of belief change, on the one hand, and truth approximation, construed as increasing (estimated) verisimilitude, on the other. We introduce the notion of ‘(verisimilitude-guided) abductive belief change’ and discuss under what conditions abductively changing our theories or beliefs does lead them closer to the truth, and hence tracks truth approximation conceived as the main aim of inquiry. The consequences of our analysis for some (...) recent discussions concerning belief revision aiming at truth approximation and inference to the best explanation are also highlighted. (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)

Approximations form an essential part of scientific activity and they come in different forms: conceptual approximations (simplifications in models), mathematical approximations of various types (e.g. linear equations instead of non-linear ones, computational approximations), experimental approximations due to limitations of the instruments and so on and so forth. In this paper, we will consider one type of approximation, namely numerical approximations involved in the comparison of two results, be they experimental or theoretical. Our goal is to lay down the conceptual and (...) formal foundations of a local theory of partial truth. This is done by introducing and exploring the concept of truth space. (shrink)

There are several conceptions of truth, such as the classical correspondence conception, the coherence conception and the pragmatic conception. The classical correspondence conception, or Aristotelian conception, received a mathematical treatment in the hands of Tarski (cf. Tarski [1935] and [1944]), which was the starting point of a great progress in logic and in mathematics. In effect, Tarski's semantic ideas, especially his semantic characterization of truth, have exerted a major influence on various disciplines, besides logic and mathematics; for instance, (...) linguistics, the philosophy of science, and the theory of knowledge. The importance of the Tarskian investigations derives, among other things, from the fact that they constitute a mathematical, formal mark to serve as a reference for the philosophical (informal) conceptions of truth. Today the philosopher knows that the classical conception can be developed and that it is free from paradoxes and other difficulties, if certain precautions are taken. We believe that is not an exaggeration if we assert that Tarski's theory should be considered as one of the greatest accomplishments of logic and mathematics of our time, an accomplishment which is also of extraordinary relevance to philosophy, as we have already remarked. In this paper we show that the pragmatic conception of truth, at least in one of its possible interpretations, has also a mathematical formulation, similar in spirit to that given by Tarski to the classical correspondence conception. (shrink)

This paper supplies a structuralist reconstruction of the Modigliani-Miller theory and shows that the economic literature following their results reports on research with an implicit strategy to come "closer-to-the-truth" in the modern technical sense in philosophy of science.

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)

We use the method of fixed points to describe a form of probabilistic truth approximation which we illustrate by means of three examples. We then contrast this form of probabilistic truth approximation with another, more familiar kind, where no fixed points are used. In probabilistic truth approximation with fixed points the events are dependent on one another, but in the second kind they are independent. The first form exhibits a phenomenon that we call ‘fading origins’, the second (...) one is subject to a phenomenon known as ‘the washing out of the prior’. We explain that the two phenomena may seem very similar, but are in fact quite different. (shrink)

Polish version, see Kuipers (2002) "O dwóch rodzajach idealizcji I konkretyzacki. Przypadek aproksymacji prawdy".

In a recent paper in this journal, entitled ‘Scientific Progress: Why Getting Closer to Truth is Not Enough’ (2017), Moti Mizrahi argues that the view of progress as approximation to the truth or increasing verisimilitude is plainly false. The key premise of his argument is that on such a view of progress, in order to get closer to the truth one only needs to arbitrarily add a true disjunct to a hypothesis or theory. Since quite clearly scientific (...) progress is not a matter of adding true disjuncts to theories, the argument goes, the view of progress as approximation to the truth is untenable. We show that the key premise of Mizrahi’s argument is false: according to verisimilitude-based accounts of progress, adding arbitrary true disjuncts to existing theories is just not enough to get closer to the truth. (shrink)

Straightforward theory revision, taking into account as effectively as possible the established nomic possibilities and, on their basis induced empirical laws, is conducive for (unstratified) 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 AGM-terms? 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. (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.

Theo AF Kuipers THE THREEFOLD EVALUATION OF THEORIES A SYNOPSIS OF FROM INSTRUMENTALISM TO CONSTRUCTIVE REALISM. ON SOME RELATIONS BETWEEN CONFIRMATION, EMPIRICAL PROGRESS, AND TRUTH APPROXIMATION (2000) ABSTRACT.

The naive structuralist definition of truthlikeness is an idealization in the sense that it assumes that all mistaken models of a theory are equally bad. The natural concretization is a refined definition based on an underlying notion of structurelikeness.In Section 1 the naive definition of truthlikeness of theories is presented, using a new conceptual justification, in terms of instantial and explanatory mistakes.

Three related intuitions are explicated in this paper. 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 deductive analogs, being ‘idealizations’. It turns out that the comparative version of the proposed HP-method amounts to the likelihood comparison (LC-) 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 analog of the deductive success theorem. (shrink)

Three related intuitions are explicated in this paper. The first is the idea that there must be some kind of probabilistic version of the HD-method, a 'Hypothetico-Probabilistic 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 deductive analogs, being 'idealizations'. It turns out that the comparative version of the proposed HP-method amounts to the likelihood comparison 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 analog of the deductive success theorem. (shrink)

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 my article entitled “Models, postulates, and generalized nomic truth approximation” :3057–3077, 2016. 10.1007/s11229-015-0916-9), 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: the traditional view: theories are postulates that exclude certain possibilities from being realizable, enabling explanation and prediction and the model view: theories are sets of models that claim to 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 to another than a third one. 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 article it will be shown that such ‘refined’ considerations can be taken into account by adapted clauses based on a ternary similarity relation between possibilities. 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. (shrink)

In this paper it is argued that the theory of truth approximation should be pursued in the framework of some kind of geometry of logic. More specifically it is shown that the theory of interval structures provides a general framework for dealing with matters of truth approximation. The qualitative and the quantitative accounts of truthlikeness turn out to be special cases of the interval account. This suggests that there is no principled gap between the qualitative and quantitative approach. (...) Rather, there is a connected spectrum of ways of measuring truthlikeness depending on the specifics of the context in which it takes place. (shrink)