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.

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)

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)

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)

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)

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 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)

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)

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)

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.

The structuralist theory of truth approximation essen-tially deals with truth approximation by theory revision for a fixed domain. However, variable domains can also be taken into account, where the main changes concern domain extensions and restrictions. In this paper I will present a coherent set of definitions of “more truth-likeness”, “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 formal aspects of theory revision strongly suggest an analogy between truth approximation and design research, for example, drug research. Whereas a new drug may be better for a certain disease than an old one, 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”, I did not find clear-cut empirical instantiations of the analogy, only, as such, very interesting, non-empirical examples. (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.

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)

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)

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 paper 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 paper 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’. (shrink)

Surprisingly enough, modified versions of the confirmation theory of Carnap and Hempel and the truth approximation theory of Popper turn out to be smoothly synthesizable. The glue between confirmation and truth approximation appears to be the instrumentalist methodology, rather than the falsificationist one.By evaluating theories separately and comparatively in terms of their successes and problems (hence even if they are already falsified), the instrumentalist methodology provides – both in theory and in practice – the straight route for (...) short-term empirical progress in science in the spirit of Laudan. However, it is 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 dynamic of science and hence on the relation between the main epistemological positions, viz., instrumentalism (Toulmin, Laudan), constructive empiricism (van Fraassen), referential realism (Hacking and Cartwright), and theory realism of a non-essentialist nature (Popper), here called constructive realism.In From Instrumentalism to Constructive Realism (2000) the above story is presented in great detail. The present synopsis highlights the main ways of theory evaluation presented in that book, viz. evaluation in terms of confirmation (or falsification), empirical progress and truth approximation. (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)

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)

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)

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)

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)

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)

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 paper presents the methodology of effective theories as a strategy used in the process of development of modern physics to reach a final theory. We present the definition and characteristic features of an effective theory, as well as the answer to the question of whether and what kind of scenario of reaching a final theory is realized by contemporary physics. We argue that the process of development of physics in the direction of a final theory is potentially final, (...) i.e. expressible in the conceptual schema of effective theories and as such it is convergent to a final theory. In each effective theory there are physical constants, however, whose status differs from logical constants. They have a dimension and are used to compare physical quantities. The structure of relevant effective theory can be interpreted in the epistemological framework of approximated truth theory. In the case study of cosmological models, the sequence of models is convergent to potentially true model. The Standard Cosmological Model is the theory of the structure and dynamics of the Universe. (shrink)

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)

Systematicity theory—developed and articulated by Paul Hoyningen-Huene—and scientific realism constitute separate encompassing and empirical accounts of the nature of science. Standard scientific realism asserts the axiological thesis that science seeks truth and the epistemological thesis that we can justifiably believe our successful theories at least approximate that aim. By contrast, questions pertaining to truth are left “outside” systematicity theory’s “intended scope” ; the scientific realism debate is “simply not” its “focus”. However, given the continued centrality of that (...) debate in the general philosophy of science literature, and given that scientific realists also endeavor to provide an encompassing empirical account of science, I suggest that these two contemporary accounts have much to offer one another. Overlap for launching a discussion of their relations can be found in Nicholas Rescher’s work. Following through on a hint from Rescher, I embrace a non-epistemic, purely axiological scientific realism—what I have called, Socratic scientific realism. And, bracketing the realist’s epistemological thesis, I put forward the axiological tenet of scientific realism as a needed supplement to systematicity theory. There are two broad components to doing this. First, I seek to make clear that axiological realism and systematicity theory accord with one another. Toward that end, after addressing Hoyningen-Huene’s concerns about axiological analysis, I articulate a refined axiological realist meta-hypothesis: it is, in short, that the end toward which scientific inquiry is directed is an increase in a specific subclass of true claims. I then identify a key feature of scientific inquiry, not generally flagged explicitly, that I take to stand as shared terrain for the two empirical meta-hypotheses. And I argue that this feature can be informatively accounted for by my axiological meta-hypothesis. The second broad component goes beyond mere compatibility between the two positions: I argue that, in want of a systematic account of science, we are prompted to find an end toward which scientific inquiry is directed that is deeper than what systematicity theory offers. Specifically, I argue that my refined axiological realist meta-hypothesis is required to both explain and justify key dimensions of systematicity in science. To the quick question, what is it that the scientific enterprise is systematically doing? My quick answer is that it is systematically seeking to increase a particular subclass of true claims. (shrink)

The qualitative theory of nomic truth approximation, presented in Kuipers in his, 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 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” :183–222, 2011). (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)

§1. Introduction. The problem raised by the liar paradox has long been an intriguing challenge for all those interested in the concept of truth. Many “solutions” have been proposed to solve or avoid the paradox, either prescribing some linguistical restriction, or giving up the classical true-false bivalence or assuming some kind of contextual dependence of truth, among other possibilities. We shall not discuss these different approaches to the subject in this paper, but we shall concentrate on a kind (...) of formal construction which was originated by Kripke's paper “Outline of a theory of truth” [11] and which, in different forms, reappears in later papers by various authors.The main idea can be presented as follows: assume a first order language ℒ containing, among other unspecified symbols, a predicate symbolTintended to represent the truth predicate for ℒ. Assume, also, a fixed modelM= 〈D, I〉 whereDcontains all sentences of ℒ andIinterprets all non-logical symbols of ℒ exceptTin the usual way. In general,Dmight contain many objects other than sentences of ℒ but as that would raise the problem of the meaning of sentences in whichTis applied to one of these objects, we shall assume that this is not the case. (shrink)

This paper primarily deals with theconceptual prospects for generalizing the aim ofabduction from the standard one of explainingsurprising or anomalous observations to that ofempirical progress or even truth approximation. Itturns out that the main abduction task then becomesthe instrumentalist task of theory revision aiming atan empirically more successful theory, relative to theavailable data, but not necessarily compatible withthem. The rest, that is, genuine empirical progress aswell as observational, referential and theoreticaltruth approximation, is a matter of evaluation andselection, and possibly (...) new generation tasks forfurther improvement. The paper concludes with a surveyof possible points of departure, in AI and logic, forcomputational treatment of the instrumentalist taskguided by the `comparative evaluation matrix''. (shrink)

We start with a nearly arbitrary standard classical first order "language" $C\sb{o},$ which is expanded to $C\sb{M,T}$ = "$C\sb{o}+M+T$", where for any variable x, M and T are unary formulas. We start also with a model ${\cal T}\sb{o},$ which together with $C\sb{o}$ represents a fixed non-problematic interpreted first order language. For each $\mu,\tau\subseteq U\sb{o},$ the universe of discourse for ${\cal T}\sb{o},$ the model ${\cal T}\sb{\mu,\tau}$ over $C\sb{M,T}$ is given so that its reduct to $C\sb{o}$ is just ${\cal T}\sb{o},$ and so (...) that for any $C\sb{M,T}$-variable x, the set-extensions of M and T are $\mu$ and $\tau$ respectively. For each $C\sb{M,T}$-expression e, $\vec e$ is its distinctly chosen representative in $U\sb{o},$ and $\lbrack\!\lbrack e\rbrack\!\rbrack$ is a constant $C\sb{o}$-term which names $\vec e.$ ;The goal is to find $\mu\sb*$ and $\tau\sb*,$ such that $\mu\sb*$ and $\tau\sb*$ plausibly and "self-referentially" approximate meaningfulness and truth respectively for any interpreted language represented by ${\cal T}\sb{\mu\sb*,\tau\sb*},$ by satisfying at least the following conditions. ; $\tau\sb*\subseteq\mu\sb*,$ and for each $C\sb{M,T}$-sentence $\sigma$ such that ${\cal T}\sb{\mu\sb*,\tau\sb*}\models M\lbrack\!\lbrack\sigma\rbrack\!\rbrack,$ $$\eqalign{&\ {\cal T}\sb{\mu\sb*,\tau\sb*} \models\sigma\Longleftrightarrow{\cal T}\sb{\mu\sb*,\tau\sb*}\models T\lbrack\!\lbrack\sigma\rbrack\!\rbrack,\ {\rm and}\cr&\ {\cal T}\sb{\mu\sb*,\tau\sb*}\models T\lbrack\!\lbrack\sigma\\leftrightarrow T\lbrack\!\lbrack\sigma\rbrack\!\rbrack\rbrack\!\rbrack.\cr}$$ ; There is a class of expression representatives $\mu\sp{D}\subseteq\mu\sb*$ containing every $C\sb{o}$-expression representative, such that the set $\tau\sp{D}=\mu\sp{D}\ \cap\ \tau\sb*$ itself satisfies the following properties. ;First, for each $\vec\sigma$ such that $\sigma$ is a $C\sb{M,T}$-sentence, if for all $\mu,\tau\subseteq U\sb{o}$ satisfying $\mu\supseteq\mu\sb*$ and $\tau\supseteq\tau\sp{D},$ it is the case that ${\cal T}\sb{\mu,\tau}\models\sigma,$ then $\vec\sigma\in\tau\sp{D}.$ ;Second, whenever $\vec\sigma\in\tau\sp{D},$ then also $\sp{\vec{\enspace}}\ \in\tau\sp{D}.$ ;Third, $\tau\sp{D}$ is "upwardly closed" with respect to the strong-Kleene rules for the truth-value evaluation of Boolean combinations of formulas. For example, for $C\sb{M,T}$-sentences $e\sb1$ and $e\sb2$: $$\eqalign{&\ \vec e\sb1\in\tau\sp{D}\Longleftrightarrow)\sp{\vec{\enspace}}\ \in\tau\sp{D}.\cr&\ {\rm If}\ \vec e\sb1\in\tau\sp{D}\ {\rm or}\ \vec e\sb2\in\tau\sp{D},\ {\rm then\ so\ is}\ \sp{\vec{\enspace}}\ \in\tau\sp{D}.\cr&\ {\rm If}\ \sp{\vec{\enspace}}\ \in\tau\sp{D}\ {\rm and}\ \sp{\vec{\enspace}}\ \in\tau\sp{D},\ {\rm then}\ )\sp{\vec{\enspace}}\ \in\tau\sp{D}.\cr}$$ ; For each $C\sb{M,T}$-expression e not involving T, ${\cal T}\sb{\mu\sb*,\tau\sb*}\models M\lbrack\!\lbrack e\rbrack\!\rbrack$; in particular, for any $C\sb{M,T}$-expression e whatsoever, ${\cal T}\sb{\mu\sb*,\tau\sb*}\models M\lbrack\!\lbrack\\neg M\lbrack\!\lbrack e\rbrack\!\rbrack\rbrack\!\rbrack.$ ; ;In this dissertation, it is shown for the first time that there are in fact $\mu\sb*$ and $\tau\sb*$ which simultaneously satisfy all three conditions , , and , even when the consequent of the Godel fixed point theorem must hold. (shrink)

According to scientific realists, the predictive success of mature theories provides a strong epistemic basis for thinking that such theories are approximately true. However, we know that many theories once regarded as well-confirmed and predictively successful were eventually replaced with successor theories, and some claim this undermines the epistemic confidence we should have in the approximate truth of current science. Selective scientific realists in turn argue that if one can show that the predictive success of (...) some rejected theory T is a function of theoretical claims consistent with current science, then T’s failure doesn’t undermine the claim that current successful theories are approximately true. As such, Selective Scientific Realism (SSR) can be tested through historical examples. Showing that the predictive success of a failed theory is the result of theoretical features later rejected provides a counterexample to SSR. Conversely, SSR is supported if its explanation of the predictive success of failed theories--namely, that the factors which lead to predictive success in the failed theory survive in the successor theory--is able to handle a wide array of historical cases. (shrink)

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.

What is the relation between coherence and truth? This paper rejects numerous answers to this question, including the following: truth is coherence; coherence is irrelevant to truth; coherence always leads to truth; coherence leads to probability, which leads to truth. I will argue that coherence of the right kind leads to at least approximate truth. The right kind is explanatory coherence, where explanation consists in describing mechanisms. We can judge that a scientific theory is (...) progressively approximating the truth if it is increasing its explanatory coherence in two key respects: broadening by explaining more phenomena and deepening by investigating layers of mechanisms. I sketch an explanation of why deepening is a good epistemic strategy and discuss the prospect of deepening knowledge in the social sciences and everyday life. (shrink)

Abstract: We propose a view of vagueness as a semantic property of names and predicates. All entities are crisp, on this semantic view, but there are, for each vague name, multiple portions of reality that are equally good candidates for being its referent, and, for each vague predicate, multiple classes of objects that are equally good candidates for being its extension. We provide a new formulation of these ideas in terms of a theory of granular partitions. We show that this (...) theory provides a general framework within which we can understand the relation between vague terms and concepts and the corresponding crisp portions of reality. We also sketch how it might be possible to formulate within this framework a theory of vagueness which dispenses with the notion of truth-value gaps and other artifacts of more familiar approaches. Central to our approach is the idea that judgments about reality involve in every case (1) a separation of reality into foreground and background of attention and (2) the feature of granularity. On this basis we attempt to show that even vague judgments made in naturally occurring contexts are not marked by truth-value indeterminacy. We distinguish, in addition to crisp granular partitions, also vague partitions, and reference partitions, and we explain the role of the latter in the context of judgments that involve vagueness. We conclude by showing how reference partitions provide an effective means by which judging subjects are able to temper the vagueness of their judgments by means of approximations. (shrink)

Scientific realism is a thesis about the success of science. Most traditionally: science has been so successful at prediction and guiding action because its best theories are true (or approximately true or increasing in their degree of truth). If science is in the business of doing its best to generate true theories, then we should turn to those theories for explanatory knowledge, predictions, and guidance of our actions and decisions. Views that are popular in contemporary philosophy (...) of science about scientific modeling and the centrality of idealization create several challenges for this traditional form of scientific realism. Yet the basic idea behind scientific realism that science has been and will continue to be epistemically successful is deeply appealing. This chapter explores the challenges posed by idealization and scientific modeling to motivate a scientific realism fully divorced from the idea that science is in the business of generating true theories. On the resulting view, the objects of scientific knowledge are causal patterns, so this knowledge only ever provides partial, simplified accounts of a complex reality. This variety of selective realism better accommodates the nature of our present-day scientific successes and offers an interpretation of scientific progress that resists the antirealist’s pessimism. (shrink)

The aim of this essay is to argue for a new version of ‘inference-to-the-best-explanation’ scientific realism, which I characterize as Best Theory Realism or ‘BTR’. On BTR, the realist needs only to embrace a commitment to the truth or approximate truth of the best theories in a field, those which are unique in satisfying the highest standards of empirical success in a mature field with many successful but falsified predecessors. I argue that taking our best theories (...) to be true is justified because it provides the best explanation of the predictive success of their predecessors and their own special success. Against standard and especially structural realism, I argue against the claim that the best explanations of the success of theories is provided by identifying their true components, such as structural relations between unobservable, which are preserved across theory change. In particular, I criticize Ladyman's and Carrier’s structural account of the success of phlogiston theory, and Worrall's well-known structural account of the success of Fresnel’s theory of light. I argue that these accounts tacitly assume the truth of our best theories, which in any case provides a better explanation of these theories’ success than the structural account. Structural realism is now defended as the only version of realism that is able to surmount the pessimistic meta-induction and the general problem that successful theories involve ontological claims concerning unobservable entities that are abandoned and falsified in theory-change. I argue that Best Theory Realism can overcome the pessimistic meta-induction and this general problem posed by theory-change. Our best theories possess a characteristic which sharply distinguishes them from their successful but false predecessors. Furthermore ‘inference-to-the-best-explanation’ confirmation can establish the truth of our best theories and thus trumps the pessimistic inductive reasoning which is supposed to show that even our best theories are most likely false in their claims concerning unobservable entities and processes. (shrink)

This book offers a close and rigorous examination of the arguments for and against scientific realism and introduces key positions in the scientific realism/antirealism debate, which is one of the central debates in contemporary philosophy of science. On the one hand, scientific realists argue that we have good reasons to believe that our best scientific theories are approximately true because, if they were not even approximately true, they would not be able to explain and predict natural phenomena with such (...) impressive accuracy. On the other hand, antirealists argue that the success of science does not warrant belief in the approximate truth of our best scientific theories. This is because the history of science is a graveyard of theories that were once successful but were later discarded. The author eventually settles on a middle ground position between scientific realism and antirealism called "relative realism.". (shrink)

The main formal notion involved in qualitative truth approximation by the HD-method, viz. ‘more truthlike’, is shown to not only have, by its definition, an intuitively appealing ‘model foundation’, but also, at least partially, a conceptually plausible ‘consequence foundation’. Moreover, combining the relevant parts of both leads to a very appealing ‘dual foundation’, the more so since the relevant methodological notions, viz. ‘more successful’ and its ingredients provided by the HD-method, can be given a similar dual foundation. According to (...) the resulting dual foundation of ‘naive truth approximation’, the HD-method provides successes (established true consequences) and counterexamples (established wrongly missing models) of theories. Such HD-results may support the tentative conclusion that one theory seems to remain more successful than another in the naive sense of having more successes and fewer counterexamples. If so, this provides good reasons for believing that the more successful theory is also more truthlike in the naive sense of having more correct models and more true consequences. (shrink)

Truth in the Making represents a sophisticated effort to map the complex relations between human knowledge and creative power, as reflected across more than half a millennium of philosophical enquiry. Showing the intimacy of this problematic to the work of Nicholas of Cusa, Bacon, Galileo, Descartes, Hobbes, Leibniz, Vico and David Lachterman, the book reveals how questions about creation apparently diluted by secularism in fact retain much of their potency today. If science could counterfeit or synthesize nature precisely from (...) its smallest nuts and bolts, as Descartes and Hobbes implied and as modern science increasingly suggests, would it create an identical world to that we live in now Robert C. Miner offers a precise genealogy of modern thought on truth and creation: from medieval theology's identification of human creativity with divine initiative to the radical Leibnizian contention that human ideas are 'not little copies of God's', and may at once exceed mimesis and produce things new, unpredictable and unseen. He considers how the theological importance given to creation interacts historically with the secularisation and instrumentalisation of modes of discovery and method, and asks how knowledge is understood between different disciplines, from the allegorical discipline of poetry to the constructible field of mathematics. The book is an eloquent reminder of the ways in which theology continues to fling a wild card at philosophical understandings of reality, countering theories of metaphysical equivalence of the 'real' and 'artificial' with theologies in which human making is always fallible, and strives only for approximate participation in divine truth. As a strenuous and informative breakdown of leading theories of knowledge, Truth in the Making shows the continuing influence of theological questions upon philosophical, scientific and aesthetic disciplines, whilst raising topical questions about the ultimate nature of our reality and our freedom to modify and define it. (shrink)

Realists regarding scientific knowledge – those who think that our best scientific representations truly describe both observable and unobservable aspects of the natural world – have special need of a notion of approximate truth. Since theories and models are rarely considered true simpliciter, the realist requires some means of making sense of the claim that they may be false and yet close to the truth, and increasingly so over time. In this paper, I suggest that traditional approaches (...) to approximate truth are insensitive to two crucial features of scientific knowledge, and that for each of these, analogies between representational practices in the sciences and in art prove useful to understanding how this situation can be remedied. First, I outline two distinct ways in which representations deviate from the truth, commonly referred to as ‘abstraction’ and ‘idealization’. Second, I argue that these practices exemplify different conventions of representation, and that for each, the conditions of approximation relevant to explicating the concept of approximate truth must be understood differently. The concept is thus heterogeneous; approximate truth is a virtue that is multiply realized, relative to different contexts of representation. This understanding is facilitated, I suggest, by considering the distinction between realistic and non-realistic representation in art. (shrink)

Aspects of a formal theory of approximate generalizations, according to which they have degrees of truth measurable by the proportions of their instances for which they are true, are discussed. The idealizability of laws in theories of fundamental measurement is considered: given that the laws of these theories are only approximately true "in the real world", does it follow that slight changes in the extensions of their predicates would make them exactly true?