This book is a sustained defense of the compatibility of the presence of idealizations in the sciences and scientific realism. So, the book is essentially a detailed response to the infamous arguments raised by Nancy Cartwright to the effect that idealization and scientific realism are incompatible.

In "Bayesian Confirmation of Theories that Incorporate Idealizations", Michael Shaffer argues that, in order to show how idealized hypotheses can be confirmed, Bayesians must develop a coherent proposal for how to assign prior probabilities to counterfactual conditionals. This paper develops a Bayesian reply to Shaffer's challenge that avoids the issue of how to assign prior probabilities to counterfactuals by treating idealized hypotheses as abstract descriptions. The reply allows Bayesians to assign non-zero degrees of confirmation to idealized hypotheses and to capture (...) the intuition that less idealized hypotheses tend to be better confirmed than their more idealized counterparts. (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)

In this paper, a criticism of the traditional theories of approximation and idealization is given as a summary of previous works. After identifying the real purpose and measure of idealization in the practice of science, it is argued that the best way to characterize idealization is not to formulate a logical model – something analogous to Hempel's D-N model for explanation – but to study its different guises in the praxis of science. A case study of it is then made (...) in thermostatistical physics. After a brief sketch of the theories for phase transitions and critical phenomena, I examine the various idealizations that go into the making of models at three difference levels. The intended result is to induce a deeper appreciation of the complexity and fruitfulness of idealization in the praxis of model-building, not to give an abstract theory of it. (shrink)

This book examines the philosophical conception of abductive reasoning as developed by Charles S. Peirce, the founder of American pragmatism. It explores the historical and systematic connections of Peirce's original ideas and debates about their interpretations. Abduction is understood in a broad sense which covers the discovery and pursuit of hypotheses and inference to the best explanation. The analysis presents fresh insights into this notion of reasoning, which derives from effects to causes or from surprising observations to explanatory theories. The (...) author outlines some logical and AI approaches to abduction as well as studies various kinds of inverse problems in astronomy, physics, medicine, biology, and human sciences to provide examples of retroductions and abductions. The discussion covers also everyday examples with the implication of this notion in detective stories, one of Peirce’s own favorite themes. The author uses Bayesian probabilities to argue that explanatory abduction is a method of confirmation. He uses his own account of truth approximation to reformulate abduction as inference which leads to the truthlikeness of its conclusion. This allows a powerful abductive defense of scientific realism. This up-to-date survey and defense of the Peircean view of abduction may very well help researchers, students, and philosophers better understand the logic of truth-seeking. (shrink)

Two types of idealization in theory construction are distinguished, and the distinction is used to give a critique of Ron Laymon's account of confirming idealized theories and his argument for scientific realism.

Truthlikeness is a property of a theory or a proposition that represents its closeness to the truth. We start by summarizing Niiniluoto’s proposal of truthlikeness for deterministic laws, which defines truthlikeness as a function of accuracy, and García-Lapeña’s expanded version, which defines truthlikeness for DL as a function of two factors, accuracy and nomicity. Then, we move to develop an appropriate definition of truthlikeness for probabilistic laws based on Niiniluoto’s suggestion to use the Kullback–Leibler divergence to define the distance between (...) a probability law X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X$$\end{document} and the true probability law T\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T$$\end{document}. We argue that the Kullback–Leibler divergence seems to be the best of the available probability distances to measure accuracy between PL. However, as in the case of DL, we argue that accuracy represents a necessary but not sufficient condition, as two PL may be equally accurate and still one may imply more true or truthlike consequences, behaviours or true facts about the system than the other. The final proposal defines truthlikeness for PL as a function of two factors, p-accuracy and p-nomicity, in intimate connexion with García-Lapeña’s proposal for DL. (shrink)

General Relativity and the Standard Model often are touted as the most rigorously and extensively confirmed scientific hypotheses of all time. Nonetheless, these theories appear to have consequences that are inconsistent with evidence about phenomena for which, respectively, quantum effects and gravity matter. This paper suggests an explanation for why the theories are not disconfirmed by such evidence. The key to this explanation is an approach to scientific hypotheses that allows their actual content to differ from their apparent content. This (...) approach does not appeal to ceteris-paribus qualifiers or counterfactuals or similarity relations. And it helps to explain why some highly idealized hypotheses are not treated in the way that a thoroughly refuted theory is treated but instead as hypotheses with limited domains of applicability. (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.

Truthlikeness is a property of a theory or a proposition that represents its closeness to the truth. According to Niiniluoto, truthlikeness for quantitative deterministic laws can be defined by the Minkowski metric. I present some counterexamples to the definition and argue that it fails because it considers truthlikeness for quantitative deterministic laws to be just a function of accuracy, but an accurate law can be wrong about the actual ‘structure’ or ‘behaviour’ of the system it intends to describe. I develop (...) a modification of Niiniluoto’s proposal that defines truthlikeness for quantitative deterministic laws according to two parameters: accuracy and nomicity. The presented proposal solves the counterexamples and defines a new way of understanding scientific progress. (shrink)

The aim of this essay is to emphasize a number of important points that will provide a better understanding of the history of philosophical thought concerning scientific knowledge. The main points made are: (a) that the principal way of viewing abstraction which has dominated the history of thought and epistemology up to the present is influenced by the original Aristotelian position; (b) that with the birth of modern science a new way of conceiving abstraction came into being which is better (...) characterized by the term idealization, the name that was later, in fact, to be used by scientists to describe their scientific activity; (c) that, however, on account of the influence of empirical and inductive philosophy, scientists have often not had sufficient methodological awareness of this new way of viewing abstraction; (d) that this new concept of abstraction has frequently been expressed in the framework of philosophies that lie outside the mainstream of contemporary epistemology or even exhibit marked anti-scientific tendencies; (e) that the theme of idealization has been taken up again in the last few decades and a great contribution in this direction has been made by the so-called Pozna school of methodology. (shrink)

General Relativity and the Standard Model often are touted as the most rigorously and extensively confirmed scientific hypotheses of all time. Nonetheless, these theories appear to have consequences that are inconsistent with evidence about phenomena for which, respectively, quantum effects and gravity matter. This paper suggests an explanation for why the theories are not disconfirmed by such evidence. The key to this explanation is an approach to scientific hypotheses that allows their actual content to differ from their apparent content. This (...) approach does not appeal to ceteris-paribus qualifiers or counterfactuals or similarity relations. And it helps to explain why some highly idealized hypotheses are not treated in the way that a thoroughly refuted theory is treated but instead as hypotheses with limited domains of applicability. (shrink)

Questions concerning the epistemological status of computer science are, in this paper, answered from the point of view of the formal verification framework. State space reduction techniques adopted to simplify computational models in model checking are analysed in terms of Aristotelian abstractions and Galilean idealizations characterizing the inquiry of empirical systems. Methodological considerations drawn here are employed to argue in favour of the scientific understanding of computer science as a discipline. Specifically, reduced models gained by Dataion are acknowledged as Aristotelian (...) abstractions that include only data which are sufficient to examine the interested executions. The present study highlights how the need to maximize incompatible properties is at the basis of both Abstraction Refinement, the process of generating a cascade of computational models to achieve a balance between simplicity and informativeness, and the Multiple Model Idealization approach in biology. Finally, fairness constraints, imposed to computational models to allow fair behaviours only, are defined as ceteris paribus conditions under which temporal formulas, formalizing software requirements, acquire the status of law-like statements about the software systems executions. (shrink)

The modern history of verisimilitude can be divided into three periods. The first began in 1960, when Karl Popper proposed his qualitative definition of what it is for one theory to be more truthlike than another theory, and lasted until 1974, when David Miller and Pavel Trichý published their refutation of Popper's definition. The second period started immediately with the attempt to explicate truthlikeness by means of relations of similarity or resemblance between states of affairs (or their linguistic representations); the (...) work within this similarity approach was summarized in the books of Graham Oddie [1986] and Ilkka Niiniluoto [1987]. During the subsequent third period, studies in verisimilitude have been actively continued, and interesting results and applications have been achieved, but not many dramatic novelties. While it is now obsolete to claim that truthlikeness with reasonable properties cannot be defined at all, there is still a lot of controversy about the best and least arbitrary approach to doing this. (shrink)

The problem of distance from the truth, and more generally distance between hypotheses, is considered here with respect to the case of quantitative hypotheses concerning the value of a given scientific quantity.Our main goal consists in the explication of the concept of distance D(I, ) between an interval hypothesis I and a point hypothesis . In particular, we attempt to give an axiomatic foundation of this notion on the basis of a small number of adequacy conditions.

Surprisingly, modified versions of the confirmation theory (Carnap and Hempel) and truth approximation theory (Popper) turn out to be smoothly sythesizable. The glue between the two appears to be the instrumentalist methodology, rather than that of the falsificationalist. The instrumentalist methodology, used in the separate, comparative evaluation of theories in terms of their successes and problems (hence, even if already falsified), provides in theory and practice the straight road to short-term empirical progress in science ( à la Laudan). It is (...) also argued that such progress is also functional for all kinds of truth approximation: observational, referential, and theoretical. This sheds new light on the long-term dynamics of science and hence on the relation between the main epistemological positions, viz., instrumentalism (Toulmin, Laudan), constructive empiricism (Van Fraassen), referential realism (Hacking, Cartwright), and theory realism of a non-essentialist nature (constructive realism à la Popper). Readership: Open minded philosophers and scientists. The book explains and justifies the scientist's intuition that the debate among philosophers about instrumentalism and realism has almost no practical consequences. (shrink)

Stipulating universal propositions with a ceteris paribus clause is normal practice in science and especially in economics. Yet there are several problems associated with the use of ceteris paribus clauses in theorising and in policy matters. This paper first investigates three questions: how can ceteris paribus clauses be non-vacuous? How can ceteris paribus laws be true? And how can they help in formulating successful policy interventions in a diversity of contexts? It turns out that ceteris paribus clauses are not always (...) used legitimately. They are meant to fence off a theory from disturbing factors, but economists who do not specify the clause well enough tend to fence variables in rather than off. In such cases, it would be better to use theoretical abstraction, which is something very different from the use of ceteris paribus clauses. However, abstract theorising conceptually leads one away from the concrete detail of real world situations in which policies take place. Hence, a fourth question arises: how can policy interventions be properly designed on the basis of abstract laws? To answer this question, I defend interdisciplinarity in concept choice. (shrink)

My thesis is that some methodological ideas of the Pozna school, i.e., the principles of idealization and concretization (factualization), and the correspondence principle can be represented rather successfully using the relations of theoretization and specialization of revised structuralism.Let n(i), t(j)> (i=1,...m, j=1,...k) denote the conceptual apparatus of a theory T, and a class M={} (i=1,...m, j=1,...k) the models of T. The n-components refer to the values of dependent variables and t-components to the values of independent variables of the theory. The (...) n- and t-components in turn represent appropriate concepts. Consider T * as a conceptual enrichment of T with concepts n(i *), t(j *)> (ii * or jj *) and models M *={D *, n(i *), t(j *)>}. If the classes M and M * are suitably related, then the situation illustrates both the case of the theoretization-relation of (revised) structuralism and of the factualization-principle of the Pozna school. (shrink)

The continuity thesis of the Poznań school threshold model of the growth of scientific knowledge is considered in the light of the example of Van der Waals' and Boyle-Mariotte's laws. It is argued - using both traditional logical means and the structuralist reconstruction of the example - that the continuity thesis does not hold. A distinction between 'a historical and a systematic point of view' is introduced and it is argued that the continuity thesis of the threshold model presupposes the (...) systematic point of view. However, looking at matters from the systematic point of view need not yield the original theory, looked at from the historical point of view. Applied to the case of Van der Waals/Boyle-Mariotte laws, it turns out that the latter law is not a true idealizing special case of the former, contrary to the continuity thesis. The structuralist analysis of the example indicates that Boyle-Mariotte's law is a false factual law from the historical point of view. However, viewed from the systematic point of view, Boyle-Mariotte's law turns out to be a law which is expandable, adding the relevant new concepts, to an idealized version of Van der Waals' law. This idealizing version of Van der Waal's law in turn is a structuralist specialization of the (general) Van der Waals' law. (shrink)

We revive the idea that a deductive-nomological explanation of a scientific theory by its successor may be defensible, even in those common and troublesome cases where the theories concerned are mutually incompatible; and limiting, approximating and counterfactual assumptions may be required in order to define a logical relation between them. Our solution is based on a general characterization of limiting relations between physical theories using the method of nonstandard analysis.