Described by the philosopher A.J. Ayer as a work of 'great originality and power', this book revolutionized contemporary thinking on science and knowledge. Ideas such as the now legendary doctrine of 'falsificationism' electrified the scientific community, influencing even working scientists, as well as post-war philosophy. This astonishing work ranks alongside The Open Society and Its Enemies as one of Popper's most enduring books and contains insights and arguments that demand to be read to this day.

To explore the relation between mathematical models and reality, four different domains of reality are distinguished: observer-independent reality, personal reality, social reality and mathematical/formal reality. The concepts of personal and social reality are strongly inspired by constructivist ideas. Mathematical reality is social as well, but constructed as an autonomous system in order to make absolute agreement possible. The essential problem of mathematical modelling is that within mathematics there is agreement about ‘truth’, but the assignment of mathematics to informal reality is (...) not itself formally analysable, and it is dependent on social and personal construction processes. On these levels, absolute agreement cannot be expected. Starting from this point of view, repercussion of mathematical on social and personal reality, the historical development of mathematical modelling, and the role, use and interpretation of mathematical models in scientific practice are discussed. (shrink)

A scientific community cannot practice its trade without some set of received beliefs. These beliefs form the foundation of the "educational initiation that prepares and licenses the student for professional practice". The nature of the "rigorous and rigid" preparation helps ensure that the received beliefs are firmly fixed in the student's mind. Scientists take great pains to defend the assumption that scientists know what the world is like...To this end, "normal science" will often suppress novelties which undermine its foundations. Research (...) is therefore not about discovering the unknown, but rather "a strenuous and devoted attempt to force nature into the conceptual boxes supplied by professional education". (shrink)

Thomas S. Kuhn's classic book is now available with a new index.

I argue against theories that attempt to reduce scientific representation to similarity or isomorphism. These reductive theories aim to radically naturalize the notion of representation, since they treat scientist's purposes and intentions as non-essential to representation. I distinguish between the means and the constituents of representation, and I argue that similarity and isomorphism are common but not universal means of representation. I then present four other arguments to show that similarity and isomorphism are not the constituents of scientific representation. I (...) finish by looking at the prospects for weakened versions of these theories, and I argue that only those that abandon the aim to radically naturalize scientific representation are likely to be successful. (shrink)

This paper aims to defend scientific realism against two versions of agnostic empiricism: a naive agnostic position, which suggests that the only rational option is to remain agnostic as to the truth of theoretical assertions, and van Fraassen's more sophisticated agnostic empiricism - which may be called "Hypercritical Empiricism". It first argues that given semantic realism, naive agnostic empiricism cannot be maintained: there is no relevant epistemic difference between theoretical assertions and observational ones. It then focuses on van Fraassen's more (...) sophisticated alternative to scientific realism and suggests that an attitude towards science which involves less than aiming at theoretical truth and believing in theories would be, in some concrete respect that empiricists should recognize, worse off than the recommended realist attitude. To this end, the paper develops the so-called conjunction argument into a diachronic argument for scientific realism. (shrink)

Review of T. S. Kuhn's The Essential Tension.

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)

Scientific representation is a currently booming topic, both in analytical philosophy and in history and philosophy of science. The analytical inquiry attempts to come to terms with the relation between theory and world; while historians and philosophers of science aim to develop an account of the practice of model building in the sciences. This article provides a review of recent work within both traditions, and ultimately argues for a practice-based account of the means employed by scientists to effectively achieve representation (...) in the modelling sciences. (shrink)

This article focuses on the role of statistical concepts in both experiment and theory in various scientific disciplines, especially physics, including astronomy, and psychology. In Sect. 1 the concept of uncertainty in astronomy is analyzed from Ptolemy to Laplace and Gauss. In Sect. 2 theoretical uses of probability and statistics in science are surveyed. Attention is focused on the historically important example of radioactive decay. In Sect. 3 the use of statistics in biology and the social sciences is examined, with (...) detailed consideration of various Chi-square statistical tests. Such tests are essential for proper evaluation of many different kinds of scientific hypotheses. (shrink)

Detectives and scientists are in the business of reasoning from observations to explanations. This they often do by raising cunning questionsduring their inquiries. But to substantiate this claim we need to know how questions arise and how they are nurtured into more specific hypotheses. I shall discuss what the problem is, and then introduce the so-called interrogative model of inquiry which makes use of an explicit logic of questions. On this view, a discovery processes can be represented as a model-based (...) game in which an inquirer subjects a source of information to a series of strategically organized questions. Strategic principles and why-questions are especially important in heuristical reasoning. Why-questions have their own peculiar nature among questions. They indicate that the inquirer's expectations are somehow disappointed, and that is cognitively challenging. In a finished argument why-questions can be omitted, but in the search for more specific questions they are highly important. As a detetective example I shall analyze Sherlock Holmes reasoning in Silver Blace, the scientific one is A.R. Wallace's discovery of the principle of natural selection. In both of these examples the meaning of questions, especially of well-chosen why-questions, of strategic principles, and of highly structured background knowledge come to the fore. Good questions frequent those who have orderly expectations, based on experience and expertise (detectives!) or highly structured background theories (scientists!). (shrink)

The process of abstraction and concretisation is a label used for an explicative theory of scientific model-construction. In scientific theorising this process enters at various levels. We could identify two principal levels of abstraction that are useful to our understanding of theory-application. The first level is that of selecting a small number of variables and parameters abstracted from the universe of discourse and used to characterise the general laws of a theory. In classical mechanics, for example, we select position and (...) momentum and establish a relation amongst the two variables, which we call Newton’s 2nd law. The specification of the unspecified elements of scientific laws, e.g. the force function in Newton’s 2nd law, is what would establish the link between the assertions of the theory and physical systems. In order to unravel how and with what conceptual resources scientific models are constructed, how they function and how they relate to theory, we need a view of theory-application that can accommodate our constructions of representation models. For this we need to expand our understanding of the process of abstraction to also explicate the process of specifying force functions etc. This is the second principal level at which abstraction enters in our theorising and in which I focus. In this paper, I attempt to elaborate a general analysis of the process of abstraction and concretisation involved in scientific- model construction, and argue why it provides an explication of the construction of models of the nuclear structure. (shrink)

There is a very plausible principle of the transitivity of justifying reasons. It says that if "p" is better justified than "q" (all things considered) and "q" better than "r", then "p" is better justified than "r" (all things considered). There is a corresponding principle of rational theory choice. Call one theory "a better theory than" another theory if all criteria of theory choice considered (explanatory power, simplicity, empirical adequacy, etc.), the first theory meets the criteria better than the second (...) theory. The corresponding transitivity principle says that if theory A is a better theory than theory B and if theory B is a better theory than theory C, then A is a better theory than theory C. I argue against this principle. It turns out that whenever there are 2 or more relevant and independent criteria of theory evaluation, and whenever at least of one the criteria is "non-linear" in a certain sense, there may be violations of transitivity which do not violate any standards of rationality (of theory choice). This shows, again, that theory choice cannot be seen as merely the application of given rules of rational theory choice. (shrink)

The epistemological problems of unification of two distinct theories are discussed. An approach related to the work of Soviet authors (Stepin, Podgoretzky and Smorodinsky) is used and developed. The notion of ‘crossbred objects’—theoretical objects with contradictory properties which are part of the domain of application of two independent theories—is introduced which helps to describe the dynamics of revolutionary theory change. The occurrence of the cross-contradiction of two theories is reconstructed and the reductionistic and the synthetic means of its elimination are (...) proposed. The results of the methodological analysis are applied to the paradox of equivalence. (shrink)

The problem of idealization in empirical sciences is very rarely taken up in works concerned with the methodology of those sciences. It seems to be common knowledge that in advanced natural sciences references are made to concepts such as “perfectly rigid body,” “material point,” “perfect gas,” etc., but it remains a fact that the most important methodological concepts, concepts which have determined the present-day form of the philosophy of science, have been advanced without regard to the peculiarities of the procedure (...) mentioned above. And yet a moment's consideration suffices to raise doubts as to Carnap's physicalism and/or Popper's falsificationism if we just realize the trivial and commonly known truth that empirical sciences resort to idealizationism. For how are we to imagine a reduction of idealizational concepts to observation terms? And how are we to imagine that theorems which include idealizational concepts imply observation statements which refute, or at least are at variance with, those theorems? But it is a fact that such doubts have neither been raised by the authors of the conceptions mentioned above, nor have they been raised against them. (shrink)

I argue that the contrast between models and theories is important for public policy issues. I focus especially on the way a mathematical model explains just one aspect of the data.

Prandtl's work on the boundary layer theory is an interesting example for illustrating several important issues in philosophy of science such as the relation between theories and models and whether it is possible to distinguish, in a principled way, between pure and applied science. In what follows I discuss several proposals by the symposium participants regarding the interpretation of Prandtl's work and whether it should be characterized as an instance of applied science. My own interpretation of this example (1999) emphasised (...) the degree of autonomy embedded in Prandtl's boundary layer model and the way it became integrated in the larger theoretical context of hydrodynamics. In addition to extending that discussion here I also claim that the characterization of applied science which formed the basis for the symposium does not enable us to successfully distinguish applied science from the general practice of 'applying' basic scientific knowledge in a variety of contexts. (shrink)

A popular line in philosophy championed by Jackson and his followers analyses concepts as networks of propositions. It takes even network-propositions characterizing ordinary empirically applicable concepts to be a priori, in contrast to statements of empirical science. This is meant to guarantee both the autonomy of conceptual analysis, and its substantial and informative character. It is argued here, to the contrary, that empirically applicable and entrenched concepts owe the acceptability of their own network precisely to its empirical pedigree. Promoting an (...) empirical proposition into a network proposition does not make it ultimately a priori: no matter how entrenched the network is, it owes its ultimate justification to its empirical pedigree. Autonomy from experience and informativeness clash with each other: the stipulative "knowledge" is a priori in a weak sense, but not informative and substantial, the factual knowledge is substantial but not a priori. (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 has been little research into the weak kindsof negating hypotheses. Hypotheses may be unfalsifiable. In this case it is impossible tofind a contradiction in some area of the conceptualsystems in which they are incorporated.Notwithstanding this fact, it is sometimes necessaryto construct ways of rejecting the unfalsifiablehypothesis at hand by resorting to some external forms of negation, external because wewant to avoid any arbitrary and subjectiveelimination, which would be rationally orepistemologically unjustified. I will consider akind of ``weak'''' (unfalsifiable) hypotheses that (...) arehard to negate and the ways for making it easy. Inthese cases the subject can ``rationally'''' decide towithdraw his hypotheses even in contexts where it is``impossible'''' to find ``explicit'''' contradictions: theuse of negation as failure (an interestingtechnique for negating hypotheses and accessing newones suggested by artificial intelligence) isilluminating. I plan to explore whether this kind ofnegation can be employed to model hypothesiswithdrawal in Poincaré''s conventionalism of theprinciples of physics and in Freudian analyticreasoning. (shrink)

I first give a brief summary of a critique of the traditional theories of approximation and idealization; and after identifying one of the major roles of idealization as detaching component processes or systems from their joints, a detailed analysis is given of idealized laws – which are discoverable and/or applicable – in such processes and systems (i.e., idealized model systems). Then, I argue that dispositional properties should be regarded as admissible properties for laws and that such an inclusion supplies the (...) much needed connection between idealized models and the laws they `produce'' or `accommodate''. And I then argue that idealized law-statements so produced or accommodated in the models may be either true simpliciter or true approximately, but the latter is not because of the idealizations involved. I argue that the kind of limiting-case idealizations that produce approximate truth is best regarded as approximation; and finally I compare my theory with some existing theories of laws of nature.We seem to trace [in KingLear] ... the tendency of imagination toanalyse and abstract, to decomposehuman nature into its constituentfactors, and then to construct beings in whomone or more of these factors isabsent or atrophied or only incipient. (shrink)

This paper is the second of a two-part series on models and theories, the first of which appeared in International Studies in the Philosophy of Science, Vol. 11, No. 2, 1997. It further explores some of themes of the first paper and examines applications, including: the relations between “similarity” and “isomorphism”, and between “model” and “interpretation”, and the notion of structural explanation.

The paper, as Part I of a two-part series, argues for a hybrid formulation of the semantic view of scientific theories. For stage-setting, it first reviews the elements of the model theory in mathematical logic (on whose foundation the semantic view rests), the syntactic and the semantic view, and the different notions of models used in the practice of science. The paper then argues for an integration of the notions into the semantic view, and thereby offers a hybrid semantic view, (...) which at once secures the view's logical foundations and enhances its applicability. The dilemma of either losing touch with the practice of science or yielding up the benefits of the model theory is thus avoided. (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)

I present a justification for the intution that more-varied data are more valuable than the same number of less-varied data by showing that the more-varied data help to improve the accuracy of our predictions.

Knowledge of many facts does not amount to understanding unless one also has a sense of how the facts fit together. This aspect of coherence among scientific observations and theories is usually overlooked in summaries of scientific method, since the emphasis is on justification and verification rather than on understanding. I argue that the inter-theoretic coherence, as the hallmark of understanding, is an essential and informative component of any accurate description of science.

Two views of scientific theories dominated the philosophy of science during the twentieth century, the syntactic view of the logical empiricists and the semantic view of their successors. I show that neither view is adequate to provide a proper understanding of the connections that exist between theories at different times. I outline a new approach, a hybrid of the two, that provides the right structural connection between earlier and later theories, and that takes due account of the importance of the (...) mathematical models of a theory and of the various distinct formulations that pick out these models. (shrink)

Popper, Polanyi and Duncker represent the widely held position that theoretical and experimental scientific research are motivated by problems to which discoveries are solutions. According to the argument here, their views are unsupported and - in light of counter-instances, anomalous chance discoveries, and the force of curiosity - over-generalized.

I argue here for a number of ways that modern computational science requires a change in the way we represent the relationship between theory and applications. It requires a switch away from logical reconstruction of theories in order to take surface mathematical syntax seriously. In addition, syntactically different versions of the same theory have important differences for applications, and this shows that the semantic account of theories is inappropriate for some purposes. I also argue against formalist approaches in the philosophy (...) of science and for a greater role for perceptual knowledge rather than propositional knowledge in scientific empiricism. (shrink)

In pure science, the standard approach to non-epistemic values is to exclude them as far as possible from scientific deliberations. When science is applied to practical decisions, non-epistemic values cannot be excluded. Instead, they have to be combined with scientific information in a way that leads to practically optimal decisions. A normative model is proposed for the processing of information in both pure and applied science. A general-purpose corpus of scientific knowledge, with high entry requirements, has a central role in (...) this model. Due to its high entry requirements, the information that it contains is sufficiently reliable for the vast majority of practical purposes. However, for some purposes, the corpus needs to be supplemented with additional information, such as scientific indications of danger that do not satisfy the entry requirements for the corpus. The role of non-epistemic values in the evaluation of scientific information should, as far as possible, be limited to determining the level of evidence required for various types of practical decisions. (shrink)

A conceptual analysis of falsificationism is performed, in which the central falsificationist thesis is divided into several components. Furthermore, an empirical study of falsification in science is reported, based on the 70 scientific contributions that were published as articles in Nature in 2000. Only one of these articles conformed to the falsificationist recipe for successful science, namely the falsification of a hypothesis that is more accessible to falsification than to verification. It is argued that falsificationism relies on an incorrect view (...) of the nature of scientific inquiry and that it is, therefore, not a tenable research methodology. (shrink)

Most recent philosophical thought about the scientific representation of the world has focused on dyadic relationships between language-like entities and the world, particularly the semantic relationships of reference and truth. Drawing inspiration from diverse sources, I argue that we should focus on the pragmatic activity of representing, so that the basic representational relationship has the form: Scientists use models to represent aspects of the world for specific purposes. Leaving aside the terms "law" and "theory," I distinguish principles, specific conditions, models, (...) hypotheses, and generalizations. I argue that scientists use designated similarities between models and aspects of the world to form both hypotheses and generalizations. (shrink)

Paul Feyerabend's globally acclaimed work, which sparked and continues to stimulate fierce debate, examines the deficiencies of many widespread ideas about scientific progress and the nature of knowledge. Feyerabend argues that scientific advances can only be understood in a historical context. He looks at the way the philosophy of science has consistently overemphasized practice over method, and considers the possibility that anarchism could replace rationalism in the theory of knowledge. -- Amazon.com.

Many arguments found in the physics literature involve concepts that are not well-defined by the usual standards of mathematics. I argue that physicists are entitled to employ such concepts without rigorously defining them so long as they restrict the sorts of mathematical arguments in which these concepts are involved. Restrictions of this sort allow the physicist to ignore calculations involving these concepts that might lead to contradictory results. I argue that such restrictions need not be ad hoc, but can sometimes (...) be justified by considering some of the metaphysical issues surrounding the question of the applicability of mathematics to physical reality. 1 Introduction 2 Rejecting inferential permissiveness 3 The agreement problem 4 Independent objections to the liberal view. (shrink)