Structure Of Scientific Theories Research Articles

The connection of mathematics and logic in the structure of axiomatized and formalized theories

The aim of the research is to study the relationship between logic and mathematics in the structure of axiomatized and formalized scientific theories. The object of the study is the explication of this connection and its explanation. The subject of the study is syntactic and semantic views on the structure of scientific theories, the relationship between logic and mathematics has not been studied in detail in them. In the syntactic view, the structure of the theory is understood as a linguistic construct build from various logical propositions of the theoretical level, correspondence propositions and observation propositions. The structure of the theory does not take into account the variety of model representations of the theory that generate a variety of language constructs. The semantic view overcomes this disadvantage, and in it the structure of the theory is presented as a hierarchy of models: from axioms to theoretical-level models, experimental models and data models. The structure of the theory, the connection of logic and mathematics were studied using comparative analysis, methods of interpretive analysis and reconstruction of scientific theories. The methods made it possible to explicate mathematical concepts in the structure of the theory and correlate them with logic and natural language. Comparative analysis has shown that in the syntactic view, the connection between logic and mathematics lies in the fact that mathematical concepts of physics are interpreted in the language of logic of first-order predicates with equality. The connection between mathematical concepts is provided by the axiomatic method, which serves as a means of formalizing concepts. Mathematics comes down to logic. In the semantic approach, in order to identify the connection between mathematics and logic, it was necessary to reconstruct the structure of non-relativistic quantum mechanics. With the help of the set-theoretic predicate of Suppes, its axioms were determined, the connection between mathematical structures, postulates of the theory, axioms, and observable quantities was established. Logic and mathematics are related to each other in such a way that metamathematics or linguistics is a part of mathematics. Mathematics includes set theory and model theory, i.e. mathematical logic. The connection of mathematical formalisms with phenomena and with natural language remains problematic, and there is this drawback in the syntactic approach. The novelty lies in the fact that the research contributes to the methodology and logic of science, to the explanation of the connection between logic and mathematics in scientific theory, which was illustrated by various examples from various fields of physics.

Structure of the Scientific Theories

A scientific theory consists of a symbolic framework containing laws and concepts that are derived by deductive reasoning from fundamental laws and primitive concepts, and complemented by the correspondence or the relation between the symbolic concepts and the real objects. The symbolic framework is understood as a representation of the real, constructed by our minds like a realistic painting. In accordance with this point of view, scientific laws are not discovered but conceived or created by our minds. We show how this approach is organized by rational thinking, which is understood as an innate ability of the mind that emerges between childhood and adolescence. We also examine with some detail the structure of the past scientific theories, pointing out their postulates, or fundamental laws, and the primitive concepts. We will restrict ourselves to some of the physical theories, starting with those that emerged in the Hellenistic period, and then proceed to examine other theories until the end of the seventeenth century.

Is “Analytic Philosophy” a Philosophy?

The article discusses the issue of the nature of analytic philosophy. It is shown that in the 1920s–1940s it was a certain philosophical school, whose representatives were united by some initial principles. Analytic philosophers saw the main task of philosophy in the analysis of the language of natural sciences, in establishing logical connections between scientific propositions, in the empirical substantiation of scientific theories and in the elimination of speculative concepts and proposals from the language of science. The tool for such analysis was the mathematical logic created at the beginning of the 20th century by G. Frege, A.N. Whitehead, B. Russell. Another characteristic feature of the analytic tradition was a negative attitude toward philosophical speculation. Adherents of this tradition believed that philosophy does not provide knowledge about the world, therefore, it is not a science. Analytic philosophers have made a significant contribution to the methodology of scientific knowledge, offering an accurate description of the hypothetical-deductive structure of scientific theory, methods of scientific explanation and prediction, verification, confirmation and refutation of scientific statements. In the late 1930s, most of the analytic philosophers emigrated to England and the United States. The analytic movement is gradually losing its integrity and loses the features of a philosophical school. There is a rejection of mathematical logic as the main means of analysis, the connection with the natural sciences has been lost. In the second half of the 20th century, analytic philosophy from a specific philosophical school turns into a certain style of thinking of the philosophers of various philosophical research areas and orientations.

Taxonomies, Networks, and Lexicons: A Study of Kuhn’s Post-‘Linguistic Turn’ Philosophy

ABSTRACT In his mature works, Kuhn abandons the concept of a paradigm and becomes more interested in the analysis of the conceptual structure of scientific theories. These changes are interpreted as resulting from a ‘linguistic turn’ that Kuhn underwent sometimes around the 1980s. Much of the philosophical discussions about Kuhn’s post-‘linguistic turn’ philosophy revolves around his views on taxonomic concepts. Apart from taxonomy, however, the mature Kuhn introduces other concepts, such as conceptual networks and lexicons. This article distinguishes these three concepts and shows that adopting each one of them has different impacts on Kuhn’s model of science. After distinguishing and assessing the concepts of taxonomy, network, and lexicon, it will be argued that the latter not only fits the Kuhnian model of science better, but it also helps capture the wide sense of Kuhn’s early concept of a paradigm.

Causal explanation and the periodic table

The periodic table represents and organizes all known chemical elements on the basis of their properties. While the importance of this table in chemistry is uncontroversial, the role that it plays in scientific reasoning remains heavily disputed. Many philosophers deny the explanatory role of the table and insist that it is “merely” classificatory (Shapere, in F. Suppe (Ed.) The structure of scientific theories, University of Illinois Press, Illinois, 1977; Scerri in Erkenntnis 47:229–243, 1997). In particular, it has been claimed that the table does not figure in causal explanation because it “does not reveal causal structure” (Woody in Science after the practice turn in the philosophy, history, and social studies of science, Routledge Taylor & Francis Group, New York, 2014). This paper provides an analysis of what it means to say that a scientific figure reveals causal structure and it argues that the modern periodic table does just this. It also clarifies why these “merely” classificatory claims have seemed so compelling–this is because these claims often focus on the earliest periodic tables, which lack the causal structure present in modern versions.

The Structure of Scientific Theories about Religion, Compared with Classical Religious Studies(Section 1,THE PROCEEDINGS OF THE SEVENTY-THIRD ANNUAL CONVENTION OF THE JAPANESE ASSOCIATION FOR RELIGIOUS STUDIES)

The Structure of Scientific Theories about Religion, Compared with Classical Religious Studies(Section 1,THE PROCEEDINGS OF THE SEVENTY-THIRD ANNUAL CONVENTION OF THE JAPANESE ASSOCIATION FOR RELIGIOUS STUDIES)

The Structure of Scientific Theories, Explanation, and Unification. A Causal–Structural Account

What are scientific theories and how should they be represented? In this article, I propose a causal–structural account, according to which scientific theories are to be represented as sets of interrelated causal and credal nets. In contrast with other accounts of scientific theories (such as Sneedian structuralism, Kitcher’s unificationist view, and Darden’s theory of theoretical components), this leaves room for causality to play a substantial role. As a result, an interesting account of explanation is provided, which sheds light on explanatory unification within a causalist framework. The theory of classical genetics is used as a case study.

On the interpretation of mathematical entities in the formalisation of programming and modelling languages

This paper analyses the interpretation of mathematical entities in the formalisations of languages. Four case studies are considered, covering both denotational and axiomatic approaches. We argue that the usual interpretation consists of direct statements about the language concepts and, occasionally, about the real world; some problems of this approach are discussed. Applying results from philosophical studies into the structure of scientific theories, we propose an alternative interpretation of mathematical entities as statements defining constructed concepts, which can be employed in turn as theoretical models of the language concepts and the world. Though this approach requires us to write hypotheses claiming some similarity between the models and the represented subjects, we reason that it is more adequate for formalising certain languages.

The Role of Efficacy vs. Effectiveness Research in Evaluating Psychotherapy.

A sound base of evidence for different kinds of psychotherapy is a fundamental prerequisite for adequate access to treatment. The present article addresses the question of what kind of evidence is required to demonstrate that a specific method of psychotherapy works. Referring to recent conceptualisations of the logical structure of scientific theories, the authors argue that randomised controlled trials (RCTs) and effectiveness studies refer to different domains of intended applications. In RCTs the efficacy of a treatment under controlled experimental conditions is tested, whereas in effectiveness studies the outcome of a treatment under the conditions of clinical practice is examined. Accounting for the different domains of intended applications has several important implications. These implications refer to methodological questions of research (e.g. internal and external validity, study design type), but also the possibility of transferring results from experimental to field settings, and the criteria for evaluating the evidence-base of treatments. They also address the important question of the degree to which the presently available forms of psychotherapy can be regarded as evidence-based. The considerations presented in this article primarily refer to psychotherapy; however, they are also relevant to the evidence-based treatment approach in general.

Falsificationism and the structure of theories: the Popper–Kuhn controversy about the rationality of normal science

Many controversies within philosophy of science have been attempted to be explained in terms of the metaphilosophical prescription/description distinction over the goal of philosophy of science. The aim of this paper is to show that the controversy between Popper and Kuhn about the ir/rationality of Normal Science cannot be fully explained in these terms, not even if we also take the truth/problem-solving distinction over the goal of science into account. It is argued that, to gain full understanding of this controversy, it is necessary to take into account their differences regarding a topic apparently not involved in it, namely the structure of scientific theories. The conclusion is that both Popper and Kuhn were descriptive/prescriptive at the same time in their attempt to make the rules of (a specific part of) scientific practice explicit, yet Kuhn did it better because he had a richer and more accurate idea of what scientific theories are. Although this work is mainly a piece of history of philosophy of science, it also aims at shedding some light on epistemological issues. If the conclusion is sound, it also shows how structural aspects of scientific theories may be relevant to the epistemology of science.

Semantic approaches in the philosophy of science

In this article I give an overview of some recent work in philosophy of science dedicated to analysing the scientific process in terms of (conceptual) mathematical models of theories and the various semantic relations between such models, scientific theories, and aspects of reality. In current philosophy of science, the most interesting questions centre around the ways in which writers distinguish between theories and the mathematical structures that interpret them and in which they are true, i.e. between scientific theories as linguistic systems and their non-linguistic models. In philosophy of science literature there are two main approaches to the structure of scientific theories, the statement or syntactic approach—advocated by Carnap, Hempel and Nagel—and the non-statement or semantic approach—advocated, among others, by Suppes, the structuralists, Beth, Van Fraassen, Giere, Wójcicki. In conclusion, I briefly review some of the usual realist inspired questions about the possibility and character of relations between scientific theories and reality as implied by the various approaches I discuss in the course of the article. The models of a scientific theory should indeed be adequate to the phenomena, but if the theory is ‘adequate’ to (true in) its conceptual (mathematical) models as well, we have a model-theoretic realism that addresses the possible meaning and reference of ‘theoretical entities’ without relapsing into the metaphysics typical of the usual scientific realist approaches.

Explanation, Causation, and Evolution

For the past three decades or so, the structure of scientific theories and their modes of explanation have received considerable attention from philosophers of science. The publication of Nagel’s The Structure of Science (1961) and Hempel’s Aspects of Scientific Explanation (1965) has led most philosophers of science to address questions such as whether all sciences can be reduced to physics, what is a good scientific explanation, what is the function and scope of laws in scientific theories, and so on. And so it appeared just natural when, a couple of years later, thanks to ground-breaking works by Ruse (1973) and Hull (1974), the very same questions were raised in light of the specific challenges that biology and evolutionary theory posed to the “received view” of scientific theories. Are there laws in biology? Is biology doomed to become a chapter of physics? Or is it autonomous? What is the role of functional and teleological descriptions in biology and why don’t we find such things in physics? These were some of the questions debated at that time. Now, the first striking feature of Kenneth Schaffner’s recent book, Discovery and Explanation in Biology and Medicine, is that it is primarily devoted to addressing most of these issues once again. Indeed, it seems to be Schaffner’s intention to revitalize the sort of problems which concerned philosophers of science thirty years ago, by giving them a new twist in light of recent approaches to these issues. In this respect, then, one cannot say that the subject matter of this book is newfangled. However, on a more innovative level, two interesting aspects of this book bear emphasis from the outset. First, its account of explanation and theory structure is supplemented with a focus on the context of discovery in the biomedical sciences. Second, against the general complaint that philosophers of biology have put too much emphasis on evolutionary theory, while neglecting disciplines such as immunology and

W. SALMON and G. WOLTERS, (Eds.), Logic, Language, and the Structure of Scientific Theories. University of Pittsburgh Press and Universitätsverlag Konstanz, 1994, cloth $59.95

W. SALMON and G. WOLTERS, (Eds.), <i>Logic, Language, and the Structure of Scientific Theories</i>. University of Pittsburgh Press and Universitätsverlag Konstanz, 1994, cloth $59.95

Logic, language, and the structure of scientific theories: proceedings of the Carnap-Reichenbach Centennial, University of Konstanz, 21-24 May 1991

This volume honors and examines the founders of the philosophy of logical empiricism. Historical and interpretive essays clarify the scientific philosophies of Carnap, Reichenbach, Hempel, Kant, and others, while exploring the main topics of logical empiricist philosophy of science.

On Pluralism and Competition in Evolutionary Explanations

A controversy arose concerning the adaptive significance of clitoral orgasm, disputing whether the presence of the trait in females is explained by appeal to developmental processes or natural selection (Gould, 1987 a, b ; Alcock, 1987). In response, Sherman (1988) offered a pluralistic solution in terms of levels of analysis in which Gould and Alcock's disagreement was construed as semantic and not substantial. I argue that Sherman's solution is mistaken. I suggest that the nature of the Gould/Alcock dispute is better understood by considering the abstract structure of scientific theories and their role in explanation. This account leads to a representation of science as having a plurality of theoretical models which are integrated piecemeal in the explanation of concrete phenomena.

The metatheoretical bases of social psychological theory

The present article deals with theory concerning interpersonal interactions of systems at the levels of individual human organisms, groups, and organizations. It involves all subsystems of these systems. It examines a number of metatheoretical constraints that may limit the development of social psychology as an empirical science. It begins by describing the sentences of one of the more classical languages used to define the structure of scientific theory, as well as criteria that are employed to evaluate these sentences. It then reviews and evaluates a number of epistemological constraints that limit the development and formulation of theories. For example, it considers the issue of complexity as a constraint, and briefly notes three possible ways to overcome complexity: (1) the construction of minitheories, (2) the use of systems theory, and (3) the development of ‘fuzzy models.’ Finally, the paper considers, given these various constraints, whether it is indeed possible for social psychologists to formulate and test sentences in a manner more or less consistent with the positivistic goals of science.

Presentations and the Status of Theories

Accounts of the structure of scientific theories in twentieth century philosophy of science have tended to focus on epistemological questions to the near exclusion of the metaphysical consequences of their solutions. This emphasis can be understood as resulting from the interest and concerns of the logical positivist movement and continued by proponents of the so-called “received view” of theories (Suppe 1977). One area where this division of interest has been a barrier to progress is understanding the growth of scientific knowledge.While philosophers as diverse as Nagel, Hempel, Kuhn, and Lakatos have attempted to explain the historical course of science, they have largely built their views on foundations designed to explicate the relation between theories (paradigms, scientific research programs) and the world. Thus, the received view's model of progress via theory (or indeed, whole science) reduction (e.g., Nagel 1961) rests on its largely syntactic/logical account of theory structure.

Van Fraassen's Semanticism

Bas van Fraassen has formulated a semantical or model theoretic analysis of the structure of scientific theories. He contrasts his semantical approach with the syntactic approach of the logical positivists and argues that his theory is preferable on a number of grounds. My aims in this paper will be threefold. First, I will present a brief description of van Fraassen's approach. Secondly, I will compare his theory with that of the logical positivists and, in so doing, identify the virtues that van Fraassen believes recommend, his theory over the positivist theory. Finally, I will raise an objection that is positivist in spirit which suggests that, epistemically, his account is indistinguishable from classical historicism.For van Fraassen, “To present a theory is to specify a family of structures, its models; and secondly, to specify certain parts of these models (the empirical substructures) as candidates for the direct representation of observable phenomena.

Gamtotyros teorijų sandara (sisteminis požiūris)

Straipsnyje autorius aptaria gamtotyros teorijos sandarą. Teigiama, kad svarbiausia kiekvienoje teorijoje yra tam tikra teorinė konstrukcija, sudaryta iš abstrakčių idealizuotų elementų. Konkrečiu pažinimo momentu eksperimentiškai fiksuojami materialiojo pasaulio ryšiai gali būti vienodai sėkmingai išreikšti skirtingomis matematinėmis formulėmis. Tačiau anksčiau ar vėliau prieinama prie gilesnių, išsamesnių materialiojo pasaulio ryšių, tuomet ir išaiškėja, kad matematinės funkcijos išraiškos, kurios buvo ekvivalenčios konkrečių materialiojo pasaulio ryšių, fiksuojamų konkrečiu pažinimo momentu, atžvilgiu, pasirodo esančios neekvivalentiškos išsamesnių ryšių atžvilgiu. Autorius išskiria teorinę sistemą (svarbiausią mokslo teorijų sandaros dalį), kuri apima ir teorinę konstrukciją, ir matematinį aparatą. Aptariamos „sistemos“, „sandaros“, „struktūros“ bei „funkcijos“ sąvokos. Sistema išreiškia tam tikrą esminį bet kokios prigimties daikto aspektą, ji yra priešingų sąvokų „sandara“ ir „funkcija“ sintezė. Sistemos funkcija suprantama kaip sistemos vidinis persitvarkymas, išėjimo parametrų kitimas pakitus įėjimo parametrams.

The Structure of Scientific Theories.

The Structure of Scientific Theories.