Coherent, well organized text familiarizes readers with complete theory of logical inference and its applications to math and the empirical sciences. Part I deals with formal principles of inference and definition; Part II explores elementary intuitive set theory, with separate chapters on sets, relations, and functions. Last section introduces numerous examples of axiomatically formulated theories in both discussion and exercises. Ideal for undergraduates; no background in math or philosophy required.

Two chief problems of the theory of knowledge are the question of meaning and the question of verification. The first question asks under what conditions a sentence has meaning, in the sense of cognitive, factual meaning. The second one asks how we get to know something, how we can find out whether a given sentence is true or false. The second question presupposes the first one. Obviously we must understand a sentence, i.e. we must know its meaning, before we can (...) try to find out whether it is true or not. But, from the point of view of empiricism, there is a still closer connection between the two problems. In a certain sense, there is only one answer to the two questions. If we knew what it would be for a given sentence to be found true then we would know what its meaning is. And if for two sentences the conditions under which we would have to take them as true are the same, then they have the same meaning. Thus the meaning of a sentence is in a certain sense identical with the way we determine its truth or falsehood; and a sentence has meaning only if such a determination is possible. (shrink)

From a logical point of view, Stone duality for Boolean algebras relates theories in classical propositional logic and their collections of models. The theories can be seen as presentations of Boolean algebras, and the collections of models can be topologized in such a way that the theory can be recovered from its space of models. The situation can be cast as a formal duality relating two categories of syntax and semantics, mediated by homming into a common dualizing object, in this (...) case 2.In the present work, we generalize the entire arrangement from propositional to first-order logic, using a representation result of Butz and Moerdijk. Boolean algebras are replaced by Boolean categories presented by theories in first-order logic, and spaces of models are replaced by topological groupoids of models and their isomorphisms. A duality between the resulting categories of syntax and semantics, expressed primarily in the form of a contravariant adjunction, is established by homming into a common dualizing object, now Sets, regarded once as a boolean category, and once as a groupoid equipped with an intrinsic topology.The overall framework of our investigation is provided by topos theory. Direct proofs of the main results are given, but the specialist will recognize toposophical ideas in the background. Indeed, the duality between syntax and semantics is really a manifestation of that between algebra and geometry in the two directions of the geometric morphisms that lurk behind our formal theory. Along the way, we give an elementary proof of Butz and Moerdijkʼs result in logical terms. (shrink)

Das Ziel: Konstitutionssystem der Begriffe Das Ziel der vorliegenden Untersuchungen ist die Aufstellung eines erkenntnismäßig-logischen Systems der ...

Bas C. van Fraassen presents an original exploration of how we represent the world.

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)

Suppe, F. The search for philosophic understanding of scientific theories (p. [1]-241)--Proceedings of the symposium.--Bibliography, compiled by Rew A. Godow, Jr. (p. [615]-646).

Achinstein, Putnam, and others have urged the rejection of the received view on theories (which construes theories as axiomatic calculi where theoretical terms are given partial observational interpretations by correspondence rules) because (i) the notion of partial interpretation cannot be given precise formulation, and (ii) the observational-theoretical distinction cannot be drawn satisfactorily. I try to show that these are the wrong reasons for rejecting the received view since (i) is false and it is virtually impossible to demonstrate the truth of (...) (ii). Nonetheless, the received view should be rejected because it obscures a number of epistemologically important features of scientific theorizing. I show this by sketching an alternative analysis which reveals some of these features and gives a more faithful picture of scientific theorizing. (shrink)

Different conceptions of scientific theories, such as the state spaces approach of Bas van Fraassen, the phase spaces approach of Frederick Suppe, the set-theoretical approach of Patrick Suppes, and the structuralist view of Joseph Sneed et al. are usually put together into one big family. In addition, the definite article is normally used, and thus we speak of the semantic conception of theories and of its different approaches . However, in The Semantic Conception of Theories and Scientific Realism , starting (...) from certain remarks already made in “Theory Structure” , Current Research in Philosophy of Science, East Lansing: Philosophy of Science Association, 1979, pp. 317–338), Frederick Suppe excludes the structuralist view as well as other “European” versions from the semantic conception of theories. In this paper I will critically examine the reasons put forward by Suppe for this decision and, later, I will provide a general characterization of the semantic family and of the structuralist view of theories in such a way as to justify the inclusion of the structuralist view as a member of this family. (shrink)

According to the semantic view of scientific theories, theories are classes of models. I show that this view -- if taken seriously as a formal explication -- leads to absurdities. In particular, this view equates theories that are truly distinct, and it distinguishes theories that are truly equivalent. Furthermore, the semantic view lacks the resources to explicate interesting theoretical relations, such as embeddability of one theory into another. The untenability of the semantic view -- as currently formulated -- threatens to (...) undermine scientific structuralism. (shrink)

Halvorson argues that the semantic view of theories leads to absurdities. Glymour shows how to inoculate the semantic view against Halvorson's criticisms, namely by making it into a syntactic view of theories. I argue that this modified semantic-syntactic view cannot do the philosophical work that the original "language-free" semantic view was supposed to do.

This chapter contains sections titled: Introduction The Once Received View (ORV) Criticisms of the ORV The “Model Model” of Scientific Theories Mechanisms: Investigating Nonformal Patterns in Scientific Theories Conclusion.

Models represent their target systems in one way or another. But what does it mean for a model to represent something beyond itself? This paper details different aspects of this problem and argues that the semantic view of theories does not provide us with an adequate response to any of these.

An early, very preliminary edition of this book was circulated in 1962 under the title Set-theoretical Structures in Science. There are many reasons for maintaining that such structures play a role in the philosophy of science. Perhaps the best is that they provide the right setting for investigating problems of representation and invariance in any systematic part of science, past or present. Examples are easy to cite. Sophisticated analysis of the nature of representation in perception is to be found already (...) in Plato and Aristotle. One of the great intellectual triumphs of the nineteenth century was the mechanical explanation of such familiar concepts as temperature and pressure by their representation in terms of the motion of particles. A more disturbing change of viewpoint was the realization at the beginning of the twentieth century that the separate invariant properties of space and time must be replaced by the space-time invariants of Einstein's special relativity. Another example, the focus of the longest chapter in this book, is controversy extending over several centuries on the proper representation of probability. The six major positions on this question are critically examined. Topics covered in other chapters include an unusually detailed treatment of theoretical and experimental work on visual space, the two senses of invariance represented by weak and strong reversibility of causal processes, and the representation of hidden variables in quantum mechanics. The final chapter concentrates on different kinds of representations of language, concluding with some empirical results on brain-wave representations of words and sentences. (shrink)

Peter Vickers examines 'inconsistent theories' in the history of science--theories which, though contradictory, are held to be extremely useful. He argues that these 'theories' are actually significantly different entities, and warns that the traditional goal of philosophy to make substantial, general claims about how science works is misguided.

It is now part and parcel of the official philosophical wisdom that models are essential to the acquisition and organisation of scientific knowledge. It is also generally accepted that most models represent their target systems in one way or another. But what does it mean for a model to represent its target system? I begin by introducing three conundrums that a theory of scientific representation has to come to terms with and then address the question of whether the semantic view (...) of theories, which is the currently most widely accepted account of theories and models, provides us with adequate answers to these questions. After having argued in some detail that it does not, I conclude by pointing out in what direction a tenable account of scientific representation might be sought. (shrink)

This impressive volume presents the results of a symposium on the structure of scientific theories held at the University of Illinois, Urbana, on March 26-29, 1969; lest this create the wrong impression, let it be noted at the outset that the volume is much more than a collection of papers. Indeed, when one takes into account Frederick Suppe’s book-length introduction, the editing of the critical comments, the extensive bibliography, and the fine index, the work must be seen as the best (...) account of scientific theory now available, one that surely commends itself to every philosopher of science with the slightest interest in metaphysics. The thrust of the symposium was to examine the view of scientific theories that has enjoyed great vogue among logical positivists, who have seen such theories as "axiomatic calculi in which theoretical terms and statements are given a partial observational interpretation by means of correspondence rules." Suppe refers to this as the "Received View," although it has been increasingly questioned in recent years, particularly by philosophers who have some proficiency in the history of science and by scientists who question its fidelity to actual scientific practice. One of the major aims of the symposium was to subject the Received View to analysis and debate by its proponents and by its critics, to assess its present status, and to see if any consensus has begun to develop on this topic—which plays such a key role in the philosophy of science. Suppe performs the analytic function in his critical introduction, and Stephen Toulmin adds a postscript that attempts to chart a course for future research. The message seems to be that the Received View has run its course and has proved to be more a hindrance than a help to philosophizing about science; what will take its place, however, does not emerge with any clarity. Participants in the symposium include all the luminaries in the philosophy of science movement: Carl Hempel, Patrick Suppes, David Bohm, Hilary Putnam, Thomas Kuhn, and Dudley Shapere, among others. Especially noteworthy are Suppe’s account of the development of the Received View and the criticisms that have been lodged against it, viz., its reliance on the analytic-synthetic distinction; the tenability of the observational-theoretical distinction; the notion of partial interpretation; its failure to include models as integral components; its analysis of correspondence rules; and its reliance on axiomatization. Suppe also details some of the proposed alternatives to the Received View, giving in the process lucid expositions of the thought of Toulmin, Kuhn, Hanson, Popper, and Feyerabend—all of which he treats under the rubric of "Weltanshauungen [[sic]] Analyses." Those interested in the relationships between history of science and philosophy of science will find the interchange between I. Bernard Cohen and Peter Achinstein stimulating as well as illuminating. Kuhn takes this occasion to offer his "Second Thoughts on Paradigms," and Shapere continues his criticism of both Kuhn and logical positivism—now more constructively than heretofore—with a penetrating essay entitled "Scientific Theories and their Domains." About the only thing that is lacking is a treatment of recent developments in England, particularly the work of Rom Harré at Oxford and related thinkers, who likewise reject the Received View and offer interesting alternatives to it that have yet to be appreciated and critiqued in the U.S.—W.A.W. (shrink)

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The structure of evolutionary theory has proved difficult to characterize. Most available analyses focus on the existence of evolutionary laws and on the axiomatizability of the theory; such analyses pay insufficient attention to mathematical evolutionary models and their structure, and to the structural complications arising from the variety of evolutionary sub-theories. ;The primary goal of this dissertation is to introduce and develop an analysis of the structure of evolutionary theory that is both precise and useful. The secondary goal is to (...) offer further evidence of the appropriateness and utility of the semantic view of theories, as developed by P. Suppes, B. C. van Fraassen, and F. Suppe, in which the theory is viewed as a family of related mathematical models. ;After reviewing the semantic approach, I provide a formal framework for describing and distinguishing among population genetics models. The interrelations among the models are described through a set of notions developed and made precise through the analysis of several evolutionary sub-theories, including genic selection and species selection. The framework of model specification, combined with the notions describing formal relations among models, are offered as a system capable of describing any part or aspect of the structure of evolutionary theory. ;Finally, I present a view of confirmation that relies on the distinctions present in the above system of theory description. I argue that this view of confirmation has two advantages over a hypothetico-deductive view of confirmation. First, it is possible to establish the reasonableness of viewing a variety of evidence as a form of confirmation. Second, as I show in the analysis of a controversial model, distinctions can be made due to the subtlety of the view that do not appear under the usual approaches. ;I conclude that a semantic approach to the structure of theories offers a natural, precise framework for the characterization of contemporary evolutionary theory. As such, it may provide a means with which progress on outstanding theoretical and philosophical problems can be achieved. (shrink)