This junior/senior level text is devoted to a study of first-order logic and its role in the foundations of mathematics: What is a proof? How can a proof be justified? To what extent can a proof be made a purely mechanical procedure? How much faith can we have in a proof that is so complex that no one can follow it through in a lifetime? The first substantial answers to these questions have only been obtained in this century. The most (...) striking results are contained in Goedel's work: First, it is possible to give a simple set of rules that suffice to carry out all mathematical proofs; but, second, these rules are necessarily incomplete - it is impossible, for example, to prove all true statements of arithmetic. The book begins with an introduction to first-order logic, Goedel's theorem, and model theory. A second part covers extensions of first-order logic and limitations of the formal methods. The book covers several advanced topics, not commonly treated in introductory texts, such as Trachtenbrot's undecidability theorem. Fraissé's elementary equivalence, and Lindstroem's theorem on the maximality of first-order logic. (shrink)

This paper analyzes the generation and function of hitherto ignored or misrepresented interfield theories , theories which bridge two fields of science. Interfield theories are likely to be generated when two fields share an interest in explaining different aspects of the same phenomenon and when background knowledge already exists relating the two fields. The interfield theory functions to provide a solution to a characteristic type of theoretical problem: how are the relations between fields to be explained? In solving this problem (...) the interfield theory may provide answers to questions which arise in one field but cannot be answered within it alone, may focus attention on domain items not previously considered important, and may predict new domain items for one or both fields. Implications of this analysis for the problems of reduction and the unity and progress of science are mentioned. (shrink)

Introduction: Science and Common Sense Long before the beginnings of modern civilization, men ac- quired vast funds of information about their environment. ...

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 have not attempted to provide here an analysis of the methodology of molecular biology or molecular genetics which would demonstrate at what specific points a more reductionist aim would make sense as a research strategy. This, I believe, would require a much deeper analysis of scientific growth than philosophy of science has been able to provide thus far. What I have tried to show is that a straightforward reductionist strategy cannot be said to be follwed in important cases of (...) theory development in molecular biology, and that in at least one important case, the Jacob-Monod operon theory, the methodology followed was more biological than chemical. It should be noted in closing, however, that since biological systems are thought by molecular biologists to be nothing but chemical systems, in the long run detailed investigations of such systems will be in full accord with the dictates suggested by the general reduction model. (shrink)

Theories in the usual sense, as characterized by a language and a set of theorems in that language ("statement view"), are related to theories in the structuralist sense, in turn characterized by a set of potential models and a subset thereof as models ("non-statement view", J. Sneed, W. Stegmüller). It is shown that reductions of theories in the structuralist sense (that is, functions on structures) give rise to so-called "representations" of theories in the statement sense and vice versa, where representations (...) are understood as functions that map sentences of one theory into another theory. It is argued that commensurability between theories should be based on functions on open formulas and open terms so that reducibility does not necessarily imply commensurability. This is in accordance with a central claim by Stegmüller on the compatibility of reducibility and incommensurability that has recently been challenged by D. Pearce. (shrink)

The notion of reduction in the natural sciences has been assimilated to the notion of inter-theoretical explanation. Many philosophers of science (following Nagel) have held that the apparently ontological issues involved in reduction should be replaced by analyses of the syntactic and semantic connections involved in explaining one theory on the basis of another. The replacement does not seem to have been especially successful, for we still lack a plausible account of inter-theoretical explanation. I attempt to provide one.

The paper presents an example of unified theory bearing interest from both a historical and systematic point of view. The example is chosen from evolutionary population genetics (neo-Darwinian synthetic theory). It exhibits various aspects of theoretical change in science that have been shown in Part I (Geiger, 1988) to be characteristic of syntheses of theories.

The paper presents an example of unified theory bearing interest from both a historical and systematic point of view. The example is chosen from evolutionary population genetics (neo-Darwinian synthetic theory). It exhibits various aspects of theoretical change in science that have been shown in Part I (Geiger, 1988) to be characteristic of syntheses of theories.

The conditions are examined under which one theory is said to be replaceable by another, while preserving those features of the original theory which made it serviceable for a given purpose. Among such replacements, special attention is given to ones which qualify as so-called reductions of a theory, and some theorems are proved concerning the notion of a reduction.

The recent sociobiology debate has raised fundamental and previously unresolved conceptual problems. Evolutionary Instability - Logical and Material Aspects of a Unified Theory of Biosocial Evolution - offers ap- proaches for their solution. The scientific applications comprise the dynamics and evolutionary instability of hierarchically organized systems, especially systems of interacting behavioural phenotypes in animals and man. The technical apparatus is thoroughly explained in intuitive terms within the text, and illustrated by numerous familiar examples and graphical representations, supplemented by an informal (...) summary and discussion. The analyses offer new theoretical perspectives to such diverse fields as philosophy of science, evolutionary biology, general system theory and sociology. (shrink)

How many miles to Babylon? Three-score and ten. Can I get there by candle-light? Yes, and back again. If your heels are nimble dnd light, You may get there by candle-light. Any philosopher who takes more than a fleeting interest in the sciences and their development must at some stage confront the issue of incommensurability in one or other of its many manifes tations. For the philosopher of science concerned with problems of conceptual change and the growth of knowledge, matters (...) of incommensurability are of paramount concern. After many years of skating over, skimming through and skirting round this issue in my studies of intertheory relations in science, I decided to take the plunge and make the problem of incommensurability the central and unifying theme of a book. The present volume is the result of that decision. My interest in problems of comparability and commensurability in science was awakened in the formative years of my philosophi cal studies by my teacher, Jerzy Giedymin. From him I have learnt not only to enjoy philosophical problems but also to beware of simpleminded solutions to them. The vibrant seminars of Paul Feyerabend held at Sussex University in 1974 left me in no doubt that incommensurability was, and would remain, a major topic of debate and dispute in the philosophical study of human knowledge. (shrink)

The author's concept of incommensurability is explicated by elaborating the claim that some terms essential to the formulation of older theories defy translation into the language of more recent ones. Defense of this claim rests on the distinction between interpreting a theory in a later language and translating the theory into it. The former is both possible and essential, the latter neither. The interpretation/translation distinction is then applied to Kitcher's critique of incommensurability and Quine's conception of a translation manual, both (...) of which take reference-preservation as the sole semantic criterion of translational adequacy. The paper concludes by enquiring about the additional criteria a successful translation must satisfy. (shrink)