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.

Four current accounts of theory reduction are presented, first informally and then formally: (1) an account of direct theory reduction that is based on the contributions of Nagel, Woodger, and Quine, (2) an indirect reduction paradigm due to Kemeny and Oppenheim, (3) an "isomorphic model" schema traceable to Suppes, and (4) a theory of reduction that is based on the work of Popper, Feyerabend, and Kuhn. Reference is made, in an attempt to choose between these schemas, to the explanation of (...) physical optics by Maxwell's electromagnetic theory, and to the revisions of genetics necessitated by partial biochemical reductions of genetics. A more general reduction schema is proposed which: (1) yields as special cases the four reduction paradigms considered above, (2) seems to be in better accord with both the canons of logic and actual scientific practice, and (3) clarifies the problems of meaning variance and ontological reduction. (shrink)

In this paper the concept of supervenience is employed to explain the relationship between fitness as employed in the theory of natural selection and population biology and the physical, behavioral and ecological properties of organisms that are the subjects of lower level theories in the life sciences. The aim of this analysis is to account simultaneously for the fact that the theory of natural selection is a synthetic body of empirical claims, and for the fact that it continues to be (...) misconstrued, even by biologists, for a tautological system. The notion of supervenience is then employed to provide a new statement of the relation of Mendelian predicates to molecular ones in order to provide for the commensurability and potential reducibility of Mendelian to molecular genetics in a way that circumvents the theoretical complications which appear to stand in the way of such a reduction. (shrink)

The present paper has two aims. First, we reconstruct the core of molecular genetics (MOLGEN) i.e. the array of theoretical assumptions which underly all or most applications of molecular genetics. Second, we define a reduction relation p reducing character-factor genetics (CFG) to MOLGEN. That p is a reduction relation is proved by establishing that p satisfies the two major conditions which are discussed in the literature as necessary or ‘essential’ for reduction. This substantiates the claim that molecular genetics is ‘better (...) than’ or ‘more progressive-than’ character-factor genetics-which is commonly held true today. The paper continues, and relies heavily on the definitions given in part 1 (Balzer and Dawe [1985]). The enumeration of the definitions and sections in the present paper continues that of part 1. References to definitions with numbers smaller than 8 and to sections number I-4 always refer to part 1. (shrink)

Explores the development of the ideas of evolutionary biology, particularly as affected by the increasing understanding of genetics and of the chemical basis of inheritance.