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.

In this article, we redefine classical notions of theory reduction in such a way that model-theoretic preferential semantics becomes part of a realist depiction of this aspect of science. We offer a model-theoretic reconstruction of science in which theory succession or reduction is often better - or at a finer level of analysis - interpreted as the result of model succession or reduction. This analysis leads to 'defeasible reduction', defined as follows: The conjunction of the assumptions of a reducing theory (...) T with the definitions translating the vocabulary of a reduced theory T' to the vocabulary of T, defeasibly entails the assumptions of reduced T'. This relation of defeasible reduction offers, in the context of additional knowledge becoming available, articulation of a more flexible kind of reduction in theory development than in the classical case. Also, defeasible reduction is shown to solve the problems of entailment that classical homogeneous reduction encounters. Reduction in the defeasible sense is a practical device for studying the processes of science, since it is about highlighting different aspects of the same theory at different times of application, rather than about naive dreams concerning a metaphysical unity of science. (shrink)

For nearly thirty years, there has been a consensus (at least in English-speaking countries) that reductionism is a mistake and that there are autonomous special sciences. This consensus has been based on an argument from multiple realizability. But Jaegwon Kim has argued persuasively that the multiple realizability argument is flawed.1 I will sketch the recent history of the debate, arguing that much --but not all--of the anti-reductionist consensus survives Kim's critique. This paper was originally titled "Anti-Reductionism Strikes Back", but in (...) the course of writing the paper, I came to think that the concepts used in the debate would not serve either position very well. (shrink)

This is a new release of the original 1949 edition.

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)

CURRENT CONTROVERSIES about the Mind-Body Identity Theory form a case-study for the investigation of the methods practiced by linguistic philosophers. Recent criticisms of these methods question that philosophers can discern lines of demarcation between "categories" of entities, and thereby diagnose "conceptual confusions" in "reductionist" philosophical theories. Such doubts arise once we see that it is very difficult, and perhaps impossible, to draw a firm line between the "conceptual" and the "empirical," and thus to differentiate between a statement embodying a conceptual (...) confusion and one that expresses a surprising empirical result. The proponent of the Identity Theory are identical with certain brain-processes) holds that his opponents' arguments to the effect that empirical inquiry could not identify brain-processes and sensations are admirable illustrations of this difficulty. For, he argues, the classifications of linguistic expressions that are the ground of his opponents' criticism are classifications of a language which is as it is because it is the language spoken at a given stage of empirical inquiry. But the sort of empirical results that would show brain processes and sensations to be identical would also bring about changes in our ways of speaking. These changes would make these classifications out of date. To argue against the Identity Theory on the basis of the way we talk now is like arguing against an assertion that supernatural phenomena are identical with certain natural phenomena on the basis of the way in which superstitious people talk. There is simply no such thing as a method of classifying linguistic expressions that has results guaranteed to remain intact despite the results of future empirical inquiry. Thus in this area there is no method which will have the sort of magisterial neutrality of which linguistic philosophers fondly dream. (shrink)

One of the central problems in the philosophy of psychology is an updated version of the old mind-body problem: how levels of theories in the behavioral and brain sciences relate to one another. Many contemporary philosophers of mind believe that cognitive-psychological theories are not reducible to neurological theories. However, this antireductionism has not spawned a revival of dualism. Instead, most nonreductive physicalists prefer the idea of a one-way dependence of the mental on the physical.In Psychoneural Reduction, John Bickle presents a (...) new type of reductionism, one that is stronger than one-way dependency yet sidesteps the arguments that sank classical reductionism. Although he makes some concessions to classical antireductionism, he argues for a relationship between psychology and neurobiology that shares some of the key aims, features, and consequences of classical reductionism. Parts of Bickle's "new wave" reductionism have emerged piecemeal over the past two decades; this is his first comprehensive statement and defense of it to appear. (shrink)

The Three Papers comprising this series, together with my earlier [34] also published in this journal, constitute an attempt to set out the major issues in the theoretical domain of reduction and to develop a general theory of theory reduction. The fourth paper, [34], though published separately from this trio, is integral to the presentation and should be read in conjunction with these papers. Even so, the presentation is limited in scope – roughly, to intertheoretic reduction among empirical theories – (...) and informal in presentation – not least because a satisfying formal account of theories has yet to be offered. And despite the length, the treatment is still condensed; often corroborating and/or intuitively helpful detail has had to be consigned to footnotes or omitted. I approach the problem from within my own naturalistic realist philosophy of science and formal analysis of abstract hierarchy in theory. The sources for the former are [25], [29], [31], and [32] and those for the latter essentially [27] and [30]. Hierarchical notions played a significant role in the already published [34]. (shrink)

I hope to show that supervenience and determination, as I have here intuitively characterized them, are really different expressions of the same core idea which one may make more precise in a great number of different ways, depending on the interpretation one puts on the catchall parameters “cases”, “truth of kind P”and “truth of kind S”.