Reduction

Reduction and reductionism have been central philosophical topics in analytic philosophy of science for more than six decades. Together they encompass a diversity of issues from metaphysics and epistemology. This article provides an introduction to the topic that illuminates how contemporary epistemological discussions took their shape historically and limns the contours of concrete cases of reduction in specific natural sciences. The unity of science and the impulse to accomplish compositional reduction in accord with a layer-cake vision of the sciences, the seminal contributions of Ernest Nagel on theory reduction and how they strongly conditioned subsequent philosophical discussions, and the detailed issues pertaining to different accounts of reduction that arise in both physical and biological science (e.g., limit-case and part-whole reduction in physics, the difference-making principle in genetics, and mechanisms in molecular biology) are explored. The conclusion argues that the epistemological heterogeneity and patchwork organization of the natural sciences encourages a pluralist stance about reduction

Intertheoretic Reduction, Confirmation, and Montague’s Syntax-Semantics Relation

Intertheoretic relations are an important topic in the philosophy of science. However, since their classical discussion by Ernest Nagel, such relations have mostly been restricted to relations between pairs of theories in the natural sciences. This paper presents a case study of a new type of intertheoretic relation that is inspired by Montague's analysis of the linguistic syntax-semantics relation. The paper develops a simple model of this relation. To motivate the adoption of our new model, we show that this model extends the scope of application of the Nagelian (or related) models and that it shares the epistemological advantages of the Nagelian model. The latter is achieved in a Bayesian framework

Intertheoretic Reduction, Confirmation, and Montague’s Syntax-Semantics Relation

Intertheoretic relations are an important topic in the philosophy of science. However, since their classical discussion by Ernest Nagel, such relations have mostly been restricted to relations between pairs of theories in the natural sciences. This paper presents a case study of a new type of intertheoretic relation that is inspired by Montague's analysis of the linguistic syntax-semantics relation. The paper develops a simple model of this relation. To motivate the adoption of our new model, we show that this model extends the scope of application of the Nagelian (or related) models and that it shares the epistemological advantages of the Nagelian model. The latter is achieved in a Bayesian framework

Reduction

This is a contribution to the encyclopedia of systems biology on reduction

On Hamiltonian cycles in hypergraphs with dense link graphs

We show that every $k$-uniform hypergraph on $n$ vertices whose minimum $(k-2)$-degree is at least $(5/9+o(1))n^2/2$ contains a Hamiltonian cycle. A construction due to Han and Zhao shows that this minimum degree condition is optimal. The same result was proved independently by Lang and Sahueza-Matamala.Comment: Dedicated to Endre Szemer\'edi on the occasion of his 80th birthda

Levels of explanation in biological psychology

Until recently, the notions of function and multiple realization were supposed to save the autonomy of psychological explanations. Furthermore, the concept of supervenience presumably allows both dependence of mind on brain and non-reducibility of mind to brain, reconciling materialism with an independent explanatory role for mental and functional concepts and explanations. Eliminativism is often seen as the main or only alternative to such autonomy. It gladly accepts abandoning or thoroughly reconstructing the psychological level, and considers reduction if successful as equivalent with elimination. In comparison with the philosophy of mind, the philosophy of biology has developed more subtle and complex ideas about functions, laws, and reductive explanation than the stark dichotomy of autonomy or elimination. It has been argued that biology is a patchwork of local laws, each with different explanatory interests and more or less limited scope. This points to a pluralistic, domain-specific and multi-level view of explanations in biology. Explanatory pluralism has been proposed as an alternative to eliminativism on the one hand and methodological dualism on the other hand. It holds that theories at different levels of description, like psychology and neuroscience, can co-evolve, and mutually influence each other, without the higher-level theory being replaced by, or reduced to, the lower-level one. Such ideas seem to tally with the pluralistic character of biological explanation. In biological psychology, explanatory pluralism would lead us to expect many local and non-reductive interactions between biological, neurophysiological, psychological and evolutionary explanations of mind and behavior. This idea is illustrated by an example from behavioral genetics, where genetics, physiology and psychology constitute distinct but interrelated levels of explanation. Accounting for such a complex patchwork of related explanations seems to require a more sophisticated and precise way of looking at levels than the existing ideas on (reductive and non-reductive) explanation in the philosophy of mind