A classification of models of reduction into three categories — theory reductionism, explanatory reductionism, and constitutive reductionism — is presented. It is shown that this classification helps clarify the relations between various explications of reduction that have been offered in the past, especially if a distinction is maintained between the various epistemological and ontological issues that arise. A relatively new model of explanatory reduction, one that emphasizes that reduction is the explanation of a whole in terms of its parts is (...) also presented in detail. Finally, the classification is used to clarify the debate over reductionism in molecular biology. It is argued there that while no model from the category of theory reduction might be applicable in that case, models of explanatory reduction might yet capture the structure of the relevant explanations. (shrink)

The aim of this paper is to clarify the role of category theory in the foundations of mathematics. There is a good deal of confusion surrounding this issue. A standard philosophical strategy in the face of a situation of this kind is to draw various distinctions and in this way show that the confusion rests on divergent conceptions of what the foundations of mathematics ought to be. This is the strategy adopted in the present paper. It is divided into 5 (...) sections. We first show that already in the set theoretical framework, there are different dimensions to the expression foundations of. We then explore these dimensions more thoroughly. After a very short discussion of the links between these dimensions, we move to some of the arguments presented for and against category theory in the foundational landscape. We end up on a more speculative note by examining the relationships between category theory and set theory. (shrink)

This volume tackles the slippery subject of 'meaning'.

It is argued that complexity has only a limited use as a paradigm against reductionist approaches and that it has a much richer potential as a comparable property. What can complexity be usefully said to be a property of is discussed. It is argued that it is unlikely to have any useful value as applied to real object or systems. Further that even relativising it to an observer has problems. It is proposed that complexity can be only usefully applied to (...) constructions within a given language. It is argued that complexity is usefully differentiated from the concepts of size, ignorance, variety, minimum description length and order. A definition of complexity is proposed which can be summarised as follows: That property of a language expression which makes it difficult to formulate its overall behaviour even when given almost complete information about its atomic components and their inter-relations.. Some of the consequences of this definition are discussed. It is shown that this definition encompasses several existing varieties of complexity measures and is then applied to some examples pertaining to the evolution of complex' systems including: "What is the complexity that has evolved in organisms and has it increased?". (shrink)

What is life? For four centuries, it has been believed that the only possible scientific approach to this question proceeds from the Cartesian metaphor -- organism as machine. Therefore, organisms are to be studied and characterized the same way "machines" are; the same way any inorganic system is. Robert Rosen argues that such a view is neither necessary nor sufficient to answer the question. He asserts that life is not a specialization of mechanism, but rather a sweeping generalization of it. (...) Above all, Rosen argues that renouncing mechanism does not mean abandoning science. A radical alternative is proposed, drawn equally from experience in biology, physics, and mathematics; an alternative which draws attention to a new class of complex systems, which are radically different from mechanism. (shrink)

There has been much discussion recently about the scope and limits of purely symbolic models of the mind and about the proper role of connectionism in cognitive modeling. This paper describes the symbol grounding problem : How can the semantic interpretation of a formal symbol system be made intrinsic to the system, rather than just parasitic on the meanings in our heads? How can the meanings of the meaningless symbol tokens, manipulated solely on the basis of their shapes, be grounded (...) in anything but other meaningless symbols? The problem is analogous to trying to learn Chinese from a Chinese/Chinese dictionary alone. A candidate solution is sketched: Symbolic representations must be grounded bottom-up in nonsymbolic representations of two kinds: iconic representations, which are analogs of the proximal sensory projections of distal objects and events, and categorical representations, which are learned and innate feature-detectors that pick out the invariant features of object and event categories from their sensory projections. Elementary symbols are the names of these object and event categories, assigned on the basis of their categorical representations. Higher-order symbolic representations, grounded in these elementary symbols, consist of symbol strings describing category membership relations. Connectionism is one natural candidate for the mechanism that learns the invariant features underlying categorical representations, thereby connecting names to the proximal projections of the distal objects they stand for. In this way connectionism can be seen as a complementary component in a hybrid nonsymbolic/symbolic model of the mind, rather than a rival to purely symbolic modeling. Such a hybrid model would not have an autonomous symbolic module, however; the symbolic functions would emerge as an intrinsically dedicated symbol system as a consequence of the bottom-up grounding of categories ' names in their sensory representations. Symbol manipulation would be governed not just by the arbitrary shapes of the symbol tokens, but by the nonarbitrary shapes of the icons and category invariants in which they are grounded. (shrink)