The context of an operational description is given by the distinction between what we consider as relevant and what as irrelevant for a particular experiment or observation. A rigorous description of a context in terms of a mathematically formulated context-independent fundamental theory is possible by the restriction of the domain of the basic theory and the introduction of a new coarser topology. Such a new topology is never given by first principles, but depends in a crucial way on the abstractions (...) made by the cognitive apparatus or the pattern recognition devices used by the experimentalist. A consistent mathematical formulation of a higher-level theory requires the closure of the restriction of the basic theory in the new contextual topology. The validity domain of the so constructed higher-level theory intersects nontrivially with the validity domain of the basic theory: neither domain is contained in the other. Therefore, higher-level theories cannot be totally ordered and theory reduction is not transitive. The emergence of qualitatively new properties is a necessary consequence of such a formulation of theory reduction (which does not correspond to the traditional one). Emergent properties are not manifest on the level of the basic theory, but they can be derived rigorously by imposing new, contextually selected topologies upon context-independent first principles. Most intertheoretical relations are mathematically describable as singular asymptotic expansions which do not converge in the topology of the primary theory, or by choosing one of the infinitely many possible, physically inequivalent representations of the primary theory (Gelfand–Naimark–Segal-construction of algebraic quantum mechanics). As examples we discuss the emergence of shadows, inductors, capacitors and resistors from Maxwell’s electrodynamics, the emergence of order parameters in statistical mechanics, the emergence of mass as a classical observable in Galilei-relativistic theories, the emergence of the shape of molecules in quantum mechanics, the emergence of temperature and other classical observables in algebraic quantum mechanics. (shrink)

The role of contingent contexts in formulating relations between properties of systems at different descriptive levels is addressed. Based on the distinction between necessary and sufficient conditions for interlevel relations, a comprehensive classification of such relations is proposed, providing a transparent conceptual framework for discussing particular versions of reduction, emergence, and supervenience. One of these versions, contextual emergence, is demonstrated using two physical examples: molecular structure and chirality, and thermal equilibrium and temperature. The concept of stability is emphasized as a (...) basic guiding principle of contextual property emergence. (shrink)

Had more philosophers of science come from chemistry, their thinking would have been different. I begin by looking at a typical chemical paper, in which making something is the leitmotif, and conjecture/refutation is pretty much irrelevant. What in fact might have been, might be, different? The realism of chemists is reinforced by their remarkable ability to transform matter; they buy into reductionism where it serves them, but make no real use of it. Incommensurability is taken without a blink, and actually (...) serves. The preeminence of synthesis in chemistry could have led philosophers of science to take more seriously questions of aesthetics within science, and to find a place in aesthetics for utility. The necessary motion twixt macroscopic and microscopic views of matter in modern chemistry leads to the coexistence of symbolic and iconic representations. And in another way to the deliberate, creative violation of categories. (shrink)

The debate between emergentists and reductionists rests on the observation that in many situations, in which it seems desirable to work with a coherent and unified discourse, key predicates fall into different groups, such that pairs of members one taken from each group, cannot be co-predicated of some common subject. Must we settle for ‘island’ discourses in science and human affairs or is some route to a unified discourse still open? To make progress towards resolving the issue the conditions under (...) which such segregations of predicates seem inexorable must be brought out. The distinction between determinable and determinate properties throws light on some aspects of this problem. Bohr’s concept of complementarity, when combined with Gibson’s idea of an affordances as a special class of dispositional properties is helpful. Several seeming problems melt away, for example, how it is possible for a group of notes to become hearable as a melody. The mind-body problem and the viability of the project of reducing biology to chemistry and physics are two issues that are more difficult to deal with. Are mental phenomena, such as feelings and memories emergent from material systems or are they actually material properties themselves? Are the attributes of living beings emergent from certain accidental but long running collocations of chemical reactions, or are they nothing but chemical phenomena? If emergent, in what way are they distinctive from that from which they emerge? (shrink)

La philosophie n'est ni contemplation, ni réflexion, ni communication. Elle est l'activité qui crée les concepts. Comment se distingue-t-elle de ses rivales, qui prétendent nous fournir en concepts? La philosophie doit nous dire quelle est la nature créative du concept, et quels en sont les concomitants : la pure immanence, le plan d'immanence, et les personnages conceptuels. Par là, la philosophie se distingue de la science et de la logique. Celles-ci n'opèrent pas par concepts, mais par fonctions, sur un plan (...) de référence et avec des observateurs partiels. L'art opère par percepts et affects, sur un plan de composition avec des figures esthétiques. La philosophie n'est pas interdisciplinaire, elle est elle-même une discipline entière qui entre en résonance avec la science et avec l'art, comme ceux-ci avec elle : trouver le concept d'une fonction, etc. C'est que les trois plans sont les trois manières dont le cerveau recoupe le chaos, et l'affronte. Ce sont les Chaoïdes. La pensée ne se constitue que dans ce rapport où elle risque toujours de sombrer. (shrink)

Mulliken proposed an Aufbauprinzip for the molecules on the basis of molecular spectroscopy while establishing, point by point, his concept of molecular orbit. It is the concept of electronic state which becomes the lever for his attribution of electronic configurations to a molecule. In 1932, the concept of orbit was transmuted into that of the molecular orbital to integrate the probabilistic approach of Born and to achieve quantitative accuracy. On the basis of the quantum works of Hund, Wigner, Lennard-Jones and (...) group theory, he suggested the fragment method to establish the characteristics of molecular orbital for polyatomic molecules. These developments make it possible to bring elements of thought on the relation between a molecular whole and its parts . An operational realism combined with the second law of thermodynamics can pave the way for interesting tracks in the mereological study of chemical systems. (shrink)

“Ontological emergence” of inherent high-level properties with causal powers is witnessed nowhere. A non-substantialist conception of emergence works much better. It allows downward causation, provided our concept of causality is transformed accordingly.

Scientists employ a variety of procedures to eliminate degrees of freedom from computationally and/or analytically intractable equations. In the process, they often construct new models and discover new concepts, laws and functional relations. I argue these procedures embody a central notion of reduction, namely, the containment of one structure within another. However, their inclusion in the philosophical concept of reduction necessitates a reevaluation of many standard assumptions about the ontological, epistemological and functional features of a reduction. On the basis of (...) the reevaluation, I advocate a continuum of reduction which proceeds from the eliminative to the constructive. The metaphysical aspects of theory use in constructive reductions are sketched. (shrink)

Does chemistry reduce to physics? If this means ‘Can we derive the laws of chemistry from the laws of physics?’, recent discussions suggest that the answer is ‘no’. But sup posing that kind of reduction—‘epistemological reduction’—to be impossible, the thesis of ontological reduction may still be true: that chemical properties are determined by more fundamental properties. However, even this thesis is threatened by some objections to the physicalist programme in the philosophy of mind, objections that generalize to the chemical case. (...) Two objections are discussed: that physicalism is vacuous, and that nothing grounds the asymmetry of dependence which reductionism requires. Although it might seem rather surprising that the philosophy of chemistry is affected by shock waves from debates in the philosophy of mind, these objections show that there is an argumentative gap between, on the one hand, the theoretical connection linking chemical properties with properties at the sub-atomic level, and, on the other, the philosophical thesis of ontological reduction. The aim of this paper is to identify the missing premises (among them a theory of physical possibility) that would bridge this gap. Introduction: missing elements and the mystery of discreteness The refutation of physicalism A combinatorial theory of physical possibilia Combinatorialism and the Bohr model Objections The missing premises and a disanalogy with mind. (shrink)

I claim that the question of whether chemistry is reduced to quantum mechanics is more ambiguous and multi-faceted than generally supposed. For example, chemistry appears to be both reduced and not reduced at the same time depending on the perspective that one adopts. Similarly, I argue that some conceptual issues in quantum mechanics are ambiguous and can only be laid to rest by embracing paradox and ambiguity rather than regarding them as obstacles to be overcome. Recent work in the reduction (...) of chemistry is also reviewed, including discussions of the ontological reduction of chemistry and the question of the emergence of chemistry from physics. (shrink)

In Neither Physics Nor Chemistry, Kostas Gavroglu and Ana Simoes examine the evolution of quantum chemistry into an autonomous discipline, tracing its development from the publication of early papers in the 1920s to the dramatic changes ...

Abstract Philosophers have paid little attention to the kind of reduction involved in transforming an analytically intractable equation into solvable form. I argue that this practice is important because it involves the design of a basic level theory for use in a specific domain. The design process can lead to the construction of a new theory. As a result of my analysis, theory design emerges as an important category of analysis for scientific methodology. Similarities between design in technology and science (...) are explored to illuminate the heuristic function of such reductions. (shrink)

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)