Emergence in exact natural science
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
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.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library||
References found in this work BETA
No references found.
Citations of this work BETA
Robert C. Bishop (2010). Whence Chemistry? Studies in History and Philosophy of Science Part B 41 (2):171-177.
Similar books and articles
Fritz Rohrlich (1997). Cognitive Emergence. Philosophy of Science Supplement 64 (4):346-58.
Bryon Cunningham (2001). The Reemergence of 'Emergence'. Philosophy of Science 3 (September):S63-S75.
C. A. Hooker (2004). Asymptotics, Reduction and Emergence. British Journal for the Philosophy of Science 55 (3):435-479.
Ion C. Baianu (2007). Categorical Ontology of Levels and Emergent Complexity: An Introduction. [REVIEW] Axiomathes 17 (3-4):209-222.
Harald Atmanspacher (2006). Contextual Emergence in the Description of Properties. Foundations of Physics 36 (12):1753-1777.
Robert C. Bishop & Harald Atmanspacher (2006). Contextual Emergence in the Description of Properties. Foundations of Physics 36 (12):1753-1777.
C. Ulises Moulines (2006). Ontology, Reduction, Emergence: A General Frame. Synthese 151 (3):313-323.
John Kekes (1966). Physicalism, the Identity Theory, and the Concept of Emergence. Philosophy of Science 33 (December):360-75.
Added to index2009-01-28
Total downloads10 ( #146,903 of 1,101,768 )
Recent downloads (6 months)0
How can I increase my downloads?