Emergence in exact natural science

Abstract
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)
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history
Request removal from index
Download options
Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 27,215
External links

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.

Add more references

Citations of this work BETA
Forms of Quantum Nonseparability and Related Philosophical Consequences.Vassilios Karakostas - 2004 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 35 (2):283 - 312.
Complex Systems, Modelling and Simulation.Sam Schweber & Matthias Wächter - 2000 - Studies in History and Philosophy of Science Part B 31 (4):583-609.
Whence Chemistry?Robert C. Bishop - 2010 - Studies in History and Philosophy of Science Part B 41 (2):171-177.
Complex Systems, Modelling and Simulation.Sam Schweber & Matthias Wächter - 2000 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 31 (4):583-609.

View all 7 citations / Add more citations

Similar books and articles
Asymptotics, Reduction and Emergence.C. A. Hooker - 2004 - British Journal for the Philosophy of Science 55 (3):435-479.
The Reemergence of 'Emergence'.Bryon Cunningham - 2001 - Philosophy of Science 3 (September):S63-S75.
Cognitive Emergence.Fritz Rohrlich - 1997 - Philosophy of Science Supplement 64 (4):346-58.
Physicalism, the Identity Theory, and the Concept of Emergence.John Kekes - 1966 - Philosophy of Science 33 (December):360-75.

Monthly downloads

Added to index

2009-01-28

Total downloads

26 ( #194,987 of 2,164,577 )

Recent downloads (6 months)

1 ( #347,948 of 2,164,577 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Order:
There  are no threads in this forum
Nothing in this forum yet.

Other forums