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Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods
13:04

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Published on: September 19, 2012

Entailment of ambiguity.

Stephen W Kercel1

  • 1Endogenous Systems Research Group, University of New England, University Campus, Biddeford, ME 04005, USA. kercel1@suscom-maine.net

Chemistry & Biodiversity
|October 24, 2007
PubMed
Summary
This summary is machine-generated.

This study clarifies Rosen's principle of closure to efficient cause, a key feature of complexity and organisms. The (M,R)-system reveals this closure's inherent ambiguity, explaining complex properties like non-computability.

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Area of Science:

  • * Theoretical Biology
  • * Systems Biology
  • * Philosophy of Science

Background:

  • * Rosen's principle of 'closure to efficient cause' is central to understanding complexity and organisms.
  • * Existing interpretations of this principle have led to confusion among scholars.
  • * The (M,R)-system provides a formal framework to elucidate this concept.

Purpose of the Study:

  • * To clarify the principle of 'closure to efficient cause' using the (M,R)-system.
  • * To demonstrate how this principle underlies the characteristics of complex systems.
  • * To identify and explain an inherent property of this closure, namely ambiguity.

Main Methods:

  • * Formalization of Rosen's closure using a set of three algebraic maps, termed the (M,R)-system.
  • * Analysis of the structural properties of the (M,R)-system, revealing a circular hierarchy of containment.
  • * Examination of the implications of this structure for the nature of efficient cause and complexity.

Main Results:

  • * The (M,R)-system clarifies the structure of closure to efficient cause as a circular hierarchy.
  • * Each map in the (M,R)-system represents an efficient cause, defined by morphology and laws of nature.
  • * A critical, observable property of this closure is its inherent ambiguity, previously unnoticed.
  • * This ambiguity provides a foundation for understanding properties of complexity such as non-computability and undecidability.

Conclusions:

  • * The (M,R)-system offers a clear and formal understanding of Rosen's closure to efficient cause.
  • * The inherent ambiguity of this closure is a fundamental aspect explaining the nature of complexity.
  • * This framework potentially simplifies proofs for complex system properties compared to Rosen's original work.