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Notes on Logic:

Informal, Deductive, and Inductive

Posts tagged with "induction"

The Thesis of Econophysics: Analogy and Division in Action

Saturday, 1. July 2006, 14:59:13

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In recent years, there has been an attempt by a few physicists to reduce economics to the principles of physics. The effort has been dubbed "econophysics."

As Philip Ball reports in Nature:

The idea that physics might have something useful to contribute to economics arises because both fields are concerned with systems of many interacting components that obey specific rules. Statistical physics describes the behaviour of bulk-matter based on the forces acting between atoms and molecules. Economics studies the interactions between economic 'agents'--market traders, say, or businesses.

Arguably, deriving microeconomic principles from the behaviour of individual agents should pose similar problems to deriving thermodynamic laws from interatomic forces.

(Philip Ball, "Culture Crash," Nature 441 No. 7094 (8 June 2006), 686-687.)

Reducing or mapping economics to physics-based formulae may well be more than the extension of the mathematics of physics to the sphere of economics. The enterprise of econophysics illustrates a number of interesting pragmatic issues in scientific reasoning: (1) mathematics as the architecture of the sciences, (2) the theory of levels of phenomena as reflected in levels of organization, (3) the logical issues of composition and division, and (4) finally, the quest for the unity of science.

All reasoning seems to be ultimately analogical. The interesting question in this regard is whether there can be uniform classification of analogical methods.

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Heuristic and Composition

Friday, 30. June 2006, 14:05:07

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Breakthroughs in the sciences often come from the use of analogy between one level of phenomena and another. Levels of phenomena are more or less described by the successful theories which get results at that size of organization. (Levels of phenomena are often listed as something like these: (1) subatomic, (2) atomic, (3) chemical, (4) biological, and (5) social.)

As science progresses, one science becomes translated and reduced to another. An important twentieth century goal was the unification of all science. In a sense, this goal was first recognized in the nineteenth century with four main discoveries described by Frederich Engles as the "deterministic" and "materialistic" basis of science:

(1) Discovery of the Transformation of Energy: From the boring of cannons, it was noticed that a specific amount of motion produced a specific amount of heat through friction. In fact, the energy of motion explains a number of forces: mechanical, force, heat, radiation, electricity, and magnetism and establishes a "mechanical equivalent of heat." Heat was once thought to be a subjective quality. Now subjective or mental qualities are explainable in terms of forms of energy.

(2) Discovery of the Cell as the Biological Basis of Living Things: Theodor Schwann and Matthias Schleiden found that almost all organisms arise and develop in cellular form. The so-called miracle of life is seen in terms of cellular laws of development.

(3) Discovery that the Forms of Life Evolved: The variety of all living things and their adaptive features is now explainable with a few principles according to Charles Darwin's theory of evolution. The development of the human brain itself is, itself, thought to be explainable and reducible to these principles.

(4) Discovery of the Unity of the Organic and Inorganic: When Friedrich Wöhler accidentally created the organic compound urea by heating the inorganic compound ammonium cyanate, vitalism (the belief that the process of life cannot be chemically explained) became suspect. Chemistry is now beginning to account for the origin of life itself according to chemical principles. With Wöhler's discovery of the synthesis of an organic compound comes the expectation that the distinction between the living and the non-living is not a mystery or a miracle.

(See Frederich Engles, "Science of Natural Processes" in Introduction to Ethical Studies: An Open Source Reader, ed. Lee Archie and John G. Archie, 2004. URL=<http://philosophy.lander.edu/ethics/ethicsbook/c1826.html>.)

With Engles's imaginative synthesis, something amazing becomes possible. Each of these reductions:

Inorganic <--- Organic <-- Biological <-- Psychological

heralds the possibility of the unity of the sciences. If political science could be reduced to sociology, and sociology to psychology, and psychology to biology, and biology to biochemistry, and biochemistry to chemistry, and chemistry to physics, and physics to particle physics, then we will have a theory of everything based on fundamental physics.

A problem with a theory of everything (other than the incompatibility of general relativity and quantum mechanics) is that each of these levels of discovery have their own theories of organization. But the successes in linking levels by quantum physics and biochemistry in the past century sustains the use of Division and Composition for heuristic hypotheses, even though they are prima facie fallacies in formal logic.

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