The Myth of Reduction: Or Why Macro-Probabilities Average over Counterfactual Hidden Variables

This page was last edited on 02/20/02 by Malcolm R Forster



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Table of Contents

  1. Introduction
  2. A Frequentist Definition of Optimality
  3. Those Confounding Hidden Variables
  4. Why Average over Hidden Variables?
  5. Learning is Not by Conditionalization
  6. Macro-Regularities are Different from Micro-Regularities
  7. Reduction in Science

Publication Data

Conditionally accepted in Philosophy of Science (10/4/01).  (Submitted on 23/12/00.)


 We prove that a probabilistic average over possible, but not actual, hidden variable distributions maximizes predictive accuracy (defined in terms of the Kullback-Leibler discrepancy) within a context in which only the relative frequencies of hidden variables are known.  Our detailed analysis of the Bernoulli model (e. g, coin flipping) reveals striking similarities with the derivation of thermodynamics from microphysics.  In both cases, the macroscopic description is derived from a probabilistic average over possible microstates, or counterfactual hidden variables.  In neither case is the macroscopic description deducible from a description of the microstate.

The example of thermodynamics has always been the example par excellence of reduction in science.  It has also been the bugbear of the special sciences in encouraging the view that psychology and biology should enjoy the same reductive relationship to physics.  In the meantime, probabilistic modeling has become increasingly successful in the special sciences in spite of its perception as being anti-reductionist.  It is therefore enlightening to see that not only does probabilistic modeling have a rationale, but it is the same rationale that explains the predictive accuracy of thermodynamics in terms of the underlying microphysics.

If reductionism is the view that macro-models should be deducible from, or determined by, disjunctive features of the underlying microstates, then it is a myth.  If this definition of reduction is denied, and reductionism is viewed more liberally as the claim that the underlying theory explains the empirical success of macroscopic models, then there is still a myth about reduction.  The myth is that reduction works by the deducibility of macro-descriptions from micro-descriptions, or the supervenience of macrostates on microstates.  This is the view that we have tried to replace with a more realistic picture.


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