Introduction to Reductionism
Abstract
In this article, my aim is to clarify the reader on the concept of Reductionism. By Reductionism, I mean the evolution of a theory into something more simple, more compact, and flawless. It might seem an easy subject at first, but its subtleness is worth careful analysis.
1. What is Reductionism? - Introduction
Reduction: Reduction can be seen as a process of altering a former theory into a theory that with "less" explains the same and normally even more. This view on the evolution of theories is named Reductionism.
An example of this is the Geocentric theory that explained the apparent revolving movement of the sun around the earth but could not explain the relative movement of the planets simply. After a reduction, the Heliocentric Theory prevailed, explaining both phenomena with the same simplicity.
In science, people are used to working with postulates and assumptions, normally taken from observation. From these, models are built to explain the greatest number of effects. To achieve this, concepts must be created to give explanations. The reduction method is a constant reshaping of these concepts and how we associate them to make them simpler but still faithful to observation.
The main concern in the study of Reduction is its Ontological problem, and how the perception of Reduced and Reducing are interpreted by different views.
In literature, the terms Reduced and Reducing are the elements of Reduction. The first one is the initial theory that after being reduced by a scientific advance (change of paradigm, experimental discovery) is subjected to a reduction process that creates the Reduction theory.
Examples:
- Newton's Gravitation Theory (Reduced) and Einstein's General Relativity (Reduction)
- Optical Theory of light (Reduced) and Electromagnetism (Reduction)
Since the two terms, Reduced and Reduction, sometimes create an alliteration, I will use Initial Theory for the Reduced Theory and Final Theory for the Reducing Theory. The process that leads from one to the other is a Reduction.
Thus, the process takes the following order:
- Initial Theory → Reduction → Final Theory
Questions:
Reduction becomes problematic when the process starts explaining the same phenomena using different definitions and ontological meanings. For instance, the Reduction of the Geocentric Model into the Heliocentric model involves the same concepts but different causality, while in Quantum Mechanics, the photon’s particle and wave interpretations introduce new concepts.
Key Example:
The reduction from thermodynamics to statistical physics changes a deterministic picture into a probabilistic one, which has important implications.
2. Evolution of Reduction
Positivism:
The Positivist ideas provide a starting point for studying Reduction in theories. According to Positivists, knowledge comes from logic, mathematics, and empirical experiments. A Final Theory describes all observational consequences of an Initial Theory but in a superior way (simpler, more accurate, easier to understand, and with greater systematic power).
However, Positivism has its limits. In Statistical Physics, a canonical ensemble (probabilistic system) has no direct counterpart in thermodynamics. Similarly, General Relativity (reduction of Newton’s theory) simplifies yet also rejects parts of Newton’s paradigm.
The Modern Idea:
Modern theoretical models often use sophisticated mathematical methods that can sometimes confuse the interpretation of Reduction. For example, General Relativity can approximate Newton’s equations, but Newton’s theory is wrong. The key issue lies in how we interpret the ontology of the concepts in the Final Theory versus the Initial Theory.
The Ontological Problem:
The main problem lies in the change of Ontology between theories and finding a way to connect the concepts without over-defining them. Bridge Laws, proposed by E. Nagel, are mechanisms that allow the deduction of both the Initial and Final Theories from each other. However, this approach is not always effective.
3. The Role of Reduction - Conclusion
According to S. Sahrkar, there are three categories of Reductionism:
-
Theoretical Reductionism: Transformation of one theory into another by identities or replacement of concepts.
Example: Newton’s Gravitation → Einstein's General Relativity -
Methodological Reductionism: Decomposition of a theory into more fundamental elements.
Example: Biology → Chemistry → Physics -
Ontological Reductionism: Search for the essential elements of reality.
Example: Understanding the meaning of "space", "time", "movement", etc.
By subdividing Reductionism into these three categories, a simple picture of the entire process is clarified. Each form of reductionism operates on different levels, depending on the focus, from practical to ontological.
References
- Sklar, Lawrence, Physics and Chance, pp. 33-45, Cambridge University Press
- Sarkar, Sahotra, Synthese, Vol. 91, No. 3 (Jun., 1992), pp. 167-194, Springer