Reduction and Unity of Science

Reduction

Paradigm examples of reduction:

• Reduction of Kepler's Laws of planetary motion to Newton's laws
• Reduction of thermodynamics to statistical mechanics or, as is often said, to Newton's laws
• Reduction of chemistry to quantum mechanics
• Reduction of Mendelian genetics to molecular biology

So, what is the reduction of one theory to another? According to Nagel there are two parts to a reduction (though the second requires the first, and so the first is redundant).

1. The observational terms of the theory to be reduced are connected to the theoretical terms of the theory to which the other theory is being reduced. (planet is small point mass, sun is large point mass; temperature is average kinetic energy of the molecules; valence is difference in number of electrons in the outermost shell from 8; a gene is a sequence of base pairs on the nuclear DNA of a germ cell).
2. The laws of the theory to be reduced are derived from the connectability conditions of part 1, the laws of the theory to which the reduction is being performed, and any auxiliary assumptions hanging around.

That is the Nagel model of reduction. The article is a wonderful example of how positivist theories are related to the received view---in each case he starts with that and falls back.

What is the nature of the connectability conditions? Nagel lists three possibilities (112–113): logical connections, conventions, or factual. If there are multiple connecting links that lead to interlocking laws, the links themselves may become subject to empirical test, and hence of type 3 instead of type 2. One really nice example of something that starts as a conventional link and becomes empirically testable is Avogadro's number, which is the number of molecules in a liter of gas at one atmosphere pressure at room temperature.

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Kemeny and Oppenheim proposed a different model of intertheoretic reduction. It is much like Nagel's, although the hedges are less sophisticated, but the main difference is that instead of the weak requirement of conditions of connectability, they require "bridge laws" connecting the observational terms of the reduced theory to the theoretical terms of the reducing theory by biconditionals, that is, necessary and sufficient conditions. The requirement is much too strong (that is, according to it, we haven't reduced Mendelian genetics to biochemistry, but we have), but it leads to a much simpler account of reduction, the one assumed by Putnam and Oppenheim.

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Unity of Science

There are many things that have been called the unity of science: unity of language, unity of laws, unity of methods, unitary science. Most of the types of unity have two versions: a descriptive one—that is how things actually are (or will turn out to be)—and a normative one—we should conduct our scientific inquiries in such a way as to try to show that unity is true.

Unity of language

Unity of language is the claim that all the "terms," that is, all the referring terms of all theories can be reduced to terms of a single theory. One example would be that all terms in all theories can be reduced to physical terms. That would mean that no theory refers to anything that is not definable in purely physical terms, that is, all things are physical things. There aren't, for example, if that is true, any mental entities that aren't particular configurations of electrical and chemical potentials in neurons, or some such. Another version would be reducing all terms to psychological terms about sense data.

Unity of Laws

This requires, Putnam and Oppenheim seem to think, unity of language. It is the idea that the laws of every science are reducible to the laws of a lower-level science (except, of course, the bottom science). Given connectability conditions short of bridge laws, the relationship between the two kinds of unity is more complex.

Unity of Methods

This is a completely separate issue. It is the idea that there is only one legitimate way to do science that needs to be applied in all the sciences.

Unitary Science

If the terms of each theory are definable in terms of the lowest-level theory and the laws are derivable from those laws, then there won't be many different sciences, but one ultimate theory of everything (physics) and the other areas of study are just particular parts of physics studying particular conditions.

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I moved straight to the lowest level because the Kemeny-Oppenheim model of reduction is transitive: if you can reduce A to B and B to C, then you have reduced A to C. That need not be the case according to Nagel's model, where you can have reduction of laws without complete reduction of language.

Putnam and Oppenheim deny that unity of laws implies that there is a unitary science. Why? The laws of a higher level may not be interesting in full generality. They may not be obvious in the ultimate, fully reduced form. Example: The laws of Mendelian genetics do follow, even in our present state of knowledge, from biochemical laws. However, the biochemical versions are of no interest.

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What is the status of the unity of laws? Putnam and Oppenheim argue that it is far from verified, but we have some evidence to suggest it is worth exploring further, that is, that it is a plausible and valuable scientific hypothesis. They say things that suggest, but they do not argue, that it is a legitimate norm of scientific research.

According to Putnam and Oppenheim we have metascientific (science of science) evidence for the unity of science.

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Microphysics

They point out that there is a long history of a certain scientific strategy: entities are taken to be composed of smaller, simpler entities, and the laws are to follow from simpler laws about the smaller entities, and data about how the big things are made up out of the smaller ones.

-- ShaughanLavine - 02 Feb 2006