Nagel's Model of Inter-Theoretic Reduction Nagel's Model of Inter-Theoretical Reduction

Reductionism has to do with the classification of knowledge, particularly the classification of scientific knowledge. Many philosophers, such as Nagel, believe that the all current scientific knowledge can be broken down into discrete theories. Accordingly, progress in science is measured by the development of new theories.

These theories are used to explore and control the phenomena in their domains and to systematise, organise and summarise our knowledge about them. In fact, mastering any field of science requires an understanding of its fundamental theories.

Examples of scientific theories are the quantum theory in physics, the evolutionary theory in biology, and the general equilibrium theory in economics.

Definition of a Theory

The first issue which all must face is defining a theory and its constituents. The second issue, often resolved in the definition of the theory, is the relation of a theory to reality. That is, in what sense does a theory represent its subject matter?

The Syntactic View of Theory

The Syntactic View of Theories posits that scientific theories provide us with descriptions of their subject matter. Accordingly, a theory is a linguistic entity; more specifically, it is a set of sentences.

However, not any description qualifies as a scientific theory and not any set of sentences will do.

According to the Syntactic View, theories are interpreted deductive axiomatic systems. That is, a theory must have: i) A formal language, usually first order logic with equality and set of rules of inference; ii) Axioms formulated in this language; iii) A set of semantic rules providing an interpretation of the language in terms of items in the theory's subject domain.

The Semantic View of Theories

Contrasted with the Syntactic View is the Semantic View of Theories. The Semantic View posits that theories are a family of models rather than sentences.

In other words, scientific theories are not mere descriptions of processes, they are representations of actual, real processes. In general, the Semantic View of Theories indicates that scientific theories, as inherently inadequate symbols representing ineffable processes, would be much more difficult to accurately define than the Syntactic View would indicate.

Nagel's Inter-Theoretical Reduction

Reductionism, as it is used by Thomas Nagel, is the notion that certain complex materials or processes are not fundamental in themselves, but are actually the product of interactions between simpler materials or processes, some of which are truly fundamental. Reduction in science involves the absorption of one process into another. For example, Kepler's laws of motion and Galileo's theories of motion can be explained completely by a more fundamental theory, Newtonian theories of mechanics. Moreover, the Newtonian explanation is superior because it is more simple and elegant, leaving out extraneous details such as planets and orbits, while still being able to explain their operation.

Richard Feynman, the great particle physicist and pioneer in quantum theory, gave a great explanation of reduction without mentioning the word "reduction." He compared the law of physics to the rules of Chess. When the game starts, we observe that the bishop always maintains its color, forming a rule out of it. We later observe that the bishop only moves diagonally, which also explains why it always maintains its color.

The principle of Reduction is illustrated in the hierarchy of entities across all scientific fields. This hierarchy starts with social groups (sociology, anthropology), which can be broken down into human beings, which are multicellular organisms (biology). These human beings can broken down into to living cells, such as T-cells, (biology), which can be broke down into molecules, such as water (chemistry). Water can be broken down into atoms such as hydrogen and oxygen (physics) and atoms can be further broken down into, elementary particles, such as quarks (particle physics).

In this way, the laws of chemistry could be explained by the law of physics.

The Syntactic View and Vocabulary

In order for the base theory (e.g. chemistry) to be reduced to the target theory (physics), one simply needs to the claims of the target theory entail all the claims of the base theory. However, this is impossible initially because two theories can employ entirely different vocabularies, as is the case with chemistry and physics.

Their distinctive vocabularies make it impossible to fully express chemistry concepts in new laws of physics using exclusively physics vocabulary.

Nagel's Solution: Bridge Laws

To overcome the limitations of unique vocabularies, Ernest Nagel proposed that theoretical reduction requires "bridge laws" to enable translation between these vocabularies. These bridge laws are true statements of the unalterable...

Because the laws of each theory are tied to a unique vocabulary, bridge laws must be added to the laws of the base science by offering a new term and explaining the relation between the new term and the terms already present in the base science. This process allows for the derivation of the base theory's laws into the target theory's laws.
Homogeneous and Heterogeneous Reductions

Nagel, however, did not think that all reductions would first require a translation of terms. He distinguished between homogeneous reductions and heterogeneous reductions. According to Nagel, it is only in heterogeneous reductions that terms in the target science are not already included in the base science.

Thus, translation through bride laws may not necessarily be required for every inter-theoretical reduction.

Nagel's Definition of Reduction

According to Nagel, true reduction is effected when the target theory's laws (T1) are shown to follow logically from the base theory's assumptions (T2).

This observation demonstrates that one basic set of principles is sufficient to account for truths in both theories. For example, taking 'B1' and 'B2' as terms in the languages of 'T1" and 'T2', B1 causes the occurrence of a B2. This statement of the relation between B1 and B2 also means that if something is a B1, then it is a T1, which is called a bridge law. This demonstrates that the occurrence of a T1 causes the occurrence of a T2.

Evaluation

Nagel's theory has marked an important paradigm shift in the philosophy of science and, more broadly, epistemology. Nagel's theory, if accepted, would make a universal theory of science possible, though not necessarily simple. This would make it possible that all scientific knowledge could be expressed in a common language and theoretical framework, a possibility that has been called the "Unity of Science" theory.

Although much work would have to be undertaken in order to create the bridge laws necessary for the target science to be able to express the laws of the base science in the vocabulary of the target science.

Nagel's model is grounded in the Syntactic View of Theories, which holds that scientific theories are composed merely of descriptions of their subject matter. This is why such a huge function of Nagel's Model revolves around the translation of vocabularies unique to each theory. The Syntactic View of Theories is actually at the heart of the most trenchant objections made by commentators of Nagel's model of inter-theoretic Reduction.

Critique

Although the necessity of bridge laws in the process of intertheoretic reduction is widely accepted, the Nagel's conception of these bridge laws is more problematic. Logically, bridge laws would be expressed through conditionals. However, the connectives within in the bridge laws cannot be expressed through conditionals. Rather, they are expressed through "biconditionals" or "identity statements."

Nagel identified three types of bridge laws, distinguished by their form and function. A bridge law could take the form of logical or analytic connections between terms, conventional assumptions, or empirical hypotheses.

However, only when a bridge law is in the form of a logical or analytical connection between terms is it plausible to say that the reduction is an act of translation, as is dictated by the Syntactic View of theory.

Are Bridge Laws, as Represented by Nagel's model, Sufficient to Effect Reductions?

Nagel does assumes that conditional bridge laws are sufficient for accurate reductions. Some philosophers, in responses to Nagel's Structure of Science, have held that bridge laws must have the strength of "Identities" in order effect accurate reduction.

In other words, the mere presence of any of the forms identified by Nagel in the bridge law is insufficient to effect a genuine reduction. Fodor, for instance, believed that physical descriptions "mean nothing," precluding the possibility that reduction can be achieved through bi-conditional bridge laws of the type envisioned by Nagel.

In Sklar's view, a genuine reduction would require that the occurrence of a B1 causes the occurrence of a B2 (a law in the base science). The bridge law must establish that being a B1 means it is necessarily a T1. The bridge law must also establish that a B1 mean s that it is necessarily a T1 in itself as well.

Not all commentators believe, as Sklar and Fodor do, that Nagelian reductions require identities.

Ladyman, et. al. believe that Sklar and Fodor's statement is overstated, partly because it is directed at toy examples instead of realistic scientific situations of the type envisioned in Nagel's Model .

They believed that physical descriptions of a process can be the source of meaningful statements of bridge laws.

However, Nagel himself admitted that the reduction of a theory to physical science does require the use of…