Nagels Model

Given the outline of Nagel s model presented above, questions (i)-(iii) can easily be answered, thereby giving a canonical re-description of Nagel s model  

The relation is derivation plus bridge-principles. Derivation is to be conceived of as syntactic derivation. Bridge-principles are usually conceived of as universally quantified bi-conditionals, or sometimes as conditionals (1961, 355, fn.5), whose predicates are predicates of the reducing as well as of the reduced theories laws. 

The primary relata of the derivation are laws or entire theories. Since derivation is a syntactical matter, these should be construed syntactically. 

Officially, instantiating the reduction relation is instantiating an explanation relation. Obviously, the reduction relation is a special case of the relation defined by Hempel and Oppenheim (1948) - a candidate for a characterization of explanation. In this sense, the reduced theory is supposed to be explained by the reducing theory. 

An interesting application of Nagelian reduction which reveals its similarity to conceptions of reduction in the philosophy of mind, namely, to functional reduction 

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The basic idea is simple A theory Tr reduces to a theory Tr iff Tr is derivable from Tb plus the relevant bridge laws (here labeled coordinating definitions ), if any, with the contention that often, theory reduction is carried out by reduction of the theory s laws. If we add the remarks Nagel opened his discussion with - namely, that reduction has to be understood as a certain kind of explanation (Nagel 1961, 338) - the core idea of the Nagel model is fully characterized. Reduction is (i) a kind of explanation relation, which (ii) holds between two theories iff (iii) one of these theories is derivable from the other, maybe under specific conditions, with (iv) the help of bridge-laws. Building on this sketch, we can easily illustrate the... 

What I have coined the real Nagel-model does not have this feature. Structuralist models, however, are, as it seems, bound to restrict the domain of the reduction-relation to full-fledged theories. Otherwise, notions of structural similarity become problematic. Only if a science or a theory can be reconstructed in structuralist terms, we have a candidate for reduction. But there are serious doubts that sciences such as economy, political science and the like can be reconstructed in this way. Thus, an extension of any structuralist reduction model to the more pedestrian parts of the scientific enterprise , (as Feyerabend (1962, 28) put it raising his criticism against Nagel), might turn out to be difficult. 

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