La reducción ontológica y sus problemas

Resumen

I try to show here how, when and why Quine’s doctrine of ontological reduction evolved, and also the links which can be traced between that doctrine, Russell’s view of reduction (or construction] as “new knowledge”, and Benacerraf’s ideas. In addition, I discuss some relevant criticisms of Quine' s position, mainly those by Tharp, Chihara and Steiner.

After a section trying to unify Quine’s main theses as proceeding from the paraphrastical methods of Russell’s theory of descriptions, I hold that Quine’s evolution towards a deeper sort of ontological reduction was a result of his attempts to clarify the difficulties of his original explanation of mathematical reduction. Thus, the doctrine of mathematical reduction in Word and Object, which was an important source of inspiration to Benacerraf and others, was only a first draft where Quine’s pragmatism shows the diverse reconstructions of the same mathematical concepts to be equivalent and also all correct, despite their possible incompatibility with the only condition to play the relevant roles. The general context then was one of increasing ontological relativity, but the underlying identification of reduction and elimination was —I think so— the main idea. A similar position was held in Set Theory and its Logic, where Quine put the emphasis on the fact that a model for arithmetic is provided simply by introducing a set-theoretical interpretation which would be able to preserve truth.

However, in 1964 a turning point appears: now there is a distinction between two different ontological reductions, one attempting only to replace certain entities by constructions playing their roles, the other attempting also to eliminate the original entities as well, by showing their dispensability. The reason was that Quine realized that through the Löwenheim-Skolem theorem we should accept that any theory can be reduced to natural numbers, which seemed to him trivial, but met his previous criterion for acceptable reductions. Then he introduced the need for a “proxy function” admitting as arguments all the objects of the universe of the first theory, taking values in the universe of the second theory, and having to be formulated in a third “inclusive” theory. As this condition is not met by the “reduction” inferred from the Löwenheim-Skolem theorem, it was not a “true” ontological reduction.

[Traducción: Gisela Hummell N.]