Poincarae's Philosophy: From Conventionalism to Phenomenology

By Elie Zahar | Go to book overview

2
Poincaré's Structural Realism
and His Logic of Discovery

So far we have addressed logical and methodological but no genuinely metaphysical questions. Twentieth-century empiricist philosophers regard metaphysics as having played—at best—a motivational role within the sciences: like art and poetry, metaphysics may inspire a scientist but it does not provide him with any meaningful information. In the present chapter, I propose to refute this empiricist thesis by demonstrating that realism—in its structural form—played a central heuristic role both in Poincaré's epistemology and in his logic of scientific discovery.


2.1 REALISM AND THE REALITY OF UNIVERSALS

Poincaré's structural realism is in a sense a reversal of Quine's slogan: to be is to be quantified over (in some first-order theory); for according to Poincaré, only the universals, and more particularly the relations occurring in a unified and empirically successful theory, mirror the ontological order of things. As for the nature of the relata, it will forever remain hidden from us.

Let us briefly examine Quine's philosophical position which closely follows Tarskian semantics, that is: the semantics of first-order languages where only the individual variables are allowed to occur bound (Quine 1980b). The domain, the basic ontological layer of any interpretation J of a first-order language, is some set D of objects. D is the class over which the individual variables range. Every name belonging to the primitive vocabulary denotes an element of D. It is well known that both names and function letters can be eliminated through the introduction of new predicate letters. Thus only the latter—which express relations—are indispensable; each one of them corresponds to some subset of the Cartesian power Dn of the basic domain D; where n refers to the number of argument-places of the predicate in question.

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