Poincarae's Philosophy: From Conventionalism to Phenomenology

By Elie Zahar | Go to book overview

APPENDIX III
The Empirical Unity of Scientific
Systems and Watkins's Organic Fertility
Requirement (OFR)

As already mentioned, the problem of the unity of scientific hypotheses has been one of the scientists' and epistemologists' main concerns. Although the simplicity of high-level theories might ultimately turn out to be an unaffordable luxury, the unity requirement remains—at any rate according to Poincaré—a transcendental presupposition of science as such. For their part, both Einstein and Popper spoke of the organic compactness of fundamental theories, while wondering whether this notion is susceptible of ever being rigorously defined. Einstein alluded to the paucity of the primitive elements occurring in a theory as to a measure of the latter's degree of unity. But unity has intuitively to do, not with a theory's basic vocabulary, but with the connections between the various components of an axiom system; the latter must be such that none of its subclasses is, in a sense yet to be defined, isolable from the rest.

In his 1984, John Watkins put forward the view that a hypothesis is unified if it satisfies an Organic Fertility Requirement (OFR), that is: if all of its postulates collaborate towards yielding empirical results not entailed by any subclass of its axioms. More precisely, Watkins starts by defining the empirical content Ct(S) of a theory S as the set of all propositions of the form e ⇒ p, where: S

(e ⇒ p), p is a prediction, and e a description of the relevant boundary conditions. Let E be the class of all the axioms of S, where E is taken to be finite. Thus S= <ΛE >, where, for any (finite) set of formulas G, ΛG denotes the conjunction of all members of G. Consider any nontrivial partition (E1,E2) of E; i.e.: E1≠Ø≠ E2E = E1∪E2,E1∩E2 =Ø.

Watkins's OFR was initially taken to be fufilled if (*) Ct(S) ≠ Ct(ΛE1)∪(Ct(ΛE2). i.e. if Ct(ΛE) ≠ Ct(ΛE1)∪Ct(ΛE2).

Since E1⊂ E, then

E)⇒ (ΛE1). From an intuitive standpoint, we must therefore require Ct(S) = Ct(ΛE) ⊇ Ct(ΛE1). Similarly: Ct(S) ⊇ Ct(AE2). Therefore: Ct(S) ⊇ Ct(ΛE)∪Ct(ΛE,). Hence (*) will be equivalent to: (**) Ct(S) Ct(ΛE1)∪Ct(ΛE2).

-233-

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