A Parting of the Ways by Michael Friedman

Author:Michael Friedman [Friedman, Michael]
Language: eng
Format: epub
ISBN: 9780812697551
Publisher: Open Court
Published: 2011-04-15T05:00:00+00:00

For Schlick, concepts are defined (implicitly) by purely formal axiom systems having no intrinsic relation to any particular empirical domain. Concepts are then related to such a domain extrinsically, in the “method of coincidences,” by invoking purely ostensive reference to intuitive subjective experience after all. For Carnap, by contrast, an empirical domain is included within his constitutional system via a single extra-logical basic relation. All other concepts are then defined (explicitly) from the given basic relation by developing a formal characterization containing this relation and stipulating that the defined concept in question is the unique concept satisfying the characterization. Thus the visual field, as we saw in chapter 5 above, is the unique sense modality (constructible from the given basic relation) having exactly five dimensions. It is in this way, in particular, that Carnap avoids all appeal to subjective ostensive reference, and how, unlike Schlick, he then has no problem at all of relating the formal system of signs constituting scientific knowledge to an extrinsic realm of “reality” lying wholly outside of this system.171 And this is one important respect, as we also saw in chapter 5, in which Carnap’s view is in fact closely analogous to that of the Marburg School.

As we have also seen, however, Carnap’s use of purely structural definite descriptions involves, at the same time, a fundamental disagreement with the “genetic” conception of knowledge. For, as is clearly indicated in the above quotation, purely structural definite descriptions suffice fully to define or “constitute” their objects at definite finite stages of Carnap’s constitutional procedure. The object of empirical knowledge is by no means an incompleteable “X” for Carnap, and it is only the further empirical specification of an already defined such “X” that entails an incompleteable task. It is precisely on this basis, moreover, that Carnap himself rejects the Kantian synthetic a priori. Purely logical or analytic definitions allow us to “constitute” the object of science, and empirical investigation then allows us further to characterize this object without end.172 But the objectivity of our scientific knowledge, and, in particular, the intersubjective meaning of the concepts we employ in articulating this knowledge, are already secured by the purely logical, purely structural definite descriptions by which we pick out relevant objects uniquely from the single empirical domain constructed on the basis of Carnap’s single non-logical primitive. So it is pure formal logic, the logic of Principia Mathematica, that definitively solves the problem of the “objectivity of meaning” in the Aufbau.

Carnap’s program for constructing explicit definitions for all concepts of empirical science using the logic of Principia Mathematica is far superior to Schlick’s conception of implicit definition in this respect. For, in the first place, not only is Schlick completely unclear about the fundamental differences between modern mathematical logic and traditional syllogistic logic,173 but he also extends the notion of implicit definition to logic itself. Logical truths, for Schlick, are themselves implicit definitions of logical concepts like negation and quantifica tion.174 And, in the second place, whereas Carnap draws a

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