Jonathan Hockey’s Reviews > Reconsidering Logical Positivism > Status Update

Accordingly, Carnap there adopts a strategy of "purely structural definite descriptions" that aims to individuate all objects of science solely on the basis of their formal or structural properties within the logic of Principia Mathematical and it is in this way, finally, that Carnap ultimately breaks decisively with both neo-Kantianism and Husserlian phenomenology.

Indeed, Carnap pushes such logical-conceptual objectification far beyond anything envisioned by Weyl; for Carnap (1928a/1967) explicitly asserts that the objectivity of science requires that all purely intuitive or ostensive elements must be completely and definitively expunged

Physical space, in particular, becomes a purely abstract mathematical object (the set of quadrupes of real numbers which is distinguished from other isomorphic relational structures only by the circumstance that our previously constituted epistemic subject is perceptually embedded within it - at a definite "point of view," as it were.

Now Carnap, in his later writings, soon leaves the intuitive space of his
dissertation completely behind. Indeed, Carnap (1928a/1967) adopts a
stepwise constitution of objectivity via purely conceptual or logical means that is parallel to both the neo-Kantianism of Cassirer and the symbolic construction of Weyl.

That this intuitively spatial structure then necessarily lacks what Weyl
calls a determinate orientation of the purely infinitesimal metrics can only mean, for Carnap, that no such orientation inheres in physically spatial reality at all - in other words, that the full metrical structure of physical space can only be conventional.

On Carnap's account, by contrast, the a priori infinitesimally Euclidean nature of space is conceived of as a direct reflection of the necessary structure of our spatial intuition. And it follows, for Carnap, that specifically spatial structure (as opposed to purely formal logical-mathematical structure) can only be intuitively spatial structure

For Weyl himself rejects the idea that physical metrical structure is conventionally stipulated, and instead sees in the general theory of relativity the culmination of Riemann's suggestive remarks according to which the metric of physical space is empirically determined by "binding forces" acting on the underlying metrical continuum.

It is against this backdrop that we should understand the
striking disagreement between Weyl and Carnap over the conventionality of physical metrical structure.

Weyl comes more and more to defend the view that, although our
mathematical-physical understanding of space must indeed begin with immediately intuitive acts (by which the subject locates and orients itself in the "here and now"), the outcome of this procedure is a wholly nonintuitive "symbolic" construction by which we represent the physical-spatial world by abstract mathematical symbols having no intuitive content.