Truth, for Carnap, must be understood as operating relative to a particular linguistic framework. Presumably, for a discursive practice or system to count as a linguistic framework it must satisfy certain formal conditions, i.e. it must have a logical syntax and be capable of generating a set of protocol sentences. Though there may be structural disparities between any two linguistic frameworks (e.g. between Newtonian systems and Einsteinian systems and hence the need for non-classical logics) all linguistic frameworks, nevertheless, should share a core universal logical structure (or family resemblance) without which these systems could not even be identified or compared as different linguistic frameworks. In addition to avoiding relativism, the discovery of such a universal logical structure would rule out as meaningless any questions asked external to it. The structure would be, so to speak, transcendental. According to Carnap, how do we know we have correctly identified this core logical structure if, indeed, all inquiry proceeds from within a given linguistic framework?
After Godel, an appeal to formalism seems to fall short. But after Gauss and Riemann (and Einstein) an appeal to synthetic *a priori* intuition (a la Kant) also seems to overstep its bounds. (Kant famously thought that space was necessarily Euclidean. But, as I understand, once you jettison the parallel postulate, you see that this is not the case.)
One solution would be to say that as humans we, as individuals, are necessarily motivated to inhabit various linguistic frameworks which, though incompatible with each other, can be cordoned off from one another for purely practical reasons (e.g. as a rational agent I am free, as a physical body I am determined; as an architect, space is Euclidean, as a cosmologist space is curved, etc). As a matter of fact, I actually think this ‘quarantine’ method works better than it is often given credit for. But alas, this solution only works on the assumption that incompatibility relations only occur at the crossroads between disparate frameworks but never within a given framework itself. Unfortunately, it is not clear that this is the case. Contradictions abound, for example, all over mathematics (e.g. 1 = 0.999…) and the mind-brain itself is now notoriously known to be a cauldron of contradictions (like a car with two-steering wheels…or more!). In light of this, it is fashionable these days to throw away the notion of a ‘transcendental’ anything and embrace the intrinsic ‘fuzziness’ of things. Though this is admittedly rather soothing, I think this tendency should be resisted. And not only on moral grounds but also on phenomenological grounds. You, as I do, experience the world from a single point of view whose formal unity is unbroken. And though this unity is entirely virtual it is not illusory. Suppose you have read thus far and ask yourself whether or not your agree with my position. Regardless of the content of your judgment, in expressing your thought, you bring to bear the structure of the “I think” onto your experience. And in order to take up your thought and understand it I must do the same.
But what is contingent in this structure, and what is essential? Does the “I think” need some form of spatial manifold (be it Euclidean or non-Euclidean)? I can kind of imagine discourse without space but I cannot imagine discourse without time, and a unidirectional one at that. Similarly, I cannot imagine discourse without some notion of rightness and wrongness, that is, normativity. And I suppose with normativity comes modality since right and wrong moves are made within a domain of possibilities. But is it safe to assume that the essential structures of the ‘I think’ (i.e. rational discourse) are also the essential structures of the world? For example, discourse may require unidirectional temporality but cosmological physics may not require this at all. How can we naturalize ourselves given these apparently irresolvable contradictions in the essential properties of mind and world?