The title of this post is a bad pun which I hope will become clear by the end of the post. Davidson’s argument (it could have been McDowell’s verison of Davidson’s argument) against their being conceptual schemes which are completely alien to ours and uninterpretable has the premise that in order for something to count as a conceptual scheme, it must be rational. This means that it must be possible to say what is a reason for what in such a way that the structure of reasons and inferential connections in the target conceptual scheme is sufficiently like the home conceptual scheme for an interpreter to recognize rationality in it. If one cannot map someone else’s conceptual scheme onto a rational structure akin to one’s own, then there is no reason to think it is a rational scheme at all. Thinking about this suggested an analogy to me. Suppose A takes the natural numbers learned as a child as basic, B takes the standard ZFC construction of the natural numbers as basic, and C takes the von Neumann version as basic. Each can interpret the others numbrs, i.e. map the foreign numbers onto theirs in such a way as to provide the right kind of structure. Now suppose D comes along with a completely alien version of things he calls natural numbers. The catch is that none of A, B, and C can map D’s numbers to their own in a way that preserves any of the expected structural features. Should A, B, or C say that D is talking about the natural numbers? Seems like the answer is no. Should we think that D is talking about natural numbers, just not those of A, B, or C? Again, no. Does this analogy extend to rationality in the way I want it to? I think so. There are some disanalogous points, mainly that in the case of natural numbers there is more (or at least the illusion of more) objectivity than our conception of rationality. Additionally, it is harder to be a pluralist, in the sense of various equally valid non-intertranslatable versions, about the natural numbers than about concepts of a nonmathematical sort. I think the basic point is preserved in the analogy however.

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