Abstract
Teitel (2021) argues that formal approaches to equivalence cannot be illuminating, since they run afoul of trivial semantic conventionality: the idea that “any representational vehicle can in principle be used to represent the world as being just about any way whatsoever.” In this paper, I consider the relationship between theoretical equivalence and convention. First, I review the notion that conventions may give rise to equivalences: in particular, that we should regard theories differing “merely by a choice of convention” as equivalent to one another. I consider the importance of this idea for both the debates over geometrical conventionalism, and for Carnap’s Principle of Tolerance (Carnap 1934). However, this idea encounters difficulties when we confront it with the following question: can there be different conventions about equivalence? That is, consider two communities which use the same representational vehicles; but whereas one community regards those vehicles as equivalent when they stand in a certain relation, the other community does not. On the face of it, affirmation of the Principle of Tolerance would appear to force the Carnapian to side with the former community, suggesting that tolerance has its limits—in other words, that it cannot tolerate the intolerant. I suggest that this conclusion is too hasty. A thoroughgoing Carnapianism is, in fact, possible. In order to do so, we should apply the Principle of Tolerance at two different ‘levels’. On the one hand, at the meta-level, it instructs us to regard these two communities as working in different frameworks, which differ from one another over which inferences are permissible but not over substantive matters of fact. On the other hand, at the object-level, it constitutes an advertisement for the more liberal framework: here, it amounts to the observation that admitting more equivalences, and hence permitting more inferences, has pragmatic advantages. I return to the question of trivial semantic conventionality. If we subscribe to the Principle of Tolerance, do we risk collapsing to the position where all representational vehicles whatsoever have the same content? I argue that this is not the case, and that the above analysis indicates why. Although the Principle of Tolerance is presented as a general injunction to regard frameworks as equivalent, there is always the possibility of semantically ascending; when we do so, we are considering the merits of a (meta-)framework that regards those frameworks as equivalent, relative to one that does not do so. And although the (object-level) Principle of Tolerance constitutes a pragmatic advantage for the more tolerant framework, it may be outweighed by other pragmatic considerations. I conclude by suggesting that this gives us the resources to understand the significance of formal work on theoretical equivalence. The existence of an appropriate formal relationship between two theories indicates that there are not significant pragmatic advantages to distinguishing them—and in particular, suggests that regarding the two theories as equivalent will not obstruct our empirical theorising. Hence, a formal equivalence is what licences application of the (object-level) Principle of Tolerance in cases such as these.
