I am having trouble understanding what 'extra-logical' actually means in the context of philosophical logic.
Case in point: Bueno and Colyvan argues in their paper Logical Non-Apriorism and the ‘Law’ of Non-Contradiction that logic is non-apriori, and that logic is revisable on 'extra-logical' grounds:
The idea is that it is possible to revise logical principles (or logical rules) on the basis of extra-logical considerations—which include empirical considerations. In other words, extra-logical considerations play a role in the selection and evaluation of logical principles (or rules).
...by ‘logical nonapriorism’ we simply mean that extra-logical considerations come to play in theory choice in logic. As it turns out , we also think that logic is non-apriori in a stronger sense (in that empirical considerations come to play). Our main purpose in this chapter, however, is to defend an account of theory change in logic that allows, and makes sense of, debates about the law of non-contradiction. It’s important for our case that the role of extra-logical considerations in these debates is appreciated. Some of these considerations are empirical, while others aremerely extra-logical.We find it convenient to use the term‘non-apriori’ to include both, but nothing hangs on this admittedly non-standard usage.
Obviously this term literally means 'something other than logic'; but exactly what is this referring to? It seems to be a catch-all phrase that literally means just that, and includes but not limited to empirical factors.
Some of the examples they gave are:
- Distributivity failing in quantum mechanics
- Natural language being semantically closed, an example they gave: 'The Earth is round' being grammatical in English is an empirical fact
The first (and perhaps to a certain extent, the third) seems to be empirical, but it is not clear exactly why the second is 'extra-logical'?
As far as I understand, this distinction is usually used to distinguish between logical constants, such as material conditional and conjunction, and other variables such as propositional constant. And this is a distinction that goes back to Tarski.
The problem is, even Tarski seems to admit in his paper On the concept of logical consequence that this distinction is problematic:
Underlying our whole construction is the division of all terms of the language discussed into logical and extra-logical. This division is certainly not quite arbitrary. If, for example, we were to include among the extra-logical signs the implication sign, or the universal quantifier, then our definition of the concept of consequence would lead to results which obviously contradict ordinary usage.
On the other hand, no objective grounds are known to me which permit us to draw a sharp boundary between the two groups of terms. It seems to be possible to include among logical terms some which are usually regarded by logicians as extra-logical without running into consequences which stand in sharp contrast to ordinary usage. In the extreme case we could regard all terms of the language as logical. The concept of formal consequence would then coincide with that of material consequence. The sentence X would in this case follow from the class K of sentences if either X were true or at least one sentence of the class K were false.
In any case, as far as I am aware Tarski never provided a precise definition for what it means to be 'extra-logical' either.
So what does 'extra-logical' actually mean? (Especially in the context of Bueno and Colyvan's paper)