Logic as "making it explicit"

In considering the very possibility of deviant logic, we face the following question: what makes us see an operator of one logical system as a deviant version of an operator of another system? Why not see it simply as a different operator? Why do we see, say, intuitionist implication as an operator 'competing' with classical implication? Is it only because both happen to be called implications?1 It is clear that if we want to make cross-systemic comparisons, we need an 'Archimedean point' external to the systems compared. Some logicians and philosophers, including Quine (1986), come close to saying that no such Archimedean point is available, and hence that there can be no deviant logics, for if two operators are governed by different axioms, then they are simply two different operators (or, if you prefer, operators with different meanings). From this viewpoint, intuitionist implication is no less different from classical implication than, say, intuitionist or classical conjunction. This conclusion is indeed plausible if we consider logical calculi simply as algebraic structures2; however, things are different if we see them as a means of accounting for something that is already 'there' before we establish the structures and is to be explicated by them. From such a perspective, two operators of different systems may be variants of the same operator in virtue of the fact that they are both means of capturing the same pretheoretical item. What might these items be? Sometimes it seems that logicians tacitly assume that there are some mythical archetypes of implication, conjunction etc., located somewhere in some Platonic heaven or somehow underlying the a priori structures of our mind, which logic tries to capture (for better or worse). However, when it comes to the comparison of the concrete outcomes of our logical efforts, say the classical and the intuitionist implications with the archetypal Implication, the latter can never be materialized so distinctly as to be of any help. A more constructive proposal is that the operators are related to elements or constructions of our language..
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