Here’s my third attempt:
Rejecting the tempting heavy weight notion of ‘diverse logics’ to mean a fundamentally ‘other’ way of going on, of thinking, of being minded, I could take my sponsors to mean something more mundane, something empirical rather than transcendental, as it were. They say:
On our part, we recognize the difference between the (explicit and mathematized) logic of textbooks and the (essentially implicit and heterogeneous) diverse logics in which we think and act, and we believe that the development of reliable methods for the study of these logics can be of great help for approaching the problems of human mentality.
So let’s assume that we are back in the vicinity of Bermudez’ distinction between procedural versus epistemic rationality (of two days ago). Taking a relaxed view of ‘logic’ to mean something like ‘grammar’ in the later Wittgenstein: the rules and surrounding practices governing correct judgements, what is the difference between the explicit logic of textbooks and implicit and heterogeneous diverse logics in which we think and act?
The difference seems to be twofold: explicit versus implicit and singular rather than plural. But why should these two distinctions align? Here’s a thought. The codified norms of procedural rationality are universal: norms, according to a Wittgensteinian view, serving as the standard of correct description. Thus arithmetic, for example, provides an additional constraint on the results of correct counting. (Are the rules of arithmetic free-floating additions to prior rules of counting as Dummett suggests Wittgenstein believes (and if I correctly recall the early Crispin Wright did hold)? No but Cora Diamond has rather a fine paper suggesting a nuanced answer to this.)
By contrast the ‘logics’ of epistemic rationality have a feature that Dancy relies on to characterise his moral particularism (and which merits the plural). A reason for a belief or an action in one context can have its force, its valence, reversed by changing the context. (The appearance of barn can justify the judgement that there is one in one context and cast suspicion on that in a land of jocular Gettierian philosophers.)
This isn’t yet to make the connection from plurality to implicitness. But that is the result of the fact attempts to codify the behaviour of reasons within epistemic rationality will themselves by relative to a broader context of reasons. Codifications, in other words, are subject to merely implicit knowledge of their appropriateness. But if so, this suggests a principled constraint with the project outlined in the brief: that of characterising these implicit logics. Any such characterisation will have to be relative to a context. And that suggests that the project is best thought of as akin to the sociology of science which takes as its aim charting the contextual nature of epistemic (and according to Bloor even procedural) rationality, itself a human, rather than a natural, science.
Bloor, D. (1973) ‘Wittgenstein and Mannheim on the sociology of mathematics’ Studies In History and Philosophy of Science Part A, 4: 173-191
Dancy, J. (1993) Moral reasons, Oxford: Blackwell
Diamond, C. (1991) The Realistic Spirit: Wittgenstein, philosophy and the mind, Cambridge, Mass.: MIT Press.
Wright, C. (1980) Wittgenstein on the Foundations of Mathematics, Cambridge, Mass.: Harvard University Press