ABSTRACT
I think you have put forward two important ideas, which I shall think about for a long time: one about how to understand what formal logic is, and one about how to understand Wittgenstein's term ‘language games’. As I understand the first idea, you propose that formal logic is not a set of ‘laws’ of anything (thought, or reasoning, or reality), but an idealized model of how a part of our language (e.g. the part consisting of certain inferences involving the so-called ‘logical connectives’) works. On your view, the question is not whether some particular laws of logic are ‘necessary’, but whether this model is or is not appropriate to any given stretch of discourse. (I take it, however, that you are not denying that in a discourse which fits the model, the substitution-instances of what we call ‘valid schemata’ are true, and that there is a good use of ‘logically necessary’ in which they can also be called ‘logically necessary’.) The point is that we should not think that, say, the so-called ‘Law of the Excluded Middle’ actually has only true substitution-instances in a natural language. It doesn't. When someone says, ‘Either you are in favor of my proposal or you aren't’, what they are saying may well be false in a particular context. (If my memory serves me right, a classical paper by Ernest Nagel called ‘Logic Without Ontology’ defended a similar view, which has unfortunately been completely neglected.) And as I understand the second idea, it is important to realize that Wittgenstein's ‘language games’ are not parts of which a language consists, but idealized models of parts of a language. (Wittgenstein called them ‘objects of comparison’, I believe.) Thus, there is a similarity between systems of formal logic (including the so-called ‘deviant logics’) and Wittgensteinian language games.
