ABSTRACT
In this book we have distinguished between natural language, which is the natural vehicle of our reasoning, and various artificial languages, calculi, and systems which we build to account for it (and perhaps also to enrich it or to replace it). It is often assumed, generally without reflection, that there is no substantial difference between what we called interpretationF and interpretationL – and more generally between concepts that are internal to the logical apparatus we put together to account for following-from and the concepts that are external to it in that they concern its relationship to the following-from. It is often assumed that while interpretingM a formal or a formalized language we map its expressions on those of a natural language and thereby on that which is denoted by the natural language expressions, interpretationF only avoids the detour via natural language and maps them directly on the denotations. Therefore, there is no need to make any categorical distinction between the two concepts. This chapter argues that this picture is amiss and that it is behind many confusions in philosophy of logic. The crucial dividing line leads not between the “syntax” (calculi) and “semantics” (natural or formal) but rather between “the natural” (natural language with its implicit semantics) and “the artificial” (formal languages with calculi and possibly explicit formal semantics). Logic, from this viewpoint, appears to be studying a natural phenomenon (human reasoning and its principal vehicle, natural language) by means of its artificial models (formal languages).
