Some Notes on the Interface
If logic comprises the most general laws of truth, abstracting from
the subject matter of the special sciences, then the properties of
human first languages, in terms of which any system of logic must be
explained and justified, will interact with logical theory both by
supplying material to be systematized and by using the tools that
logic provides for the study of syntax, proof, and semantic
interpretation. Assuming a version of linguistic theory that puts the
nature of syntactic and semantic competences, and the basis for its
acquisition, in the spotlight, there will be three major issues: (a)
the nature of the syntactic inputs to interpretation; (b) the
conception of interpretation that is in play; and (c) the nature of
the principles that mediate between these. The assumption that the
principles (c) are of a very simple character has played a significant
role in a variety of developments, crossing otherwise very different
points of view; and as syntax has once again grown more abstract, and
the properties of the lexicon more prominent, it appears more than
ever possible to maintain the view that "interface" conditions are
simple (compositional, limited in type, etc.), and even to conjecture
that the most prominent syntactic distinctions among languages are, as
it were, wiped out when it comes to interpretation (although there
must be limits to this, not least because of syncretisms). I will
illustrate these developments with examples due to various
researchers.
James Higginbotham