Permission Sentences Stand in the Way of Boolean and Other Lattice–Theoretic Semantices
Arthur Merin · Journal of Semantics · 1992
Permission sentences undermine the Fregean dogma of speech-act-independent propositional contents. I expound, develop and criticize little-read analyses of this phenomenon by Lewis (1979) and Kamp (1973, 1979). Section 2 reformulates Lewis's state-transformation paradigm for atomic commands and permissions, related as direct and inverse, namely non-monotonic theory change. Lewis's and Stalnaker's search for remedies inspired by conditional semantics is outlined. Section 3 develops Kamp's related analysis of or-coordinated permissions in diverse ways and detail, and extends them to and–coordinated permissions. Boolean or intuitionistic or even semi-latrice interpretation of or and, more drastically yet, and turns out empirically non-predictive. Permission (unlike pure command) state transformations are not (semi-)latrice homomorphisms. Implicatural, routines of doubtful provenance would carry the whole explanatory burden. The problem generalizes to similar analyses (Kamp 1973) of determiners all, every, any, and some. Inferential differences between conditional antecedents and permission clauses are demonstrated. Section 4 briefly notes problematic relations to axiomatic theories of non-monotonic theory change, and suggests desiderata for formal descriptive semantics. Hopes are pinned on a distinction between predictively overlapping theories of (rapid) understanding and (considered) inference, consistent with E. J. Lemmon's view that arguments in, not sentences of, natural languages have logical forms.