Thursday, 21 August 2014

Why Natural Logic & Propositional Logic Differ

Halliday & Matthiessen (1999: 105):
Both the difference in scope and the difference in ‘definability’ can be explained in functional terms. Sequences have evolved in the interpretation of human experience in general; consequently, they have to be flexible and powerful enough to cope with a large amount of variation, and the implicit ‘definition’ of each relation (i.e., its location in the semantic system along various dimensions) is the evolving distillation of innumerable instances where it is invoked […]. In contrast, the truth-functional connectives of propositional logic have been designed for a restricted purpose — the kind of deductive reasoning western philosophy came to focus on — and their definitions are fixed by reference to values of “true” and “false” (by means of truth tables.