ABSTRACT
Davidson’s diamonds are a recurrent pattern of inference in natural language, in which elimination of a modifier phrase or argument, the arrows in (1), is valid; but, introduction reversing the arrows is not (Davidson 1967, 1985; Castañeda 1967; Parsons 1985, 1990):
(1) Jones (slowly) buttered the toast with a knife in the kitchen. OP Jones (slowly) buttered the toast with a knife. Jones (slowly) buttered the
toast in the kitchen. PO Jones (slowly) buttered the toast. OP Jones (slowly) buttered. The toast was (slowly) buttered. PO There was a (slow) buttering. (2) e(Agent(e, x1) & slow(e) & butter(e) & Patient(e, x2) &
with (e, x3) & in(e, x4))
A Davidsonian logical form (2), being a conjunction of terms, explains that elimination of a modifier or argument is elimination of a conjunct. It further represents that all the conjuncts are about a particular e in a sentence which asserts that an e exists to satisfy them all. Introduction is thus shown to be a mistaken inference from the existence of some particulars satisfying given descriptions to the existence of a single one satisfying a conjunction of them:
(3) e(Agent(e, j) & butter(e) [an x3: knife(x3)] with(e, x3)) Jones buttered with a knife. e(Agent(e, j) & butter(e) & [the x4: kitchen(x4)] in(e, x4)) Jones buttered in the kitchen. Ӎ e(Agent(e, j) & butter(e) & [an x3: knife(x3)] with(e, x3) &
[the x4: kitchen(x4)] in(e, x4)) Jones buttered with a knife in the kitchen.
