y)): Father Ted officiated at the marriage of Jack to somebody and Father Ted officiated at the marriage of Jill to somebody. ∃x ∃y (M(x, a, b) ∧ M(y, a, c)): Somebody officiated at the marriage of Father Ted to Jack and somebody officiated at the marriage of Father Ted to Jill. To establish which is the correct translation of “Father Ted married Jack and Jill”, it would be necessary to ask the speaker exactly what was meant. Philosophical significance Atomic sentences are of particular interest in philosophical logic and the theory of truth and, it has been argued, there are corresponding atomic facts. An atomic sentence (or possibly the meaning of an atomic sentence) is called an elementary proposition by Ludwig Wittgenstein and an atomic proposition by Bertrand Russell: 4.2 The sense of a proposition is its agreement and disagreement with possibilities of existence and non-existence of states of affairs. 4.21 The simplest kind of proposition, an elementary proposition, asserts the existence of a state of affairs. — Wittgenstein, Tractatus Logico-Philosophicus. A proposition (true or false) asserting an atomic fact is called an atomic proposition. — Russell, "Introduction to Tractatus Logico-Philosophicus" See also and especially regarding elementary proposition and atomic proposition as discussed by Russell and Wittgenstein Note the distinction between an elementary/atomic proposition and an atomic fact. No atomic sentence can be deduced from (is not entailed by) any other atomic sentence, no two atomic sentences are incompatible, and no sets of atomic sentences are self-contradictory. Wittgenstein made much of this in his Tractatus. If there are any atomic sentences then there must be "atomic facts" which correspond to those that are true, and the conjunction of all true atomic sentences would say all that was the case, i.e., "the world" since, according to Wittegenstein, "The world is all that is the case". (TLP:1). Similarly the set of all sets of atomic sentences corresponds to the set of all possible worlds (all that could be the case). The T-schema, which embodies the theory of truth proposed by Alfred Tarski, defines the truth of arbitrary sentences from the truth of atomic sentences. See also Logical constant References Bibliography Benson Mates, Elementary Logic, Oxford University Press, 1972. Elliott Mendelson, Introduction to Mathematical Logic, Van Nostrand Reinhold Company, 1964. Predicate logic Sentences by type Syntax (logic) Propositions