The assertion that complex statements are reducible to statements about particulars standing in logical relations to one another is associated with logical atomism and the philosophical method of analysis popularized by Bertrand Russell, Moore and the early Wittgenstein. The doctrine is both metaphysical and methodological.
Metaphysically, logical atomism employs the method of logical analysis to discern the fundamental objects (the logical atoms) from which complex (atomic or molecular) statements are constructed and things are constituted. Traditionally, these atoms are non-inferentially known sensa. Methodologically, logical atomism proceeds by reducing complex statements into simple components (the logical atoms) in logical relations under the assumption that there exists a direct correspondence between logical language and the constitution of reality.
To Russell, there are two types of atoms. On the logical side, there are names and predicates. On the metaphysical side, there are particulars and properties. Simple names are demonstrative, denoting simple objects; simple predicates are properties, denoting qualities or sensa. The atoms are used to form complex propositions or objects. For instance, in atomic propositions a property or relation is predicated of names denoting one or more atoms. Complex propositions are formed via truth-functions, quantifiers and atomic propositions or other statements.
The doctrine of analysis was popular in analytic philosophy from Russell to the early Wittgenstein, primarily as a reaction to British Hegelianism and under the influence of recent successes in mathematical logic. Later analytic philosophers such as Wittgenstein (Philosophical Investigations), Quine (Two Dogmas of Empiricism) and Sellars (Empricism and the Philosophy of Mind) successfully attacked the fundamental epistemological assumptions underlying it. In this regard, it is not a useful method for doing philosophy, and is distinct from the method of conceptual analysis found in modern analytic philosophy. The SEP has a detailed article.