   Russell strongly intimated that it is a part of the very nature of logical analysis that if our pre-analyzed understanding of a certain phenomenon involves the postulation of entities with certain structural or modal properties, one should seek to replace talk of such entities with logical constructions specifically constituted so as to have these features by definition (PLA, 272–79; LA, 326–29). A logical construction would typically be understood as a sort of class; since discourse about classes was regarded by Russell as a convenience, which would be eliminated in a fully analyzed language in favor of speaking of their defining properties and relations, by such a process Russell believed it is possible to replace commitment to entities having “neat logical properties” with commitment to those that do not possess such features. Russell’s work on mathematics provides us with what he would have taken as many examples of this phenomenon. If we take "3 &gt; 2” and "3 &lt; 2” at face-value as expressing simple dyadic relations between simple entities named “2” and “3”, then these appear to be two atomic propositions, one necessary, one impossible, which are not independent of each other. But after analysis, “2” and “3” are revealed not to be names at all, and the necessity, impossibility, and mutual incompatibility of these statements is rendered purely logical. Assuming that there is a final terminus of analysis in absolutely simple entities and fully atomic facts, one might suppose that here  the logical necessities and relationships between them would have completely disappeared.