Valid logical inferences are made possible by the fact that the logical constants, in combination with nonlogical concepts, enable a proposition to represent reality. Indeed, this representational function may be considered their most fundamental feature. A proposition G, for example, can be validly inferred from another proposition F when all of the scenarios represented by F—the scenarios in which F is true—are also scenarios represented by G—the scenarios in which G is true. In this sense, (2) can be validly inferred from (1) because all of the scenarios in which it is true that someone envies everybody are also scenarios in which it is true that everybody is envied by at least one person.

In a still narrower sense, logic is restricted to the study of inferences that depend only on certain logical concepts, those expressed by what are called the “logical constants” (logic in this sense is sometimes called elementary logic). The most important logical constants are quantifiers, propositional connectives, and identity. Quantifiers are the formal counterparts of English phrases such as “there is …” or “there exists …,” as well as “for every …” and “for all …” They are used in formal expressions such as (∃x) (read as “there is an individual, call it x, such that it is true of x that …”) and (∀y) (read as “for every individual, call it y, it is true of y that …”). The basic propositional connectives are approximated in English by “not” (~), “and” (&), “or” (∨ ), and “if … then …” (⊃). Identity, represented by ≡, is usually rendered in English as “… is …” or “… is identical to …” The two example propositions above can then be expressed as (1) and (2), respectively: