 The motivation for the \(\lambda\)-calculus given at the beginning of the entry was based on reading \(\lambda\)-expressions as descriptions of functions. Thus, we have understood ‘\(\lambda x[M]\)’ to be a (or the) function that, given \(x\), gives \(M\) (which generally, though not necessarily, involves x). But it is not necessary to read \(\lambda\)-terms as functions. One could understand \(\lambda\)-terms as denoting relations, and read an abstraction term ‘\(\lambda x[M]\)’ as the unary relation (or property) \(R\) that holds of an argument \(x\) just in case \(M\) does (see Carnap 1947, p. 3). On the relational reading, we can understand an application term \(MN\) as a form of predication. One can make sense of these terms using the principle of \(\beta\)-conversion: