 The method of using logical notation for representing meanings has a long history, going back at least to philosophers such as Dalgarno and Leibniz who developed formal languages in order to express philosophy clearly. In the 19th century, there were several proposals for artificial languages in order to make mathematical argumentation more transparent, for instance by Frege and by Peano. Frege’s ‘Begriffsschrift’ (Frege 1879) can be seen as the birth of predicate logic: he introduced quantifiers. His motivation came from mathematical needs; he did not use his Begriffsschrift in his papers on natural language. Russell (1905) used logic to represent the meanings of natural language. A classical example in his paper is the analysis of The king of France is bald. Syntactically it has the form subject-predicate, but if it were constructed logically as a subject-predicate, then the king of France, which denotes nothing, cannot be the subject. So syntactic form and logical form may diverge: natural language obscures the view of the real meaning. This became known as the ‘misleading form thesis’. Therefore, philosophers of language saw, in those days, the role of logic as a tool to improve natural language, an aim that is alien to Montague semantics. In fact, using higher-order functional type theory (Church 1940) as the target of his translation, Montague (1970c) developed a ‘compositional’ version of Russell‘s analysis, which does preserve the constituent structure of the source language (English). An interesting overview of the history of translating natural language into logic is given in Stokhof 2007.