Frege's treatment of quantified propositions departs radically from the traditional view that grammatical structure mirrors logical structure

On Frege’s view, the proposition that Mary sang has a functional component corresponding to ‘sang’ and an argument corresponding to ‘Mary’, even if the English sentence ‘Mary sang’ has ‘Mary’ as its subject and ‘sang’ as its predicate. The proposition can be represented as follows: \(\textrm{Sang}(\textrm{Mary})\). Frege thought of the relevant function as a conditional mapping from individuals to truth values: \(\textrm{Sang}(x) = \textbf{T}\) if \(x\) sang, and \(\textbf{F}\) otherwise; where