Wittgenstein wrote the Philosophical Grammar during the years 1931 to 1934 -- the period just before he began to dictate the Blue Book. Although it is close to the Investigations in some points, and to the Phiosophische Bemerkungen at others, the Philosophical Grammar is an independent work which covers new ground. It is Wittgensteina s fullest treatment of logic and mathematics in their connection with his later understanding of a propositiona , a signa , and a systema . He also discusses inference and generality -- critisizing views of Frege and Russell as well as earlier views of his own -- and the treatment of mathematical proof in this book, especially of inductive or recursive proofs, is deeper and more extensive than previously.