The first significant event in the history of modern modal logic after Lewis 1918 is the appearance in 1930 of an article, ‘On the logic of modalities’ by Oskar Becker, which marks the beginning of modern modal logic. Becker’s principal concern was to eliminate as far as possible the iterations of modal and non-modal operators that Lewis’s system of the Survey (later known as S3) allowed. Adding axioms that ‘reduce’ strings of modalities, he presented a ‘six-modalities system’ (now known as S5) and a ‘ten-modalities system’ (known as S4.) In this era, modal logic was often studied in connection with ‘intuitionist’ theories of truth. A mathematical proposition being true if it can be proved, it is a plausible principle that if it is true, then, of necessity, it is possible that it can be proved. Adding this principle (Brouwer’s Axiom) in Lewis’s system, p implies ∼∼p gives the six-modalities system. Adding the principle that if something can be proved that it can be proved, then it can be proved, the ten-modalities system is obtained.