Free choice sequences play a key role in the intuitionistic theory of the continuum and especially in the theorems of intuitionistic analysis that conflict with classical analysis, leading many classical mathematicians to reject the concept of a free choice sequence. By treating free choice sequences as potentially infinite objects, however, they can be comfortably situated alongside classical analysis, allowing a rapprochement of these two mathematical traditions. Building on recent work on the modal analysis of potential infinity, I formulate a modal theory of the free choice sequences known as lawless sequences. Intrinsically well-motivated axioms for lawless sequences are added to a background theory of classical second-order arithmetic, leading to a theory I call $MC_{LS}$. This theory interprets the standard intuitionistic theory of lawless sequences and is conservative over the classical background theory.

Frege explained the notion of generality by stating that each its instance is a fact, and added only later the crucial observation that a generality can be inferred from an arbitrary instance. The reception of Frege’s quantifiers was a fifty-year struggle over a conceptual priority: truth or provability. With the former as the basic notion, generality had to be faced as an infinite collection of facts, whereas with the latter, generality was based on a uniformity with a finitary sense: the provability of an arbitrary instance.

The journal Compositio Mathematica was founded by Luitzen E. J. Brouwer to counter his dismissal from the Mathematische Annalen in 1928. In spite of the economic crisis, Brouwer succeeded in finding a publisher (Noordhoff), an editorial board and subscribers. The founding took place at the time of the rise of the Third Reich, which caused problems of a political nature. The German editors followed Ludwig Bieberbach in 1934 when he left the board because Brouwer refused to dismiss the Jewish editors. After a period of flourishing, the publication was suspended at the beginning of the occupation of Holland in 1940. The post-war restart of the journal led to a painful conflict between Brouwer and the publisher, which ended with Brouwer's withdrawal from power. After having founded his own journal in the early 1930s, he lost it again some twenty years later.