Using Brouwer’s continuity principle to pick stocks

This article shows that an apparent puzzle in finance and accounting is resolved by changing from classical to constructive (more specifically, intuitionistic) mathematics. Our position is that it is unproblematic if real-world actors behave inconsistently with nonconstructive mathematical results. Thus the solution to our puzzle lies in a deeper challenge to the standard view of how rational agents reason. The alternative we propose gives refutable predictions that find support in the empirical capital markets literature. Our main tool, intuitionistic mathematics, plays a similar role in the mathematical philosophy literature to that of ambiguity in decision theoretic work.