Professor James Franklin recently presented a talk, "Mathematics and Ethics: The Two Sciences with Demonstrable Truths", for Scholarship at the Cathedral.
Synopsis: Where empirical sciences like physics and sociology rely on observation and experiment, abstract sciences like mathematics and ethics don’t. The basic truths in them are accessible by pure thought which reveals necessary truths about reality (though some wisdom is needed when it comes to applications).
Plato was right: immersion in mathematics induces an understanding of the necessities underpinning reality, an understanding that is essential for distinguishing objective ethics from tribal custom. Equality, for example, is an abstract concept which is foundational for both mathematics and ethics.
Watch the talk: