In a new book published by Bloomsbury, Professor James Franklin brings together four decades of work examining necessity in mathematics, probability, and related areas of philosophy.
Professor James Franklin of the School of Mathematics and Statistics has published a new open access book, The Necessities Underlying Reality: Connecting Philosophy of Mathematics, Ethics and Probability. The volume brings together four decades of Franklin’s work across philosophy, mathematics and the history of ideas.
The essays are unified by a central theme: the existence of necessary structures in reality that ground certain knowledge of absolute truths. Drawing on an Aristotelian realist philosophy of mathematics, Franklin argues that mathematical truths are not merely abstract constructions but are directly about physical reality, while remaining provable and certain. Extending this approach beyond mathematics, the book examines probability, logic and ethics, presenting the relation of evidence to hypothesis - as found in science and law - as logical and necessary. In ethics, Franklin advances the view that fundamental moral truths, such as the worth of persons, possess a certainty comparable to that of mathematics.
Reflecting on the book’s underlying idea, Professor Franklin notes:
The idea is that in mathematics, ethics, logic and probability - but not science - there are absolute necessities, ones with no possibility at all of being otherwise. Getting in tune with them means accessing a level of reality more basic than the facts of science and history.
The book reflects insights developed over nearly 40 years of teaching and research in mathematics and statistics, and complements Professor Franklin’s earlier maths-related works, including An Aristotelian Realist Philosophy of Mathematics, Proof in Mathematics, and Introduction to Proofs in Mathematics.
Professor Franklin was the recipient of the 2005 Eureka Prize for Research in Ethics and was elected a Fellow of the Royal Society of New South Wales in 2019.
The Necessities Underlying Reality is now available open access via Bloomsbury.
