Tim Johnson — Finance and Mathematics: where is the ethical malaise?

Must-read on mathematics and finance, and the history thereof. Huge amount of information in this relatively short and accessible post.  Hopefully, Tim Johnson will expand it into a longer article or book. Many gems to be mined herein. I will be savoring this for some time.

This is a draft of an article that has been accepted by The Mathematical Intelligencer and offers an argument very similar to Romer's 'mathiness' argument as discussed in my previous post.

Money, Maths and Magic
Finance and Mathematics: where is the ethical malaise?
Tim Johnson | Lecturer (associate professor) in the Department of Actuarial Mathematics and Statistics, Heriot-Watt University, Edinburgh

James Franklin — The mathematical world

Some philosophers think mathematics exists in a mysterious other realm. They’re wrong. Look around: you can see it

Aeon Magazine

The mathematical world
James Franklin | Professor of Mathematics at the University of New South Wales in Sydney. His book An Aristotelian Realist Philosophy of Mathematics is out this month.

Here is the publisher's blurb:

An Aristotelian Philosophy of Mathematics breaks the impasse between Platonist and nominalist views of mathematics. Neither a study of abstract objects nor a mere language or logic, mathematics is a science of real aspects of the world as much as biology is. For the first time, a philosophy of mathematics puts applied mathematics at the centre. Quantitative aspects of the world such as ratios of heights, and structural ones such as symmetry and continuity, are parts of the physical world and are objects of mathematics. Though some mathematical structures such as infinities may be too big to be realized in fact, all of them are capable of being realized. Informed by the author's background in both philosophy and mathematics, but keeping to simple examples, the book shows how infant perception of patterns is extended by visualization and proof to the vast edifice of modern pure and applied mathematical knowledge.

See our debate over Aristotelian realism in the comments. 

Aristotelian realism is now being put forward in a number of fields, I think erroneously in that it has little to do with Aristotle's sophisticated explanation of intellectual intuition for his time that modern thought has rejected. I see the contemporary version of "Aristotelian realism" as being simply a reassertion of naive realism that ignores the epistemological issues that have raged since ancient times and have yet to be resolved in a way that is either logically compelling through philosophical reasoning, or on the basis of basis of scientific evidence.

Why is this important for economics? Because it is the basis for the assertion of "laws" that are supposedly logically necessary (a priori) and self-evident as principles underlying the structure of reality, hence, universal, absolute, and ahistorical. It is essentialist and structuralist thinking in contrast to contextual and constructivist. Critics also view it as dogmatic rather than scientific.