# J M Keynes’s Mathematical Platonism(Realism) in the A Treatise on Probability, Like Kurt Godel’s Mathematical Platonism, Held That All Mathematical Entities Were Independent of the Human Mind, but They Could Be Perceived or Intuited Directly From The Abstract Universe in Which They Existed: Keynes Was Both a Platonist (Logicist) and Aristotelian (Empiricist)

35 Pages Posted: 26 Jun 2019

Date Written: June 18, 2019

### Abstract

J M Keynes was never simply a Platonist or Realist like G E Moore was alleged to be. Keynes was a Mathematical Realist (Mathematical Platonist) similar to Kurt Godel, much like 95 % of all practicing mathematicians are today. Weak to Strong Mathematical Platonism has dominated the field of mathematics for the last 2,400 years, dating back to Pythagoras and Plato. Economists, who have written on Keynes, have confused and conflated Platonism with Keynes’s Mathematical Platonism, which is very close to the Mathematical Platonism of Kurt Godel, the greatest mathematical logician of the 20th century. Keynes never accepted Plato’s theory of Forms.

Keynes‘s logical relations, P(a/h) =α,and V(a/h) =w, in his A treatise on Probability are mathematical entities.Therefore, since they are mathematical entities, they must, like all other mathematical entities, exist independently from the human mind in an abstract, metaphysical universe that can be perceived or intuited directly by the human mind.

Heterodox economists, Post Keynesians and Fundamentalist Keynesians simply lack the necessary philosophical background, knowledge and training that is needed in order to grasp Keynes’s philosophy of mathematics.They have categorized Keynes as a Platonist without realizing that, as a mathematician, Keynes would naturally categorize all mathematical entities, just like Bertrand Russell and William Ernest Johnson, as existing independently from the human mind. Russell later moved from a Strong to Weak perspective on mathematical Platonism.

The other two major philosophies of mathematics, Hilbert’s formalism, which regards mathematics as being mere scribble written on a piece of paper that the practicing mathematician hopes to make some sense out of later, and Brouwer’s Intuitionism, which views mathematical entities as properties of each individual human mind’s intuition, make up the other 5 % of practicing mathematicians views of the nature of mathematical entities. Brouwer’s approach is problematic once one asks the question,”Is 2 +2 still equal to 4 if the earth is completely destroyed, so that there are no more human minds in existence? ”A “yes” answer means that the mathematical entities were never internal to the human mind.

This paper examines the flawed philosophical understanding of mathematical Platonism exhibited by O’Donnell (1989, 1990, 1992), Bateman (1996), Backhouse (2010) and Davis (1991, 1994,1997, 2003), who have confused and/or conflated Platonism with Mathematical Platonism while ignoring Keynes’s Aristotelianism.These misconceptions have appeared again in 2017 in papers published in the Journal of Markets and Morality.

Keynes was both a Platonist, mathematical Platonist, and Arietotelian. A dangerous, pseudo-scientific approach that relies on a dualism based on only binary choices has arisen since the late 1930’s in the work of G L S Shackle and Joan Robinson, and especially since the late 1970’s among Keynesian Fundamentalists. Supposedly, Keynes’s work is presented as being only one of two conflicting choices: it is either in historical time or logical time, atomic or organic, open or closed, ergodic or non ergodic, formalist or anti-formalist, mathematical or anti-mathematical, based on uncertain or certain knowledge, knowledge or unknowledge, rationalist or empiricist, Platonic or Aristotelian, all or nothing.

Aristotle himself referred to himself explicitly as a Platonist in his Metaphysics. Like Keynes after him, he maintained many aspects of Platonism (Virtue ethics), but emphasized other aspects ignored by Plato, such as physics and biology (empirical). The same holds for Keynes.

**Keywords:** Plato ,Aristotle,mathematical realism (Platonism),Platonism,rationalism,Moore,Keynes

**JEL Classification:** B10,B12,B14,B16,B20,B22

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