Conference 5th European Summer School in Process Thought in Budweis, 2018

Tuesday 7th August 2018 14:00-14:40

Michael Heather & Nick Rossiter (University of Northumbria, UK) - The Logic of Æsthetics

The first love of Alfred North Whitehead (1861-1947) was Symbolic Logic1 which he and his collaborator Bertrand Russell believed to be at the foundations of mathematics and that occupied the first half of his life explicitly and the second half implicitly. Yet although his writings were mostly technical and scientific nevertheless ‘æsthetics’ is a word that creeps in his writings everywhere but on closer examination is not as incongruous as it might seem on first sight for Whitehead treats mathematical ordering as a fundamental beauty of the Universe and yet allied with concepts like ethics, theology and even music. For when towards the end of his long life in 1944 Whitehead is asked the questionAre not Æsthetics a form of Ethics?’ his reply somewhat surprises his listeners until he elaborates. Earlier in 1937 Whitehead suggests that in the distant future the subject of Symbolic Logic would expand to examine patterns beyond space, number and quality and by the use of real variables ‘will become the foundation of æsthetics’. The phrase ‘real variables’ is perhaps an example of his belief that knowledge passes with each generation while ‘the words are retained, but with different meaning’.2 Real variables can now express formally the relationship between logic and æsthetics by adjunction in Category Theory. The Universe is the Cartesian Closed Category of a Topos initially modelled in Category Theory at first order as a sheaf over a set by Grothendieck but æsthetics in metaphysics is of higher order and requires the full Topos concept of Aristotle in impredicative mathematics first mooted by Russell (as ‘non-predicative’) but never successfully developed. Whitehead recognised the need for a robust type theory but it seems made no serious attempt to join Russell in his endeavour to achieve it.

In the natural version of Category Theory of postmodern mathematics, dialectic and aesthetics are adjoint metaphysical processes within logic: Dialectic <=> Æsthetics with the right adjoint Æsthetics as the co-unit of adjunction. In Plato’s world the highest form of pure beauty is the expression of divine eroticism whereby the human soul has sought after God from the origins of the Universe. In metaphysics God is the left exact limit and human souls are individuated (along with the other entities of creation) as right exact co-limits alienated from God: Chaos <=> Cosmos; Logic and the Erotic emerge with Logic the left-exact to creation and the Erotic as right-exact to creation: Logos <=>. Erôs. Erôs is the urge to return to God in death. These relationships can be better understood within the formal Dolittle Diagrams of Aristotelian Category Theory.

1 Analysis of Meaning, ESP99

2 Harvard: the Future ESP155