Reply to Davies: Let Platonism die

It's time to confront the series of articles on platonism published in recent issues of the EMS Newsletter. The first one that was published was E. B. Davies' article entitled Let Platonism die. Inclusion of words derived from death or dying usually indicates some zealous semi-political agitation, but let us instead focus on the arguments Davies puts forward:

Davies starts by expressing indignation over the fact that several Fields medalists have spoken positively about their platonist convictions. After quickly dismissing mystical experience as nonsense, in the best style of scientism or positivism, Davies seems to jump to conclusions when he states:

Although he is a Platonist, Roger Penrose is almost
unique in accepting that his beliefs imply that the math-
ematical brain cannot obey the known laws of physics.

It is true that Penrose is a platonist. However, it does not follow from platonism that the "mathematical brain" cannot obey the known laws of physics. Why not? Well, even though platonism postulates a type of perception with the capacity to reach beyond the physical world as currently understood, this does not imply that the mechanisms of the brain must themselves go beyond the laws of physics as currently understood. This only follows if one also assumes that the universe is causally closed, that is, that something beyond the physical universe cannot interact with the physical universe. This is something which platonism does not assert.
There are many aspects of the human mind that are currently not understood. Indeed, nobody would claim that we understand for example how human consciousness works. Platonism implies that there is a brain function which is not covered by today's explanations of the workings of the mind. This is not a very radical claim, because there are many brain functions which are currently not understood. If you claim that consciousness exists as a brain function, then you are claiming that the human brain works in ways which are not explained by current science. Does this make you an unscientific mystic? Obviously not. Does this imply that consciousness must be due to some physical laws not currently known? No. If one reads Penrose one learns that his original motivation to develop his ideas about consciousness as a product of quantum effects was to construct an alternative to the predominant view of the mind as a computer. This view of the brain as a computer does not fit well with Gödel's incompleteness theorem, and this, rather than any necessary need to defend platonism by postulating new physical laws, has been Penrose's goal.

Given the failure of Davies' claim that platonism requires some extra-physical brain mechanism, the remainder of his argument looses its relevance. Davies mentions how modern brain science has revealed mechanisms of sense perception and the perception of number. This is all very well, because of course we understand mathematics with our brains, and of course the way in which we understand certain things can be described in terms of neuro-cognitive models. Platonists would not deny such obvious facts. The point is that it is fully possible that our brains are able to produce mental states of awareness of objects whose existence is not dependent on the spacio-temporal world, but which nevertheless interact with it because these objects provide the forms in which the landscape of the universe takes shape.