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Plato and the Philosophy of the Unsayable: Discovering the radical Plato that Analytic Philosophy can never know

Lecturer: Bernard Lewin

Originally Taught: Summer School 2020

Course Aim

An invitation to get inside the extreme idealism of Plato

Course Overview

This is an introduction to Plato through selected readings from his dialogues. While no prior knowledge is required, the coverage of core themes is more than sufficient preparation for advanced and specialised courses. However, the Plato revealed here is a different character to the Plato introduced in Analytic schools. There, Plato is often presented and read as the founder of rationalism. But Plato railed against those who saw reason as the arbiter of truth. For Plato, truth is beyond what is sayable and only attainable through the powers of insight. Our first steps along his ‘mystical way’ are lit by elementary mathematical thinking. Once we begin to see how Platonic idealism is possible, the dialogues opens up to reveal a more powerful and masterful offering.

Course Suitability and Level of Difficulty

This course will suit those motivated by unresolved questions around what it is to know. No difficulties should arise due to unfamiliarity with the contemporary debate. On the contrary, those immersed in this debate may have difficulty letting go of some of its preconceptions so that Platonism might appear any less than absurd. The shift from linguistic to mathematics foundations requires no mathematical sophistication. This shift is entirely conceptual. It extends little beyond consideration of how the form of word/meaning, or the form of signifier/signified, might differ from the way that two things expressing the number two. 

Course Outline

The course begins by showing just how difficult it is to come to the Platonic vision from our post-Enlightenment milieu. We travel back through the triumph of linguistic philosophy to the Enlightenment, and all the way back to Aristotle’s modification of Academic doctrine. Engagement with Plato can only begin after a ruthless retrospective application of Socratic scepticism to linguistically framed philosophy. Not that our criticism of its compulsion to ground reality in unknowable external objects makes Plato’s internal objects – his so-called ‘Forms’ – any more credible.

The best approach to this extreme anti-materialism is found through introducing the ‘Pythagorean Plato’, where elementary mathematic entities exemplify the relationship of insensible Forms to sensible experience. After that, we take another deep dive into scepticism, twisting through the labyrinth of contradictions that is Plato’s Parmenides. On the other side of this gruelling dialogue we are not entirely ruined, and yet perhaps not entirely convinced that all is resolved by the supposed being of not-being or by Plato’s mystical same/other unity self-differentiating through alternation. But at least we have glimpsed the possibility of Platonism mathematical mysticism and rediscovered its profound influence not only on Western culture and religion but also on the development of the modern mathematical sciences.

Week 1  Introduction: the Triumph of Analytic Philosophy

Our journey back to Plato begins with Russell’s incredulity to Wittgenstein’s philosophy of the unsayable during the dying days of the ‘Foundations of Mathematics’ controversy.


  • Russell B. ‘Introduction’ in Tractatus Logico-Philosophicus by L. Wittgenstein, London: Kegan Paul; 1922.
  • Russell B. ‘Mysticism and Logic’ in Mysticism and Logic and Other Essays p. 9-37, London: Penguin Books; 1953.
  • Poincaré H. ‘The Last Efforts of the Logisticians’ in Science and Method p. 177-96, London: Thomas Nelson; 1914.

Week 2  Socratic Scepticism and Platonic insight

Socratic scepticism clears a way to consider that reality might be constructed from insensible, unprovable and ultimately ineffable ‘Forms’. We finish by reflecting on how Plato’s persuasive ‘dialectic’ mode of exposition suddenly cuts to fantastic narrative when key concepts are introduced.


  • Plato. Apology p. 20c – 24a
    (find this in Last Days of Socrates, Penguin Classics, or in various other editions and collections)
  • Plato. Republic p. 471c – 521a
  • Plato. Ion p. 530 – 36d
  • Aristotle. Prior Analytics (in Organon) p. 24 – 27

Week 3  The Pythagorean Plato

Our discussion of mathematical passages begins with the doctrine of knowing-as-remembering exemplified by the doubling of the square. The philosophical importance of ratio (logos) and proportion (ana-logia) is drawn out before finally wondering at the Republic’s ‘Divided Line’, a geometric mandala to the Form of Forms.


  • Plato. Memo p. 79a – 86b
  • Plato. Republic p. 521– 41

Week 4  Opposites and Alternation

This week we consider the various binary oppositions that keep appearing throughout the dialogues. Our survey finishes with the contradictions of being/non-being in Parmenides and their resolution in the Sophist.


  • Plato. Pheado p. 60 – 105
  • Plato. Sophist p. 218b – 221c
  • Plato. Parmenides p. 126 – 143a
  • Plato. Sophist p. 237 – 260b

Week 5 From Plato to Platonism

Aristotle’s famous account of esoteric mathematical philosophy links our ‘Pythagorean Plato’ to the Monad and Logos/Dyad emanationism of Hellenistic Platonism. The course closes by considering the extent to which our reading of the dialogues provide a workable vision of Plato’s extreme idealism.


  • Aristotle. Metaphysics p. 985b24 – 988a18
  • Proclus. The Elements of Theology Translated by E R Dodds, Oxford, Oxford, 1963 (2nd Ed). Read from Prop. 1 to Prop. 21.