Video transcription

To illustrate the nature of the Ideas-Forms and the role of the Intelligible World in human processes of knowledge, we shall make use of the game of chess, which contains all the elements required for our purpose. The board game, played with counters on a checkered surface, called by the Greeks Pesseia or Petteia, was one of Plato's passions. In it, he discerned an essential representation of mechanisms such as government, war, laws, and language. Andrea Capra writes: “The game, evoked in the Dialogues with a frequency that is nothing short of astonishing, embodied for the philosopher an activity that was purely intellectual and devoid of chance, endowed with strong strategic value, in so far as the player must know how to arrange the ‘pessoi’ in the most advantageous way. This justifies its metaphoric presence on three quite distinct planes: the cosmological, the ethical-political, and the discursive-dialectical, all amply documented in the Platonic Dialogues.”

This inclination of Plato for board games, together with his artistic disposition, are symptoms of a Synthetic Logic at work, an inferential mode that privileges vision, spatiality and structure as a logical model, whose forms are applicable both to the microcosm of the game and to the macrocosm of our reality. Let us then consider how a game may help us to understand Platonic Idealism.

Chess presupposes: a chessboard, with a finite number of black and white squares; a finite number of pieces, each with recognizable morphological features, and essential movements that define its role (King, Queen, Bishop, and so forth); two players who set the pieces in motion in turn, guided by opposing strategies; rules that govern the movement of each piece on the board and define a goal, upon the attainment of which one of the two players is declared the winner.

Let us now assign to the elements of this metaphor a correspondence with our archetypal logical structure. The chessboard represents the sphere of Being, composed of space and time: each square is a place, each turn is a moment. The set of movements of the material pieces, which are Phenomena, is Becoming. What stirs upon the board thus represents the existent, the whole Sensible World.

The second dimension is that of Thought, which encompasses what stirs in the players' minds, the representation of moves in the play of memory and imagination. Finally, the peculiar symbolic shape of the pieces, which distinguishes them in the eyes of the player, represents the sphere of Language.

What then of the rules? To understand what the rules represent, we must penetrate to the heart of Idealist thought. The rules are not the booklet that contains their description: the printed booklet is, in fact, a Phenomenon. Nor are they the words through which someone has codified them: words are Signs. Nor are they what the players remember and imagine: these are mental representations, Concepts.

The rules enclose instead the “logic of the game” and its “laws”, the constraints that transcend the material elements, that to which everything is subordinated, so that the game may express its inner essence, and thus be defined as “the game of chess” and not, for instance, “the game of backgammon”. Within the reality represented by a game of chess, these rules are “transcendent”, because they cannot in any way be found in the physical elements of the game, but only deduced; “universal”, because they apply to every possible game; “objective”, because they are recognized and shared by all players; “real”, since no element of the game can free itself from the logical concatenation they prefigure; “subsistent”, because they do not depend on any other element of the game, and remain valid even when no pieces and no board exist any longer; “causal”, because they are the source from which the game springs; “true”, because they are universally valid for every player; and finally, since they are bound to no particular place and no particular moment in time, they are “non-existent”.

Both Thought and Language thus combine two aspects: one physical, one metaphysical. On the one hand, the player's thought is divided between the rules that have been internalized, which we may describe as “pure constraints”, and the possible and impossible moves determined by the current position on the board, which we may call the “empirical situation”. On the other hand, the pieces themselves possess two attributes: one physical, one metaphysical. On one side, there is the piece as “material object”; on the other, there is its “role”, which determines its symbolic aspect.

Let us now apply the elements of our metaphor to Platonic thought. The transcendent, metaphysical constraints of the rules could never unfold, except through the interaction of physical elements, each characterized by a specific “quality” or “essence”: an Eidos, to use the Greek term. Within this Intelligible World constituted by the rules of chess, the “essences” are the “roles” of the pieces. They are not the little material figures that we can see and touch; those are Phenomena; rather, they are the “ideal roles” of King, Queen, Bishop, Knight, Rook and Pawn.

Within the microcosm of chess, there must be six eternal essences, and their number will remain unchanged until the end of time, even if all the material chessboards in the world were to be destroyed, for the existence of chess is a possibility that belongs intrinsically to the structure of this reality. Thus, the Intelligible World stands to the Sensible World exactly as the “rules” stand to the “play”. The “rules” contain the “play” in potency, whereas the “play” is the actual manifestation of the “rules”.

The rules are “legislating information”: they endow the game with form, meaning, movement and purpose. When we ask where these laws “reside”, Plato, pointing to the board and tracing its outline with a gesture, replies: “beyond this world”, in the so-called hyperouranios, that is, beyond the physical, material elements of the game. Above all, however, beyond the minds of the two players, even though the mind, through study and discipline, is capable of mirroring, more or less clearly, the logic of the game.

We have spoken of rules, and this makes it clear that Idealism conceives Reality as a rational project. Whether there is, in an anthropomorphic sense, an “author” of the project, and “who” this author might be, are questions on which Philosophy cannot pronounce without turning into Theology. We therefore leave the answer to such questions, which arise from a logic patterned upon the empirical dynamics of cause and effect, to the intimate convictions of the viewer.

What we can affirm, instead, is that for a hypothetical observer who watches a game of chess without knowing the game, and without being able to see the players, it is by no means easy to reconstruct these rules. The game may, in fact, appear as a succession of phenomena more or less coherent. The project becomes rational only if the observer makes the effort to go beyond mere sensible perception.

If the observer is a scientist, he will, for instance, be able to discover, by analyzing the piece and the recurrence of its move duly recorded, that a Bishop always moves diagonally. If, however, the scientist is also a philosopher, he may come to hypothesize the existence of an invisible connective structure that links, synchronically, all the elements of the game. This might lead him to acknowledge the presence-absence of those rules that escape the evidence of the senses. To that extent, Theoretical Physics ventures.

What, then, are the rules of this game called “reality”, as Metaphysics understands them and as they may be condensed into first principles? They are few in number, yet densely packed. First of all, Reality is a Unity. Within this Unity there acts a Duality, a polar opposition whose terms reciprocally imply one another in varying proportions.

The polarity between the Sensible and the Intelligible worlds expresses the antithesis between the infinite multiplicity of Phenomena and the unity of the supreme Idea, in which the One, universal and abstract, gathers and synthesizes all the many, singular and concrete. Thus human consciousness, through a dual process of composition and decomposition, may set in motion a “descending” movement from spiritual Unity to material Multiplicity, or an “ascending” movement, from material Multiplicity to spiritual Unity.

We find traces of this in the Philebus, in the dialogue between Socrates and Protarchus: “One example of what I mean, Protarchus, can be seen quite clearly in what you were taught as a child: the letters of the alphabet. The voice that comes from our mouth constitutes, in a certain sense, a Unity, yet at the same time it is infinitely Multiple, if we consider the individual sounds that compose it. We attain true knowledge only if we consider that both aspects, Unity and Multiplicity, are one and the same thing.”

Let us try to exemplify, with the figure that follows, the two opposing movements of what we shall call “the Dialectical Process”. The cluster at the centre represents all the objects of thought. Each letter inside a square stands for a concept which, relative to other concepts, possesses as properties both “differences” (the individual letters) and “identity” (the shared square shape).

In the figure on the right, we see the same set, but the segmented circles represent the result of the Analytic process, which focuses on differences, the letters, and produces Multiplicity. On the left, we see the result of the Synthetic process, which focuses on identity, the square shape, and produces Unity. The initial set has remained unchanged. We have chosen, consciously or unconsciously, to know it and represent it by following one of the two directions.

In conclusion, let us add an important remark. Dialectic, although it rests upon Opposition, does not halt there. It does not ask us to reason in “binary”, but in “ternary” fashion. It makes use of dichotomies, because they are the only way in which the Intellect can proceed, sharply and intolerant of contradiction.

The dialectical strategy is therefore to make use of the Intellect and then dispense with it, in two stages. At first it allows the Intellect to divide two opposing concepts: Diairesis, or “decomposition”; thereafter Reason intervenes and reconciles the oppositions, with Sinagoghe, or “composition”. In the course of our account, we shall reflect at length on this extraordinary mechanism, making it clear and evident through the archetypal diagram. “To the Principle!”