The limits of the unlimited, and the unlimitedness of the limits


Plato calls God « the Unlimited » in the Parmenidesi – but he calls him « the Limit » in the Philebusii. Contradiction? No, not really.

He calls God « Unlimited » because He receives no limit from anything, and he calls it « the Limit » because He limits all things according to their form and measure.

Marsilio Ficino notes that matter itself imitates God in this. It can be called « unlimited » because it represents « like a shadow, the infinity of the one God ». And it is « limited » as all things are, in some form.

The infinity of matter and the infinity of things can be described philosophically, using the three Platonic categories of « essence », « other » and « movement ». The world, shadow of God, generates infinitely in matter essences, alterations, transformations and movements.

The limit of matter, like the limit of all things, can also be philosophically described using the Platonic categories of « being », « same » and « rest ».

The Unlimited and the Limit are in the same relationship as the sun and the shadow. This is not an opposition ratio, but a ratio of generation. Through shade, one can probably better « see » (understand) the light of the sun than by looking at it directly.

If the « Unlimited » were a sun, then the innumerable essences, the infinite ‘othernesses’, the incessant movements would be its cast shadows.

And we would find the Limit in ideas, the idea of Being, the idea of the Same, the idea of Rest.

iParmenides 137d

iiPhilebus 16d-23c

Being Horizons


Man, stars, wisdom, intelligence, will, reason, mathematics, quarks, justice, the universe, have something precious in common: “being”. Arguably, they all have specific forms of “existence”, though very different. The diversity of their distinctive types of “being” may indeed explain their distinctive roles in the (real) world.

One could assume that the word “being” is much too vague, too fuzzy, too neutral, by allowing itself to characterize such diverse and heterogeneous entities. The verb “to be” has too many levels of meaning. This is probably a direct effect of the structure of (here English) language. For, despite an apparent homonymy, the “being” of man is not the “being” of the number pi, and the “being” of the Cosmos as a whole does not identify itself with the “being” of Wisdom or Logos.

Sensitive to this difficulty, Plato sought to analyze the variety of possible “beings” and their categories. He defined five main genres of the “Being”, which were supposed to generate all other beings through their combinations and compositions.

The first two types of “Being” are the Infinite and the Finite. The third type results from their Mixing. The Cause of the Mixing represents the fourth genre. The fifth genre is Discrimination, which operates in the opposite way to Mixing.

Infinite, Finite, Mixing, Cause, Discrimination. One is immediately struck by the heterogeneity of these five genres. It is a jumble of substance and principle, cause and effect, union and separation. But it is undoubtedly this wild heterogeneity that may give rise to a power of generation.

With its five genres, “Being” is a primary category of our understanding. But there are others.

Plato, in the Sophist, lists them five all together: Being, Same, Other, Immobility, Movement.

The Being expresses the essence of everything; it defines the principle of their existence.

The Same makes us perceive the permanence of a being that always coincides with itself, and also that it can resemble, in part, other beings.

The Other attests that beings differ from one another, but that there are also irreducible differences within each being.

TheImmobility reminds us that every being necessarily keeps its own unity for a certain duration.

The Movement means that every being has a ‘potential’ for ‘action’.

Five kinds of “Being”. Five “categories” of (philosophical) understanding. Oh, Platonic beauties!

This is only a starting point. If we are to accept their power of description, we must now show that from these “genres” and these “categories”, we may induce all the realities, all the creations, all the ideas, all the possible…

As a serendipitous thought experiment, let us conjugate these five « categories » of understanding with the five genres of “being”, in hope of bringing out new and strange objects of thought, surprising, unheard of, notions.

What about imaginary alloys such as: “Moving Cause”, “Mixed Same”, “Other Finite”, “Discriminate Being”, “Immobile Infinite”, “Cause of Otherness”, “Moving Finite”, “Infinite Otherness”, “Infinite Mixed”, “Immobile Discrimination”, or “Discriminate Immobility”?

A general principle emerges from these heuristic combinations : an abstraction piggybacking another abstraction generates “ideas”, that may make some sense, at least to anyone ready to give some sort of attention, it seems.

What do these language games teach us? It shows that genres and categories are like bricks and cement: assembled in various ways, they can generate shabby cabins or immense cathedrals, calm ports or nebulous clouds, dry chasms or acute bitterness, somber jails or clear schools, clumsy winds or soft mountains, hot hills or cold incense.

There are infinite metaphors, material or impalpable, resulting from the power of Platonic ideas, their intrinsic shimmering, and the promise of being “horizons”.