Philosophy between mathematics and poetry

Marina Gusmão, Hello Stranger, Digital illustration


Philosophy is a meditation on the existence of truths that result from the event in a given situation of being.

We will start with some considerations about philosophy as such. You know that Socrates was sentenced to death because he was accused of "corrupting youth". We have to accept this condemnation. Yes, philosophy corrupts youth and ultimately corrupts everyone. Philosophy organizes ruptures, an opening to a new life, a true life as opposed to the fallacious life that the capitalist march and the cult of money offer us today.

In order to clarify the issues and means of philosophy we will focus on the “conditions” of philosophy, which are defined by the relationship between philosophy and the four different forms of truths, scientific, artistic, loving and political truths. We will examine more precisely how philosophy, with the complexity of philosophical language, gets caught between the rigorous construction of arguments and the seduction of language.

Thesis 1. Mathematical demonstrations and rational philosophy were born at the same time in the same place, namely in Greece in the fifth century BC Philosophy emerged in Greece conditioned to mathematics, but also to the language of poetry. From then on, there was always a tension between its demonstrative or mathematical tendency and its seductive and poetic tendency. So you have Spinoza on one side, Nietzsche on the other.

Thesis 2. This tension can take the form of a conflict or a contradiction. In this way, Plato speaks of a “very ancient war between poetry and philosophy”. In turn, he violently attacked poetry, although he often declared his love for it. This conflict is therefore less objective (in the sense of the difference between two language materials) than subjective. Poetry and philosophy, in both cases, try to produce, by a single language medium, two distinct types of conversion of listeners. Philosophy's ambition is to replace authoritarian discourse with argumentative discourse. For a statement is not true because it is said by a priest, king, prophet or god. It is true because there is proof of its truth. Thus, any alleged truth must be submitted to general discussion and the subject of the statement cannot be the guarantor of the truth of a statement. It is the statements already guaranteed to be true that are proof of the veracity of a new statement. Poetry is more on the side of seduction, of subjective transformation, which is produced by the strength and beauty of language as such.

Thesis 3. The difficulty is precisely that philosophy, before Socrates, appears in a still poetic language, largely inspired by the great poems of Homer. This was the time of Empedocles or Anaximander. The transition takes place in the work of Parmenides: he also wrote a great poem. But, in fact, he proposes a proof, the logical proof that only being is, thus placing philosophy between poetry and mathematics. To prove that only being is and that there is nothing else, he uses the indirect method of reasoning by the absurd. In fact, he tries to demonstrate that non-being cannot exist and that, therefore, only being exists. The fact that non-being does not exist seems obvious, but in fact we must understand that for Parmenides “being” and “existing” are two different things.

In any case, from Parmenides on, philosophy is situated between poetry and mathematics and Plato undertakes to continue this demonstrative form, without sacrificing anything in relation to the beauty of language. In fact, the genre of poetry that Plato criticizes is not poetry in general, but poetry that he calls “mimetic”, that is, that which is placed under the pressure of a natural model, whose aim is not to create a new one. knowledge, but a new affection. For Plato, the models of this “bad” poetry are the epics on the one hand and, on the other hand, the tragic theater. It is less a question of language than a question of the subjective effects produced by poetry, since the uncontrolled seduction allows spectators and listeners to identify with models of thoughts, feelings and actions, something unacceptable for the philosopher. We must definitely admit that Plato is not opposed to poetry as such. He accepts poetry as long as it is not mimetic. His fundamental argument is that philosophy is the creation of something and not the imitation of something.

Finally, after Parmenides, the language of philosophy will be situated midway between the language of poetry and the language of mathematics. It can be said that it is a language of seduction, which provokes a transference in the speaker, and a language of demonstration, which reduces the listener to silence.

Thesis 4. Plato himself constantly made poetic use of language, particularly in the form of “myths”, which are types of fables that produce and modify concepts by inventing a fictitious account of his birth and history.

Unlike poetic stories, fables, in short, fictional language, the strength of mathematics lies in relying on symbols, letters, figures or formulas rather than words, images or sentences.

Here is an example of math language:

[(∀y) (y ∉ x)] ↔ (x = ∅)

This formula means: "Stating that, for every set y, it is not true that y belongs to x is equivalent to saying that x is an empty set". We can say that mathematics proves the power of the letter, of pure letters and symbols, of pure demonstration or symbolization, while poetry is the power of language, discourse, its images and its developments.

Thesis 5. There has never been philosophy written entirely in mathematical language, because philosophy, even demonstrative, has never reached this level of formalization. The dream or idea of ​​a purely mathematical philosophy, which would be written solely in letters and symbols and where all sentences would be theorems, is impossible. The extreme case is represented by Spinoza, who wrote his famous book Ethics in the form of Euclid's great treatise. On the other hand, there are philosophical works that are explicitly presented in a poetic form, as in Natural Rerum of Lucretius or certain parts of Thus spake Zarathustra of Nietzsche.

We can conclude that philosophy does not admit the absolute power of the letter. She needs the meaning of the words. It can certainly try to be demonstrative, but it cannot be fully formalized. That is why philosophy stands between mathematics and poetry.

Thesis 6. Mathematics, as a formal ontology of multiplicities, is an independent science, which constitutes a closed field. Poetry, on the other hand, as an extraordinary treatment of common language, can arise from any text.

Furthermore, mathematics is written in a single language while poetry is written in many languages, which raises the question of how the universality of philosophy is possible. Indeed, from the beginning philosophers claimed that what they thought or wrote had universal value. In this sense, a philosopher offers something universal beyond national languages ​​or through the differences between languages. And mathematics could accurately represent a universal language of its kind, since it is based on the power of the letter; now we have seen that for philosophical writings the letter is not enough. It's a difficult problem because if the philosophy is written heavily in a national language, its universality will be proven or verified by translations. We must, therefore, assume that, in the case of philosophy, there are translations that do not present real transformations or modifications of its universal meaning. This point opens the delicate question of the relationship between philosophy and translation.

Thesis 7. Philosophy can and should ask why mathematics, which is formalized, is used in all the natural sciences, especially physics, which deals with concrete objects and the laws of nature. I will reply that this comes from the fact that mathematics is the science of everything that exists. Not what is this or that, but what is.

From the point of view of philosophy, mathematics constitutes the demonstrative apparatus of all thought of being, of the thought of being as such, of what is as it is (it is not a tree or a person). This begins with Parmenides, for whom being is being, because not being is not. Seen from the same point of view, poetry constitutes, within language, the ability to apprehend the event*. In that sense, my own philosophy is in relation to poetry, not on the side of being, of what is, but on the side of the event, of what happens and which is not immediately identifiable as what it is. Think, for example, of artistic creations (which are creations of something that doesn't yet exist) or love (which is what happens or doesn't happen), or scientific inventions that upset all previous knowledge.

Thesis 8. The common feature of everything is that everything is multiple. Nothing in nature is absolutely one in itself. Again, from the point of view of mathematics, "everything that exists is a form of multiplicity". Nothing in nature is absolutely one, this water bottle, for example, is made up of several things. To be is to be multiple and mathematics is the science of the multiple. The question of mathematics in philosophy is therefore the question of the multiple. In other words, thinking about the multiple in its purity is an object for mathematics, whereas thinking about the multiple in philosophy is sometimes complex, sometimes simple (this is why mathematics can be useful for philosophy). Perhaps God is the only exception. If he exists, God is absolutely One. Hence the importance of God in philosophy: metaphysics deals with the absolute One in the form of God, the great One, in opposition to us because we are multiplicities. Everything that is natural or material is composed of elements that are also natural or material.

This places us before a fundamental choice between an ontology of the One and an ontology of the many. Think, for example, of the history of philosophy and the many attempts to demonstrate the existence of God (for example, on Descartes or Leibniz). In its philosophical sense, God does not arise from affection, from belief, he is related to a demonstration regarding the necessity of the great One-infinite. The mathematical side is important, as it deals with the conflict between a rational proof, from the point of view of philosophy, of the existence of the One, on the one hand, and a mathematical ontology that deals with all possible forms of the multiple, on the other hand. other side.

Poetry, for its part, testifies to the power of intellectual activity to force language to say what is impossible to say. From the point of view of philosophy, the existence of this power allows us to say that truths are universal, because they are based on events. Which means they go beyond the ontological laws of the worlds in which they appear.

Poetry is, for me, the possibility of thinking about what happens: the pure event. An event is necessarily what happens and then disappears. That's why I think it's necessary to move from the classic view of the One (God as the great One) to thinking about the pure multiple and the difficulty of thinking about the new. The history of philosophy then becomes the history of the change it proposes from fundamental questions. Old metaphysics generally deals with what is in relation to what is not, or with the One against the many, or even with the infinity of God separated from the finitude of the sensible. Today, I think a fundamental issue concerns the gap between being (what is) and event (what happens). In any case, as always happens in philosophy, my personal choice. Philosophy always imposes itself to carry out a program whose starting point is a network of questions that it asks itself.

Thesis 9. There are two possible sciences of being. If you think that God exists, there has to be a science of the forms of the One, which is called theology. Otherwise, there is only the science of all possible forms of the multiple. It's the ontology.

Escaping all forms of ontology, each poem is the name of an event. Here is an example that comes from the French poet Paul Valéry. The title of the poem is to the plane tree. The poem is the story of an attempt to enclose the big tree in the image of an object of the landscape and the site, therefore, not to attribute it to an event, but to the silent force of the world as it is. [1]:

You stoop down, great plane tree, and you emerge naked,
Like a young man from Cynthia,
Targets, but your candor is trapped and your foot is held back
By the strength of the site

But at the end of the poem, you have the tree's revolt against this objectification. The tree does not want to be a splendid prisoner, but part of an event, a violent event, a storm. And she replies: "No, I don't accept being just a piece in a structure".

– Says the tree: No! says by shining
From your haughty head
That the storm treats like every being
Just like you do with the grass!

Thesis 10. Ontology is only fully thinkable in the language and logic of mathematics. That science can make use of the power of the letter because letters are not concerned with the meaning of what is or the law of what is. Its only bet is to serve to observe, think and classify the possible forms of what is, and the possible relations between these forms. Mathematics can be literal because it is never concerned with what is singular, but only with the universality of the forms that singularities take. Philosophy, which thinks of truths as a mixture of being and event, is a kind of poeticization of mathematics.

Thesis 11. Mathematics can be used to formulate the laws of nature because all singular objects in nature are also and primarily parts of what is as it is. Any object that exists is in the possible form of a multiplicity. That is why mathematics thinks and formulates the ontological basis of physics. In the 19th century and through much of the 20th century, the reign of positivism and hence science on the one hand, of history and hence politics on the other, had the effect of creating an age of poets stretching from Hölderlin to Paul Celan and including Rimbaud, Mallarmé, Trakl, Mandelstam, Pessoa, Stevens, Vallejo and a few others. Throughout this period, poetry assumed the tasks that usually belong to philosophy, in particular: thinking about everything that is unpredictable, impossible, the workings of chance and the new figures of heroism.

Thesis 12. Philosophy must be situated beyond theology, which is the religious science of the forms of the One, but also beyond pure ontology, which is the secular science of the forms of the many (mathematics). Philosophy begins when it comes to thinking not only about what is, but the being of what is not and the effect of what is not on what is. Philosophy must therefore think about the event and clarify the importance of what happens and disappears. Because all this is not reducible to the form of multiplicity. An event is an event in a concrete context and therefore poetic in nature. That is why philosophy must know what is happening in the field of poetry. Hence also the very close relationship between poetry and love, which is the main example of what can happen as universal and creative in human life.

In the last years of the XNUMXth century, the failure of the second period of communism (that of the socialist states) and the crisis of science (left to commercial interests) restored the independence of philosophy and put an end to the age of poets.

Thesis 13. Philosophy must know mathematical ontology precisely. It is your duty to understand the thinking of all possible forms of the manifold, and especially the profound modern mathematical theories about the forms of infinity. However, philosophy is the thinking not only of what is, but also of what happens to what is. Not only of being, but also of event. Not just forms of the possible, but the conformation of what, at a given moment, is considered impossible. That is why, today more than ever, there is no philosophy worthy of the name without a meditation by poets, in particular by the prodigious poets of the era of poets. Philosophy is a meditation on the existence of truths that result from the event in a given situation of being. Truth is something new, because it is always a construction composed, on the one hand, of multiples that belong to a situation, and on the other hand, of an event that occurs to the situation. This relationship is crucial: the result of the event is the realization, within the being, of the process that gives rise to a new truth, the creation of truth within the framework of its four conditions (science, art, love and politics). Philosophy is therefore situated between poetry (what happens, the event) and mathematics (what is, being).

* Alain Badiou is a retired professor at the University of Paris-VIII. Author, among other books, of The adventure of French philosophy in the XNUMXth century (Authentic).

Translation: Diego Fagundes to the website word-plowing.


* Translator's note: we prefer to translate “evenement”, one of the author's fundamental concepts, to “event”, but there are publications in Portuguese that opt ​​for “event”.

[1]: Excerpts from the poem To the plane tree, Translated into Portuguese by Roberto Zular and Álvaro Faleiros for the bilingual edition of Spells [Charms] released by luminuras in 2020.

The two stanzas – the first and the last (eighteenth) – in the original French:

Tu penches, grand Platane, et propose nu nu,
Blanc comme un jeune Scythe,
Mais ta candeur est prize, et ton pied retenu
Par la force du site.

— Non, dit l'arbre. I said: Non! par l'étincellement
From sa tete superbe,
Que la tempête traite universellement
Comme elle fait une herb!


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