Alan Badiou is unique in modern philosophy, which is contrary to the wave of deconstruction and post-structuralism prevailing in France. These popular viewpoints (following Heidegger's viewpoint) put forward the position of subverting metaphysics and ontology in philosophy and tried to think about the external/other of traditional philosophy. Badiou, on the other hand, put forward a new set of ontology-mathematical ontology to counter deconstruction, postmodernism and other ideological trends. Badiou called these thoughts "democratic materialism" in The Logic of the World, because they believed that there was only body and language in this world, and different bodies and languages had equal rights to exist. Badiou called his philosophy materialist dialectics, thinking that there is only body and language in this world, except truth (except truth).
In an era of "skeptical hermeneutics", Badiou's reintroduction of truth is inevitably out of date. From Descartes and Foucault to Rorty and Quine, philosophy doubts the absoluteness of truth from different angles, while traditional concepts of truth, such as logic, philosophy and historical truth, do have many loopholes. Therefore, our first reaction to Badiou's philosophy is a doubt-can we still talk about truth in an era when we no longer believe in absolutes?
But from his self-proclaimed materialist dialectics, we can already see where Badiou's passion for truth comes from. From his earliest works and social movements to the present, he is a staunch capitalist. As a student of louis pierre althusser, Arthur's philosophy of * * * has a profound influence on him. Badiou even said in his book Metapolitics that all contemporary philosophy must start with Artus's philosophy. This philosophy puts forward that Marx is an important ideological revolution in the history of thought and points out the scientific basis of materialist dialectics. In the history of Artus's thought, every scientific revolution leads to a philosophical revolution, and the mission of contemporary philosophy is to try to promote a revolutionary condition through Marx's revolution in the field of philosophy (that is, politics).
But Artus's philosophy faces many difficulties, and his students know it best. On the one hand, Badiou inherited the spirit of Artus's philosophy, on the other hand, he began to re-understand the function of philosophy and build a more complete philosophy. Subject theory is the starting point of his philosophical system. Translators of the subject theory call this book "the most creative and passionate" by Badiou. This book does not have the objective detached attitude of traditional scholars, but is more like what Artus said: "Philosophy is a class struggle in theory." * * * Capitalism (Lenin, Marx, Mao Zedong and Engels) is of course one of the protagonists in this book. But besides politics, subjectivity also shows Badiou's theoretical ambition. Badiou tried to put forward a new theoretical framework to interpret the history of thought, and made in-depth and unique analysis of Hegel, Malamey, Greek tragedy and Heldring. The plan of subjectivity theory is to transform idealistic dialectics, reflect on the materialistic orientation of subjectivity and establish a set of Marxist philosophy. The philosophy after Badiou expanded this idea.
Existence and events
"Mathematics is an ontological statement ... a beam of light that illuminates the speculative scene." Mathematics is the source that enables Badiou to expand and surpass the framework of subject theory. "Mathematics is ontology" is also the center of Badiou's philosophy, which can be called his greatest ideological breakthrough. The philosophical view of mathematical ontology hides Badiou's criticism of twentieth century philosophy. Philosophy in the 20th century (whether Heidegger or Wigenstein, Deschida, Foucault, etc. ) emphasize that language is the medium to express ideas, and constantly analyze the limitations of language on ideas. Heidegger even sewed philosophy with poetry (especially Holdrin's poetry). Mathematical ontology is to establish philosophy by virtue of the absoluteness of mathematics and the variability brought by the flow of language. On the other hand, the ontology of mathematical ontology is also challenging the declaration of 20th century philosophy that metaphysics and ontology have come to an end. In Badiou's eyes, we don't need to give up ontology, we just need to establish a new set of ontology.
Four Procedures for Opening Truth
The failure of traditional ontology is just empty talk of several generations of philosophers. Metaphysics, starting from Plato, is to seek eternal truth and set this truth as the foundation of philosophy. Twentieth century philosophy found that this was no longer possible. Therefore, the foundation of philosophy itself has been shaken, and giving up metaphysical thinking mode has become the most natural way out. Badiou accepted the criticism of ontology by modern philosophy and acknowledged the absoluteness of tradition (truth, God, etc. ) is unfounded. But in Badiou's eyes, groundless talk is not a problem. Philosophy has no absolute foundation: it is based on accidental events. The emergence of truth waits for the occurrence of "events". Furthermore, philosophy cannot find truth-it is science, politics, art and love that can find truth. Badiou put the above four conditions of philosophy, or the truth procedure. Philosophy must be proficient in its conditions, but it cannot be sewn with anyone. Philosophy has no truth, but this is not a "defect" of philosophy, and philosophy can run through four conditions of truth. Artux sewed philosophy and politics together, and Heidegger sewed philosophy and art together, both of which were wrong.
Set theory of mathematical ontology
The book Being and Events attempts to prove the following philosophical viewpoints: to demonstrate the ontology of existence and events. But the foundation of Badiou's philosophy lies in accidental events; Therefore, it will not try to "prove" whether its starting point is correct. Just like Hegel's philosophy, whether the starting point is correct or not can only be seen clearly by looking back after departure. The only thing that can be pointed out is the condition of his philosophy-Cantor as the pioneer of set theory. Under the condition of such events, Being and Events constructs an ontology set based on zermelo-Frankel set theory. (Extended reading of set theory: Wayne: set theory/mathematical philosophy model)
The picture above is a simple vickers diagram. There are three sets, A, B and C, which are represented by circles, and the overlapping areas between circles are intersections. If element A meets the definition of set A, it can be contained in the circle of set A, set B or set C, otherwise it will be outside these three circles. If an element/member can be included in the set of A and B, B and C, A and C, or A and B and C at the same time, there will be overlapping areas in the diagram, that is, intersections.
From this point of view, the intuitive concept of set theory is actually very simple (this is called naive set theory): a set is a set of any different elements/members. We can turn all the books into one collection, or we can turn cats and dogs into another collection. In a more formal language (this is the set theory developed by Frege), a set is all members who satisfy any proposition. This intuitive understanding of set provides a simple foundation for mathematics: all mathematical structures are a set, but they have different propositions. A "group" in algebra is a set that conforms to four axioms, and manifolds with different geometries are sets that conform to different topological conditions.
This original simple and satisfactory foundation was overturned by Russell's paradox: the set of all sets does not exist as the set of propositions. Therefore, a set cannot be defined as a member that conforms to any proposition. In order to develop a consistent set of axioms, mathematicians formed the zermelo-Frankel axiom. Badiou uses this axiom to think about ontology.
If it seems neither fish nor fowl to think about ontology with set theory, then Badiou's interpretation of Plato's parmenides in The First Meditation of Being and Events shows the philosophical elements of set theory. The problem of one and many is closely related to set theory. Ontology always thinks that there are many performers, and the performer is a multiple of nature; The essence of presenting itself is one. Badio claims that it does not exist. "One" is the result of an operation. We can count everything as one (count-as-one), and this operation process is not necessary; We can count everything into one. Badiou called it a situation of multiplicity; The diversity presented consists of multiplicity and "number into one". There are two parts to this situation. But any such structure is subdivided into: first, those multiples are themselves "one", and they are consistent multiplicity; But in one case, we will find retrospectively that there is not one presentation itself, but many, which is the multiplicity of inconsistency. So we can say that the axiom of Zemello-frankl is a philosophy of presentation.
According to zemel-frankl axiom, Badiou reconsidered many basic issues of traditional philosophy, such as attribution/inclusion, identity and difference. The first five axioms of Zemel-frankl set theory are the concepts we use to understand that presentation itself is presented. But justice is just a form; Anything that conforms to axioms can be a set. But the existence of the set itself cannot be determined by the axiom itself. There is still a distance between axiomatic system and ontology, and axioms need to be sewn. This is the sixth axiom, which is the function of the empty set axiom. The concept we use to understand expression (that is, axiom itself) does not exist; They are just forms. But this nothingness itself exists; His existence is just a sign? . "... nothing is transmitted by the laws of ideas, but this nothingness is made possible by the assumption of a proposer's name" is the starting point of all existence. This coincides with Heidegger's and Desida's criticism of presenting metaphysics: taking nothingness as the beginning of existence means that existence itself cannot be presented.
Badiou expounded the basic concept of ontology with the simplest language and Zemel-frankl set theory, and took "one non-existence" as the basis of the whole ontology. On this basis, Badiou can grasp the essence of different beings mathematically. Badiou's understanding of truth and events with higher set theory is only an extension of this foundation. Based on set theory, Badiou divides situations into three categories: nature, history and neutrality. The event took place in a historical context. In Badiou's words, the multiplicity in historical situations is abnormal. These words have strict definitions, so I won't analyze them carefully here. A completely abnormal multiplicity is an event location where an event may occur. But this venue is not the activity itself, and the appearance of the venue does not necessarily mean that the activity will definitely appear. The event was not caused by any factors, so we can't understand the occurrence of Badio event by causality. Events occur in a certain situation, but not all the elements in the situation can be completely determined. An event is strictly defined as a site that contains its own multiplicity. Badiou used the example of the French Revolution to explain his concept: The French Revolution included the historical reality at that time-from the third-level conference, the economic situation in France, the jacoby school, to the Marseillaise, the prison, the guillotine and so on. But these are not the revolution itself; The word revolution in the French Revolution cannot be understood by lists. Calling it a revolution is part of this revolution. Therefore, an event includes his site (France, 1789- 1794), but it must include himself.
Intervention and loyalty
We can't logically judge whether the event happened or not. Every situation has its actual and concrete reality, and it is necessary to intervene in the situation if we want to judge whether an event has occurred. Loyalty is to define whether a situation is related to an event.
The truth will only appear after the incident. But truth cannot be limited by different situations and history, otherwise Badiou's whole philosophy will only return to a set of historical relativism. But Badiou's view of truth is completely different from traditional philosophy. Truth is often used in philosophy to measure the truth value of different propositions. Badiou calls this truth authenticity, which is separate from truth. Authenticity is the standard of authenticity of different propositions, and truth does exist. Truth comes from loyalty plan (general truth plan) and is a part of existence. After this process, it will become an infinite part of the situation. Since it is a part of existence, it will not change with the times.
Being and Events establishes the philosophical position of truth, event, existence and subject by re-establishing ontology, which can be said to be a brand-new beginning of modern philosophy. On the basis of this ontology, Badiou further explored different philosophical themes and analyzed the most important themes of modern philosophy, such as politics, art, philosophy history and psychoanalysis, in his books, such as Conditions, Aesthetic Handbook, Brief Introduction of Being and Metapolitics. However, Badiou gradually discovered the shortcomings of Being and Events, and this discovery finally led him to write Being and Events II, that is, The Logic of the World.
The logic of the world of existence and events
If existence and events are ontologies, then the logic of the world is phenomenology. Badiou simulated these two books as Hegel's Phenomenology of Spirit and The Great Logic, but he published the Great Logic first and then dealt with phenomenology. The framework of Badiou's reflection on existence and events stems from two main reasons: in mathematics, category theory contains the advantages of set theory as a mathematical basis, and is even more widely used than set theory; Set theory is just a category. Philosophically, Badiou has to deal with the possibility of different situations: why can different situations exist without becoming pure chaos? What gives the structure of a situation? Badiou called this situation the world in his book The Logic of the World. Therefore, these questions are asking: how did the elements of a world appear in the world? This way of appearing is the logic of this world.
The application of category theory in modern mathematics is numerous. The different structures of algebra are all categories; Different topological spaces of algebraic geometry and algebraic topology all form different categories, and the method of studying different structures by category theory is also indispensable in modern mathematics (hierarchy, homology, model category ...). The most important thing for Badiou is the importance of category theory in mathematical logic, especially the concept of topology. Topology is a category that accords with several axioms. It is characterized by its own logic. In a topology, the logical rules we use in our daily life are not necessarily correct, and law of excluded middle is not necessarily true. But this does not mean that the logic of topology is arbitrary; Its logic is based on its elements and lies in itself. For example, the category of a set is a topology, which conforms to our usual logic-this logic is not put in by us, but the mathematical structure of the set itself. If the members of a category are not sets, it can have other mathematical structures and change the logic of topology.
In Badiou's philosophy, the world is a topology (more precisely, a Grothendieck topology). Therefore, the logic of the world is the inherent logic of the world. The function given to the world structure is a priori); Structure; As a topology, each world has its own prior structure, which measures the intensity of different elements in the world.
On the basis of this new phenomenology, Badiou re-understood the meaning of being in the world. This is another interpretation of the event. In the world, the subject faces multiplicity; But events and truth are prominent in this multiplicity-the subject can affirm or deny the occurrence of this event. In other words, the subject must make a choice when facing the event. This choice turns the complex multiplicity of the whole world into affirmation and negation. Badiou calls this a point in the world-it forces the subject to make a choice. The existence of the whole world is focused on this point-all living beings have to decide whether they are right or wrong. For example, 1940 France was occupied by Germany. Faced with this complicated political and military situation, every Frenchman has to make a choice: to join or not to join the French resistance movement. The whole French political circles have to face up to this point, affirm or deny it.
There is no passion in today's world.
In Badiou's eyes, today's world is an era of refusing to face choices. Consumerism, capitalism and post-modern customs all encourage keeping a moderate distance from the world, and there is no need to remain loyal to any "truth". Badiou called this world atonal. Badiou's whole philosophy is very opposed to this world. Loyalty to events and truth is to resist indifference and nihilism in an irreconcilable world and challenge false sense of security and freedom. In Badio's profound philosophy and mathematics, it is not difficult to feel his enthusiastic affirmation of life and the joy of thought: "Sometimes I think that what I see in philosophy is just a means to re-establish the right of heroism and oppose the contemporary defense of futility and daily life. Why not? ... my wish is to let heroism exist through positive joy, which is generally produced by following the results. We can say that the epic heroism of those who gave their lives was replaced by the mathematical heroism of those who created them. "