NOTE: As with all my notes from the EGS, there will likely be mistakes because I did not record the lectures, I made notes as they spoke, so I am perhaps interpreting what they are saying as I am writing. To overcome my limitations I will embed the lecture here as well:
Aristotle's Book IV of Metaphysics, 3 Princles:
- identity: a proposition is equal to itself
- noncontradiction: it is impossible for p and non-p to exist simultaneously
- excluded middle: there is no third way - it entails double negation
Since negation of negation is affirmation we have a nullification; Hegel says it is not immediately affirmation but perhaps reflexively so - reflexive logic.
War, classically understood, is a binary - it makes no sense to say that the city is occupied by both your troops and the enemy's. If neither camps occupy, Classically we would say that the city is not at all occupied.
With paraconsistent logic we can say both camps occupy the city; and also that the city is not occupied. Think of Stalingrad during World War II, where both Germany and the Soviets claimed they occupied the city.
As we move from Classical logic to Intuitionism and then to Paraconsistent logic we have a gradual diminution of negation.
In my ontology, a thing is a possibility without any qualification, a pure multiplicity. All laws are appearing within a context. The thing exists as an object in the world. Clearly the logic of being qua being is Classical; this is because Classical is extensional, this assumes point A and point B. As a consequence of this thinking, multiplicity is seen as Classical.
In a given world, however, being appears as more or less. Being, as Plato said, is univocity, but appearing is a multivocity. The logic of being qua being is Classical, but the logic of existence is _____ (I missed it, intuitionistic? paraconsistent?)
We are examining the possibility of novelty generation within this framework. What is the destiny of an event? Events are existent and determined by their intensity. From the perspective of the event, the whole world is bifurcated between minimal and maximal intensity. The consequences of the intensity of the event, if it is maximal, is that we say it exists.
We can say that revolution is Classical and reformational change is Intuitional; 3rd case, the force of change cannot be perceived but its effects are nonetheless determinable, this is paraconsistent. We are event and nonevent simultaneously. We have a force event or a simulacrum. A true change must be Classical and weak change is Intuitional.
The unfolding of change is in the world and we must accept that these changes are Intuitionistic. Since the world's negation is within the Intuitional, we see the triumph of the Paraconsistent.
Pn(B^PnB) = the principle of noncontradiction contradicted.The point of the handout (and this talk talk which it simplifies) [I will scan it in once I have a scanner] the beginning of sentence is "non" in these cases it is a Classical logic. The Classical principles which determine it negate the entirety, the negation transcends, every total negation is Classical.
What the 3 negations have in common is their behavior when their logic is dominant, in these cases they are uniformly Classical. In my conception, when you face a choice of a creation of a work of art, when you have the necessity to discard and then continue, you have to say, "non," to a temptation when in this situation. Yes/No; when saying, "non," is a necessity to continue the creation is one in Classical logic.
When continuing to incorporate ourselves into a new project assumes we are in a Classical situation. In love, science, the context is Intuitionistic. The logic of temptation is Paraconsistent - we cannot do the two, and it is powerful in its existence.
We resist temptation, not for moral reasons but because it is illogical; sometimes there is a key moment when the priority is clearly a Classical choice situation. The world is governed by Intuititionistic logic, but at the point of decision, Classical logic carries the day.
When we have an idea that the idea of true life exists, then we know that philosophy exists. This is because the logic of desire is always Paraconsistent.
(Here begins the Q&A)
Žižek: isn't the victory of abstraction when it penetrates its opposite and so the Real begins to act abstractly? (I made a note to myself that Žižek then spoke for 15 minutes)
Badiou: It's not that abstraction destroys negation, but rather allows for another possibility given the force of its change proposed.
There was something unclear to me about the nature of the event when I began to work on this: how can we recognize the true event? How do I know this is true loved rather than simply desire? The event is the most important example of negation, the possibility of the event is also the possibility of the negation of the world. The 20th century has been that of the impaired negation and so has been overpowering in its forms of negations.Schirmacher: What was Hegel's 2nd negation?
Badiou: It's very striking that the political implications of Hegel's 2nd negation have more and more been Classical. Mao Zedong's attempt has been very interesting: to overcome the Enemy is to overcome that in us that is also that in them.
Me: What about process? That we focus on an event in a field of events?
Why do you start with negation?
Badiou: I always try to uphold the precedents of affirmation. To enter into the question of affirmation we must make a metallurgical choice, maybe by the end of this week we have affirmation. The project is to transform the relationship between Classicism, Intuitionism, and Paraconsistence.