On Kant

Synthesis and Time

We are returning to Kant. May this be an occasion for you to skim, read or re-read The Critique of Pure Reason. There is no doubt that a tremendous event in philosophy happens with this idea of critique. In going into it, ourselves, or in going back into it, I had stopped reading it a very long time ago and I read it again for you, it must be said that it is a completely stifling philosophy. It's an excessive atmosphere, but if one holds up, and the important thing above all is not to understand, the important thing is to take on the rhythm of a given man, a given writer, a given philosopher, if one holds up, all this northern fog which lands on top of us starts to dissipate, and underneath there is an amazing architecture. When I said to you that a great philosopher is nevertheless someone who invents concepts, in Kant's case, in this fog, there functions a sort of thinking machine, a sort of creation of concepts that is absolutely frightening. We can try to say that all of the creations and novelties that Kantianism will bring to philosophy turn on a certain problem of time and an entirely new conception of time, a conception of which we can say that its elaboration by Kant will be decisive for all that happened afterwards, which is to say we will try to determine a sort of modern consciousness of time in opposition to a classical or ancient consciousness of time. Why it is that it was Kant who created the philosophical concepts of this new consciousness of time, making his philosophical expression possible, does not concern us or in any case does not interest me, but what I would like to say is that it is indeed this sort of consciousness of time which takes on a philosophical status in Kant, and which is completely new. I will proceed by numbered points because I'm always working with the idea that to each point corresponds a type of concept, and once again, I will be happy if you grant me at the end of these lessons that philosophers are precisely this, that they are no less creative than painters or musicians, simply that they create in a determinable domain that is the creation of concepts. Firstly, what does Kant understand by the a priori which he opposes to the a posteriori? These are common terms. In some cases new words must be invented, and this happens with Kant when he creates the notion of the transcendental, which is a very strange notion, transcendental subject... no doubt you will tell me that the word existed before, but it was rarely used and it marked no difference from the ordinary word transcendent, whereas Kant gives it a very special sense: the transcendental subject, he almost created a word... in the case of the a priori and the a posteriori he borrows a word, but he completely renews its sense. A priori, in the first place, means: independent of experience, that which does not depend on experience. In opposition to a posteriori which means: given or givable in experience. What things are a priori? Note that I don't ask myself: does the a priori exist, which is to say, are there things independent of experience? The question of existence is secondary, we must first know what a thing is in order to be able to say and reply to the question of existence: does it exist or not? I'm saying that if it exists, what is something that would be independent of experience? Thus not givable in experience. Nothing complicated so far, Kant takes this up very quickly, the a priori in this sense is the universal and the necessary. Everything that is necessary and universal is said to be a priori. Why? It certainly fulfills the first condition of the a priori: not given in experience, because, by definition, experience only gives me the particular and the contingent. With expressions of universality and necessity it is always so necessarily, as also with certain uses of the future tense, or expressions of the type "each time": each time I bring water to 100 degrees it will boil. Philosophers have said this for a very long time: there is something in this which is not given in experience. What is it? It's the expressions: "always", "necessarily", or even the future tense. What experience has given me is, strictly speaking, that each time I have effectively brought water to 100 degrees, it has boiled, but in the formula "water necessarily boils at 100 degrees", the necessarily is not an object of experience. Similarly if I say "all objects of experience" - do I have the right to say this? We don't even know if "all objects of experience" is not nonsensical. Supposing that it is not nonsensical, "all objects of experience" are not given in experience, for the simple reason that experience is ???? Thus you can always make a summation, a sum of the objects you have experienced, but this sum is indefinite.
Thus the universal and the necessary by definition are not givable in an experience since an experience is always particular and contingent. So that gives us a second determination of the a priori. The a priori was first of all what is independent of experience, in the second place it is what is universal and necessary.
Third point: how can this universal and necessary be defined? There is already something extremely delicate here. To say that something is independent of experience doesn't prevent this something perhaps being applied to experience and only to it. The question of application is entirely different. When I say "water will always come to a boil at 100 degrees", I don't know where this idea of "always" comes from, since it is not given to me in experience, I don't know where this idea of necessity comes from, since it is not given to me in experience, this doesn't prevent the fact that "always" is applied to water, boiling, 100 degrees, all things which are given in experience. Let's suppose then that the a priori is itself independent of experience but applies to objects given in experience. In other words the universal and the necessary are said of objects of experience; perhaps they are said of other things as well, but they are said of objects of experience. What is universal and necessary? What would these universals and necessaries be which can be said of objects of experience? Here is introduced a notion which is famous in philosophy, that of the category. A certain number of philosophers have even made or proposed what are called tables of categories. There is a famous table of categories in Aristotle. With Kant, who did not escape a strong influence from Aristotle, there will be another table of categories. What is a category? A category is not just anything in philosophy, it's as rigorous as a scientific notion in another domain. What is called a category is a universal predicate, or universal attribute if you want. Which is to say a predicate which is attributed to, or predicated of, or said of any object. This notion of "any object" is bizarre. I say "the rose is red". What is that? "The rose is red" is not complicated, it's a relation between two concepts, the rose and red, and if I say "what is universal or necessary in that?" I can reply: nothing. Not all objects are roses, not all roses are red. Not all reds are the colour of roses. I would say that there is an experience of the red rose and that this experience is particular, contingent, a posteriori like all experience.
Compare this judgement: "the rose is red" to this other judgement: "the object has a cause" or even "the rose has a cause".
I see a difference straight away, which is that the concept of rose defines what will be called a class in so far as it is an a posteriori concept, the concept of rose defines a class or set. Red is a property of a subset of this set, the subset formed by red roses. I can define a set according to what it excludes and in relation to what it excludes: all that is not a rose. The set of roses is carved out of a broader set which is that formed by flowers, and the set of roses can be distinguished from the rest, which is to say all the flowers which are not roses. When I say "all objects have a cause", am I not in another domain completely? Evidently I am, I am completely in a different domain because to have a cause is a universal predicate which is applied to all objects of possible experience, to the point that I don't even need to - or I believe that - but that makes no difference because "I believe" will become an act that we will have to analyse - I believe that if an unknown object emerged in experience before my eyes, this object would not be an object if it didn't have a cause. To have a cause or to be caused is a predicate of a wholly other type than the predicate "red". Why? Because the predicate "to be caused" - to the point where we can wonder, after reflection, is that really a predicate or is it something else? - the predicate "to be caused" is predicable of any object of possible experience, to the point where it is not going to define a set or a subset within experience because it is strictly coextensive with the totality of possible experience.
Moreover, we must go back. When I said that the totality of possible experience has perhaps no sense, now we have the response: the totality of possible experience makes no sense in itself, but it is precisely to the extent that there are predicates which are attributed to all possible objects, which are thus more than predicates, and this is what Kant will call conditions, they are the conditions of possible experience, it is thus via the notion of conditions of experience that the idea of a whole of possible experience will take on a sense. There is a whole of possible experience because there are predicates or pseudo-predicates which are attributed to all possible objects and these predicates are precisely what are called categories. I'll cite some examples of categories according to Kant: unity, plurality, totality (with Kant they come in threes).
Reality, negation, limitation.
Substance, cause, reciprocity.
I'll stop there. In what sense are these categories and not predicates of the type red, green, etc...? They are categories or conditions of possible experience for the simple reason that any object is only an object to the extent that it is conceived as one, but also as multiple, having the unit parts of a multiplicity, and in this forming a totality, any object whatever has a reality. On the other hand, it excludes what it is not: negation, and by virtue of this it has limits: limitation. Any object whatever is substance, any object whatever has a cause and is itself cause of other things.
That's enough to be able to say that my notion of object is made in such a manner that if I encountered a something which did not allow the categories be attributed to it, I would say that it is not an object.
So there we have as a last determination of the a priori, they are the conditions of possible experience, which is to say universal predicates as opposed to empirical predicates or a posteriori predicates.
I could define the categories in the simplest way as being the predicates of any object whatever. Thus you can yourselves make your list of categories according to your mood, according to your character... what would be good would be to see if everybody came up with the same list of categories. In any case you do not have the right to cheat with the word. To make your list of categories is for you to ask yourselves what is for me predicable of any object whatever. I have already given a certain list of them, with nine categories. In fact, for Kant, there are twelve of them, but I left three aside for later; you see: unity, plurality, totality, affirmation, negation and limitation, substance, cause, reciprocity or community.
To finish with this first point, I am saying that the categories, qua predicates of any object whatever, are a priori, and they are conditions of possible experience; understand that it is through them that the notion of possible experience takes on a sense.
To the question: does the whole of possible experience mean something? No meaning [sens] at all if we remain in an a posteriori approach, because in an a posteriori approach I am led to make an addition: the roses, the flowers other than roses, the plants which are not flowers, the animals, etc.... I could go to infinity like that and nothing tells me that I have a whole of possible experience. On the contrary, experience is fundamentally fragmented, it is opposed to a totalisation. If Kant launches this very very new notion of a totality of possible experience it is because he is in a position to define, to say: yes, there is a level where the whole of possible experience takes on a sense, it is precisely because there are universal predicates which are attributed to all things, which is to say are attributed to any object whatever. Thus it is a priori that the notion of the totality of possible experience will be founded.
Is there anything else besides the categories that can be a priori, which is to say, universal and necessary? The reply is yes, and this other thing is space and time. Because every object is in space and in time, or at least in time. But you will say to me straight away, very well then, why not make a category of them, why not add space and time as two categories? Because space and time are also, it seems, predicates. Obviously, Kant has the most serious reasons to not want to and he will go to great pains to distinguish the categories on the one hand, and on the other hand space and time. There will thus be two sorts of a priori elements: the categories and space and time. Why doesn't he want space and time to be among the categories? I will give a reason very quickly which will become clear afterwards: it is that the categories qua predicates of possible experience are concepts, whereas Kant fundamentally holds that, these are a priori representations, a priori representations or concepts, while space and time are presentations. There you also have something very new in philosophy, it will be Kant's work to distinguish presentation and representation. So there will be two sorts of elements in the a priori.
My second point is Kant's importance at another level, which is the notion of phenomenon, and that also is very important. There Kant operates a kind of essential transformation of a word which was frequently employed previously in philosophy. Previously philosophers spoke of phenomenon to distinguish what? Very broadly we can say that phenomenon was something like appearance. An appearance. The sensible, the a posteriori, what was given in experience had the status of phenomenon or appearance, and the sensible appearance was opposed to the intelligible essence. The intelligible essence was also the thing such as it is in itself, it was the thing in itself, the thing itself or the thing as thought; the thing as thought, as phenomenon, is a Greek word which precisely designates the appearance or something we don't know yet, the thing as thought in Greek was the noumenon, which means the "thought". I can thus say that the whole of classical philosophy from Plato onwards seemed to develop itself within the frame of a duality between sensible appearances and intelligible essences. You can see clearly that this already implies a certain status of the subject. If I say that there are appearances and that there are essences, which are basically like the sensible and the intelligible, this implies a certain position of the knowing subject, namely: the very notion of appearance refers to a fundamental defect in the subject. A fundamental defect, namely: appearance is in the end the thing such as it appears to me by virtue of my subjective constitution which deforms it. The famous example of appearance: the stick in water appears broken to me. It's what is called the rich domain of sensory illusions. So much so that in order to reach the thing in itself the subject must in fact overcome this sort of constitutive infirmity which makes it live amongst appearances. It's Plato's theme: leave appearances to find essences.
With Kant it's like a bolt of lightning, afterwards we can always play clever, and even must play clever, with Kant a radically new understanding of the notion of phenomenon emerges. Namely that the phenomenon will no longer at all be appearance. The difference is fundamental, this idea alone was enough for philosophy to enter into a new element, which is to say I think that if there is a founder of phenomenology it is Kant. There is phenomenology from the moment that the phenomenon is no longer defined as appearance but as apparition. The difference is enormous because when I say the word apparition I am no longer saying appearance at all, I am no longer at all opposing it to essence. The apparition is what appears in so far as it appears. Full stop. I don't ask myself if there is something behind, I don't ask myself if it is false or not false. The apparition is not at all captured in the oppositional couple, in the binary distinction where we find appearance, distinct from essence.
Phenomenology claims to be a rigorous science of the apparition as such, which is to say asks itself the question: what can we say about the fact of appearing? It's the opposite of a discipline of appearances. What does an apparition refer to? The appearance is something that refers to essence in a relation of disjunction, in a disjunctive relation, which is to say either it's appearance or it's essence. The apparition is very different, it's something that refers to the conditions of what appears. The conceptual landscape has literally changed completely, the problem is absolutely no longer the same, the problem has become phenomenological. For the disjunctive couple appearance/essence, Kant will substitute the conjunctive couple, what appears/conditions of apparition. Everything is new in this.
To make things a little more modern, I would just as well say: to the disjunctive couple appearance/essence, Kant is the first who substitutes the conjunctive couple apparition/sense, sense of the apparition, signification of the apparition. There is no longer the essence behind the appearance, there is the sense or non-sense of what appears. Grant me at least that even if what I say remains just a matter of words, it's a radically new atmosphere of thought, to the point where I can say that in this respect we are all Kantians.
It's obvious that thought, at that time, was changing elements. People had for a long time thought in terms which didn't come from Christianity but which fit in very well with Christianity, in the appearance/essence distinction, and towards the end of the eighteenth century, prepared no doubt by all sorts of movements, a radical change takes place: for the whole appearance/essence duality which in a sense implies a degraded sensible world, which even implies if need be original sin, is substituted a radically new type of thought: something appears, tell me what it signifies or, and this amounts to the same thing, tell me what its condition is.
When Freud comes up and says that there are certain phenomena which appear in the field of consciousness, what do these phenomena refer to, Freud is Kantian. How so? In a way that is at the same time very general but also very rigorous, namely that, like all those of his era and since Kant we spontaneously think in terms of the relation apparition/conditions of the apparition, or apparition/sense of what appears, and no longer in the terms of essence/appearance.
If you don't see the enormity of the reversal, admire the fact that the subject, in my second couple, the subject is not at all in the same situation. In the disjunctive couple appearance/essence, the subject is immediately condemned to grasp appearances by virtue of a fragility which is consubstantial with it, and the subject requires a whole method, it needs to make a whole effort to get out of appearances and reach the essence. In the other case, what makes the subject take on an entirely different value? It's when I say that every apparition refers to the conditions of the appearing of the apparition, in this very statement I am saying that these conditions belong to the being to whom the apparition appears, in other words the subject is constitutive - and understand this well, otherwise it's a radical misinterpretation - the subject is constitutive not of the apparition, it is not constitutive of what appears, but it is constitutive of the conditions under what appears to it appears to it.
I mean that the substitution of the conjunctive couple phenomena-conditions, or apparitions-conditions ensures a promotion of the subject in so far as the subject constitutes the very conditions of the apparition, instead of constituting and being responsible for the limitations of appearance, or the illusions of appearance. There is indeed a subject, Kant will say, which is subordinated to appearances and which falls into sensory illusions; it will be called the empirical subject, but there is another subject which is evidently neither you nor me, which above all is not reducible to any empirical subject, which will be from that point on named the transcendental subject for it is the unity of all the conditions under which something appears, appears to whom? Appears to each empirical subject. It's already beautiful as a system of ideas. I hope you can feel its extent, it's a tremendous machine.
To finish this second point, I'll make two corrections: Kant is at the turning-point of something, so it's more complicated than I'm making it out to be because he keeps something of the old essence-appearance difference, and effectively he will say all the time: do not confuse the phenomenon with the thing in itself, the thing in itself is the pure noumenon, which is to say it is what can only be thought, while the phenomenon is what is given in sensible experience. So he maintains the disjunctive duality phenomenon/thing in itself, noumenon. It's the duality of the couple appearance/essence. But he gets out of it and he is already in another type of thought for a very simple reason for he says that the thing in itself, it is so by nature or the noumenon - the thing in itself can be thought, it is thus noumenon, but it cannot be known. So if it can be determined, it is a completely different point of view than that of knowledge; so we don't bother with it or at least we will bother about it in very special conditions.
What counts from the point of view of knowledge and of all possible knowledge is the other couple, apparition-conditions of appearing, conditions of the fact of appearing.
Once again if I sum up this reversal it's the one which consists in substituting for appearance-essence, apparition-conditions or apparition-sense of the apparition.
If you ask me what these conditions of appearing are, fortunately we have got somewhere because our first point gave the answer, the conditions of appearing, which is to say the conditions of the phenomenon, in so far as the phenomenon is what appears, we will not look for an essence behind the phenomenon, we will seek the conditions of its apparition, and in fact the conditions of its apparition are, the categories on one hand and on the other space and time.
Everything which appears appears under the conditions of space and time, and under the conditions of the categories. By this fact space and time on the one hand and on the other the categories are the forms of all possible experience and they belong not to things as they are in themselves, but as forms of all phenomena, as forms of all apparition, space and time on the one hand, the categories on the other hand are the dimensions of the transcendental subject. Time is already completely involved here. Are there any questions?

Richard: How is the difference between the transcendental subject and the empirical subject distributed? How is it very different from the domain of being?

Gilles: Obviously he needs another notion. We start from the idea: phenomenon equals apparition. The phenomenon is not the appearance behind which there would be an essence, it's what appears in so far as it appears. I can add that it appears to someone, all experience is given to someone. All experience is related to a subject, a subject which can be determined in space and time. It's here and now that I put my little saucepan on to boil and light the fire. I would say that all apparition appears to an empirical subject or to an empirical self. But all apparition refers not to an essence behind it but to conditions which condition its very appearing. The conditions of the apparition - these are thus forms since apparitions appear in these forms, or under these forms - the conditions of the apparition are space and time and the categories. In other words space and time are the forms of representation of what appears.
Given this if the apparition presupposes conditions which are not like objective essences behind it, but are like the conditions of its apparition to a given empirical self, we already have no more choice: the formal conditions of all apparition must be determined as the dimensions of a subject which conditions the appearing of the apparition to an empirical self, this subject cannot itself be an empirical self, it will be a universal and necessary self. It's for this subject that Kant feels the need to forge or to extend a word which only had a very restrained theological use till then, thus the need to invent the notion of the transcendental, the transcendental subject being the instance which the conditions of all apparition are related to, while the apparition itself appears to empirical subjects. That doesn't tell you yet very well what the transcendental subject is, you'll have to wait because it will be so involved with the problem of time.
We just need for one little thing to suddenly become concrete, we mustn't demand continuous concreteness. There is the concrete and the opposite of the concrete, the true opposite of the concrete is not the abstract, it's the discrete. Discretion is the moment of thought. My aim is to arrive at a fabulous conception of time.

Comptesse: inaudible comment

Gilles: The synthetic a priori was my third point. We have to begin somewhere. If I had begun there I would have needed a completely different organisation. Quite simply it seems to me that in all I have said I have not needed to assume synthetic judgements. Third point: what is a synthesis for Kant?
It is common to distinguish two types of judgements. Judgements which are called analytic and judgements which are called synthetic. By definition, a judgement is called analytic if it expresses a predicate which is already contained in the subject, i.e. there will be an analytic relationship between two concepts when one of these concepts is contained in the other. An example of an analytic judgement: A is A, it's the principle of identity. When I say "A is A" I don't go outside of concept A. I predicate A of itself, I attribute A to itself, I'm in no danger of making a mistake. "Blue is blue", you will say to me that that doesn't go very far, it's obvious... because when I say "Bodies are extended" what is that? We want to reply that it's an analytic judgement. Why? Because I couldn't have thought the concept "body" - we're not saying "thing" - without having already included the concept of extension, thus when I say "Bodies are extended" I am formulating an analytic judgement. I think Kant would say something very malicious like: OK all bodies are extended is an analytic judgement, but on the other hand "all phenomena appear in space or in extension" is a synthetic judgement because if it is true that the concept "extended" is in the concept "body", on the other hand the concept "extended" is not in the concept "phenomenon" nor the concept "body" in the concept "phenomenon". Well, let's suppose that "all bodies are extended" is an analytic judgement. At least we can be sure of one thing which is that an analytic judgement is perhaps useless but it's true. "A is A" is true, no one has ever denied "A is A". In Hegelian-style dialectical contradiction no one says "A is not A", they say "A is not non-A", but just that a thing includes in its being this non-being that it is not. So they take seriously the formula "A is not non-A" in saying that the being of the thing is inseparable from the negation of the negation (is not...not), but they don't deny at all the principle of identity.
In experience we have synthetic judgements, it's even in this way that we know things. When I say "Oh look, the rose is red", it's an encounter. "Red", at first glance is not contained in the concept of rose, the proof is that there are roses which aren't red. You will say that this is stupid because isn't "red" contained in the concept of this rose here? It gets complicated because is there a concept of this rose here, is there a concept of the singular? We'll leave that aside. We will say very broadly that, apparently, "the rose is red" is a synthetic judgement. You can see how this sorts itself out. All analytic judgements are a priori, it's independently of any experience that I can say that a thing is what it is. "A is A" is an a priori judgement. Still at first glance, the synthetic judgement seems by nature to be the combination of two heterogeneous concepts, the rose and the red, it establishes a link or a synthesis between two heterogeneous concepts and is by virtue of this a posteriori. The form of this judgement is "A is B". In a certain way, I'll just say very quickly, classical philosophy before Kant, just as I was saying a moment ago, is caught in the dualist couple, in the disjunctive duality essence/appearance, classical philosophy was caught, at least in appearance, in a certain duality: either a judgement is a priori and it is analytic, or it is synthetic and it is empirical or a posteriori.
It became very complicated to know in what conditions an empirical judgement could be true. There is a famous and very prodigious attempt, Leibniz' attempt, before Kant. In order to found the notion of truth, he is led to try and show that all judgements are analytic, we just don't know it, we believe in the existence of synthetic judgements because we never take the analysis far enough, which is to say to infinity, it's because of this that we believe that there are synthetic judgements. But if we could take the analysis far enough, when we truthfully affirm one concept of another, the affirmed concept is always interior and contained in the one we affirm it of, to the point that - this gives Leibniz' famous theses - Caesar crossed the Rubicon, this proposition which seems eminently to be a synthetic proposition, implies the link between two representations: Caesar crosses the Rubicon on such and such a date, at such a point in space, here-and-now, which seems to be the very signature of the a posteriori, Leibniz says that if in the concept of Caesar there was the concept "crossing the Rubicon"... is it any accident that it's the same man who is one of the creators of differential calculus, which is to say a mathematical form of infinite analysis? Evidently not, it's not an accident. What does he mean when he manages to treat "crossing the Rubicon" as a predicate which is contained in the concept Caesar exactly as "extended" is contained in the concept body? Obviously he too will have to engage in a quite astonishing sort of gymnastics of concept-creation, because afterwards he will have to save freedom, he holds to this for his own reasons, so how can Caesar be free when from the beginning of time "he crossed the Rubicon here and now" is included in his concept? And what does such a proposition of Leibniz's imply, namely: there are only analytic judgements? That necessarily implies that space and time, the here-and-now be reducible and reduced to the order of concepts. Spatio-temporal position will be treated as a predicate, which is to say as an attributable concept.
Why does Kant hold so fiercely to the heterogeneity of space and time on the one hand, and on the other hand the categories, i.e. a priori concepts. Precisely because he needs there to be something which is irreducible to the order of the concept.
Classical philosophy is a long discussion between the respective proportion of a posteriori synthetic judgements and a priori analytic judgements. The possibility of reducing one to the other, or else the impossibility of reducing...

Richard: How is it that we don't manage to derive the principle of identity from experience? In the example "A is A".

Gilles: Because it's a pure empty form, A is A. A is not at all given as a generality, it's pure thought, it's generic thought. Moreover, as soon as there is an identity in experience, it's a temporal identity, which is to say that it's not a necessary identity. So "A is A" is said to be a priori precisely because it is strictly without content, it will be a rule for all possible content.
So now Kant comes along and everything happens as if he discovered a new type, a third type of judgement, and he will have to invent the concept to designate this third type of judgement, namely synthetic a priori judgement. In doing so he effects an amazing forced takeover [coup de force]. For a classical thinker, still very broadly, analytic a priori judgement, that meant something, synthetic a priori judgement, that meant something, but synthetic a priori judgement - that's truly a monster. So a philosopher cannot but create monsters as new concepts. It's a prodigious monster. What on earth can it mean? Here I will use some examples which aren't even in Kant, in order to be more faithful, to try and be clearer than he is, because he has other things to do.
The triangle is white. If I blithely ask you what that is you will reply it's a synthetic a posteriori judgement. I'll reply: very good, you've passed the course. If I say "we call triangle a figure formed by three straight lines enclosing a space", three straight lines enclosing a space, what is that? I can say that it is an analytic judgement. Why? Because I'm not saying anything but "A is A". The concept of triangle is precisely three straight lines enclosing a space. This was broadly the distribution in the world of classical philosophy, the terminological coordinates of classical philosophy. Kant comes along and says: if I say that the three angles of a triangle are equal to two right-angles - elementary geometrical proposition - what is that? Is it an a priori analytic judgement or an a posteriori synthetic judgement? Stunned silence! And yet this was something everybody had known for a long time, but nobody had used this case to explode the insufficiency of certain philosophical categories, the a priori analytic judgement and the a posteriori synthetic judgement. Here he is in the process of finding something which really appeals to the taste of philosophy qua philosophy, namely the simplest thing in the world which bursts a conceptual frame. In effect this story is very curious: the three angles of the triangle are equal to two right angles. It is the very example of what is called a geometrical necessity. It's universal and necessary, and yet is it analytic?
As for Leibniz, he would have laughed at Kant's observation, this is why philosophy is so good. Leibniz's simple reply is: yes of course the concept of the triangle, if you take the analysis far enough, it's obvious that its angles being equal to two right angles is contained in the concept. But again, under what condition can Leibniz say that? Because he has also invented a mathematical discipline which he has determined as already being a topology, and which allows a sort of reduction of spatial determinations to conceptual ones. But under what condition?
Kant began by noting the impossibility according to him of reducing spatio-temporal determinations to conceptual ones. In other words, there is an order of space and time which is irreducible to the order of the concept. So Kant: I say that [the equation of] the three angles of the triangle is so little contained in the concept that to demonstrate it you have to extend a side of the triangle, raise a parallel on the opposite side... already Leibniz would say that he doesn't agree, and he would be right because if he accepts something here he would be screwed, but we'll let it go, we'll go along with this attempt of Kant's. So here is my concept: three straight lines enclosing a space. To demonstrate the equality of three angles to two right-angles, I take for example the base of the triangle and I extend it; at point C I raise the parallel to AB and I show that the three angles of the triangle are equal to two right-angles. Kant tells us we mustn't get carried away, the side didn't grow all by itself, the triangle is not a flower, it doesn't raise a parallel to one of its sides all alone, parallel to a side of the triangle isn't part of the concept of the triangle thus it's a synthetic judgement. But it's a very curious type of synthetic judgement, not at all of the "the rose is red" type, since it's a universal and necessary synthetic judgement. How are you going to explain such a judgement?
I'll take another example. "The straight line is black". Everyone understands, no problem: synthetic a posteriori judgement; I encounter it in experience, which is to say I come across a straight line which has been drawn in black. I take Euclid's definition: "The straight line is the line which is ex aequo in all its points", it doesn't matter if you use another definition. In any case, I would say that it's an analytic judgement, it's already contained in the concept of the straight line, it's even the statement of the concept of straight line. And then comes the monster, I say: "the straight line is the shortest path between two points." Is it analytic, can I say that the shortest path is contained in the concept "straight line"?
Once again, Leibniz would say: yes. Kant says no. Why? For several reasons. I'll give a vulgar reason and a scholarly reason. The vulgar reason: if one looks very closely at "the shortest", is it a predicate or an attribute? It's a question of diagnostics. Is it something else? When I say "the straight line is the shortest path", it's bizarre, is "the shortest" an attribute? If you managed to demonstrate that it's an attribute, it would be via a very complex route. It wouldn't be an attribute because "the shortest"... I'll try putting it another way: if you want to find the straight line, take the shortest, what does that mean? The shortest appears to be a predicate, but it's not a predicate. In fact, it's a rule of construction. It's the rule according to which I produce in experience a line as a straight line. You will say to me; we still have to know what "the shortest" is... the shortest is not a predicate that I attribute to the straight line, it's a rule of construction for constructing straight lines in experience in order to determine a line as straight. We find this example in one of his disciples, Salomon Maïmon, a great, great philosopher. So the shortest is the rule of construction of the line as straight, it's the means of producing in experience a line as a straight line. What does that mean?
It's obvious that a concept does not give the rule of construction for its object. In other words, the rule of construction is outside the concept. Once again Leibniz would say "not at all"; if he admitted that his whole system is screwed. At first glance the rules of construction are something very different from concepts because the rule of construction is the rule according to which one produces in experience an object which conforms to the concept. It's thus obligatory that it's not in the concept, by definition. You say: "the circle is where points are situated at an equal distance from a common point named centre", that is the concept of circle, that doesn't give you any means of producing a circle. We are already at the heart of the problem of time. When you say that a straight line is a line ex aequo in all its points, you have no means of producing a straight line in experience, you still need a rule to produce a line that is ex aequo in all its points, you still need a rule of construction to produce a figure such that it presents points situated at an equal distance from a common point named centre. And when you have said that the triangle is three straight lines enclosing a space, you have no means of producing a triangle in experience. The rule of construction of a triangle will be something else completely which will go via the circle, by the way. To produce a triangle you have to go via the circle. It's bizarre.
What does Kant mean when he says it's a judgement of a synthetic kind? In effect you will define the rule of construction of a triangle by saying that if you give me a segment of a straight line - it assumes the straight line, that goes without saying, and the means of producing the straight line -, if you give me a segment of straight line, if the two end-points are taken as the centre, whether of the same radius or varying radii, if the two circles cross, if you link the two ends of the straight line to the point where the circles cross, if the circles are of equal radius, this triangle will be called equilateral. (correction: if the radius is equal to the circle). There, I have a rule of construction.
You see that there is something amazing in the a priori synthetic judgement, it's that instead of operating a synthesis between two heterogeneous concepts, it operates a synthesis between the concept, between a conceptual determination, the triangle or the circle, and a group of spatio-temporal determinations. In effect, a rule of construction is a spatio-temporal determination. Why is it a synthesis? We have seen it, the rule of construction fundamentally relates heterogeneous concepts. Where does this power of necessarily relating heterogeneous concepts come from, since the only way we thought that heterogeneous concepts could be linked was through the contingency of experience: ah yes, this rose is red. But when I say that the straight line is the shortest path, I claim to be saying something necessary, in this sense a priori, it's geometrical necessity; it doesn't depend on experience. It is said of experience, I can check on any straight line that it is in fact the shortest path, but I don't need to. I know it from the first time, I know it at the same time that I understand the judgement. I know that it is necessarily and universally valid for all straight lines.
... namely what underlies the necessary relation between the concepts is a group of spatio-temporal determinations by which one of the concepts is put into a necessary relation with the other.
At this point my scholarly reason comes in. When I say "the straight line is the shortest path between two points", at first glance I don't see how that gives me the means to construct a straight line, but in fact, those who were here other years will remember that I had tried to show something quite obvious in geometry. Namely that "the straight line is the shortest path between two points" is not a Euclidean-style proposition, it's an Archimedean-style proposition because it implies a fundamental comparison between two heterogeneous concepts, that of the straight line and that of the curve. In effect, "the straight line is the shortest path between two points" only has a meaning in the very precise situation of the arc of a circle and the chord. In other words, it implies the method "the straight line is the shortest path between two points", it's what would be called an already pre-differential proposition referring to a pre-differential calculus which is the famous calculus of Archimedes, the calculus of exhaustion by which one stretches a broken line towards a curved line, to infinity, it implies the passage to the limit. That is why the straight line is the shortest path between two points even though the curve is not stated explicitly, the concept of the curve is not named. This judgement is devoid of sense if we don't see that it effects a synthesis between two concepts, the straight line and the curve, that it's uniquely in the comparison between the straight line and the curve in the very precise Archimedean situation that this judgement is expressed, with the passage to the limit and exhaustion, and that Kant's response on this level is: you can clearly see that it's not an analytic judgement because two heterogeneous concepts are... just as in the example of triangles, once again in order to demonstrate the equality of three angles to two right-angles, you have to erect a parallel, but the parallel is a concept exterior to the triangle. What welds these heterogeneous concepts together in the synthetic a priori judgement? Solely an operation which consists this: being a determination of space and time.
It's the determination of space and time, for example in the figure of the circle's arc and the chord, in the elevation of the parallel to one side of the triangle, it's this spatio-temporal determination which will make possible the necessary link between these concepts which are nevertheless not contained in each other, i.e. you will have at that moment a synthetic a priori judgement.
What are Kant's reasons for telling us that space and time are not reducible to categories, that is, that there are two sorts of a priori forms: space and time on the one hand, the categories on the other hand, or if you like space and time are irreducible to the order of concepts. He gives lots of reasons, but he invites us to engage in at least one thought-experiment, as it's the simplest it's the one I'll give you. He says, you see two hands, it's the paradox of non-superimposable symmetrical objects. You see two hands, not only do you see two hands but you think two hands. Let's suppose that, in reality, there are never two hands, there are always little differences, prints, traits, from the point of view of thought that is of no interest, you can always say that there are no two things alike. But you can still think, you can still represent to yourself two absolutely identical hands. Note that if I make Leibniz speak from off-stage, he would say: not at all, you believe you think it, but you can't think it, you've just stopped the concept. But we will accept this sort of dare of Kant's.
So you can think two hands which are strictly identical in their concept. And however far you go in the concept, in the characteristics of the concept and you can even think that such a line is on each. And yet... Leibniz would say: OK maybe, but if you do that you will see that there remains only one hand. Kant says that there is something irreducible in them. Kant says that he can think two strictly identical hands and that there are nevertheless two of them. They are strictly identical in their concept, each characteristic of the one has its identical correlate in the other. And yet there are two of them. And why are there two? One is the right hand, the other is the left. Or else one is before and the other is after or behind. How can that be thought, in the two strictly identical hands, that one is on the right and the other on the left? You know that however well they can be thought as identical in each of their characteristics, they are not superimposable. They are absolutely symmetrical in their smallest details and yet they are not superimposable. Kant will say that that's what finitude is.
That's what the irreducibility of space and time is. The right, the left. Here-now. Before, after. You can conceive of two objects whose concept is strictly the same, there are still two objects, for this very reason that the one is here and the other there. One is on the right, the other on the left, one is before, the other is after. There is a spatio-temporal order irreducible to the conceptual order.
But Kant doesn't invoke that reason. He also gives this famous example: two like trihedrons, opposed at their vertex, you cannot make them coincide. Why is it that you can't make them coincide? Because superimposing two figures or making them coincide implies a rotation, a rotation in a dimension that is supplementary to the figure's number of dimensions. When you have two triangles opposed at the vertex, you can make them coincide, which is to say put one on the other by making one of the triangles undergo a rotation in the third dimension. You have in that case a supplementary dimension to the dimensions of the figure. When you come to volumes, i.e. three-dimensional figures, like the two hands or the two trihedrons opposed at the vertex, you can easily make the two hands superimpose on each other if you have a fourth dimension of space. You would effect the rotation in the fourth dimension. Finitude is the fact that space irreducibly has three dimensions and not n dimensions, or that time has one dimension. We could always be told that there are theories or spaces with n dimensions, or else that time has several dimensions. I think that there's little interest in such a thing because the idea of a space with n dimensions already implies a system of problems and concepts which have nothing to do with Kant's system of concepts and problems.
Why are space and time irreducible to the order of the concept?
It's because spatio-temporal determinations don't allow themselves to be reduced to conceptual determinations, to the extent that however far you take the identity of two concepts, the corresponding thing or things will always be able to be distinguished not only by contingent a posteriori characters, but by their situation in space and time. By their position in space and time. Spatio-temporal position is not a conceptual property.
In which case we are assured of the following principle that the a priori synthesis happens less between two concepts, it doesn't happen between two concepts because in the first place, because it happens between the general concept on the one hand, and the spatio-temporal determination on the other hand. The true a priori synthesis is not between concepts like the empirical synthesis, the true a priori synthesis goes from the concept to the spatio-temporal determination, and vice-versa. That is why there can be a priori syntheses between two concepts, because space and time have woven a network of determinations which can make two concepts, however different they are, from the moment that there are rules of production, form necessary relations with each other. Thus space and time will acquire a constitutive power [pouvoir] which will be the constitutive power of all possible experience.
To better mark the difference between the order of the concept and the spatio-temporal order, I'll return to terms that I used just before. Space and time are the forms of appearing, or the forms of presentation of what appears. In effect, we can understand this because space and time are indeed a form of appearing, but they contain no specific unity. What appears is always diverse, an apparition is always an apparition of diversity: the red rose, a smell, a colour etc. So what appears is, by nature, diverse. Space and time are forms of perception, but you can see that space and time themselves have a diversity, namely the diversity of "heres" in space, any point in space being a possible "here", and the diversity of moments for time, any point in time being a possible moment.
We have thus to distinguish the diversity of what appears in space and in time and the diversity of space and time themselves. The first diversity will be said to be empirical diversity, the second diversity, the diversity of space itself or of time itself will be a priori diversity. Diversity of space. Diversity of time. The a priori diversity of space and of time constitute the forms of presentation. By contrast, empirical diversity belongs to what appears. The categories or concepts, which we have just seen are of another order than space-time determination, have a unity, it's even the function of the concept to unify a diversity. To the extent that you can in fact sense that the concept will have to bear, in a certain way, on space and time. Space and time as the forms of appearing of what appears are what Kant calls Forms of Intuition. Intuition is precisely the presentation, intuition is the immediate. Phenomena are immediately in space and in time, which is to say immediately appearing in space and in time. Space and time are the forms of immediacy. The concept is always what we call a mediation. The concept refers to the concept and it effects a unification. It is in this sense that it is not simply a form of presentation of what appears, it will be a form of the representation of what appears. The prefix re- indicates here the activity of the concept in opposition to the immediate or passive character of space and time which are given or which are the form of what is given.
Space and time are, Kant says, the form of our receptivity, while the concept is the form of our spontaneity or our activity.
What incredibly new thing does Kant bring to the history of time? Once it is said that determinations of space and time are irreducible to conceptual determinations, there would be no possible knowledge unless nevertheless and despite everything we were able to establish a correspondence between spatio-temporal determinations and conceptual determinations, and that's the sort of miracle of knowledge. And Kant constructed his whole system of new concepts to get to that point.
He's an austere philosopher, a severe philosopher, he uses all sorts of complicated words but they're never just for effect, he's not a lyrical type. I refer you to his secretaries who wrote things about his life, he has a very calm life, very ordered? Thomas de Quincey has translated and somewhat arranged, embellished the accounts of Kant's secretaries, in "The Last Days of Immanuel Kant". It's a splendid text.
There is an formula, a first formula about time which seems to me to be one of the most beautiful things said about time, it's Hamlet who says it. The formula suits is so well: "the time is out of joint". It's beautiful! It's a very beautiful formula if we understand it. What is the joint? The joint is, literally, the hinge [pivot]. The hinge is what the door pivots around. But the door? we have to imagine a revolving door, and the revolving door is the universal door. The door of the world is a revolving door. The door of the world swings and passes through privileged moments which are well known: they're what we call cardinal points. North, South, East, West. The joint is what makes the door swing in such a way that it passes and re-passes through the privileged co-ordinates named cardinal points. Cardinal comes from cardo; cardo is precisely the hinge, the hinge around which the sphere of celestial bodies turns, and which makes them pass time and again through the so-called cardinal points, and we note their return: ah, there's the star again, it's time to move my sheep!
"The time is out of joint", time is no longer coiled up in such a way that it is subordinated to the measure of something other than itself, such as, for example, astronomical movement. Time has ceased to be the number of nature, time has ceased to be the number of periodical movement. Everything happens as if, having been coiled up so as to measure the passage of celestial bodies, time unrolls itself like a sort of serpent, it shakes off all subordination to a movement or a nature, it becomes time in itself for itself, it becomes pure and empty time. It measures nothing anymore. Time has taken on its own excessiveness. It is out of its joints, which is to say its subordination to nature; it's now nature which will be subordinated to it. I can say, going quickly, that the whole of ancient philosophy maintained a subordination of time to nature, even in its most complex forms; that classical philosophy, however complicated its conceptions of time were, never put into question this very very general principle. The famous definition: "time is the number of movement".
With Kant there is an indescribable novelty. It's the first time that time is liberated, stretches itself, ceases to be a cosmological or psychological time, whether it's the world or the soul makes no difference, to become a formal time, a pure deployed form, and this will be a phenomenon of extreme importance for modern thought. This is the first great Kantian reversal in the theory of time.
So I take Hamlet's formula literally to apply it to Kant: "the time is out of joint". It's with Kant, from the point of view of the concept of time, that we can effectively say that time is out of joint, which is to say has ceased to be subordinated to the measure of movement, and on the contrary movement will be completely subordinated to it. And time will be this sort of form which is also pure, and this kind of act by which the world empties itself, becomes a desert. This is why one of Kant's best disciples - it won't be a philosopher, we never find those who understand philosophers among philosophers - is Hölderlin, and Hölderlin who, drawing on Kant against the Kantians, understood by developing a theory of time which is precisely the pure and empty form in which Oedipus wanders.
Next time I would like to see what the formula "the time is out of joint" means, applied to Kant. It really means something quite literal.
The second formula that I want to develop truly belongs only to Kant and it is part of his last, most obscure texts. Kant, at the end of his life, compiles a book which will appear after his death. He begins a sketch of something which will be called the Opus Postumum. And the Opus Postumum is very strange because it's a mix of everything. There are laundry lists, there are little impressions of everyday life, and then there is a wonderful page. In these texts near the end the idea that time is like the form of auto-affection appears more and more. It's the form under which the subject affects itself. If anything is mysterious, that is. It would be clear for space, but he also says it of time. See how he divides things up: space is the form under which something exterior affects me and time is the form under which I affect myself. It's even more mysterious than "the time is out of joint".
They're Kant's three oracles: firstly disguised as Hamlet, time is out of joint, secondly disguised as himself he says time is the form of auto-affection, the form under which I affect myself. But why does he say that? He couldn't do otherwise. If you followed the first point, time is out of joint, it no longer measures a movement, it is no longer subordinated to nature. Already, on the most basic level it's very new. What is new with someone must already be grasped on the most basic level. Before him, what did they say, very broadly. With Leibniz no problem, time is the order of possible successions, space is the order of possible coexistences. Kant wants nothing of this and can no longer accept it. The whole way in which he has posed the problem means that he cannot: it's obvious that to define time by the order of possible successions implies, at first glance, a subordination of time to a content which measures it, a content to which it is subordinated. It must be the case that time is subordinated to succession. So once he has conceived of formal time, the pure form of time detached from a movement to measure, once he has straightened time, once he has let it go like a spring, he can no longer define it by an order of succession. It's all the more significant given that to define time as succession means nothing but - of course succession is temporal, but it's only a mode of time, as coexistence or simultaneity by which we claim to define space, is another mode of time, it's not space. It's a very bad distribution. Space cannot be defined by the order of coexistence since coexistence is an idea which can only be understood in relation to time, it means at the same time. Time cannot be defined by succession because succession is only a mode of time, coexistence is itself another mode of time. You can see that he arranged things to make the simple distribution: space-coexistence, and time-succession. Time, he tells us, has three modes: duration or permanence, coexistence and succession. But time cannot be defined by any of the three because you cannot define a thing through its modes. Moreover space cannot be defined as the order of coexistence since coexistence is a mode of time. He is very very good on this point.
He will say - and I want you to admire the simplicity - you will define space as simply the form - and above all not the order since order still refers to a measure of something to measure in time - as the pure form, of what? Space is the form of exteriority. That doesn't mean that it comes from outside, but it means that everything which appears in space appears as exterior to whoever grasps it, and exterior from one thing to another. It is not exteriority which ???? space, it's space which constitutes the form of exteriority or which constitutes exteriority as form, as pure form. As he has just defined space as the form of exteriority, it must be the case that time is the form of interiority. It's the form under which we affect ourselves, it's the form of auto-affection. Time is the affection of self by self.
I ask you to consider that this second point follows from the first.
So, the first paradox is what does it mean that time is out of joint; the second is what does it mean that time is the form of interiority.




Why wouldn't there also be a synthesised or electronic way of handling philosophy?

Last time I tried to determine a certain number of very precise Kantian notions: a priori, synthesis, etc... but very much as a function of what seemed the essential thing to me, namely a radical reversal in the position of the problem of time in relation to philosophy. It's a critical reversal, like a critical point.
I proposed last time that we take as three arbitrary formulae, but it's very dangerous, but never mind there are three key formulae that aren't Kant's but under which, it seems to me, the three great novelties or the three great reversals that Kant operates on the notion of time group themselves.
So if we can manage to eliminate everything that is facile in this evocation of literary formulae in relation to a conceptual study of philosophy, the first formula to which Kant would give a powerful content is that of Hamlet: the time is out of joint. The second formula is anonymous, and would be something like this: till now the task we have given ourselves was to represent space, the moment has come to think time. Third famous formula, given by an author who had nothing to do with Kant: "I is an other". I believe that if we separate these expressions from their contexts, they suit Kant admirably, if you take them as abstract declarations. Maybe that will allow me to understand in itself the formula "I is an other", as well as to understand in itself the formula "the time is out of joint".
I have asked Gilles Châtelet to bring a contribution to the commentary of this first formula. So I'm taking us back to the level of the first formula "the time is out of joint", how is it that Kant's philosophy posits a time which is in the process of getting out of joint. The joint was this sort of pivot around which time turned, in other words, in a certain tradition of antiquity, time is fundamentally subordinated to something which happens in it, and this something can be determined as being change, the subordination of time to change, time will thus measure the changing of what changes, or else, which amounts to the same thing on another level, it will be subordinated to movement, the subordination of time to movement, I say that that amounts to the same thing on another level because movement qua local movement is the purest form of change, which is to say the perfect form of change; that goes back to things in Aristotle and which cover the whole of Greek philosophy. Or else, which again amounts to the same thing on another level, subordination of time to the course of the world, and it's in this sense that the classical definition of the Greeks appears: time is the number of movement. What does that imply?
That implies a subordination of time to change, to movement, to the course of the world. That implies that time is as if bent, it becomes circular. It is a time, independent or not of questions of the eternal return which are posed in a completely different manner, time is cyclical. And indeed, to the extent that it is the number of movement, it will measure the movement of the planets - see all of Plato's prose writings on the eight movements of the eight planets - and the great circle that will measure the time it takes for the eight planets to come back to the same respective position, the eight circles of the world, you would have thus a great circle of circles whose point would be assigned by the planet's return to the same respective position, you would have the world's year. But this time become circular is but one with time subordinated to change, to movement, and to the course of the world, and it's the great idea which runs through all of ancient philosophy: time as the image of eternity. The circle of time, in so far as it measures planetary movement, and the return of the same, it's precisely this time become circular. In the Timaeus there were some very beautiful pages on the arc of the Demiurge which makes circles, this bending activity.
However, this time as an image of eternity, the cyclical figure of time subordinated to movement and whose secret will be the periodic return of planets to the same position relative to each other, is indeed a time which is the image of eternity. I would say that all of the time of antiquity is marked by a modal character, and in effect the word appears all the time: time is a mode and not a being. No more than number is a being, it's a mode in relation to what it quantifies, in the same way time is a mode in relation to what it measures.
Obviously, it's not a matter of just taking Kant like that, it doesn't happen only in his head, there's a very long scientific evolution which find its philosophical expression there, but it had already found, no doubt with Newton, a scientific expression. Everything happens as if time "deployed itself" [se déployait], but we must take "deployed itself" in its strict sense, which is to say unrolled itself, which is to say lost its cyclical form. What does that mean that time becomes a pure straight line. It's exactly as if you were holding a coiled spring and you let it go.
Time becomes a pure straight line. It reminds me of Borges, the true labyrinth is the straight line. When time becomes a straight line, what does that mean and what change does that imply?
Still speaking musically, I would say that with Kant time acquires a tonal character, it ceases to be modal. We can find no other images to indicate the violence of such an operation in relation to the thought that, truly, the circle snaps, like a spring that uncoils itself, which becomes a pure straight line. You can see that the cyclical line, when time is cyclical, is a line which limits [borne] the world and just saying that time becomes a straight line means that it no longer limits the world, it will traverse it. In the first case, cyclical time is a time which limits and which thus carries out - which has always been the supreme act for the Greeks - carries out the act of limitation. When time becomes a straight line, it no longer limits the world, it traverses it, it is no longer a limit in the sense of limitation, it is limit in the sense: it's at the extremity [bout], it never ceases to be at the extremity, it's the sense of a passage to the limit. The same word "limit" radically changes in sense, it's no longer the operation which limits something, it's on the contrary the term towards which something tends, and at the same time the tendency and that towards which it tends, that's time. How can we explain that. It's precisely a matter of assigning the importance of this time become straight line. It's not a simplification, it changes everything in the very atmosphere of time and in the operation of time.
The simplest way is to refer ourselves to a poet who claims to be inspired by Kant. That's Hölderlin. For the moment our problem is solely to say what is the importance of the change when time ceases to be circular, ceases to be a circle in order to become a straight line. We must keep in mind both that Hölderlin claims to be inspired by Kant and that he has many things to say on what happens when time becomes a straight line.
Hölderlin poses the problem at the level of Greek tragedy, and in particular he opposes Greek tragedy such as it appeared in Aeschylus and Greek tragedy such as it appeared in Sophocles, and above all in Oedipus and in Antigone. You will see straight away that the schema that Hölderlin develops, and that other commentators of Sophocles took up afterwards, concerns the very heart of our problem. It amounts to telling us that there is a certain sense of the tragic for the Greeks which is the tragic element of cyclical time. We find it very easily in Aeschylus. What is the tragic cycle of time? The tragic cycle of time is, broadly, like three unequal arcs of a circle; there is the moment of limitation; limitation is nothing other than justice, it's the lot assigned to each. And then there is the transgression of the limitation, the act which transgresses.
The moment of the limit is the great Agamemnon, it's the beauty of royal limitation. Then there is the transgression of the limit, which is to say the excessive act [l'acte de la démesure]: it's Clytemnestra assassinating Agamemnon. Then there is the long atonement, and the tragic cycle of time is the cycle of limitation, of transgression and of atonement. The atonement is Orestes who will avenge Agamemnon. There will be the re-establishment of the equilibrium of the limit which for a moment was overstepped. Notice that this tragic time is modeled on astronomical time since in astronomical time you have the sphere of fixed points which is precisely the sphere of perfect limitation, you have the planets and the movements of the planets which, in a certain way, break through the limit, then you have the atonement, which is to say the re-establishment of justice since the planets find themselves in the same position again.
And in this formula of the famous tragic destiny, as they say, it's settled from the beginning, and when the tragedy begins it's already done: as Aeschylus' text itself says, at the moment when Agamemnon goes into his palace and is about to be assassinated by Clytemnestra, it's already done. But at the moment when Clytemnestra assassinates him, an act of excess and injustice, of violation of the limit, the atonement is already there. It's this sort of cyclical destiny. Time is a curve.
Whereas in some splendid pages, Hölderlin says: what is the novelty of Sophocles? In what respect does Sophocles found in the end the modern sense of the tragic? He is the first to un-curve [décourber] time. It's the time of Oedipus. He says that before Sophocles, in the Greek sense of the tragic, it's man who eludes the limit. You can see, in the limitation-limit, man transgresses the limit and in so doing eludes the limit; but with Oedipus one can no longer say that it has the atmosphere of someone who transgresses the limit, who eludes the limit. In the case of Oedipus, it's the limit which is elusive. Where is it? It's the limit which becomes passage to the limit. Splendid expression of Hölderlin's: in Oedipus, the beginning and the end no longer rhyme. And the rhyme is precisely the arc of the time bending in such a way that beginning and end rhyme with each other. There was atonement for the injustice. In Oedipus time has become a straight line which will be the line on which Oedipus wanders. The long wandering of Oedipus. There will no longer be any atonement, even if only in the form of a brutal death. Oedipus is in perpetual suspension, he will travel his straight line of time. In other words, he is traversed by a straight line which drags him along. Towards what? Nothing. Heidegger will be able to say later that it's towards death. Heidegger for his part will draw from the straight line the idea, which is not wholly un-Kantian, the idea of a sort of being-towards-death.
We can see well indeed that in the case of Oedipus, in Sophocles' tragedy, the beginning and the end do not rhyme, and moreover there is a zero-instant. Hölderlin adds that this un-curved time, such that the beginning and the end no longer rhyme together, and it's precisely because there is a caesura in this time, thus a pure present, that there will be - and it's this caesura that will distribute it - a before and an after, and it's this before and this after which do not rhyme. For the schema of cyclical time is substituted a time as straight line, marked by a caesura, a caesura which distributes a non-symmetrical before and after. It's very important for us for time as a straight line contains the possibility of distributing a non-symmetrical before and after, of producing a non-symmetrical before and after using a caesura. We can call this caesura the pure present. Hölderlin's analysis is admirable however because he tries to show that this form of time, the caesura which distributes a before and an after, thus the linear form of this time marked by a pure present according to which a past and a future are produced in time, well this time is that of the modern consciousness in opposition to the consciousness of antiquity.
Since I borrowed the formula from Hamlet, what strikes me, independently of dates, is the extent to which the whole schema that Hölderlin constructs for us to understand what he considers to be the novelty of Oedipus, the extent to which that applies to Hamlet. For those who remember Hamlet, it's curious the extent to which it's a linear time where something is always elusive, it is no longer Hamlet who eludes the limit, it's the limit which eludes Hamlet, as if it was spinning the straight line. And there is a caesura. For Oedipus, Hölderlin assigns the moment of the caesura to the intervention of Tiresias, the intervention of the seer. It will constitute the pure instant, the pure present from which a past and a future will be produced on the straight line, which is to say a before and an after which no longer rhyme together. And in Hamlet there is a moment which seems extraordinary to me: Hamlet hesitates a great deal in his task of avenging his father: the limit is literally elusive. When he hesitates a great deal to avenge his father it's the same story as Oedipus. For a long time it's as if it's the time before, but we can't yet say "before" since the before and after are only distributed by the caesura which is to say the moment of the pure present; and then his step-father, who wants to get rid of him, sends him on a sea trip. Well the sea trip is so fundamental that Hamlet returns from it saying: "there is something dangerous in me", which he would never have said before, as if the sea trip had made him capable of something which he was not capable of before. The sea trip has played the function of the caesura and has distributed on the straight line of time a before and an after which are non-coincident, non-symmetrical.
We will see all that in this quite beautiful, obscure but beautiful text of Hölderlin's: "At the extreme limit of the rift nothing in fact remains any more except the conditions of time or of space [here Hölderlin is speaking like a Kantian]. At this limit man forgets himself because he is wholly inside the moment. God forgets because he is nothing but time. And there is infidelity on both sides, etc." The categorical turning-away [détournement], what is it? It's that in so far as time is cyclical, there is a sort of God-man relationship which is one with destiny in Greek tragedy. When time becomes a straight line, there is also something which separates. In Hölderlin's very beautiful commentary it's the double deviation in the same course of linear time which will separate man and God, God turns away from man who turns away from God. Which is why Oedipus is said by Sophocles to be "atheos", which does not mean atheist, but he who is separated from God. So much so that God is no longer the master of time, the one who curves time, and man is longer himself ???? encircled in a sort of harmony with God, in this sort of relationship with God, man is no longer anything but the caesura which prevents the before and after from rhyming together, which distributes a before and an after which do not rhyme together.
I would simply like you to begin to feel the importance of this time which becomes a straight line. It doesn't mean simplification of the figure of time at all, on the contrary I would like you to feel an intense complication of the figure of time. Time is no longer subordinated to something which happens in it, on the contrary it's everything else which is subordinated to time. God himself is no longer anything but empty time. Man is no longer anything but a caesura in time. In The Critique of Pure Reason, there is a very famous passage, also very very beautiful, which is called "Anticipations of Perception". I would just like to show that, at a completely different level, Kant tells us a story which is the same one that Hölderlin told afterwards. But it's not in relation to Greek tragedy. Oddly enough it happens to be in relation to scientific physics. So there are twelve extraordinary pages entitled "Anticipations of Perception". Kant tells us that space and time are what are called extensive magnitudes. What does extensive magnitude mean? It's not complicated, in Latin an extensive magnitude is one which accepts the formula "partes extra partes", the exteriority of parts, which is to say an extensive magnitude is one whose parts are apprehended successively so that, all quantity being at the same time multiplicity and unity - when you say, for example, this is twenty metres long, it's the unity of a multiplicity - extensible magnitude or extensive magnitude will be defined in the following way: the multiplicity refers to a gathering of parts into a whole. That's an extensive quantity. But time is like that: a minute, another minute, and then you say that's it, that an hour has passed. You can see the succession of parts in their apprehension, the gathering into a whole: an hour.
Space and time are extensive quantities, no difficulty there. Kant adds: but there you have it, the real in space and time - you recall that the real in space and time is what appears in space and time, it's the phenomenon since with Kant the phenomenon is no longer an appearance, it's the fact of appearing - the real in so far as it appears in space and time, no doubt it also has an extensive quantity, there is the space of the table. There's no more to go over on this point; it's precisely what Kant calls a synthesis. But the real in space and in time doesn't only have an extensive quantity, it also has an intensive quantity. What is an intensive quantity? It's what fills space and time to such or such a degree.
We can see straight away the difference between extensive quantity and intensive quantity since the same extensive space can be filled to varying degrees. An example: the same space can be filled by a more or less intense red, the same room can be filled with a more or less intense heat, the same volume can be filled with a more or less dense matter. Kant will even distinguish the two questions fundamentally: can emptiness in space and time be conceived, and another question, namely that space and time can be filled without there being any void in them, can be filled varying degrees.
So what is the intensive quantity of the real in so far as it fills space and time? Moreover, there is not just a real which fills space and time, there is a real of space and time, it's intensive quantity. In opposition to what we have just said about extensive quantity, the two fundamental characteristics of intensive quantity according to Kant - and this will be very important for all subsequent theories of intensity - first characteristic: the apprehension of an intensive quantity is instantaneous, which is to say that its unity no longer comes from the sum of its successive parts, the unity of a given intensive quantity is apprehended in an instant. Which amounts to saying that when I say "it's 30 degrees", the 30-degree heat is not the sum of three times ten degrees, it's at the level of extensive quantities that thirty is 10+10+10, but thirty degrees is not three 10-degree heats. In other words, the rules of addition and subtraction are not valid for intensive quantities. The apprehension of the unity of an intensive quantity happens in an instant. Second characteristic: the multiplicity contained in an intensive quantity is no longer referred to a succession of parts exterior to each other, but refers to a variable proximity to degree zero. I can say that each time there is something which fills space and time, I would say or rather Kant would say that he has before him an empirical intuition. Intuition, you will recall, is the faculty of receiving what is given, but the given is given in space and time, so intuition is not at all a magical faculty, it's the faculty of receptivity. I receive something which is given, and in this sense I have an empirical intuition. But to the extent that what is given has an intensive quantity, which is to say a degree, I grasp it in a relation to its production starting from zero, or its extinction... or the real which fills space and time from the point of view of its intensive quantity is grasped as produced starting from degree zero or as extinguishing itself, i.e., rejoining degree zero.
At that point the question is not at all one of knowing if there is an empty space and time, the question is of knowing that in any case there is an empty consciousness of space and time. And there is an empty consciousness of space and of time as consciousness determined by and as a function of degree zero as the principle of production of all reality in space and time - production starting from zero or the principle of extinction.
I don't want to make associations that are too forced, but at the physical level of intensity in Kant, you can do what Hölderlin ?????, namely the straight line of time marked by a caesura which is intuition = 0; what he will call the empty formal intuition, from which the real which fills space and time will be produced, and it's this intuition = 0, this empty intuition which constitutes the caesura. It's according to this caesura, this degree zero implied by all intensive quantity, which is naturally correlated with time as empty form, as pure line. So on time as a pure line the caesura of degree zero is marked, which will mean that before and after will no longer rhyme together. Again the question is not: is there an empty time and space, the question is whether there is an empty consciousness of time, by virtue of the nature of time itself. In other words God has become time, at the same time that man became caesura. It's hard, we understand nothing, but it's beautiful. That's all I wanted to say on time that's out of joint.
Intensive quantity effects a synthesis between the degree zero that it implies, from which it is produced, and time as pure line or empty form. Intensive quantity as degree of the real which fills a space and a time effects the synthesis between a degree zero from which this real is produced or in which it extinguishes itself, and on the other hand time as empty form or pure line. So much so that there will be a complementarity between the function of the caesura which intensive consciousness plays in time and the empty linear form that time takes on. Hence, as Hölderlin will say: man (the consciousness of time) is no more than a caesura, God is no more than empty time. It's the double turning-away [détournement]. Kant didn't go as far as that, for a simple reason that I will explain: in effect Kant subtracted God and the soul from knowledge. He gave them a function in the field of knowledge, but God and the soul were not known as such since we only know phenomena, we only know what appears. But he didn't suppress either God or the soul since he was to give them a quite different function, a moral, practical function. But from the point of view of knowledge, Gods passes into empty time just as the soul passes into the caesura.
Is that any better? True lived experience [le vécu] is an absolutely abstract thing. The abstract is lived experience. I would almost say that once you have reached lived experience, you reach the most fully living core of the abstract. In other words, lived experience represents nothing. And you can live nothing but the abstract and nobody has ever lived anything else but the abstract. I don't live representation in my heart, I live a temporal line which is completely abstract. What is more abstract than a rhythm?
For the Stoics, they are at once so new in relation to antiquity, and at the same time they have nothing to do with it, they employ "limit" in a wholly different sense. The limit for them is no longer the limit assumed by philosophers of the Platonic type, neither is it the other limit... Kant's ?Anticipations of Perception? means something very simple, which is that you can't say anything about perception, a priori, if there is a colour that is called red and another that is called green, that's to do with the given, you cannot say it independently of experience, it's given in experience. There are two things that you can say a priori, which are: whatever there is that is given in space and time, what is given in space and time is an extensive quantity, but also has a degree, which is to say an intensive quantity. That is an a priori judgement. Which is to say nothing would come and fill space and time as extensive quantities if what comes to fill them did not also have a degree. So I anticipate perception since in this I have a determination, it's the only a priori thing I can say. So there is anticipation. With Epicurus it's not at all in this sense. The Epicurean definition of time will not even be the novelty of a Stoic form of time, it's typically modal time. Here I would very much like Gilles Châtelet to come in and say, from his rather mathematical point of view, precisely how this conception of time as straight line is fundamental.

Gilles Châtelet (summarised because the taped recording is inaudible): With Plato there is a time which is created, which is to say there is a transcendence somewhere which is above time and which has, in correlation with this, a higher dimension. This time of Plato's measures periods, it's a set of periods and it assures the repetition of identities in the stars, the calendar. The fundamental thing to retain is that time is a number. This time above the market measures order. Time in Plato describes order, chaos has no time for example. Time is a sort of calendar that expresses the order of the world: it's a system of coordinates of order, it is in the world, it's a worldly being.
In Aristotle everything is set out through movement and time is in movement, it is interior to mass. Time is attached to the body. Time will be purely astrological, but we owe to Aristotle the notion of an eternal, infinite and uniform time. But with Plato and Aristotle we have a cyclical representation.
In Plotinus there is an abstract operator which is called the One, which is without any qualification and something degrades once we leave the One. Certainly time measures degradation in relation to eternity. Plotinus says that time is the irreparable addition of being to itself. Time is a fall, i.e. a degradation, and Plotinus speaks of aspiring towards God. The mathematical figure which would go with what Plotinus says is called a projective straight line, time is a straight line, but a straight line which has been curved. It's not a circle either. It's a circle minus one point (the One). Time in Plotinus would be a sort of projective time, there is already the idea of irreversibility. In Plotinus time flows from the One and the One is transcendent to time. Time is not exactly a cosmic being, it's the soul which appreciates time in so far... Time is already an equivalent of eternity, it has neither beginning nor end and the point outside the circle is not in time, the One is above, we never begin. It's rather paradoxical. In Kant time becomes a condition of possibility of phenomena. The succession of phenomena implies time, so it is time which is transcendent. Time is what is called a multiplicity, it's clearly said, it is uni-dimensional and above all it is ordered. In the end he says that it tends towards a straight line. But what is a straight line?... Time as a parameter gives the trajectory... The real straight line is a function, time becomes the condition of a function; it's not the image of representation, it's the function itself. There is the possibility of having a function of time. In what sense is Kant completely modern? Because temporality is defining a topology... a straight one... But Kant's essential idea is that his abstract space is pure parameter.
There are two things in Kant: firstly a technological revolution in the sense that it is clearly affirmed that time is a real straight line, but there is also a notion of function.

Gilles Deleuze: You're saying something very important, namely that with Kant time ceases to be a number or measure and becomes parameter. I would like you to explain the difference between a number or measure and a parameter?

G. Châtelet: The parameter is not a result. A number, for the Greeks, is simply a measure, here the measure of time is possible because... In mathematics parameter has no definition, it's simply a notion. Time become parameter is no longer a result, it becomes an initial given. A parameter is what is given, what varies.

Deleuze: I think that it amounts to exactly the same thing: to say that time ceases to be a number or that time ceases to measure something and thus is subordinated to what it measures, and that time becomes a parameter, time is related to a problem of constitution. When I said that time un-curves itself, becomes a straight line... There is something equivalent in this modern conception of time where it is at the same time that an empty form of parametric time appears and a complementarity with something which makes a function, whether it is the caesura in the tragedy, or else the cut in mathematical instrumentation. I am just a bit bothered by the key role that Gilles Châtelet gives to Plotinus. In antiquity it is much more complicated than has been said till now. There were in fact two directions and the two directions had at least something in common: in the two directions time only has a modal character and never a ???? character. However the two directions are time as number of movement, thus subordinated to the physical cosmos, subordinated to physis, and then Plotinus breaks away there, but he is not the first to break away, and he makes a conception of time which is subordinated not to physis but to the soul. I wouldn't completely agree with Gilles Châtelet on the importance of this point, of Plotinus, and on the one hand the two attempts: time subordinated to the soul, time subordinated to physis maintain or at least have in common the affirmation of a purely and uniquely modal character of time, thus time as the image of eternity, a secondary and derived character of time, and the two have a point of convergence in the Antique theory of the soul of the world. I would not make of Plotinus a...

Comptesse: [inaudible comment]

Gilles: Transcendent in relation to Kant. Once again there are two notions. The Kantian notion is transcendental, time is transcendental, but the whole Kantian notion of the transcendental is created in order to refute the classical notion of the transcendent. The transcendental is above all not transcendent.
I would like to move very quickly to the second point. I'm going very quickly. I would say that the second formula that I would like to apply to Kant is... but thinking time is really the most difficult thing - it's the phase of philosophy as critical philosophy, as modern philosophy defined by Kant under the form of a critical philosophy. In classical philosophy, what is the other of thought. The other of thought is above all space. It's space. Space is conceived as limitation. It was conceived as an obstacle and a resistance, it is also limitation. Why? Because it happens that my thought is referred to a thinking substance that is itself unextended, thought is the attribute of a thinking substance that is itself unextended, but this thinking substance is finite in body. It is finite in body: it's the famous problem which will poison classical philosophy, namely the union of the soul as thinking substance and the body as extended substance. And the fact that the soul is finite in body, even though the soul is in itself unextended (you can see that it's an inextricable problem: how is it that something unextended can be finite in something extended, it will produce all sorts of paradoxes), this in fact introduces a fundamental limitation of thought since it will be the source of all the errors, of all the illusions which not only create an obstacle to thought, but limit thought. Third characteristic: if space is the other of thought, I'm saying that it's an other of, literally, alterity. Extended substance is other than thinking substance even though it is uni-substantially opposed, hence the well-known position of Descartes in which there were three substances: thinking substance, extended substance and the union of thinking substance and extended substance. With the Kantian transformation the aspect of everything changes. Why? We remember time become straight line, and I can no longer say that what is important is space as obstacle or resistance to thought, or as limitation of thought. Here it's time which ceases to be subordinated to space, it takes on an independence at the same time that it acquires this form that we have seen, this pure form, and it's not time which takes the place of space, it is not an obstacle to thought, it is the limit which works thought from the inside. For the notion of external limitation is substituted the notion of internal limit. Time is the limit which works thought over, which traverses thought through and through, it is the inherent limit, a limit interior to thought, whereas in classical philosophy it's space which is determined as the exterior limitation of thought.
So everything happens as if the "enemy" of thought was within. It does not receive it from outside. There we have a sort of fundamental change. To think time means to substitute for the classical schema of an exterior limitation of thought by the extended, the very very strange idea of an interior limit to thought which works it from the inside, which doesn't at all come from outside, which doesn't at all come from the opacity of a substance. As if there was in thought something impossible to think. As if thought was worked over from the inside by something that it cannot think. From this point the problem, in Kant, will no longer be that of the union of the soul and the body, which is to say the union of two substances one of which is extended and the other unextended. The problem will no longer be the union of two distinct substances, it will be the coexistence and the synthesis of two forms (they're completely different, two forms and two substances) of one and the same subject. Instead of the union of two substances, the synthesis of two forms of the same subject, which implies that the subject is not substance.
What are these two forms which will have to unite - I can no longer even say in the same subject since substance will not be inherent in the subject - they are two forms for the same subject. Now this subject will be traversed by this line of time; the subject is as if traversed by two forms and is himself nothing other than the synthesis, namely the most mysterious point, the synthesis of these two forms. What are these two forms? They're on the one hand the form of thought, and on the other hand the form of the internal limit of thought. What does that mean in concrete terms? The form of thought is in the first place the act of "I think", the "I think" as act or as determination. To say "I think" is to determine something. What? We will see later.
The form of equal thought, in the most universal sense "I think" which is to say that it's thought in so far as it is related to a subject; but I don't have the right to say that it's a substance. Second determination of the form of thought: as Kant says, "I think" is the slightest [la plus pauvre] of representations, it's the slightest of thoughts which accompanies all thoughts. Self = self, it's the "I" of "I think". The "I think" is the universal form of determination, but in a sense I determine nothing and in "I think" the determination is at its emptiest.
Concretely acts of thought are concepts. We have seen that a priori acts of thought are particular concepts called categories. So the form of thought is the "I think" and the categories taken together, the "I think" together with what it is that "I think", namely the categories or the predicates of any given object. These are what the forms of thought are. Kant will also use the term ?forms of spontaneity?, when "I think" is the act of determination and that implies an activity which is the activity of thought. Kant will reserve the word ?spontaneity? to qualify the form of thought in these two cases. But what else is there besides these two forms of thought? We have seen the form of receptivity or the form of intuition. In the form of intuition we also have two things, just as a moment ago we saw that the form of thought is the self, the "I" of "I think" and it's also the concept as act of thought, the a priori concepts, which is to say the categories, the forms of receptivity are space and time.
There are two forms twice. Last time I said that space is the form of exteriority, time is the form of interiority, this doesn't prevent these two forms from having in common the fact of being two forms of intuition or two forms of receptivity. The form of receptivity is double: form of exteriority = space, form of interiority = time, but the two together are the form of receptivity. On the other hand there is the form of spontaneity which is the "I think" and the categories. You can see, and this is very important, how it unfolds: you have a first great duality: form of intuition and form of spontaneity, form of receptivity and form of spontaneity, and each one of these two great forms has two aspects. The form of receptivity has two aspects: exteriority-space, interiority-time, the form of spontaneity has two aspects: the self of the "I think", the I = I, and the concepts that I think, the a priori concepts.
Kant's problem is howthe same subject, or self, can have two forms which are irreducible to each other (irreducibility of space and time on the one hand, and of the concept on the other hand), how = the same subject can have two forms, principally the form of time and the form of thought, and that according to the form of time, it is receptive, it is accepted, and according to the form of thought it is spontaneous, it is determining, it effects determinations. It is no longer at all a matter of knowing how the soul is united to the body, the answer to the union of the soul and the body will evidently follow from the problem reworked in this way, namely the synthesis of the two irreducible forms of the same subject, or for a subject. Which amounts to saying that for the same subject there is the form of spontaneity of thinking and the form of receptivity of time.
It is by virtue of this that time is already the author of thought. And the Kantian synthesis is obvious: the synthesis is something which separates or rends and this sort of Kantian self is rent by these two forms which traverse it and which are completely irreducible to each other. So where does the harmony come from, how can this limping subject function, he who can think nothing without what he thinks having a correlate in space and time, who finds nothing in space and time without it having a correlate in thought, and yet space and time and thought are two absolutely heterogeneous forms. It's literally a subject who is fundamentally split, it is traversed by a sort of line which is precisely the line of time. So much so that I would say, as a third point, that in classical philosophy the other of thought was the other of alterity; with Kant something absolutely new begins: the other within thought. It's an other of alienation. Of course Kant does not use this word, but the post-Kantians will produce a fundamental theory of alienation which will be revealed in its most perfect state in Hegel.
The difference between the other of alterity, which is really an exterior other which creates an obstacle for thought, it is the other of alienation which is this interior limit.
What is this alienation? The alienation of the subject in Kant is precisely this fact that it is as if torn by the duality of the two forms, each of which belongs to it as much as the other, form of receptivity and form of spontaneity. Suddenly we are on the verge of understanding what Rimbaud's formula "I is an other" could mean. "I is an other" is in the first place a formula of Rimbaud's, it's in the letters. It's the most classical context possible, it is purely Aristotelian for the two times Rimbaud comments on the expression "I is an other", he issues this formula with an extremely classical philosophy as its philosophical support. It is obvious that Rimbaud had a teacher who gave him a course on Aristotle. It's letter II in the Pléiade edition, 1971: "I is an other. Too bad for the wood which finds itself a violin." Letter to Paul Dominique: "For I is an other. If the tiger awakens... I witness the hatching of my thought, I watch it, I study it."
Aristotle tells us that there is matter and then there is form which informs [informe] matter. Matter is the copper, the bugle is the copper which has been poured into this form. Nothing could be more classical, and Rimbaud assimilates himself to a matter and says: thought forms me. In the other example, the wood becomes violin, it is given the form of the violin and it receives its capacities.
Rimbaud draws from this the formula "I is an other" which obviously exceeds the context. His business is to find the poem, the appropriate poetic act. It's Kant who will do the philosophical work which corresponds to the formula "I is an other".
We must at all costs, for Kant makes reference to this, without even saying it, we must start from the cogito in Descartes. Obviously I would like to spare you a lesson on Descartes, but everything comes from this formula: "I think therefore I am", I am a thing that thinks. That is the Cartesian development exactly, but it is summarised as "I think therefore I am". But the complete formula is "I think therefore I am", it being understood that in order to think it is necessary to be, what am I? I am a thing that thinks. You can see the progression: I think, I am, I am a thing which thinks. I think = determination. ?I am? is the position of something indeterminate; I am a thing which thinks, the thing qua determined. Follow me, there are three terms: a determination, I think; a thing to determine, namely an existence or a being; thirdly the determined, namely the thinkable thing.
The determination determines something to be determined. You will tell me that if that's all there is, that doesn't go very far. I have indeed three things then: I think, I am, I am a thing that thinks. The "I think" determines the "I am" as a thing that thinks. At first glance that seems to be impeccable. And now Kant comes along and says: not at all, he has forgotten a term, it's not at all complicated enough. And Kant will correct, he says, OK, I think = determination - and here we are fully in the future of German philosophy - in order to think it is necessary to be, OK, so the determination implies something indeterminate which is to be determined by the determination. I need this complicated formula for a very simple thing. You can see, I think therefore I am, it's quite simple, I think is a determination, the determination implies something indeterminate which is precisely to be determined by the determination. So, I think, I am, that works. At that point he makes a cut, a caesura: he says: I think therefore I am, very well, but you cannot conclude from this "I am a thing that thinks". Kant saw a flaw there in what the other believed to be a sort of continuity that nobody could refuse him.
Why does it go from "I think" to "I am"? Once again, OK, the determination implies something indeterminate to be determined by the determination. But, Kant says, that doesn't yet tell us the form, under what form the indeterminate (which is to say the I think) is determinable by the determination.
... The determination, the indeterminate existence, the existence determined by the determination, and Descartes thought he had a continuum of thought. The determination was the "I think", the indeterminate existence was the "I am", the determination determined the indeterminate: I am a thing which thinks. Kant says: I think = determination, I am = indeterminate existence implied by the I think; in order for there to be a determination there must indeed be something to be determined. But now, we still must be told under what form the indeterminate, the to-be-determined, what must be determined, we still must be told under what form the indeterminate existence is determinable by the determination. Descartes has only forgotten one thing, namely to define the form of the determinable. So there were not three terms, the determination, the indeterminate and the determined, there were four terms: the determination, the indeterminate, the determinable form and the determined.
If you understand that you have understood everything because you have Kant's reply. Under what form is the indeterminate existence such as it is implied by the I think, under what form is it determined?
The "I think" is a determination, which is to say a spontaneous act. It implies an "I think", but a completely indeterminate "I think". Descartes told us: well yes it's completely indeterminate, but what difference does that make? Since the determination "I think" is enough to determine its determinate, "I am a thing that thinks"... What he has forgotten is that "I think" is a determination which implies something indeterminate, but also that does not tell us under what form the "I am" is determinable by the determination "I think".
Kant's reply: the form under which the "I am" is determinable is obviously the form of time. It will be the form of time; and you will come across this paradox that Kant will himself define in an admirable formula: the paradox of inner sense, the paradox of interior sense, namely the active determination "I think" determines my existence, the active determination "I think" actively determines my existence, but it can only determine my existence under the form of the determinable, which is to say under the form of a passive being in space and in time. So "I" is indeed an act, but an act that I can only represent to myself in so far as I am a passive being. I is an other. Thus I is transcendental.
In other words, the active determination of the "I think" can only determine my existence under the form of existence of a passive being in space and in time. Which amounts to saying that it's the same subject which has taken on two forms, the form of time and the form of thought, and the form of thought can only determine the existence of the subject as the existence of a passive being.






Kant was very interested in a bizarre author called Swedenborg, and Swedenborg had a certain conception not only of spirits, in the spiritualist sense, but he had a conception of space and time as a function of spiritualism. To answer your question: it seems to me that you aren't posing the problem in Kantian terms. When you say, for example: "I'm thinking of someone", and then this someone comes into the room. You are using "thinking" in an extremely general sense, that is, any activity of any given faculty referable to a so-called thinking subject, whatever the mode of thought. When you say that I am thinking of someone that means that I am imagining someone, or I remember someone, and then by chance, by coincidence, this someone comes into the room. "Thinking" can very well be used in vague and general terms. At the point we are at in our analysis, Kant has substituted a restricted use, in which to think does not mean to imagine or to remember, or to conceive, but in which thinking means solely to produce concepts. To feel means solely: to receive a sensible diversity, to apprehend a sensible diversity. To imagine means: either to produce images, or else to produce the concept's corresponding spatio-temporal determinations.
So grant me that, at the level that we are on, whatever these restricted definitions and their value are, to think, to imagine, to feel, are not treated by Kant as modes of a same type of thought which could be substituted for one another, but as specific faculties. So that when you say "I remember someone", and this someone comes in, there is no activity of thought, there is an act of imagination, there is suddenly the sensible diversity which gives me this someone. That's what Kant would say.
Kant says, in a text of the Critique of Pure Reason: "if cinnabar was sometimes red, sometimes red and sometimes black, sometimes heavy and sometimes light... I would never have the opportunity to associate - i.e. my imagination would never have the occasion to associate - the heavy cinnabar with the colour red..." If nature was not subject to concrete rules, there would be no associations of ideas. In other words, when I have an association of ideas, this implies that things, and no longer ideas, that things are themselves subject to rules analogous to the rules which are associated in us. Which is to say if Pierre did not come to Vincennes, or had not come to Vincennes, I would never have had the opportunity to associate the idea of Vincennes and the idea of Pierre.
I will try to clarify this story of faculties, but you can well see that you can't invoke the example that you just gave as transforming the problem of the thought-imaginary relationship, because in fact it would be a matter of one of the forms of thought. When I think "of Pierre" and then Pierre is there, in fact I haven't thought anything since I haven't formed any concept at all. I imagined or remembered.
There's something very, very curious in Kant. When Kant writes his three great critiques, the Critique of Pure Reason is in 1781, Kant is 57 years old, the Critique of Practical Reason is in 1788, and finally the last very great work by Kant is the Critique of Judgement in 1799, he is 76 years old. I was saying to myself that there aren't that many precocious philosophers. If he had died at the age of 50 he would be a sort of secondary philosopher, a good disciple of Leibniz, a good run-of-the-mill philosopher. There is only one case, the extraordinary case of Hume. With him, he has his whole system, all his concepts, at the age of 22-25, after which he only repeats, improves.
Today, I would like to speak about this extraordinary book that is the Critique of Judgement; if I say that it is an extraordinary book it's because it is a book which founds a discipline, even if the word existed before. There is a particular discipline which will be radically founded by the Critique of Judgement, namely the foundation of all possible aesthetics. Aesthetics came into existence as something different from the history of art with the Critique of Judgement. It's really a very difficult book, don't try to understand each line of it, follow the rhythm. I would like to develop a bit the difference between the Cartesian "I think", such as it appears in Descartes, and the "I think" such as it appears in Kant. We must schematise at the level of a certain labor of thought. Already with Descartes, something appears which, it is said, will be of very great importance in the evolution of philosophy, namely: substance, that certain substances are therein determined as subjects. We can say very schematically that these formulae have been helpful. Not all substances, but a type of substance called thinking substance (?). Thinking substance is determined as subject. It's the discovery which will mark all philosophy said to be modern, from the 17th century onwards, it is the discovery of subjectivity. Why the discovery of subjectivity, why would subjectivity have to be discovered? It's the discovery of a subjectivity which is not the subjectivity of the empirical self, namely you and me. From the point of view of the labor of the concept, if I say: the Cartesian cogito is the assignation of substance as subject: "I think", the Kantian I think is very different. Everything happens as if a further step was taken, namely that the form of subjectivity breaks away from substance. The subject is no longer determinable as a substance. Subjectivity liberates itself from substantiality. Philosophers do not contradict each other, it's like with scholars, there is a whole labor of the concept. I will try to express Descartes' "I think" very concretely. Descartes' point of departure is a famous operation called doubt. He says, in some very beautiful texts, "perhaps this table on which I rap does not exist", and "perhaps my hand which raps on this table does not exist"; everyone knows very well that this is a manner of speaking. There is necessarily a discrepancy between the style and the content. It's not a matter of saying the table doesn't exist. Descartes' problem is something else entirely, it's the ground [fondement] of certainty, which is to say a certainty which would be exempted from all possible doubt. If I say "the table exists", its existence is of no matter to me, I am wondering whether it is a certainty which contains in itself its own ground. No. Certainly the table exists, it's understood, but this certainty does not contain in itself its own ground. Are there certainties which contain their own ground in themselves? At this point I move up a level: we say that we are sure that two and two make four; Dostoyevsky's heroes say: "I don't want two and two to make four". Can one not want two and two to make four? And when he says: I am certain that two and two make four, is that also a certainty which has its own ground in itself? Why would two and two make four? In this case one can demonstrate that two and two make four, which is complicated. On the other hand Descartes thinks that it is the operation of doubt which will give us a certainty which contains in itself its own ground. Namely that there is one thing which I cannot doubt, I can doubt the existence of the table, I can doubt the proposition "two and two make four", I cannot doubt one thing, which is that in so far as I doubt, I think. In other words, the operation of doubt, in so far as doubting is thinking, will provide me with a certainty which contains in itself its own ground: I think! "I think" - it's a funny sort of formula. In certain texts Descartes goes so far as to say that it is a new mode of definition. It's a definition of man. Why is it a definition of man? Before Descartes philosophy proceeded by definitions, scholasticism, definitions were given above all through generic and specific differences. Man is a rational animal. Animal is the genus, rational is the specific difference. Descartes says that when a definition of this type is given we are always referred to something else that we are supposed to know. In order to understand that man is a rational animal, we are supposed to know what an animal is, we must know what rational is. He will substitute a definition of another form entirely: I think. It's very curious, this "I think", because there is no need to know what thinking is. It is given in the act of thinking. There is a kind of implication, which is not at all an explicit relation between concepts, it's an act which is one with the act of thinking.
With doubt, when I doubt, there is one thing which I cannot doubt, which is that as a self who doubts, I think. Self, what is the self? Is it my body, is it not my body? I have no idea since I can doubt my body. The only thing I cannot doubt is that since I doubt, I think. You can see that it is absolutely not a matter of an operation in which doubt would come to bear on ?????, but of an operation which consists in requiring a certainty which contains in itself its own ground as certainty. "I think" is thus an act through which I determine my certainty. The "I think" is a determination. It's an active determination. Not only can I not doubt my thought, but I cannot think without it, which is to say that the same implicit relation which goes from doubting to thinking, goes from thinking to being. In the same way that doubting is thinking, in order to think one must be. You can see the progression of the Cartesian formulae: I doubt, I think, I am. I doubt, I think, I am, I think is the determination, I am is the indeterminate existence, I am what? Well, the determination will determine the indeterminate existence. That the determination determines the indeterminate means: I am a thing that thinks. I am a thinking thing.
Thus it is that what I am is determined by the determination "I think", is determined as the existence of a thinking thing. Descartes is told that that's all very well, but what proves to us that it is not the body which thinks in us? A materialist of the time says this to him. And Descartes replies - as soon as anyone makes an objection to him, he is very rude - he says: you haven't understood anything, I never claimed that it is not the body which thinks in us, he says exactly this: what I am claiming is that the knowledge which I have of my thought cannot depend on things which are not yet known. In other words, it is not a matter of knowing if it is the body or not the body which thinks in us, it is a matter of observing that, within the perspective of the Cartesian method, the consciousness which I have of my thought cannot depend on things which are not yet known, namely the body since doubt [also bears on this?]. Thus this procedure, from a logical point of view, but a new type of logic since it is no longer a logic that operates through genera or differences, it's a logic of implications since Descartes is in the process of... in opposition to classical logic which was a logic of explicit relations between concepts. He launches a new type of logic which is a logic of implicit relations, a logic of implication.
So, he has determined with the "I think", which is a determination, he has determined the existence of what thinks, and the existence of what thinks is determined as the existence of the thinking thing. He thus goes from the determination to the indeterminate, from the determination "I think" to the indeterminate "I am" and to the determined: I am a thing that thinks. He threads along his logic of implications: I doubt, I think, I am, I am a thing that thinks. He has thus discovered the zone where substance was subject.
And Kant appears.
What Descartes affirms is that the soul and the body are really distinct. It's more than an ontological separation. But what is it that he calls a real distinction, in conformity with the whole tradition? Again, words here are as defined as in science. A real distinction is not the distinction between two things, it's the distinction, a mode of distinction, between two things, it's the distinction, a mode of distinction, between two ideas and representations : two things are said to be really distinct when I can form the idea of one of them, which is to say when I can represent to myself the idea of one of them without introducing anything about the other. Representations thus form the criteria for real distinction. Two things being completely distinct is a proposition which, ultimately, has no meaning. We will get to the level of substance, Comptesse, you who know Descartes as well as I, after the fifth meditation. In the second meditation, there is absolutely no way of knowing if it is the body which thinks in me. Descartes says it categorically. The soul and the body, thought and extension are really distinguished - which is not the same thing as really distinct - as two ontologically separate, or separable, substances. He is not able to say this before the end of the meditations. In the second meditation, when he discovers the "cogito", the "I think", he absolutely cannot say it yet, and it's for this reason that among the novelties of Descartes' text, there is something which he very much insists on, and this is the true novelty of the meditations, even if you don't like Descartes very much, namely that it is the first book which introduces time into philosophical discourse.
There is something tremendous in this. What he says in the second meditation, then what he says in the fifth, there is a temporality which has unfolded which meant that he could not say in the second what he will say in the fifth.
This is not true of all philosophies; if I take Aristotle or Plato, there is a succession in the reading, but this succession corresponds to a chronological order and that's all. In Descartes there is the establishment of a temporal order which is constitutive of the metaphysical dimension.
Broadly speaking, during the whole of the middle ages, there was a theory of forms of distinction, each author will create his own forms of distinction, but broadly there were three major types of distinction: real distinction, modal distinction and the distinction of reason. And if you relate these three types of distinction to things themselves, you produce an absurdity, if you give them an ontological bearing, they don't have an ontological bearing yet, they only have a representative bearing, namely: there is a real distinction between A and B when I can think A without thinking B, and B without thinking A. You can see that it is a matter of a criterion of thought, a criterion of representation. For example: two things are really distinct, and not truly distinguished, two things are really distinct when you can form the representation of one without introducing anything of the other, and reciprocally. This lighter is on this book, are they really distinct? Yes, I can represent the lighter to myself without introducing anything of the representation of the book, they are really distinct. It's possible that they are also truly distinguished, it would be enough for me to put the lighter in my pocket. Between the front and back of a piece of paper, there is a real distinction, I can represent to myself one side of the paper without having the least representation of the other. In things, front and back are not separate, but in my representation front and back correspond to two representations. I would say that there is a real distinction between the front and back of the paper. So there can be a real distinction between two things which are not truly distinguished.
Second type of distinction: modal distinction. There is a modal distinction when I can think A, I can represent A to myself without B, but I can't represent to myself B alone. For example: extension and the figure. Let's suppose, broadly, that I can represent to myself extension without figure, I cannot represent to myself a figure without extension. I would say that between extension and figure there is a modal distinction. In relation to this, we must not transport it to the level of ontology too quickly, it does not mean at all that there is an extension without figure in things, perhaps there isn't. You can see it's the same gesture, it's the criteria of representation.
Third distinction: the distinction of reason. When I represent to myself as two, two things which are one in the representation. In other words, the distinction of reason is abstraction. When I distinguish the front and back of the piece of paper, I do not make an abstraction since they are given as two in my representation, since there are two representations, but when you speak of a length without breadth, however small this length, there you make an abstraction. When you can have no possible representation of a length which would have no breadth, however small. Thus between length and breadth there is a distinction of reason.
The way people talk about abstraction is amazing, they have absolutely no idea what it is. Philosophy has a kind of technique and a terminology like mathematics. Generally the word abstract is used for things in which there is no abstraction. The problem of abstraction is how can I make two things out of what only exists as one in my representation. It's not difficult to make a thing into two when I have two representations, but when I say the back of the piece of paper, I am not abstracting at all since the back is given to me in a representation which itself exists. When I say a length without thickness, there I am abstracting because I am separating two things which are necessarily given in each other in my representation.
There is indeed a philosopher who started the theory of distinctions. And then the theologians of the middle ages were not guys concerned with God, that's like saying that the painters of the Renaissance were guys who thought about God, no, they thought about colours, they thought about lines, and they draw out the most bizarre things from Christ's body. What we call theologians are people who are in the process of inventing a logic, a physics, a dynamics, and one of the great things in the theology of the middle ages is the theory of distinctions... ok... up to this point it's completely independent of the question of knowing if things are truly distinguished or confused in themselves, so that in the whole story of the cogito, I doubt, I think, I am, I am a thing that thinks, Descartes can only conclude: the representation that I have of my thought, and the representation that I have of an extended body, are such that I can represent my thought to myself without representing anything to myself of extension; I can represent to myself an extension without representing anything to myself of my thought. This is enough for Descartes to say that thought and extension are really distinct. He cannot add yet that it is not the body which thinks in me...

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So he will have to, in order to draw from the real distinction between representation-substance the ontological separation between substances, he will have to go through a whole analysis of the concept of God in which he says: if the real distinction between representation and substance was such that there was no corresponding true separation in things, an ontological separation in things, then God would be deceitful, God would be lying to us since the world would be double, God would be duplicitous, God would be full of duplicity since he would have made two non-conforming worlds: the world of representations and the world of things. You can see what that implies, philosophically, if God is deceitful... it would imply an entirely new way of posing of the problem of evil. But if I had the power to establish real distinctions between representations without there being a corresponding true separation between things, the world would be double: there would be the world of my representations and the world of things, so God would be always misleading me since he would inspire true ideas in me and these true ideas would correspond to nothing in things.
To reply to Comptesse, I'm just saying that it's true that it's a story of ontological separation, but not so quickly, it will become a matter of ontological separation when Descartes is able to conclude: since I can represent thinking substance as really distinct from extended substance, then thinking substance and extended substance are two substances ontologically, and from that point on it is not the body which thinks in me. But before having gone through [the fifth meditation?], he absolutely cannot say this, he can only say: I conceive thinking substance as really distinct from extended substance, they are really distinct, since, once again, to be really distinct is the same thing as to be conceived as really distinct, two things whose representations are caused without one implying anything of the other are really distinct, he cannot yet affirm that it is not extension which thinks in me, that it is not the body which thinks in me.
The one thing that seems interesting to me is this idea of implicit relations, but Descartes does not call it that, and from this the promotion of an order of time in the writing of philosophy... You are going to tell me that you understand everything.
What does Kant do here? Kant wants to go further. It's inevitable, he wants to go further in relation to a previous philosopher, only this further has no pre-existence, he must create it. One of Kant's most beautiful texts is: "What does it mean: to orient oneself in thinking?" In this very beautiful text he develops a whole geographical conception of thought; he even has a new orientation, we must go further, Descartes did not go far enough: since he determined certain substances as subject, we must go further and break the link between the subject and substance. The subject is not substance. OK. What does that mean? He takes it up again and I will try to mark the stages: he says: "I think", fine. Which is to say that it is an active determination, and it's in this sense that Kant will name the "I think" as the form of spontaneity. It seems strange when he says that "I think" is the form of spontaneity, but everything is clear if you stick closely to the terminology; it means precisely: "I think" is a determination - he takes that from Descartes - and the "I think" accompanies each production of concepts. I cannot think a concept without thereby including the "I think". In other words, the "I" of the "I think" is the subject of all concepts, or, as he will say, it's the unity of the synthesis. Thus on this point, he changes the vocabulary, but he remains in agreement with Descartes. Why does he change vocabulary? It was to be expected, if he changes vocabulary while remaining in agreement with Descartes, it's because he will need this vocabulary for the moment when he will not agree, that's the first point.
Second point: in order to think one must be, in other words, there is a relation of implication between the determination "I think" and the position of an indeterminate existence "I am". Kant says it all the time: the "I think" implies - often the words vary - a feeling of existence (here we can clearly see the lineage, between Descartes and Kant there was Rousseau). Sometimes he says a consciousness of an indeterminate existence; the "I think" implies a pure consciousness of an indeterminate existence. Agreement with Descartes up to this point. From this point on Descartes has no more problems, and it's when a philosopher has no more problems that the next philosopher is about to arrive. Descartes has no more problems because he has a determination, and he has posited an indeterminate existence hence something to be determined, and he will say that the determination determines the indeterminate. The determination: I think, the indeterminate: I am, the determination determines the indeterminate: I am a thing that thinks.
Here Kant says no; it's the birth of German philosophy. I'm thinking of Leibniz. There are objections which are like reproaches. Beneath objections there are always theoretical reproaches. Leibniz already said of Descartes: he is too quick. It's like a judgement of taste. Kant takes on something of this, it's too quickly said. Kant: "I think" is a determination, agreed, determination implies the positing of an indeterminate existence "I am", agreed, but this doesn't tell me under what form this indeterminate existence is determinable, and this Descartes doesn't care about because he hasn't seen the problem. I think, I am, agreed. But what am I? Descartes replied: "I am a thing that thinks" since he applied the determination to the indeterminate. Now what I'm saying is becoming very clear: Descartes carried out an operation whereby he directly applied the determination to the existence to be determined. He directly applied the "I think" to the "I am" in order to get "I am a thing that thinks."
Kant says OK, I think, I am. But what am I, what is it that I am? A thing that thinks? But by what right can he say that? Descartes would have become angry... Kant says to him: but you're stuck, you have posited an indeterminate existence and you claim to determine it with the determination "I think". You have no right to do that. You have a determination, you have posited an indeterminate existence, you can turn it around as much as you like, you will not make any headway. You are stuck there. Why? Because to draw from this the conclusion "I am a thing that thinks", it assumes - and you have no right to assume it - it assumes that the indeterminate existence is determinable as a substance or a thing. Res cogitans, in Latin, the thinking thing.
Kant says, in accordance with all that has come before, which is to say what I tried to say the last time - the extraordinary change in the notion of phenomenon, the phenomenon no longer designating the appearance but the apparition, what appears in space and time - Kant can now say to us that the form under which an existence is determined within the conditions of our knowledge (what happens with angels, we have no idea), well, the form under which an existence is determinable under the conditions of our knowledge is the form of time. Thus the "I think" is the form of spontaneity or the most universal form of determination, but time is the most universal form of the determinable. Descartes' fatal conclusion was to confuse the indeterminate and the determinable, but the determination can only bear on the indeterminate as the mediation of the form of the determinable. In other words, I think, I am, the determination must determine the indeterminate existence "I am", but the indeterminate existence "I am" is only itself determinable under the form of time. It is only under the form of time, as the form of the determinable, that the form of thought will determine the indeterminate existence "I am".
This is how my existence can be determined only as time. But if time is the form of the determinable, under which my indeterminate existence can be determined by the "I think", what form do I receive from the determinable? The form that I receive from the determinable is that of a phenomenon in time, since time is the form of apparition of phenomena. I appear and I appear to myself in time. But what is it to appear and to appear to oneself, to appear in time?
They are the coordinates of a receptive, which is to say passive, being. Namely a being which has a cause, which does not act without also undergoing effects. Ok, we're at the end, and it's here that Kant will name the paradox of inner sense, the paradox of intimate sense: the "I think" is an active determination, it's the same form of the active determination, but the existence which it implies, the "I am", the indeterminate existence that the active determination of the "I think" implies, is only determinable in time, which is to say as the existence of a passive subject which undergoes all its modifications following the order and the course of time. In other words, I cannot - there is one sentence which is splendid, it's the Kantian version of what I was saying last time, namely that I is an other. This is what Kant says in the Critique of Pure Reason: "I cannot determine my existence as that of a spontaneous being, I only represent the spontaneity of my act of thinking". It's exactly "I is an other". I cannot determine my existence as that of an I, but I only represent the I to myself. The spontaneity of my act of thinking. The fact that I represent to myself the spontaneity of my act of thinking means that I represent the active determination of the "I think" to myself as the determination which determines my existence, but which can only determine it as the existence of a being which is not active, but a being on time [tre sur le temps]. This is the line of time which separates the "I think" from the "I am". It's the pure and empty line of time which traverses, which effects this sort of crack in the I, between an "I think" as determination and an "I am" as determinable in time.
Time has become the limit of thought and thought never ceases to have to deal with its own limit. Thought is limited from the inside. There is no longer an extended substance which limits thinking substance from the outside, and which resists thinking substance, but the form of thought is traversed through and through, as if cracked like a plate, it is cracked by the line of time. It makes time the interior limit of thought itself, which is to say the unthinkable in thought.
From Kant onward, philosophy will give itself the task of thinking what is not thinkable, instead of giving itself the task of thinking what is exterior to thought. The true limit traverses and works thought from within.
We rediscover what I tried to say the last time, namely: we find a sort of tension between two forms: the active form of spontaneity, or if you prefer, the "I think" as form of active determination, or form of the concept since "I think" is the formal unity of all concepts, so on the one hand the active form of determination, on the other the intuitive or receptive form of the determinable, time. The two are absolutely heterogeneous to each other, and yet there is a fundamental correlation: the one works in the other. Thought shelters in itself what resists thought.
In what sense is Heidegger Kantian? There are famous phrases such as: "we are not yet thinking"; when he talks about time in relation to thought, it's in this way that he is Kantian. The direct line from Kant to Heidegger is truly the problem of time and its relation to thought. The big problem that Kant discovers is the nature of the relation between the form of determination, or activity, or spontaneity, and on the other hand the form of receptivity, or form of the determinable, time. If I shift slightly, I would no longer say the form of determination and the form of determinable, but: two types of determination which are heterogeneous. You will ask me by what right I can make this shift; passing from the form of determination: I think, form of the determinable: time, the idea that there are two types of determination remains to be seen, but you can sense that it is the outcome of a series of shifts which must be justified, namely the two types of determination, in this case the conceptual determination, as all concepts refer to the "I think", concepts are the acts of the "I think", thus on the one hand a conceptual determination, and on the other hand a spatio-temporal determination. The two are absolutely heterogeneous, irreducible, the conceptual determination and the spatio-temporal determination are absolutely irreducible to each other, and yet they never cease to correspond to each other in such a way that for each concept I can assign the spatio-temporal determinations which correspond to it, just as, the spatio-temporal determinations being given, I can make a concept correspond to them. In what way, this is what remains to be seen.
If you grant me these shifts which we will define in a moment, it amounts to the same thing to say that Kant poses the problem of the relation between the form of determination "I think" and the form of the determinable = time, and in so doing completely upends [bouleverse] the element of philosophy, or to say, on a more precise level: no longer the "I think" but concepts, no longer time but the determinations of space and time, in this case it is a matter of the relation between the conceptual determination and the spatio-temporal determination.

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Our point of departure is this: how can we explain that conceptual determinations and spatio-temporal determinations correspond with each other when they are not at all of the same nature? What is a spatio-temporal determination? We will see that there are perhaps several kinds. Kant poses the question concerning the relation between the two types of determination on very different levels. One of these levels will be called that of the synthesis, another of these levels he calls that of the schema, and it would be disastrous for a reader of Kant to confuse the synthesis and the schema. I'm saying that the schema and the synthesis are operations which, in a certain way, put a conceptual determination and a spatio-temporal determination into relation, but then it's as if the synthesis will be shattered, pierced, will be overcome by a stupefying adventure which is the experience of the sublime. The experience of the sublime will knock over all the syntheses. But we do not live only on this. We live only on the syntheses and then the experience of the sublime, which is to say the infinity of the starry vault, or else the furious sea... The other case, the schema, is another case where spatio-temporal determinations and conceptual determinations come into correspondence, and there again there are conditions where our schemas shatter, and this will be the astonishing experience of the symbol and of symbolism. But the whole analysis of the sublime, and the whole analysis of the symbol and symbolism, the English had analyzed the sublime before him, but the whole novelty of Kant's analysis is obvious: it will be the Critique of Judgement, in his last book, as if to the extent that he aged, he became aware of the catastrophe. Of the double catastrophe of the crushing of the sublime, the sublime crushes me, and the irruption of the symbol, where our whole ground, the whole ground of our knowledge which we had constructed with syntheses and schemas, starts to shake.
What is the synthesis? It's the synthesis of perception. But don't think that that goes without saying. I'm saying that it's from this level of the analysis of the synthesis of perception that Kant can be considered as the founder of phenomenology. That is, that discipline of philosophy which has as its object the study, not of appearances, but apparitions and the fact of appearing. What is the synthesis of perception? All phenomena are in space and time. There is strictly speaking an indefinite diversity in space and time. Moreover, space and time are themselves diverse: they are not only the forms in which diversity is given, but they also give us a properly spatial and temporal diversity: the diversity of heres and the diversity of nows; any moment in time is a possible now, any point in space is a possible here. Thus not only is there an indefinite diversity in space and time, but also an indefinite diversity of space and time itself. Thus for perception, certainly the diverse must be given to me, but if I had nothing but this given diverse, this receptivity of the diverse, it would never form a perception. When I say "I perceive", I perceive a hat, I perceive a book, for example, this means that I constitute a certain space and a certain time in space and time. Space and time are indefinitely divisible: any portion of space is a space, any portion of time is a time. So it is not space and time themselves which account for the operation by which I determine a space and a time. I perceive a piece of sugar: I perceive a complex of space and time. You will tell me: that works for space, I can see that, there is the form, the grain; but why time? Because it forms part of my perception to wait for the sugar to melt. When I perceive a thing, I perceive a certain temporality of the thing and a certain spatiality of the thing. So there we have, according to Kant, a properly logical order, not at all chronological, he doesn't say that we must start with one.
There are three operations which constitute the synthesis, the synthesis operating on diversity in space and in time, and diversity in space and time at the same time. The synthesis consists in limiting a diversity in space and in time, and a diversity of space and time themselves, in order to say: it begins, it ends, etc.... The first aspect of the synthesis is what Kant calls the successive synthesis of the apprehension of parts, that is: every thing is a multiplicity and has a multiplicity of parts; I perceive parts, my eye runs over the thing. You will tell me that there are things small enough for me to perceive them at once. Yes and no, perhaps not, maybe so; moreover, however small something is, my perception can begin from the right or begin from the left, from the top or the bottom; it doesn't take very much time, it's a very contracted temporality. I carry out a synthesis of successive apprehension of parts.
But by the same stroke things already become complicated, we must distinguish two cases, we have not finished. In any case the apprehension of parts is successive. There are cases where the succession is objective, this already complicates things. I perceive a house, for example: ... the foreground, the background, the perspective, the foreground becoming background etc. ... there is a kind of subjective apprehension. But I begin from the right, or I begin from the left, and I keep going; in both cases my apprehension is successive, but the succession has only a subjective value. I can begin with the top or the bottom, with the right or the left; this will be reversible or retrograde, whether from right to left or from left to right, I can say that it's the wall in front of me. The succession is in my apprehension, it is not in the thing, it is not in the phenomenon. By contrast, you are sitting on ?????, there again you have a succession, a successive apprehension of parts, but the succession is objective. When the succession is objective, you will say: I perceive an event. When the succession is grasped as solely [subjective?], you perceive a thing. We could say that an event is a phenomenon whose successive apprehension of parts is such that the succession therein is objective. By contrast a thing is such that the succession therein is only subjective.
Thus the first aspect of the synthesis which consists in determining the parts of a space and a time is the synthesis of apprehension. Through this I determine the parts of a space. Let's suppose that you have carried out your successive apprehension of parts, suppose that you are in a curious situation, suppose that is that when you have arrived at the following part you have forgotten the previous one, you would not be able to perceive. There must in fact be an operation of contraction such that when you come to the following part, the preceding one is conserved, otherwise if you lose on one side what you gain on the other, you will never manage to determine a space and a time. This second aspect of the synthesis is the synthesis of reproduction. You must reproduce the preceding part when you come to the following part, so not only must you produce successive parts, but you have to reproduce the preceding parts with the following ones. The two aspects of the synthesis refer to the synthesis as the act of what? Not receptivity, receptivity is solely space and time and what appears in space and time is intuition. The concept is something else. The synthesis refers to the imagination, it is the act of the imagination. This act of the imagination is bizarre; see what he means: it's that through the two aspects, the apprehension of parts and the reproduction of parts, I effectively determine a space and a time. But according to Kant, to imagine is not to fabricate images, it is not to think of Pierre who is not there. To imagine is to determine a space and a time in space and time. There is certainly an empirical imagination. Empirical imagination is when Pierre is not there, I think of Pierre, or else I imagine Pierre, I dream. But the imagination which Kant will call transcendental is the act by which the imagination determines a space and a time, and it determines a space and a time through the synthesis of apprehension and the synthesis of reproduction. But something else again is needed. I am no longer in the situation of a diversity in space and in time, or a diversity of space and time itself, I am in the situation of a space and a time determined by the synthesis of the imagination. And yet I cannot yet say that I perceive. In order to perceive we still need for this space and this time, determined by the synthesis, or what comes to the same thing, that which contains this space and this time, must be related to a form, to a form of what? Not to a form of space or time since we have the form of space and time. What other form? You can see the progression. We started from the form of space and time in general, as the form of intuition, then the act of imagination determines a space, a given space and a given time, through the two aspects of the synthesis. In this case it's a form - not the form of space and time - but a spatio-temporal form, the form of a house or the form of a lion for example, but we need yet another form in order for there to be perception. It is necessary for this space and time, or what contains this determined space and time, to be related to the form of an object.
At this point it becomes difficult to understand. What does it mean that I have to relate it to the form of an object? We can imagine a number of sensations where the sensible givens, the diverse, sensible diversity, are not related to the object-form. It's my perception which is constituted in such a way that sensible diversity is related to the form of an object. In other words, I do not perceive an object, it is my perception which presupposes the object-form as one of its conditions, it's not something, it's an empty form. The object-form is precisely the index by which sensible qualities, such as I experience them, are supposed to refer to something. What something? Precisely a something = nothing. Kant will invent the splendid formula: a something = x. You will tell me that it's not a something = x when I say it's a table or it's a lion, it's not nothing, but the any-object-whatever [l'objet quelconque], the object = x, only receives a determination as lion, table or lighter by the diversity that I relate to it. When I relate to the object = x a diversity comprising: long hair in the wind, a roar in the air, a heavy step, a run of antelopes, well, I say it's a lion. And then I say: look a mouse! What I would like you to understand is that in any case there is an any-object-whatever, the object = x is a pure form of perception. I do not perceive objects, and it's my perception which presupposes the object-form. So the object is specified and qualified by myself according to a given diversity, a given space and time that I relate it to; when I relate a given spatio-temporal diversity, when I relate a given spatio-temporal form to the object = x, the object = x is no longer x, I can say that it's a lion or a house. But inversely I could never say that it's a lion or a house if the empty form of the object = x, the any-object-whatever was not available to me, for it is not the sensible diversity and it is nothing in the sensible diversity which accounts for the operation by which the sensible diversity goes beyond itself towards something that I call an object. Thus, apart from the form of space and of time (the form of intuition), apart from the determined spatio-temporal form (the synthesis of the imagination), I also need a third form: the form of the any-object-whatever such as this form is related to the spatio-temporal form in saying "it's this".
Such that the third aspect of the synthesis, after apprehension and reproduction, is what Kant calls recognition. To recognize. I effect a recognition when I say: "it's this". But "it's this" implies an operation whereby I go beyond what is given to me, I go beyond the forms of space and time, I go beyond purely spatio-temporal forms towards the form of an any-object-whatever that the spatio-temporal form will determine as such or such an object. But just as the two first acts of the synthesis, apprehension and reproduction, refer to the imagination, because it consists in determining a space and a time, so recognition is an act of the understanding. Why? You remember the concepts which are the representations of the understanding, they are the predicates of the any-object-whatever, of the object = x. Not every object is a lion, not every object is red, but every object has a cause, every object is one, every object is a multiplicity of parts, etc.... The predicates that you can attribute to any-object-whatever are the categories of the understanding, they are the concepts of the understanding. So recognition, the form of recognition, the form of the any-object-whatever is no longer in this case the synthesis of the imagination but the unity of the synthesis of ????? [understanding?].
It's the three aspects, apprehension, reproduction and recognition which constitute perception under the conditions [of an other of perception?].
A small note in parenthesis: above all never confuse, in the Kantian vocabulary, the object = x and the thing in itself. The thing in itself is opposed to the phenomenon since the phenomenon is the thing as it appears, whereas the object = x is not at all opposed to the phenomenon, it is the referring of all phenomena to the object-form. The thing in itself is situated outside of our possible knowledge, since we only know what appears, the form of the any-object-whatever is on the contrary a condition. The form of the object = x is a condition of our knowledge. We begin again from zero. I have all the elements [ensemble] of the synthesis: apprehension of successive parts, reproduction of preceding parts in the following ones, reference to the form of an any-object-whatever. So I have referred a spatio-temporal form to a conceptual form: the object-form. So Kant says to himself... let's begin again at the beginning. We have tried to analyze an edifice which emerges from the ground: the edifice which emerges from the ground is the synthesis. What is underneath it? I have said: in order to perceive an object I apprehend its successive parts, but how do I choose these parts? It's a funny sort of thing because it varies greatly according to the object. Apprehending successive parts implies, even at the level of perception, it already implies something like a lived evaluation of a unit of measure. But in following the nature of objects there is no constant unit of measure. In reflection, yes; from the point of view of the understanding, yes, I indeed have a constant unit of measure. I can fix a standard and even so, we will see that this is not even true, but we could fix a standard, put it into place for example and say that there are so many meters. But this is obviously not what Kant means by the successive apprehension of parts. It's like a sort of qualitative measure according to the object. What does that mean? When I see a tree, for example, I carry out my apprehension of successive parts, I begin with the top, then I go towards the bottom, or the other way round, and I say that this tree must be as big as ten men... I choose a kind of sensible unit to carry out my successive apprehension of parts. And then, behind the tree, there is a mountain, and I say how big this mountain is, it must be ten trees tall. And then I look at the sun and I wonder how many mountains it is; I never stop changing the unit of measure according to my perceptions. My unit of measure must be in harmony with the thing to be measured; there are some amazing variations.
Kant tells us in the Critique of Judgement, he is very careful not to before, he tells us that the most elementary act of the synthesis of perception presupposes a logical act. This synthesis of perception is in spite of everything a logical synthesis. I say in spite of everything because at the same time he gives "logic" an entirely new meaning. So once again I must choose a unit of measure, and this unit of measure is variable in each case in relation to the thing to be perceived, just as the thing to be perceived depends on the chosen unit. Beneath the successive apprehension of parts, which is a logical synthesis, even though it refers to the imagination, we need an aesthetic comprehension... this is no longer of the same order as measure; the aesthetic comprehension of a unit of measure such as it is supposed by measuring... Kant is in the process of discovering a sort of basis for the synthesis of apprehension, how an aesthetic comprehension of the unit of measure can be carried out because an aesthetic comprehension of the unit of measure is presupposed by the synthesis of the imagination in perception, namely the apprehension of an [evaluation of a rhythm?]. The evaluation of a rhythm will allow me to say: yes, I'll take that as a unit of measure in a given case; and the rhythms are always heterogeneous, we plunge into them in a sort of exploration. Beneath measures and their units, there are rhythms which give me, in each case, the aesthetic comprehension of the unit of measure. Beneath the measure there is the rhythm. But this is the catastrophe. Again we can no longer stop. We had the synthesis, we remained on the ground and the synthesis was established on the ground; we wanted to dig a bit and we discovered the phenomenon of aesthetic comprehension, and we can no longer stop. The rhythm is something which comes out of chaos, and the rhythm is something which can indeed perhaps return to chaos? What could happen? Let's approach this like a story. I look at something and I tell myself that I'm dizzy, or else my imagination wavers. What happens? In the first place I cannot choose a unit of measure. I don't have a unit of measure; it goes beyond my possible unit of measure. I look for an appropriate unit of measure and I don't have one. Each time I find one it is destroyed. So I am pushed as if by a wind at my back to choose bigger and bigger units of measure, and none is adequate. By the same stroke I cannot carry out my synthesis of apprehension. What I see is incommensurable to any unit of measure. Second catastrophe. In my panic I can perhaps distinguish parts, completely heterogeneous parts, but when I come to the next one everything happens as if I was struck by a dizzy spell: I forget the preceding one; I am pushed into going ever further and losing more and more. I can no longer carry out either my synthesis of apprehension or my synthesis of reproduction. Why? Because what I grasped, what struck my senses, was something which goes beyond any possibility of aesthetic apprehension!
We have seen that aesthetic comprehension was - even though Kant does not say it, but it is what he is thinking of - was the grasping of a rhythm as basis of measure and the unit of measure. You can see the whole of the synthesis of perception: I can no longer apprehend the successive parts, I cannot reproduce the preceding parts as the following ones arrive, and finally I can no longer say what it is, I can no longer qualify the any-object-whatever. My whole structure of perception is in the process of exploding. Why? My whole structure of perception is in the process of exploding because we have seen that it was founded - not in the sense of a ground [fondement], but in the sense of a foundation [fondation] - we have seen that this whole perceptive synthesis found its foundation in aesthetic comprehension, which is to say the evaluation of a rhythm.
Here it's as if this aesthetic comprehension, as evaluation of a rhythm which would serve as a foundation of measure, thus the synthesis of perception, is compromised, drowned in a chaos. The sublime.
Two things are said to be sublime. Kant's response: two things are said to be sublime: the "mathematical" sublime (said to be mathematical because it is extensive), and what is called the dynamical sublime (an intensive sublime). Examples: the infinite spectacle of the calm sea is the mathematical sublime; the starry celestial vault when the sky is clear is the mathematical sublime; it inspires a sentiment close to respect within me, it's a dynamical [?] sublime. In this case the infinity of an expanse gives way to the infinity of material forces, the intensive infinity of forces which fill space and time. The dynamical sublime is the tumultuous sea, it's the avalanche. In this case it's terror. Think to what extent Kant is at the centre of a certain conception of German Romanticism. I'll pass over the reasons why the dynamical sublime is more profound than the mathematical sublime. My second question on the sublime is : what effect does it have on me? We can move forward. I can no longer apprehend parts, I can no longer reproduce parts, I can no longer recognize something, and in effect the sublime, as Kant says, is the formless and the deformed. It is the infinite as encompassing all of space, or the infinite as overturning all of space; if my synthesis of perception is suppressed, this is because my aesthetic comprehension is itself compromised, which is to say: instead of a rhythm, I find myself in chaos.
Everything happens as if the imagination (the synthesis of perception) was pushed to its own limit. Great, we are in the process of rediscovering on the level of the faculty of the imagination something which we found on the level of the faculty of thought: it is not only thought which has a consubstantial relation, a fundamental relation, with an interior limit, the imagination is itself traversed by a limit specific to it, and the sublime confronts the imagination with its own limit. The beautiful, according to Kant, is not this at all, the beautiful is a reflection of the form of the object in the imagination. The sublime is when the imagination is in the presence of its own limit, it is alarmed. There was an enormous ambiguity between rhythm and chaos; I refer you to Paul Klee's famous text, how rhythm emerges from chaos, the way in which the grey point jumps over itself and organizes a rhythm in chaos. The grey point having the double function of being both chaos and at the same time a rhythm in so far as it dynamically jumps over itself; it will organize chaos and allow rhythm. Cézanne tells us that we never look at a landscape, it looks at something, and it is absolute chaos, "iridescent chaos". Cézanne says that it's like a landslide, a cave-in.
At this point I am one with the painting - this is Cézanne speaking - we are an iridescent chaos, etc. ... geological strata... translated into Kantian terms, it's really: I go from the synthesis of perception to [aesthetic?] comprehension...
Fortunately we are not caught up in the sublime all the time, this would be terrible, fortunately we hang on to our perception. At the moment that Kant says that in the sublime the imagination is taken to its own limit, and by the same stroke panicked, like a panicked compass, it is in the process of imagining what cannot be imagined; well at that moment, Kant says, in the respect of the mathematical sublime, or in the terror of the dynamic sublime, we suffer [éprouvons].
At the same time that my imagination is crushed by its own limit, it is a limit which is like its founding kernel, it is the bottomless [sans fond]. What is this bottomlessness of the imagination? It's something which makes me discover in myself something like a faculty which is stronger than the imagination, and this is the faculty of ideas.

Question:Can we say that music is the art of the sublime?

Gilles: That wouldn't be difficult. If I think, out of convenience for you, in terms of the history of philosophy, we can distinguish the arts of the beautiful and the arts of the sublime. However, about the arts of the beautiful and the arts of the sublime, you will find a long history with Schopenhauer and Nietzsche. But how do they make the distinction? Broadly, if you like, all art rests on an Idea; but in the arts of the beautiful it's as if the Idea is mediated, which is to say it is represented. There is a representation of the Idea. In the sublime the will appears for itself. Nietzsche, in so far as he is concerned with the origin of tragedy, will remain with this idea of a preeminence of music over all the arts because music makes the Idea appear as such, in opposition to the other arts which are condemned to representation.
You should sense that an Idea is not from the imagination, but neither is it a concept of the understanding, it's something else still. We thus need a very particular status for the Idea since the whole game of the sublime is this: the imagination is vanquished and derailed before its own limit, but the joy which we experience is because an awareness arises in us of a superior faculty, which Kant will call the super-sensible faculty and which is the faculty of the Idea. With Kant we cease to think the problem of evil in terms of exteriority. Very broadly, in the classical tradition, there is a tendency rather to say that evil is matter, evil is the body, it's what opposes, it's what resists. It's with Kant that this very curious idea appears, which obviously comes from Protestantism, of reform, the idea that evil is something spiritual. It is truly within spirit and not matter as exterior. This is precisely what I was trying to say with the notion of limit in Kant: the limit is not something outside, it is something which works from within. Here evil is fundamentally bound to spirituality; it is not at all as it is in Plato, where if there is evil it is because souls fall, and obviously they incarnate themselves in a body. With the reform the devil is taken seriously, only taking the devil seriously can be a philosophical operation. Evil is not the body, evil is truly in thought qua thought.
Question: Can you give the definitions of causality in Kant?
Gilles: There are several. The first definition of causality is: causality is the faculty of making something begin in the order of phenomena. It's a simple definition which implies two causalities: a causality which Kant calls phenomenal, namely that phenomena follow on from each other, and a phenomenon begins something which will be called its effect, and, second causality, the so-called free causality - because phenomenal causality is a determined causality and free causality is the faculty of beginning something in the order of phenomena on the basis of something which is not itself caused.
Second definition of causality, those before were nominal definitions, second definition: it's the relation between phenomena when the succession in their apprehension corresponds to an objective rule. Example: the boat which goes down the flow of the river, there the succession corresponds to an objective rule in opposition to succession in the perception of reason, where there is no causality. I would not say that the right side determines the left side, whereas in the perception of the boat I would say that the preceding state determines the following state.




Today I would like to be as clear as possible within a problem which is nevertheless complicated. I have only one idea at best which I would like to develop today, and which is not only linked to the desire to help some of you in speaking about Kant in a precise way, but also to try and show a kind of development of an amazing problem throughout Kant's philosophy. The centre of everything I would like to say today is precisely this: if we stay with the Critique of Pure Reason, Kant's famous book, we can well see, in relation to the themes which concern us involving time, we can well see that there are two great operations. What these two great operations of knowledge have in common - since pure reason is concerned with knowledge - what these two great operations of knowledge have in common is that in both cases a correspondence is created, despite their heterogeneous elements, despite their difference in nature, between conceptual determinations and spatio-temporal operations. These two great operations by which a correspondence is created - whatever the difficulties this correspondence involves given their heterogeneity - between spatio-temporal determinations and conceptual determinations are both synthetic operations. They are synthetic for very simple reasons, they are necessarily synthetic since, as we have seen, spatio-temporal determinations on the one hand and conceptual determinations on the other hand, space-time and concepts, are heterogeneous, so the act which puts them into correspondence can only be a synthesis of heterogeneities. These two synthetic operations have names. These two operations also have in common the fact of being acts of the imagination. Obviously imagination no longer means making up ideas or imagining something, since Kant gives a fundamentally new meaning to the act of imagination, since it is the act by which spatio-temporal determinations will be put into correspondence with conceptual determinations. You will ask me why he calls that "imagination"? Understand that he is already at a level where he grasps imagination at a much deeper level than in the preceding philosophies; imagination is no longer the faculty by which we produce images, it is the faculty by which we determine a space and a time in a way that conforms to a concept, but that does not flow from the concept which is of another nature than the determination of space and time. It is really the productive imagination in opposition to the reproductive imagination. When I say: I imagine my friend Pierre, this is the reproductive imagination. I could do something else besides imagine Pierre, I could say hello to him, go to his place, I could remember him, which is not the same thing as imagining him. Imagining my friend Pierre is the reproductive imagination. On the other hand, determining a space and a time in conformity to a concept, but in such a way that this determination cannot flow from the concept itself, to make a space and a time correspond to a concept, that is the act of the productive imagination. What does a mathematician or a geometer do? Or in another way, what does an artist do? They're going to make productions of space-time.
The two synthetic operations which establish the correspondences of space-time to concepts. I said that Kant gives them very strict names, and it would be very unfortunate to confuse these two operations. One is designated under the name of synthesis strictly speaking, synthesis as the act of the productive imagination and the other - which is no less synthetic - Kant saves another name for it, that of the Schema. A schema. It is also an operation of the productive imagination. One of our problems is what the difference is between a synthesis strictly speaking and a schema. We have seen what they have in common: in both cases it is a matter of determining a space and a time in correspondence with a concept. But my second problem is that if we don't stay with the Critique of Pure Reason, if we go on to one of Kant's last works, where Kant goes deeper and deeper, which is to say if we effect a confrontation with the ultimate work, the Critique of Judgement, and if we see its effect on the Critique of Pure Reason, we realise that Kant reveals to us in the Critique of Judgement an amazing double adventure: how synthesis, as act of the imagination, can be overwhelmed by a fundamental experience which is the experience of the sublime; thus that there is an operation of extreme fragility in the synthesis: something which comes from the depths [le fond] puts ???? this operation at risk at each instant, drowning it. Drowning it in a simple destruction? No, in favour no doubt of the revelation of another level which is the revelation of the sublime and thus that the synthesis of the imagination risks being overwhelmed by another act, or rather by another passion, by a sort of passion of the imagination which is the spectacle and the experience of the sublime, where the imagination vacillates on its own ground.
On the other hand, it is quite curious how it's both inspired and works in symmetry; it is really the hinge of Classicism and Romanticism. The Critique of Judgement is really the great book which all the Romantics will refer to. They had all read it, it will be determining for the whole of German Romanticism. But on the other hand as well we experience the same adventure, but under another form. The schema, which is the other act of the imagination, risks being overwhelmed by something which comes from the depths of the imagination in the same way as the synthesis, namely the experience of the sublime, the schema - [the] other act of the imagination from the point of view of knowledge - also risks being overwhelmed by something monstrous, which Kant is the first to analyse, to my knowledge. It is symbolism. In the same way that the sublime threatens at each instant to overwhelm the imagination's act of synthesis, the operation of symbolism and symbolisation threatens at each instant to overwhelm this other act of imagination which is the schema. So much so that between symbolism and the sublime, there will obviously be all sorts of echoes, as if they brought about the emergence of a sort of ground [fond] which is irreducible to knowledge, and which will testify to something else in us besides a simple faculty of knowing. Feel how beautiful it is.
So first we must go via something more reasonable, duller: what is the difference between the schema and the synthesis? The last time I tried to show what the synthesis was. The synthesis as act of the imagination consists precisely in this - but I want this to be very concrete, which is good if one is in the world and in the world there are Kantian phenomena; if you come across a typically Kantian moment in the world, then it's very good, at that moment you must speak in Kantian terms; they are phenomena which can only be grasped through Kantian spectacles, if not you pass on by. The synthesis and the schema are always the forming of a correspondence between, on the one hand conceptual determinations, and on the other spatio-temporal determinations. What defines the synthesis as distinct from the schema? The synthesis is an act of the imagination which operates here and now; there is no synthesis if it is not an operation of your imagination that you do here and now. For example, here and now, you see a diversity; or else here and now you see an organisation of space and time. You will recall that this space and this time are not yet determined: there is something in space and time. A synthesis must yet be effected which will give you a certain space and time, in such a way that you carry out a sort of isolation: if you say "that is a table", you have carried out a synthesis of space and time in conformity with a concept. There is the concept table, and then you have synthesised, you have carried out a synthesis of a certain diversity. So the principle of the synthesis is recognition, it is this. The synthesis has as its rule the process of recognition. Given this, it is obligatory that the synthesis operates here and now: look, it's a house. What does the synthesis consist in? We saw it last time: successive apprehension of parts, synthesis of apprehension, reproduction of the preceding parts in the following parts; thus the two aspects of the synthesis, apprehension and reproduction, are what I use to determine a finite space and time.
The concept is the form of the object which I qualify according to the diversity whose synthesis I have effected: it's a table, it's a house, it's a small dog.
So, in the synthesis, I have indeed effected a correspondence between a determination of space and time and a conceptual determination, the determination of space and time being carried out by the synthesis of apprehension and reproduction, and the conceptual determination referring to the form of the any-object-whatever in so far as this form of object will be determined by the diversity upon which I effect the synthesis. I would almost say that in the synthesis I go from the spatio-temporal determination to the conceptual determination and that my point of departure is here and now. You can see that, at the beginning, I only have a concept of any-object-whatever; I only have the form of an any-object-whatever which is the empty form of the concept, object = x. Why is this a concept? Because it is not at all contained in the sensible diversity. So as the form of the pure concept I have only the form of the any-object-whatever, and the synthesis of the imagination will make a spatio-temporal determination correspond to the any-object-whatever in such a way that the any-object-whatever will be specified as such or such an object: this is a house, this is a table.
There is something quite curious in Kant. When things don't work, he invents something which doesn't exist, but it doesn't matter. The schema. Put yourself in the reverse situation. You have the concept, you start from the concept. So the path of the schema will no longer be the here and now, not what your productive imagination does here and now, that is determine space and time, the schema will be on the contrary an operation that you carry out, when you carry it out, as valid at all times. "This is a house" is not valid at all times. You recall the rule of the synthesis, it's a rule of recognition. The schema: you have a concept, and the problem is to determine the spatio-temporal relation which corresponds to this concept. The synthesis is just the opposite, it's this: you carry out a spatio-temporal operation and you specify the concept according to this determination. So the operation of the synthesis, valid here and now, will correspond with, in the other direction, the determination of the schema, valid at all times. There you have a concept and you are looking for the spatio-temporal determination which is likely to correspond to it. What does that mean? When I say: the straight line is equal in all its points, Euclid's definition, I have a concept of a straight line. You will tell me, yes, but it's already spatial. Yes it's spatial, but with space, I can make a concept of space for myself. A straight line defined as a line equal in all its points doesn't yet give me any determination, and while the synthesis went from the space-time intuition to the concept carried out by a rule of recognition, the schema on the contrary will operate by a rule of production. Given a concept, how can I produce it in intuition? Which is to say in space and in time, an object conforming to the concept. Producing in space and time, that is the operation of the schema. In other words, the schema does not refer to a rule of recognition, but refers to a rule of production. The synthesis of a house is the rule of recognition according to which I say "it's a house". You say "it's a house" in front of very different things. You effect a synthesis of the given such that you relate them to the any-object-whatever "it's a house". The schema of the house is very different, it is not a rule of recognition over random diversities. The schema of the house is a rule of production, namely that you can give yourself a concept of house. For example I can take a functional definition: house = apparatus made for sheltering men, this doesn't yet give us a rule of production. The schema of the house is what allows you to produce it in experience, in space and in time, something, objects conforming to the concept. But that definition does not get out of the concept; you can turn the concept around all you like in all directions, apparatus made for sheltering men, you will not draw rules of production from it, the rules of construction of the house. If you have the rule of production you have a schema. It is very interesting from the point of view of a study of judgement. Consider the two following judgements: the straight line is a line equal in all its points; there you have a logical or conceptual definition, you have the concept of the straight line. If you say "the straight line is black", you have an encounter in experience, not all straight lines are black. The straight line is the shortest path from one point to another, it's a type of judgement, a quite extraordinary one according to Kant, and why? Because it cannot be reduced to either of the two extremes that we have just seen. What is the shortest path? Kant tells us that the shortest path is the rule of production of a line qua straight. If you want to obtain a straight line, you take the shortest path. It is not a predicate at all. When you say: the straight line is the shortest path, you seem to treat the shortest path like an attribute or a predicate, when in fact it is not a predicate at all, it's a rule of production. The shortest path is the rule of production of a line qua straight line in space and in time.
Why in time? Here you must understand why time is involved in this, and even more deeply still than space. You can't define the shortest independently of time. How is it a rule of production? If someone says to you: you want to draw a straight line, very well, take the shortest! We no longer understand the judgement; we say so many things without knowing that we say them. Once again it is true historically that the judgement "the straight line is the shortest path between one point and another" has very very precise implications from a geometrical point of view, namely that while the Euclidean or conceptual definition of the straight line is indeed a line equal in all its points, the straight line as the shortest path from one point to another is an Archimedean notion, and Archimedean geometry has quite different principles than Euclidean geometry. The notion "the straight line is the shortest path" is purely nonsensical if you separate it from a whole calculus which is a comparison of heterogeneous elements. Here you find the theme of the synthesis again. The heterogeneous elements are not the different sorts of lines, straight or not straight, it's the confrontation of the curve and the straight line. It's the Archimedean theme of the minimal angle, of the smallest angle which is formed by the tangent and the curve. The shortest path is a notion which is inseparable from the calculus which in antiquity was called the calculus of exhaustion in which the straight line and the curve are treated in a synthetic confrontation. Given this, tracing the tangent to the curve is indeed a rule of production. So it is in this sense that I can say, despite appearances, that the straight line is the shortest path, we must see that the shortest path is not an attribute of the line and this is not surprising since "the shortest" is a relation. A relation is not an attribute. If I say Pierre is smaller than Paul, "smaller" is not an attribute of Pierre. Even Plato said that if Pierre is smaller than Paul, he is bigger than Jean. A relation is not an attribute. "The shortest" is the rule according to which I produce a line qua straight line in space and in time. In other words, I make a correspondence between a conceptual determination, that is the straight line defined as equal in all its points, and a spatio-temporal determination by which I can produce as many straight lines as I like in experience.
In one of Kant's distant successors, namely Husserl, there is something like this which also interests me very much, but I think Husserl has let something slip away. Husserl said to us: take two ends, at the two extremities of the chain, you have pure essences. For example the circle, as pure geometrical essence. And then, at the other end, you have things in experience which correspond to the circle. I can make an open-ended list of them: a plate, a wheel of a car, the sun. I would say, in technical terms, that all of these things in experience, a wheel, the sun, a plate, are subsumed under the concept of a circle. Can you not see a series of intermediaries between these two extremes, which will be of great importance from Kant onwards. But notions, they must be lived, the abstract is lived, it's really the same. At the moment when something becomes very very abstract, then you can say that it concerns something lived. We already know that "between the two" is not a mixture, that it will be a zone discovered by Kant. Take a word: "the ring" [le rond]. I can always say that the circle is a ring. The conceptual determination of the circle is: where points are situated at equal distance from a common point named centre. That's the conceptual determination, the empirical determination or determinations are the plate, the wheel and the sun. When I say: "oh what a beautiful ring [rond] !" - I was saying just before that the two extremes are the line conceptually defined as equal in all its points, and then "the straight line is black" which is an encounter in experience, a case of a straight line. But between the two, as a perfectly specific region, there is "the straight line is the shortest path."
Now between the circle and the illustrations of the circle in experience, I would almost say the images of the circle : the plate is an image of a circle, the wheel is an image of a circle, but I have this bizarre thing: a ring [rond]! It is very curious to do the logical analysis of a ring. I would say the same thing: if we go far enough in our analysis of the round, we will see that it's a rule of production; for example a round is the circumference [le tour], no, the round is what allows us to make a circumference.
The circumference is what allows us to make certain materials round. The ring must obviously be lived dynamically, as a dynamic process; in the same way that "the straight line is the shortest path" implies an operation by which the length of a curve is compared to that of a straight line, which is to say by which there is a linearisation of the curve, the ring implies an operation by which something in experience is rounded. It's a process of production of the circumference-type which allows the production in experience of things corresponding to the concept circle.
Where Husserl is obviously wrong is when he discovers this sphere of the ring - we have just shown how the ring is completely in the same domain as the shortest, it's the same domain of being - Husserl is wrong because he makes them into inexact essences, like subordinate essences. The direction that Kant went in seems much stronger to me, making them precisely into acts of the productive imagination. Here you can see in what respect the productive imagination is more profound than the reproductive imagination. The reproductive imagination is when you can imagine circles, concrete circles; you can imagine a circle drawn on a blackboard with red chalk, you can imagine a plate... all that is the reproductive imagination. But the circumference that allows you to make rounds, which allows you to round things, which is to say to produce in experience something conforming to the concept of circle, that doesn't depend on the concept of circle, that doesn't flow from the concept of circle, it's a schema, and that is the act of productive imagination.
You can see why Kant feels the need to discover a domain of the productive imagination distinct from the simply empirical or reproductive imagination. You can see the difference between a schema and a synthesis, if you have understood that I have finished with my first point: what the difference was between the two fundamental acts, within the context of knowledge: the schematism and the synthesis.
The schematism is not a case of reflective judgement, it is a dimension of determining judgement. I will do the story of reflective judgement on request.
The a posteriori is what is in space and in time. It's the plate, the wheel, the sun. A rule of production is solely a determination of space or of time conforming to the concept. Take another case. You make yourself a concept of a lion; you can define it by genus and specific difference. You can define it in this way: big animal, mammal, with a mane, growling. You make a concept. You can also make yourself lion images: a small lion, a big lion, a desert lion, a mountain lion; you have your lion images. What would the schema of a lion be? I would say in this case, not in all cases, that the concept is the determination of the species, or its the determination by genus and specific differences. The image in experience is all the individuals of this species, the schema of the lion is something which is neither the examples of a lion... [end of tape] ... there are spatio-temporal rhythms, spatio-temporal attitudes [allures]. We speak both of an animal's territory and an animal's domain, with its paths, with the traces that it leaves in its domain, with the times that it uses a particular path, all that is a spatio-temporal dynamism that you will not draw from the concept. I am not going to draw from the concept of a lion the way it inhabits space and time. From one tooth you can draw something of a mode of living: this is a carnivore. But really the spatio-temporal dynamism of an animal, that is really - I can't say its rule of production - but it's something productive, it's the way in which it produces a spatio-temporal domain in experience in conformity with its own concept. The lion is Kantian, all the animals are Kantian. What is the schema of the spider? The schema of the spider is its web, and its web is the way it occupies space and time. The proof is that the concept of the spider, I don't know how, but you can take the concept of a spider; the concept of a spider will include all of its anatomical parts and even the physiological functions of the spider. Thus one will encounter that funny sort of organ with which the spider makes his web. But can you deduce from it what we can now call the spatio-temporal being, and the correspondence of the web with the concept of a spider, which is to say with the spider as organism. It's very curious because it varies enormously according to the species of spider. There are cases of very extraordinary spiders which, when you mutilate one of their legs, which is nevertheless not used for fabrication, make abnormal webs in relation to their own species, they make a pathological web. What happened? As if a disturbance in space and time corresponded to the mutilation. I would say that the schema of an animal is its spatio-temporal dynamism.
Where Kant was determining, after Husserl, there were all sorts of experiments and I'm thinking of a funny sort of school which, at one time, had some success. It was the psychologists of the WŸrzburg school, they were closely linked to a Kantian lineage. They carried out psychological experiments. They said that there are three sorts of things: there's thought which operates with concepts, and then there's perception which grasps things, and if need be there is the imagination which reproduces things: but they said that there is also another dimension which they gave a very curious name to. They spoke of the direction of consciousness, or even of the intention of consciousness, or even of an empty intention. What is an empty intention? I think of a lion and an image of a lion comes to me; I think of a rhinoceros and I can see the rhinoceros very well in the image which comes to my mind, that is an intention. I have a conscious intention and an image comes to fill it, the image of the rhinoceros. So they carried out experiments on this, it was experimental psychology. They set the rules of the game, you're going to laugh: you stop yourself from having an image, you are given a word and you take a view which both excludes any image, and which nevertheless is not purely conceptual; what does that produce? It produces sorts of conscious orientations, i.e. spatio-temporal directions. The more abstract it was, the better. It was in order to persuade us that there were three possible attitudes of conscious: abstract thinking consciousness, for example proletariat, where one had to work for the proletariat. First reaction: proletariat = the class defined by... etc... I would say that that is the conceptual definition of the proletariat; it is a certain attitude of consciousness towards a word: I aim at the concept through the word. Second attitude of consciousness: through the word proletariat I evoke one, a proletarian: "ah yes, I've seen one!" That is really the empirical attitude, an image. Sartre, in his book The Psychology of Imagination, describes the third attitude, that of the WŸrzburg-type experiments, and he gives descriptions of people's responses; I see a sort of black wave advancing; it defined a sort of rhythm. Managing to grasp an attitude of consciousness, a sort of way of occupying space and time: the proletariat doesn't fill space and time in the same way as the bourgeoisie. At that moment you have the schema. Or else another method was to take a word that is empty for you, whose meaning you don't know: in a precious poem, and you carry out the direction of consciousness, you don't make an association, but a vague direction of consciousness, a sort of purely lived spatio-temporal opening. How does a consciousness orient itself following the sound of an understood word? There you have a whole dimension of spatio-temporal dynamisms which are somewhat similar to the schema. The schemas are subdivided, but while the concepts are subdivided according to genus and species, the schema will have another mode of division. In fact when I said that the true schema of the circle was the circumference, it is in fact a sub-schema because the circumference already implies certain modes, the circumference is the rule of production in order to obtain things in experience, but in these conditions of suitable materials. In other cases, something else would be required. I don't know how bicycle wheels are made? When phenomenology and then Heidegger, then all sorts of psychiatrists go on to define ways of being in space and in time, complexes or blocks of space-time, rhythmic blocks, I'd say that all that derives from Kant. Indeed the ethnologist constructs schemata of men to the extent that he describes manners: a civilisation defines itself, amongst other ways, by a block of space-time, by certain spatio-temporal rhythms which will vary the concept of man. It's obvious that an African, an American or an Indian won't inhabit space and time in the same way. What is interesting is when, in a limited space, we see the coexistence of different types of space-times. I could equally say that an artist operates through blocks of space-time. An artist is above all a rhythmicist. What is a rhythm? It's a block of space-time, it's a spatio-temporal block. But each time you have a concept, you don't yet have the rhythmicity of the things which are subordinated to it. A concept, at best, will give you the beat or the tempo. Which is to say a homogeneous beat, but rhythmicity is something entirely different from a homogeneous beat, something entirely different from a tempo.
I'll go on to my second point. You remember that we saw, in relation to the synthesis, this adventure of the sublime. Kant realises that the synthesis of the imagination, such as it arises in knowledge, rests on a basis of a different nature, namely that the synthesis of the imagination in all its aspects assumes an aesthetic comprehension, an aesthetic comprehension both of the thing to be measured and the unit of measure. You must be clear that aesthetic comprehension is not part of the synthesis, it's the basis [sol] that the synthesis rests on. I would say that it is not the ground [fondement] of the synthesis but that it is the foundation [fondation] of synthesis. At the same time that he discovers this basis, he discovers the extraordinary viability of this basis. He doesn't discover this basis without also seeing that this basis is ????? Why? Because what the synthesis rests on is fundamentally fragile, because the aesthetic comprehension of the unit of measure, assumed by all effective measurement, can at each instant be overwhelmed, which is to say that between the synthesis and its basis there is the constant risk of the emergence of a sort of thrust coming up from underground [sous-sol], and this underground will break the synthesis. For the synthesis rests on the aesthetic comprehension of the unit of measure, an aesthetic comprehension which is irreducible to the operations of knowledge. Why is this very fragile? Because at every instant there are types of phenomena in space and in time which risk overturning the aesthetic comprehension of the unit of measure, and it's the sublime, where the imagination finds itself before its limit. It is confronted with its own limit, it can no longer be at the service of the concepts of the understanding. To be at the service of the concepts of the understanding is to determine space and time in conformity with the concepts of the understanding, and here it can no longer do this: the imagination finds itself blocked before its own limit: the immense ocean, the infinite heavens, all that overturns it, it discovers its own impotence, it starts to stutter. And it is thus at the same time that the basis of the synthesis, namely aesthetic comprehension, and the underground of the synthesis, namely the sublime in so far as it overturns the base, is discovered. But there's a consolation; at the moment that the imagination finds that it is impotent, no longer able to serve the understanding, it makes us discover in ourselves a still more beautiful faculty which is like the faculty of the infinite. So much so that at the moment we feel for our imagination and suffer with it, since it has become impotent, a new faculty is awakened in us, the faculty of the supersensible.
When the storm is over, when the avalanche is finished, I rediscover my syntheses, but for a moment the horizon of knowledge will have been traversed by something which came from elsewhere, it was the eruption of the sublime which is not an object of knowledge. We must put ourselves in Kant's place, assuming that he has discovered all of this. He says to himself that there must be something analogous for the schema. The schema is also an operation of knowledge, we saw its relation to the synthesis; the schema must also follow its own limit and have something overwhelm it. It must be something different, a different adventure. There is no reason to treat philosophy in a different way from art or science. There are differences but they aren't at the level we think they are. Here is the schema of the schema: I make a big white ring [rond] up top and I put A on the side. To explain: this big white ring called A is the concept of a. Concept of a. Vertically, I make a dotted line, above all dotted, with an arrow at the end, and at the end of the arrow, beneath, I put a. I'll explain, but for those who want the complete schema: from the a which is beneath the end of my arrow, I make a filled line this time, a spray of little arrows, and under each of the little arrows I put a', a'', a '''. The big A is the concept a, at the end of my dotted arrow I have a, it's the schema of A, that is, the spatio-temporal determination A. If I take an example: A = concept of the circle, a = the ring or the schema of the circle, which is to say the rule of production. Then a', a'', a''' are the empirical things which conform to the schema, and led back to the concept by the schema. So a' = plate, a'' = wheel, a''' = sun, in our previous example. Why is it that the arrow which goes from the concept to the schema was dotted? Precisely in order to indicate subtly that the symbol which he opposes [to] or which he explicitly distinguishes from the schema in the Critique of Judgement, and it's among the most admirable pages in Kant. Well that's going to complicate things and here are the two schemas.
A = concept. a = schema of the concept, which is to say spatio-temporal determinations. B, dotted arrow and b. We need that to make a schema. I'll give examples. First example: A = the sun. a = to rise (spatio-temporal determination). Let's say that this is the auto-schema of the concept. B, the virtue of the concept, b: schema or intuition = x?
Second example: A = the sun, a = to set. You can see that these are two sub-schemas, I could have taken rising and setting in a single schema. B = death. b = intuition = x of death. Third example: A = a mill. a = a type of mill which implies a certain space-time, which is to say not the general schema of a mill, but a certain schema corresponding to category of mills = hand-mill. B = despotic constitution. b: intuition = ? = x.
I have two remarks to make if you understand these examples. There would be symbolisation when you use the schema or intuition a, not in relation to the corresponding concept A, but in relation to the quite different concept B for which you have no intuition of a schema. At that moment the schema ceases to be a rule of production in relation to its concept, and becomes a rule of reflection in relation to the other concept. So much so that you have the Kantian sequence: the synthesis refers to a rule of recognition, the schema refers to rules of production, the symbol refers to rules of reflection.
Why don't I have any intuition corresponding to the concept? Two possible cases: either because I don't in fact have one, because I lack the necessary knowledge, but I could have it, I could form a schema of the concept. Or else by virtue of the special nature of this concept.

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