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.