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Outline of Critique Of Pure Reason:
Prefaces

Introduction (I VII)
/ \
Part I Part II
Transcendental Doctrine of Elements Transcendental Doctrine of Method
/ \ (see below)
First Part Second Part Transcendental Aesthetic Transcendental Logic
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1. Space 2. Time
Introduction
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Division I Division II
Transcendental Analytic Transcendental Dialectic
 
Introduction Introduction
/ \ / \
Book I Book II Book I Book II
Analytic of Concepts Analytic of Principles Concepts of Pure Reason Dialectical Inferences of Pure Reason
/ \ /  \
version A version B Chapt. I Chapt. II Chapt. III Transcendental Deduction Paralogisms Antimonies Ideal
Chpt I Chpt II Chpt III
Schematism System Noumena/Phenomena
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1 2 3
Analytic Synthetic Systematic Representation Part II
Transcendental Doctrine of Method
Axioms
Anticipations i. Permanence of Substance
Analogies ii Succession in time and Causality
Postulates iii. ReciprocityCommunity
Refutation of Idealism
HYPERLINK \l "gobackwiggle" gobackwiggle
HYPERLINK \l "goback2330" goback2330 (part 2) HYPERLINK \l "gobackanalogies" gobackanalogies HYPERLINK \l "gobackrefutation" gobackrefutation
00:00Logistics1:30Today we will polish off the B Deduction and transition in to the Schematism
Then in the next two weeks we will look at the Analogies and the Refutation of Idealism.
The final week we will take a look at the 3rd Antimony.
We will frame next week by almost relaunching the entire project of this course. That is we will try to show next week how you go via the Analogies and the Refutation and the problem of freedom into German Idealism and beyond.
In a way we are restarting the whole course next week.2:30Last week we left off with 20.
On our reading, just as a reminder, 19 is a reworking or rather an insertion of the argument of the Metaphysical Deduction into Transcendental Deduction. So that the notion became one of realizing that the categories are the very functions for judging, and they play the role they do by determining the representational content of a cognition, namely its form.
Thereby there is such a thing as an essential structure or a general form to judgment and hence, just to set up the equation, the thought is:
Making a judgment = the application of a category = spontaneously grasping an intuitive manifold (as the presentation of an object).
What we are trying to claim here is that in all of this there is just one act, there is just the act of judging. And the act of judging just is the application of a category, because categories are the things that structure via the logical functions of judgment.
They involve the application of categories, and the application of categories just is the spontaneously grasping of the manifold in an intuition as the presentation of an object.
This is to say that it is not the case that every time we say S is P we are using the categoriesthat is plainly false. But it is to say that every time we grasp something as a substance with a property, it is tied up with the subjectpredicate form of judgment. So it is the other way around.
Every use of a logical functions, in order to grasp the manifold in an intuition involves the presentation of states of affairs, hence involves an application of categories.8:00So that is why it is helpful to think of the logical functions of judgment as like the rules of chess, which tells you nothing about any game of chess.
They are pure form. And every game is totally contingent, but nonetheless you couldnt get any game started without the rules, how each piece can move, etc. 9:00So judgment is importantnot because all cognition is judgment, although that is in fact truejudgment is important because all cognition involves both receptivity and spontaneity, and spontaneity can only be objective if it is grounded in the essential structures of judgment.
That is the thought to get clear on, the crucial piece of the puzzle.
And that should bring us up to 20.10:0020 HYPERLINK \l "a1" a1
All Sensible Intuitions are subject to the Categories,
as Conditions under which alone their Manifold can come
together in one Consciousness.
The manifold given in a sensible intuition is necessarily subject to the original synthetic unity of apperception, because in no other way is the unity of intuition possible (17) [ HYPERLINK \l "a2" a2]. But the act of understanding by which the manifold of given representations (be they intuitions or concepts) is brought under one apperception, is the logical function of judgment (cf. 19) [ HYPERLINK \l "a3" a3]. All the manifold, therefore, so far as it is given in a single empirical intuition, is determined in respect of one of the logical functions of judgment, and is thereby brought into one consciousness [ HYPERLINK \l "a4" a4]. Now the categories are just these functions of judgment, in so far as they are employed in determination of the manifold of a given intuition (cf. 13) [ HYPERLINK \l "a5" a5]. Consequently, the manifold in a given intuition is necessarily subject to the categories[ HYPERLINK \l "a6" a6].
HYPERLINK \l "goback5300" goback53:00[a1] 20 is just the summary of the argument and it looks like it should be the completion of the argument. We will have to explain in what sense it is not.[a2] notice it is the unity of intuition, that is there. That is importantit is not the unity of sense data herebecause intuition is a representation.
The crucial point is that the reason it has got to be grasped by the original synthetic unity of apperception is because it is a unity of intuition, namely the unity of a representing.
And a unity of a representing is only possible by something holding together, of the various parts hanging together. That is the notion of representational unity. 11:30[a3] So the kind of unity, the kind of hanging together that is cognitively significant for us human beings is judgmental unitythat is what counts as unified; subject is predicate; that is the kind of unity that is at stake.
HYPERLINK \l "gobacksec20" gobacksec2012:30[a4] So given this story about judgment, then one of the logical functions of judgment must be operative in any judgment.13:00[a5] That is the movement from logical functions of judgment to categories. This, again, is what the Metaphysical Deduction is all about.
That is, the point of the Metaphysical Deduction is that the categories are the sensible and material counterparts of the logical functions of judgment.
HYPERLINK \l "gobacksec20" gobacksec2013:30[a6] Thats it. We dont need anything else. 14:00Question: whats the difference between the logical functions of judgment and the unity of apperception?The unity of apperception is accomplished via the logical functions of judgment.
That is, how does my mind sweep them all up? It gathers them together by judging. So the notion of unity that I need, the notion of synthesis
The TUA = synthesis of the manifold = making a judgment.
We want to be absolutely clear on this point.
And our claim has been that the I think becomes making a judgment and that making a judgment is something that is done always by an individual from a point of view.
So that my judgment this is a cupthis is the great objectification. Although that objectivates it in space and time as independent from my subjectivitythat is what he said about the copula is: I saying, e.g. the cup is round I am saying something of the object that is true irrespective of the state of my subjectivity. That is what the copula means.
On the other hand, only I can do that. So it is my judgment from a point of view. And that is Kants way of claimingand this is the fullest burgeoning of the Cartesian cogitois that the heart of subjectivity, the subjectivity of the subject, the I think, is itself an objectivity that generates worldhood.
That is the great moment in modern philosophy.
This is why in their different ways even Heidegger and MerleauPonty are fully moderns because they are trying to find in the very core of subjectivity an objectivityan exteriority.
So at the very place I look to abstract myself most completely from the worldmy spontaneitythat is the very thing that reaches out and gives me a world in general. And that is just what Descartes wanted.
That is why Descartes thought that the cogito ergo sum ended skepticism and introduced certainty. That is what Descartes meant by suddenly finding at the very point in which the evil demon was reaching into his soul he says no exist anyways you SOB.
This is actually an argument against faith which is why we know Descartes was an atheist. The evil demon and doubt must be an argument about the relationship between faith and reason and it must be an argument concerning why the very idea of faith is a repudiation of self and therefore the affirmation of the cogito is an affirmation of the self against any conceivable deity.
That has got to be what is going on in Descartes.19:00What Kant is trying to do is carry out that Cartesian project where you find the resources just at this moment [of spontaneity, of subjectivity] for objectivity.
Question:
[i] all analysis presupposes a prior synthesis [e.g. B130]
[ii] the force of the Deduction is that it is all just an analysis of what is wrapped up in the I think.
[iii] Therefore, mustnt the analysis of the I think assume a prior synthesis? So what is this prior synthesis that gets us the I think?20:30
The quick and facile response here it so to keep in mind the motto (and dont underestimate the value of the vulgar in philosophy):
no unity without unification
Analytic unity is a form of unityone thin is contained in another. And so the Kantian dictum says that nothing is going to count as analytically unified unless we have unified it.
So every form of givenness in Kant turns into an activity. This will come out again in Hegelevery form of givenness becomes something we do rather than something we suffer.
So he does want to do a form of analysis, but he does want to show that underlying what looks like analytic truths there is synthetic activity.22:30Question on disjunctive and hypothetical judgmentsKant thinks that these logical functions are either judgments or the basic logical relations between judgments.
So ifthen is for him an irreducible relation between judgment.
If X is the case then Y is the case. Here X is a judgment (#1) and Y is also a judgment (#2) [and the ifthen form is a judgment about the relation between categorial judgments.]
These [disjunctive and hypothetical judgments] are the exemplary forms of spontaneity.
Spontaneity here is the case if the relationshipKant didnt have modern symbolic logic, so he didnt have the law that (X v Y) is true if either X is true or Y is true or both are true [so long as both are not false (X&Y)], but nonetheless, he thought that anything like that was exemplary of spontaneity.24:30
Just remember where we started. We said that Kants starting point is that cognition is discursive. Discursivity is a matter of doing something with concepts, not mental vision.
So Kant doesnt think that having a truth is seeing, having a mental perception of a truth, but rather it is making a judgment and/or following certain logical laws.
It is always a doing of something and of connection of concepts in particular ways.25:30
So Kant seems to have completed the task of the Deduction when he said ( HYPERLINK \l "gobacksec20" gobacksec20) in concluding 20:
Consequently, the manifold in a given intuition is necessarily subject to the categories.
That looks like QED for the whole deduction.
Needless to say that in the Kant scholarship there are dozens of different interpretations of why the Deduction goes on.
We will largely let these interpretations go because they all more or less assume that the Deduction continues after 20 because something has been left unshown.26:30So each interpretation has to say that Kant really hasnt shown everything yet. Allison, for example, thinks that he hasnt shown that we have objects in the weighty sense of external to us. Howell thinks he hasnt shown that it applies to human sensibility. Heinrich thinks that he hasnt shown that it applies to more than one given intuition that is unified by itself.
For Jay these are all farfetched.The right account, rather, is that 20 reaches an unrestricted conclusion about discursive cognition in general.
That is, the manifold of a given intuition stands under categories.
The puzzle then is what then 26 adds? 28:00
We will go through it piece by piece (over the next few weeks) but the overview is that what 26 adds is that the spatiotemporal structure of all possible human cognition is a particular determination of the abstract determined structure that is common to all possible discursive cognition.
29:00
So the claim is that in 20 we reach an unrestricted conclusion and what 26 simply adds is a further determination. That is, it is a move from the abstract to the concrete. It is not a newer, extra thought.
It is not solving a new problem. Rather it is a making more precise by making more concrete what we already knowit is already assumed that this holds.
We are talking about intuition, so we are talking about sensible intuitionof course, because this is the only kind of intuition we can have.
So we cant not be talking about sensible intuitions (as Dieter Heinrich would have it).But what we havent done is said anything concrete about sensible intuitionsnamely, that they are spatiotemporal.
So all this is is a form of further determination or further concretion of the original argument. 30:00
So what 26 is going to argueand this is our summary of the first , which we will presently turn tobut what Kant says 26 is going to argue is that the spatiotemporal structure of experience is not independent of its categorydetermined structure.
Instead it is a particular determination of it.
So the spatiotemporal structure of human experience is a particular determination of the categorydetermined structure of all cognition.
Therefore it follows automatically that we can know a priori a particular range of truths about space and time.32:0026
Transcendental Deduction of the Universally Possible
Employment in Experience of the Pure Concepts of the
Understanding.
In the metaphysical deduction the a priori origin of the categories has been proved through their complete agreement with the general logical functions of thought [ HYPERLINK \l "b1" b1]; in the transcendental deduction we have shown their possibility as a priori modes of knowledge of objects of an intuition in general (cf. 20, 21) [ HYPERLINK \l "b2" b2]. We have now to explain the possibility of knowing a priori, by means of categories, whatever objects may present themselves to our senses, not indeed in respect of the form of their intuition, but in respect of the laws of their combination, and so, as it were, of prescribing laws to nature, and even of making nature possible [ HYPERLINK \l "b3" b3]. For unless the categories discharged this function, there could be no explaining why everything that can be presented to our senses must be subject to laws which have their origin a priori in the understanding alone [ HYPERLINK \l "b4" b4].[b1] This is step 1.[b2] So he is saying this is how far weve got. In the next sentence then he is going to make it more precise.33:00[b3] So we are going to discover general laws about space and time, meaning the kind of unity they must have. Because if we did notthis is what the next sentence discusses[b4] So here is the little trick.
How are the categories going to determine nature in general? How is that possible?
Because the first action of the categories is going to be on space and time.
The categories are going to determine space and time and indeed they can determine space and time because they are already a priorithey are our forms of intuition: nothing can effect us except by being spatial and temporal.
So anything that could appear must appear as in space and in time.
And now we show that the unity of space and time is not given but is itself a product of the categories. So the categories, as it were, get at everything, the whole world, but determining space and time.35:30Question:We need to recall the distinction between forms of intuition and formal intuition.36:00
So what is going to go on here is an explanation of how our a priori knowledge of the category determined structure of our experiencethat is what we have already. We know our experiencewe know there is the a priori categorydetermined nature of experience, we know that already.
We are going to discover how that is at the same time an a priori knowledge of the laws of the combination of whatever objects may appear before our senses.37:00
That is, the way in which objects can be related or combined in space and time.
Before we turn to the third paragraph, where Allison has got it right that each sentence is just one step in the cumulative argument, the simple argument again is that space and time are forms of sensibility. Nothing can appear that doesnt appear as a somewhere or a some when.
We have discovered that the categories structure our experience necessarily, via the notion of judgment.
And now what we are doing is simply taking that story about judgment and applying it to space and time, of which the consequences the very notion of the very unity of space and time, that is, the nature of how things are related in space and time, that is for Kant the very idea of nature as a lawgiven whole, is determined by the a priori structures that determine categorial synthesis.39:00
What Kant is going to do in this third of 26 is state this thesis in general and then give it a little bit of wiggle, and that is what he calls the Schematism ( HYPERLINK \l "outline" outline), where he is going to go from a formal account of the determination to a more substantive account.
And then in the Analogies it is as though he is going to start all over and show that you have three categories namely, substance (duration), succession, and community that themselves structure temporal determination and therefore structure the very idea of the unity of nature. 40:30So this question about the unity of nature being the structure of the categories is what we are doing for the next 3 weeks.
So we dont have to squeeze it all of this 3rd . The Transcendental Deduction promises more than it delivers. 41:3026, 3. Here we have 5 sentences, each of which is a step in the argument. Allison has a good account of this. But nowadays, most everyone agrees on this.B 160:
In the representations of space and time we have a priori forms of outer and inner sensible intuition [ HYPERLINK \l "c1" c1]; and to these the synthesis of apprehension of the manifold of appearance must always conform, because in no other way can the synthesis take place at all [ HYPERLINK \l "c2" c2]. But space and time are represented a priori not merely as forms of sensible intuition [ HYPERLINK \l "c3" c3], but as themselves intuitions which contain a manifold [of their own] [ HYPERLINK \l "c4" c4], and [d2]therefore are represented with the determination of the unity of this manifold (vide the Transcendental Aesthetic) [ HYPERLINK \l "c5" c5].a Thus unity of the synthesis of this manifold, without or within us [ HYPERLINK \l "d3" d3], and consequently also a combination to which everything that is to be represented as determined in space or in time must conform [ HYPERLINK \l "d4" d4], is given a priori as the condition of the synthesis of all apprehensionnot indeed in, but with these intuitions[ HYPERLINK \l "d5" d5]. This synthetic unity [ HYPERLINK \l "d6" d6] can be no other than the unity of the combination of the manifold of a given intuition in general in an original [ursprnglichen] consciousness, in accordance with the categories, in so far as the combination is applied to our sensible intuition [ HYPERLINK \l "d7" d7]. All synthesis, therefore, even that which renders perception possible, is subject to the categories [ HYPERLINK \l "d8" d8]; and since experience is knowledge by means of connected perceptions, the categories are conditions of the possibility of experience, and are therefore valid [ HYPERLINK \l "d9" d9] a priori for all objects of experience [ HYPERLINK \l "e1" e1].
a Space, represented as object (as we are required to do in geometry), contains more than mere form of intuition; it also contains combination of the manifold [ HYPERLINK \l "c6" c6], given according to the form of sensibility, in an intuitive representation, so that the form of intuition gives only a manifold, the formal intuition gives unity of representation [ HYPERLINK \l "c7" c7]. In the Aesthetic I have treated this unity as belonging merely to sensibility [ HYPERLINK \l "c8" c8], simply in order to emphasize that it precedes any concept, although, as a matter of fact, it presupposes a synthesis which does not belong to the senses but through which all concepts of space and time first become possible [ HYPERLINK \l "c9" c9]. For since by it means (in that the understanding determines the sensibility) space and time are first given as intuitions, the unity of this a priori intuition belongs to space and time, and not to the concept of the understanding (cf. 24) [ HYPERLINK \l "d1" d1].[c1] That is just the argument of the Transcendental Aesthetic.[c2] So this is first sentence is the argumentspace and time as a constraint upon the synthesis of the manifold.
It runs from space and time as pure forms of intuition to them saying to synthesis that if it is going to synthesize anything it is going to have to synthesize through them because only through them can anything be present to consciousness.
Because time is even the form of inner sense. So nothing can be present or presented to consciousness that is not either somewhere or some when.
Therefore whatever spontaneity works on, it works on it via the forms of intuitionnamely space and time.
So that is the constraint on it. It has got to connect up with that.44:00And now comes the turn
This next sentence is a rewriting of the entire Transcendental Aesthetic.
HYPERLINK \l "gobackB160" gobackB160[c3] That is not merely as conditions of the possibility of receptivity but as themselves intuitions, ones.
So in order for space to be a pure form of intuitionthat in which anything must appearit must simultaneously be something that we actually intuit. Something that is itself an intuition, a one and therefore itself in need of synthesis. 45:00[c4] Space and time are complex ones. They have about them a manifoldness[c5] Because space and time are intuitions they are complex. And as complex they have to be unified.
And it is the unity of their manifold that is going to be the work of synthesis. This is where he has this long footnote ( HYPERLINK \l "footnotea" footnotea):[c6] So we want to be clear here. The least awareness of spacesay of a line, or of a pointis a synthesis of a manifold.
The same with time.
So it is not merely the form in which anything might appearlets call that its mode of givennessit is also something that requireshas complexity and requires unification.
Therefore we have the idea ( HYPERLINK \l "footnotea2" footnotea2).48:00[c7] And then we get the backtracking over the Aesthetic.
( HYPERLINK \l "footnotea2" footnotea2)[c8] That was the fudge. ( HYPERLINK \l "footnotea2" footnotea2)49:00[c9] So in the Aesthetic he wanted to make sure that we got the intuitive aspect of space and time.
The ways in which space and time were irreducible to conceptuality. Hence we went through the long story even of left and right. (Although it turns out you can have mathematical representations of left and right).
But that irreducibility to conceptuality is an aspectit is not the total storythe total story says in fact that any actual unity of a representation presupposes synthesis and therefore conceptual determination. ( HYPERLINK \l "footnotea2" footnotea2)50:00[d1] So he is trying here to struggle with the thought of the relationship between givenness and therefore the sensible and therefore its sensible determination.
So the thought here is that space and time are represented a priori not merely as forms of intuitions, but as intuitions themselves. Which therefore contain a manifold... Reading from [ HYPERLINK \l "d2" d2] above.[d3] That is space and time, respectively.
HYPERLINK \l "gobackB160" gobackB16051:00[d4] Remember everything that is to be represented as determined in space in time is everythingit doesnt leave anything out.
HYPERLINK \l "gobackB160" gobackB160[d5] So that nothing can even be apprehendedand remember that apprehension is the most minimal form of sensible awareness.
In that notion of threefold synthesis, apprehension is the minimal encounter with anything given. So even the minimal encounter with anything given is bound up with the laws of combination of synthesis.
HYPERLINK \l "gobackB160" gobackB160[d6] So the synthetic unity of even the most minimal apprehended whatever53:00[d7] So this synthetic unity is nothing other than this very same category determination that holds of intuition in general.
Remember that 20 ended with intuition in general ( HYPERLINK \l "gobacksec20" gobacksec20).
So that notion of intuition in general turns out to be even true of that which is apprehended where apprehension is the first moment of any possible spatial or temporal awareness.
HYPERLINK \l "gobackB160" gobackB16054:00
[d8] So this structure at the end of 20 is subject to categories. Therefore every synthesis is subject to categories.
HYPERLINK \l "gobackB160" gobackB16055:00[d9] Notice the conclusion[e1] This is Kants famous extra.
The necessary conditions for the possibility of experience are at the same time the conditions for the possibility of the objects of experience.
So that which structures my judgmental awareness of the worldbecause that is the operation of the categories on the intuitive manifold
And it turns out that the first, the a priori intuitive manifold, is the manifold of space and timethen by showing that anything that appears so that I must have a unification of them, then if follows that the categories apply to anything that can appear in them.
But since they are the conditions of anything appearing to me whatsoever, then the categories apply to anything that can appear.
That is the Transcendental Deduction. end of part 1******BREAK***part 200:00For the time being we are going to jump over 24, but we are skipping over it in order to set it up by talking first about the Schematism Problemif we get clear on what this problem of the schematism is, we can make more sense then of 24.1:30So our claim here has been that the structures of space and time in general are particular determinations of the more abstract categorydetermined structure that is common to all experience.
The structures of space and time in general are a more particular case of the more abstract categorydetermined structure that is common to all experience.
And thereforethis is a huge therefore because this is why Kant says that we give laws to natureit follows that the structures of space and time are human expression of discursive categories.2:30To show this point is what the next three weeks of the course are going to be all about.We want to show how the structures of space and time are a human expression of discursive categories.3:00To look briefly at 24.
The question here is how do we get from logical functions of a judgment to applications of categories to intuitive manifolds.
How do we get from something purely intellectual to something that is partially intellectual and partially sensible?
4:00So first we want to just say up front how do we do it. Then we will go on to give content to this how do we do it.
And the simple answer to the how do we do it is via the imagination.
And that in a way makes senseto get the intuitive idea out thereif we think of this moment (?) as the moment of spontaneity and if we think about what we want to happen is for the spontaneity to affect our forms of sensibility which are our forms of passivity and receptivity, then the question emerges how can something purely intellectual encounter something purely sensible?
In short, how can we cross Platos Divided Line (Republic book VI)? All philosophy is a footnote on Plato. That is obviously true.
But Kant feels this in an almost unbearable way. That really is the nugget here of the struggles of the rest of the book.6:30That is, the problem is how the intellectual human activity and human passivity get connected.
We could go through a long story here, but we already know that the relation between activity and passivity already was the debate between rationalists and empiricists.
For rationalists, everything happened up here (?), for empiricists it was all sensibility.
And the whole idea of discursive cognition is that thoughts without intuitions are empty, intuitions without thoughts are blind.
So the very notion of overcoming the duality of active and passive is what the whole project is all about, (without spontaneity and reason, and this is the senses ???) and there has got to be something that is both intellectual and sensible at the same time, and Kant calls that imagination.8:00
In particular, he calls it the productive imagination. So we should feel that phrase productive imagination as an oxymoron.
That is, the production of something that is itself sensible.
And this is one way of saying that we care about art. Art is a heightening of an oxymoron.
Art is about the oxymoronic structure of human discursivity. Or you may say it is about the aporetic structure of9:00
So the question of 24 is how the categories can apply to the sensesthat is all he is talking about here. Thus he is preparing the way for 26. And he says that synthesis is at once both transcendentali.e. a necessary condition for the possibility of knowledgeand also purely intellectual.
But since there lies in us a certain form of a priori sensible intuition, which depends on the receptivity of the faculty of representation, the understanding as spontaneity is able to determine inner sensethe manifold of given representationsin accordance of the unity of apperception.
And that just is a statement, a claim. Pure intellectuality determines inner sense, our temporal consciousness. 10:30
Next paragraph of 24.
So spontaneity first works out (here?) in the middle. Spontaneity is going to work first on inner sense and he is going to call this figurative synthesis.
So we have an intellectual synthesisby intellectually we mean just S is P. But now we have got to take that intellectuality, that pure human rationality, and have it encounter somehow, and how is really going to be what we are working out in the schematism and the analogies.
It has got to encounter sensibility, and it is going to encounter it via the imagination. 12:00
So he says that this figurative synthesis is directedand he wants this figurative synthesis to be nothing more than the original synthetic unity of apperception.
So the figurative synthesis is literally a kind of sensibilization of original spontaneity. So it is via the imagination that we move from the purely intellectualby purely intellectual we mean something is merely intellectual if it is merely a rule.
So every concept is a rule, categories are superrules. So they are rules without anything attached. And these rules can a priori determine a manifold via the imagination. 14:00So looking then at B 152:
imagination is to that extent a faculty which determines the sensibility a priori; and its synthesis of intuitions, conforming as it does to the categories, must be the transcendental synthesis of the imagination.
So it is as if the first thing I must do is unify my imagination.
This synthesis is an action of the understanding on the sensibility; and is its first applicationand thereby the ground of all its other applicationsto the objects of our possible intuition. As figurative, it is distinguished from the intellectual synthesis, which is carried out by the understanding alone, without the aid of the imagination. In so far as imagination is spontaneity, I sometimes also entitle it the productive imagination, to distinguish it from the reproductive imagination15:30
So, to get concrete, lets turn to B 154:
We cannot think a line without drawing it in thought [ HYPERLINK \l "f1" f1], or a circle without describing it [ HYPERLINK \l "f2" f2]Even time itself we cannot represent save in so far as we attend, in the drawing of a straight linemerely to the act of the synthesis of the manifold whereby we successively determine inner sense, and in so doing attend to the succession of the determination in inner sense [ HYPERLINK \l "f3" f3].
[f1] So first sentencenothing can be spatially imaginedand he is taking the notion of geometrical figures to be as simple as it gets, after all geometry represents the pure form of the spatial whole.
So this first statement here is that we can imagine, perceive, or think a line without drawing it in thought.
What he means by this is that anything that is spatially given also includes a temporal dimension. So what appears to be just something that is there has to also get there. Again, no unity without unification.17:30
[f1continued] So what is the most spatially simple thinga linehas to be drawn.
HYPERLINK \l "gobackB154" gobackB154[f2]
Here we have got the same thought.What does he mean here? What does it mean that we cant think a circle without describing it?
The mathematical definition of a circle is on object in which all points are equidistant from the radius (from the center, more accurately).
But given just that definition, what the hell is a circle? (What if we had not yet ever seen one and someone gave us that description?)
It is just this:
Kant says that the pure rule, that move from purely intellectual, purely temporal, has to be spatialized, just as in the case of the line, what is spatialized can only be thought if thought temporally.
In each case we are joining a rule and an image. We are joining a moment of passivity to a moment of activity.
19:30
And in joining a moment of activity to a moment of passivity, we are showing how every moment of spatial awareness depends upon a temporal understanding. And every moment of temporal understanding requires spatial awareness.
HYPERLINK \l "gobackB154" gobackB15421:00
[f3] So the imagination, drawing a circle, drawing a line
This is the way in which my activitythe rules, the shortest distance between two points, or all points equidistant to the centerreceive their sensible realization. And it is where any sensible realization gets brought back into an intellectual rule.
So the productive imagination is the means by which we give original structure to our sensibility.22:00So imagination is going to be the inbetween.
And now the question is going to be, how does the imagination work, what is going to be necessary here. How is this categorial determinationhow can we make explicit the categorial determination of sensibility.Question:23:30So how is Kant going to make explicit this categorial determination of space and time?
It turns out that it is going to be a bit more complicated then we had thought.
Kant claims that all knowledge is subject to time. Because time is the form of inner sense. And yet, that argumentthat time is the form of inner sense, all knowledge is subject to timeplays no structuring role in the justification of the categories.
What is going to happen in the schematism and the analogies (see HYPERLINK \l "outline" outline above) is that they are going to argueand this is Jays argument against the completeness problemthe schematism and the analogies really argue for particular categories by offering a two stage theory of time determination.
On the one hand, the schematism is going to continue the regressive strategy of the transcendental deduction by claiming that we have knowledge of the temporal relation of objects distinct from our representations of them.25:00
What we mean by this is that the order of my representations is not the temporal order of the objects. This is the principle of everything that is going to follow.
So the temporal order or relations of objects is not the same as the order of my representations of them.
To illustrate this point, look for instance at an object on one side of the room, say a hat. Then turn your head and look at an object on the other side of the room, like a projector.
First we see the hat, then we see the projector.
The order of my representations is first the hat, and second the projector. And I cant see them both at the same time because they are too wide for my peripheral vision.
But what is the temporal order of those two objects?
They are simultaneoushow do we do that? How are objects that are represented in an order get taken as simultaneous? 27:00
How we do that is the argument for the next two weeks.
Because it certainly seems as if we suddenly have knowledge of the structure of the world that is different from the order and structure of our representations.
So our representations really do represent something independently of us.
If that wasnt clear up to now, that really makes it clear that we have knowledge of an order of the world independent of our order of representations.
Now having that knowledge, Kant is going to argue, requires three principles of temporal determination.
And the three principles of temporal determination is the claim that the objectively real is ultimately composed of permanent substance of a determinate magnitude and that these substances of a determinate magnitude all stand in relations of causation and interaction.
(See the HYPERLINK \l "outline" outline of the Analogies above)
Axioms
Anticipations i. Permanence of Substance
Analogies ii Succession in time and Causality
Postulates iii. ReciprocityCommunity
Refutation of Idealism28:30The relationship between the hat and the projector is a relationship of interaction. Those three principles substance, succession, and interaction, are the three analogies.
And the three analogies together generate the unity of time.
They are the conditions for determining that all objects are in one time. That is to say that since time is an intuition, it is a one, that all objects have to be temporally related to one another. And these three principles will give us how they are so relatedhow they all belong to one time, and therefore stop the universe from exploding into different times, which would be unintelligible.30:30
So stage 2, and this is all a schematic comments setting up the schematism, is to say that these same principles provide the necessary conditions for the possibility of experience, not just in the strong sense of the unity of time, but even in the weak sense of, without these three principles I could not even have minimal selfawareness.
Even having the slightest of ideas is going to require all three principles. And that is going to be the argument of the Refutation of Idealism. HYPERLINK \l "outline" outline
That is, my inner awareness is dependent on my outer awareness of this whole elaborate temporal structure.
So that is where we are going in the next few weeks.32:00
The Schematism shows exactly how categories can be manifested in or as sensible intuition.
That is, what the goal of the schematism is, is to give each of the categories sufficient spatiotemporal content.
We might say its goal is to give each of the categories a temporal semantics. We might also say that its goal is to give each of the categories a temporal interpretation.
These are all more or less equivalent formulations.33:00
So Kant thinks that there is no general problem of concept applicationto be clear, people misread the schematism as doing this.
Kant does not think that there is a general problem of concept application because Kant thinks that mathematical concepts, and ordinary empirical concepts, and even the empirical concepts of natural science just are rules for applying predicates to particular objects.
That is what they are. To have the rule for red is to pick out red objects. To have the rule for circular is to draw a circle.
34:00They just are rules for the application of concepts to experience.
And that is what Kant says when he talks about the dog. Finally Kant mentions something concrete.
So at A 141
And this is meant also to be Kants solution to the problem of abstract ideas. 35:00You might remember Berekeleys criticism of Locke as how can you have an idea of a dog that is not a Labrador or a Bulldog, etc.
And of course if you think ideas are images then this problem looks insuperable.
Kant says that this is not what concepts are. Concepts are not images, they are rules.
A 141:
The concept dog signifies a rule according to which my imagination can delineate the figure of a fourfooted animal in a general manner, without limitation to any single determinate figure such as experience, or any possible image that I can represent in concreto, actually presents.36:00
So ordinary empirical concepts just are their own schematism. What does that mean?A 141, cont:
This schematism of our understanding, in its application to appearances and their mere form, is an art concealed in the depths of the human soul, whose real modes of activity nature is hardly likely ever to allow us to discover, and to have open to our gaze.
Of course, there is something missing here.
We take it that our concept of a dog is something like a fourfooted mammal with fur, etc., etc.
And when we give that description, we might be tempted to ask how that definition is different than the description of a horse? How is it that we get from that rather abstract conceptwe can call it the dictionary definitionto this dog here in front of me, Fido?
How does that happen?37:30Kant has shown that concepts are not images, and if they are rules, they look then as if they underdetermine particular cases.
How does that underdetermination get accounted for?The answer occurs at A 133, B 172:
Here Kant is suddenly talking about judgment, but not judgment in the way that we have been talking about it, but judgment not just as the faculty of rules, but as the faculty of subsuming under rules.
So to judge something is to subsume it under a rulethe rule that something that has this, that, and the other property is a cup.
That is the act of judgment as subsuming under rules.39:00
And then he says, which seems shocking, that the general understanding contains no rules for judgment.
So judgment is the subsuming of objects under rules. But the understanding contains no rules for the application of rulesno rules for judgment.
Why is this the case?40:00
Kants first answer is that to ask for a rule for the application of a rulewhen do I apply the rule dogthis is going to be a problem because it opens up an infinite regress.
Because if I need a rule for when I apply the rule of dogthen I would need a rule for when I apply the rule of applying the rule of a dog, and we get an infinite regress.
So there cannot be a rule for the application of rules. Thus judgment requiresand this is what he is saying at A 133and that is why he is saying that judgment must be:
a peculiar talent which can be practiced only, and cannot be taught. It is the specific quality of socalled motherwit; and its lack no school can make good.41:00
This is very close to Aristotle on phronesis and his critique of Plato. You cannot be a rationalist all the way. You cannot have an algorithm for everything, you cannot have a rule for everything.
There is a notion of motherwit involved. Practice, training, discrimination. 42:00
If this is right, there really is no fundamental problem about empirical concepts.
You learn them, you learn how to use them.
And now you can see why suddenly Wittgensteinians come together. Because just as meaning is use, so he is saying here, concepts are use.
So Kant is not a rationalist (but?) much closer to Wittgensteinthe meaning of a concept is its use. It is a rule, but a rule thatand this is the very problem of the Philosophical InvestigationsWittgenstein is going to want to say that a rule does not project itself infinitely into the future, to determine all future cases.
The belief that rules determine all future cases is just what generates skepticism.
That is how you generate skepticism about meaning. Meaning is impossible because you cannot predict whether a rule will apply to some future case. 43:00
And the Kantian answer right here is that it is logical error to even expect that. It is a logical error because of the infinite regress argument. If it were a rule, then there would have to be a rule for the application of that rule, ad infinitum.
So ordinary concepts are in great shape, they fit experience just beautifully.
There are certain complications. We can call that the Third Critique, the Critique of Judgment.
The Critique of Judgment is about trying to think a bit about that raw talent.44:00
So the Schematism only applies where there is a genuine gap between concept and object.
And the question is where is there a genuine gap between concept and object.
Well, it is in the special concepts of transcendental philosophynamely the pure concepts of the understanding.
And now the notion of pure concepts should make us kind of nervous because these are categories not cast in terms of properties and relations that can actually be manifested by objects given through sensibility.
45:00
Or, to go back to Humes problem. There is no sensible impression or idea of a causal connection.
There is no impression above and beyond having the representation of this object that tells me that this particular set of properties belong to an external object.
Hume wanted an impression of externality. He couldnt find one.So there are certain properties that Hume expected to find in empirical intuition, and he could not find them. That was his skepticism.
Those are the concepts for which we need a schematism.46:00We can stop there for today, and pick up there next week.
11 Kants CPR B Deduction (20, 26, 24)
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