The Critique of Pure Reason – Transcendental Logic – On the Deduction of the Pure Concepts of the Understanding

On the Deduction of the Pure Concepts of the Understanding

With the categories of the pure concepts of the understanding outlined, Kant’s next move is to provide arguments supporting his thesis that these concepts are indeed a priori and provide the framework for how we are to understand the world.  Kant makes an important distinction about what sort of examination this is going to be; just as in legal debates where there is a difference between questions of law and questions of fact, so too here can there be questions of the fundamental laws which govern epistemological claims and what we can factually say about them.  Kant’s concern is with the former which he refers to as deduction (A84/B116).  Hence, the deduction of the pure concepts of the understanding is an examination into what are the laws governing a priori concepts of our understanding which allow us to understand and order the world around us.  It is important to keep in mind that this examination is concerned with how concepts relate to objects a priori, and as such, is a transcendental deduction.

From what has been said in so far in the Critique, there are two structures which play a role in our ability to gain knowledge:  There are the pure forms of intuition known through sensibility (i.e. space and time) and there are the categories which are the pure concepts of the understanding.  The former are given to us while the latter are products of the spontaneity of thought.  What is important for Kant here is to show how exactly the pure forms of intuition and the pure concepts of the understanding interact with each other and provide us with epistemological access to the world.  It cannot be that the intuitions act alone in giving us sensible input, for then there would be no formable cognitions about the representations we receive; and conversely without pure intuition we would possess pure concepts that could not tell us anything at all.  Thus, finding the connecting point for the two is crucial for Kant.

This connection point is going to be centered on the roles played by “the synopsis of the manifold (of representations) through sense…the synthesis of this manifold through the imagination…(and) the unity of this synthesis through original apperception.” (A94/B127)  Thus we see a tri-part system involving the senses, the imagination, and apperception, and it will be through this collaborative process of the sense and understanding that we will discover how the categories are not only the subjective conditions of thinking, but that they also have objective validity and thus provide the conditions necessary for the possibility of cognition.

Side note: Kant rewrote the deduction substantially in the second version of the Critique.  Here I will expound the arguments as they appear in each version to both highlight similarities and differences.

On the a priori grounds for the possibility of experience <A>

In order to deduce the objective validity of the pure concepts of the understanding, we must “inquire (into) what are the a priori conditions on which the possibility of experience depends and that ground it even if one abstracts from everything empirical in experience.” (A96)  Stripped away of all empirical content, these concepts would only possess the “formal and objective condition universally and sufficiently (necessary to) be called a pure concept of understanding.” (A96)  Thus, what Kant is looking for here are those concepts that serve as the foundations for the empirical world (e.g. that objects of sense have attributes like form and substance, operate causally, exist, etc.).  These concepts cannot be borrowed from experience in any way; they must be a priori if they are to provide any sort of necessary law-like structure upon which a posteriori can be placed.  Hence, (as mentioned above) the categories are the pure concepts of the understanding that have objective validity and allow us to experience the world in the manner that we do.  Before delving into the arguments proper Kant tells us at the end of the introductory part of this section that if “I ascribe a synopsis to sense, because it contains a manifold in its intuition, a synthesis must always correspond to this, and receptivity can make cognitions possible only if combined with spontaneity.  This is now the ground of a threefold synthesis, which is necessarily found in all cognition: that, namely, of the apprehension of the representations, as modifications of the mind in intuition; of the reproduction of them in the imagination; and of their recognition in the concept.” (A97)  Thus we see that the arguments for the deduction are going to be based on these three activities which, when combined, show how epistemological knowledge can indeed have objective validity.

  • On the synthesis of apprehension in the intuition

Kant’s first point about the representations that are given to us, rather they be empirical or a priori, all belong to the inner sense and therefore all belong in time.  Hence, all cognitions are ultimately subject to time.  Kant points this out to remind us that time will be the ground for which the rest of the argument will be built upon.

Next Kant tells us that there are a manifold of representations given to us in intuition and that this manifold would not be possible if they were not in time, for only in time can succession occur.  If the manifold were given out of time, then the only representation we would have is that of “absolute unity.” In other words, outside the intuition of time all that would be possible is a static representation that would be incapable of change.  But this does not mean unity is excluded completely, for through the “synthesis of apprehension” the manifold is “first…run through and then take(n) together.” (A99)  This statement seems a bit cryptic, but I think it can be taken like this:  We perceive a unified consciousness that consists of a various representations of objects moving about doing whatever it is they are doing.  In order for this sort of unity to occur (i.e. the unity of consciousness), it has to be in time, otherwise all we would perceive would be one unchanging image.  Kant seems to make this explicit where he talks of the manifold having to be contained “in one representation.” (A99)

Now, this synthesis of apprehension also has to extend to a priori representations, otherwise we could not have the representations of space and time since they occur “only through the synthesis of the manifold that sensibility in its original receptivity provides.” (A100)  In other words, if the synthesis of apprehension did not extend past empirical representations, then there would be no way to have pure intuition, and without pure intuition there would be no way to show the objective validity of knowledge statements.  Hence, there is a pure synthesis of apprehension.  To formalize the argument:

  1. All representations occur in time.
  2. If all representations occur in time, then representations are given in succession.
  3. Representations are given in succession (1,2)
  4. If representations are given in succession, then this is only possible through a unifying consciousness containing a synthesis of apprehension.
  5. There is a unifying consciousness containing a synthesis of apprehension. (3,4)
  6. If there is a unifying consciousness containing a synthesis of apprehension, then the synthesis of apprehension must be pure in order to give the representations of space and time.
  7. The synthesis of apprehension is pure. (5,6)

Note here that (7) tells us that the synthesis of apprehension has pure (non-empirical) grounding which gives it objective validity.

  • On the synthesis of reproduction in the imagination

The first move here is to highlight the purposefulness of “empirical law.” (A100)  As we go through our daily lives, we are presented certain representations that are inevitably associated with other representation, and we tend to follow a rule that when one representation appears, the other will accompany it (smoke follows fire, what goes up falls back down, dark clouds mean rain, etc.).  All this falls under what Kant terms the law of reproduction, and contra Hume he wants to say that there is something fundamentally grounding these sorts of empirical observations that is objective.  He tells us that “this law of reproduction, however, presupposes that the appearances themselves are actually subject to such a rule, and that in the manifold of their representations an accompaniment takes place according to certain rules; for without that our empirical imagination would never get to do anything suitable of its capacity, and would thus remain hidden in the interior of the mind, like a dead and to us unknown faculty.” (A100)  If we are to make sense of reproduction, then we are going to need something that grounds it a priori, otherwise there is nothing to stop reproductions from not occurring as we observe them.

In order to ground reproduction a priori, we need to “demonstrate that even our purest a priori intuitions provide no cognition except insofar as they contain the sort of combination of the manifold that makes possible a thorough-going synthesis of reproduction.” (A101)  Kant goes on to argue by way of example that in order to represent a train of thought to ourselves we must first possess the manifold of preceding representations, then the proceeding representations in order for that train of thought to exist.  For example, if I am counting to ten and by the end have forgotten the first five numbers, then I have not properly represented to myself the activity of counting to ten.  Thus, reproduction presupposes recognition in order to function.  This is even true of the purest of representations (space and time) for if those representations were not already present, then it would not be possible to add any representations to them (e.g. substance and succession).

Just as the synthesis of apprehension provides the possibility for all representations encountered through sensibility, the synthesis of reproduction adds rules about how those representations are encountered.  The latter is possible because of the former and since the former “constitutes the transcendental ground of the possibility of all cognitions in general…the reproductive synthesis of the imagination belongs among the transcendental actions of the mind.” (A102)  To continue with the formal argument:If there are empirical laws regulating how representations are given, then there must be some non-arbitrary law (i.e. reproduction) giving this regulation necessity.

8. There are empirical laws regulating how representations are given.
9. If there are empirical laws regulating how representations are given, then there must be some non-arbitrary law (i.e. reproduction) giving this regulation necessity.
10. There must be some non-arbitrary law (i.e. reproduction) giving this regulation necessity. (8,9)
11. If there must be some non-arbitrary law (i.e. reproduction) giving this regulation necessity, then this non-arbitrary law (i.e. reproduction) requires the recollection of previous representations.
12. This non-arbitrary law (i.e. reproduction) requires the recollection of previous representations. (10,11)
13. If this non-arbitrary law (i.e. reproduction) requires the recollection of previous representations, then the purest representations of space and time can be reproduced.
14. The purest representations of space and time can be reproduced.  (12,13)
15. If the purest representations of space and time can be reproduced, then the synthesis of apprehension is inseparably combined with the synthesis of reproduction.
16. The synthesis of apprehension is inseparably combined with the synthesis of reproduction. (14,15)
17. If the synthesis of apprehension is inseparably combined with the synthesis of reproduction, then the synthesis of reproduction is pure.
18. The synthesis of reproduction is pure. (16,17)

Conclusion (16) is possible due to the synthesis of apprehension and synthesis of reproduction both being constituents of the unity of consciousness.  The act of reproduction (and the memory that comes along with it) presupposes the unified synthesis of apprehension that is the basis for all possible cognitions.  Without this unity reproduction would not even be possible, and without reproduction rules or laws about how representations relate cannot be given objective validity.

  • On the synthesis of recognition in the concept

So far we have seen that there is a unity of consciousness that consists of an apprehension in the intuition and the imagination actively reproducing concepts in order that we may recognize certain relationships that exist between representations.  These relationships exist necessarily because are grounded a priori.  In the apprehension of intuition we encounter all the representations that are given to us through sensibility and in reproduction we think about how these representations relate within the pure intuitions of space and time.  We can now add to this the recognition of concepts that was presupposed in Kant’s arguments for reproduction.

Kant first points to the importance of recognition in the reproduction of representations:  “Without consciousness that that which we think is the very same as what we thought a moment before, all reproduction in the series of representations would be in vain.  For it would be a new representation in our current state, which would not belong at all to the act through which it had been gradually generated, and its manifold would never constitute a whole, since it would lack the unity that only consciousness can obtain for it.” (A103)  Thus without the faculty of recognition there would be no way to link newly acquired representations to past representations which means reproduction could not take place.  Speaking more broadly, we would be unable to order the world in the way in which we do, for we would have no frame of reference to work with.

Kant goes even further on this point arguing that concepts themselves are only possible within “this one consciousness that unifies the manifold that has been successfully intuited, and then also reproduced, into one representation.” (A103)  This makes sense in light of earlier comments made about how concepts are even able to be formed.  It is the combination of what is given through sensibility and the active process of thinking that produce concepts in our understanding.  Since both the receptive nature of the sensibility and the active functions of the understanding are connected a priori and are encountered in a unified consciousness, it makes sense that concepts are only accessible within this framework.

Next Kant has wants to elucidate what is meant by the term “object of representation.”  The question here is what exactly does Kant mean when he talks about the “object” that is to be represented.  He cannot be pointing to anything about the object in-itself for that is realm that is beyond human access.  However, since his transcendental idealism does point to the fact that there is indeed some thing-in-itself out there beyond the world of sense, it is alright to speak of the object as an abstraction (something in general = X according to Kant).  This abstract link is important for being able to provide necessity between cognitions and their relations to objects.  According to Kant “since we have to do only with the manifold of our representations, and that X which corresponds to them, because it should be something distinct from all of our representations, is nothing for us, the unity that the object makes necessary can be nothing other than the formal unity of the consciousness in the synthesis of the manifold of representations.” (A105)  Thus cognizing the object requires the synthetic unity of intuition.  But that is only possible if done so within the framework of the unity of consciousness where apprehension, reproduction, and recognition reside.  Thus there is a “unity of rule (that) determines every manifold, and limits it to conditions that make the unity of apperception possible.” (A105)

The first sentence of the next paragraph helps tie things together nicely:  “All cognition requires a concept…but as far as its form is concerned the latter is always something general, and something that serves as a rule.” (A106)  As we shall see quite shortly, it is within the realm of concepts that Kant is going to place his categories of understanding (which have yet to make an appearance in this argument).  Now, all rules require necessity to ground them and all necessity has as its ground in transcendental conditions.  This transcendental ground –or transcendental apperception- can be best summed up by Kant:  “Now no cognitions can occur in us, no connection and unity among them, without that unity of consciousness that precedes all data of the intuitions, and in relation to which all representation of objects is alone possible.  This pure, original, unchanging consciousness I will now name transcendental apperception.” (A107)  This can be contrasted with the inner sense or empirical apperception, which is “the consciousness of oneself in accordance with the determinations of our state in internal perception.” (A107)  In other words, empirical apperception is the introspection of our inner selves we do when we are, for example, thinking about all these topics in Kant’s Critique.   Transcendental apperception is the framework that forms the unity of consciousness which we need in order to even think about these topics.  With this we can now formalize the next leg of the argument:

19. Reproduction requires the recollection of previous representations. (12)
20. If reproduction requires the recollection of previous representations, then recollection also resides within the unity of consciousness.
21. Recollection also resides within the unity of consciousness. (19,20)
22. If recollection also resides within the unity of consciousness, then the synthesis of recollection is pure.
23. The synthesis of recollection is pure. (21,22)
24. Concepts and sensibility are possible only within the unity of consciousness.
25. If concepts and sensibility are possible only within the unity of consciousness, then cognition is only possible within the unity of consciousness.
26. Cognition is only possible within the unity of consciousness. (24,25)

This argument has thus far been suffered from quite a bit of meandering, and I only mean here to construct it as faithfully to the letter of the text as possible.  It is definitely possible to interpret these arguments in such a way as to give them a firmer formal structure, but that is not the goal here.  Also there is one further premise that can be drawn concerning concepts being law-like, but as that premise would fit better alongside the next set of premises, I will hold off for a moment.

  • Provisional explanation of the possibility of the categories as a priori cognitions

We are now at the point in the argument where we have a unity of consciousness in which all perceptions are represented in “thoroughgoing and lawlike connection, just as there is only one space and time, in which all forms of appearance and all relation of being or non-being take place.” (A110)  This begs the question as to what exactly these law-like connections (or concepts from above) are.  Here Kant asserts “that the categories …are nothing other than the conditions of thinking in a possible experience, just as space and time contain the conditions of intuition for the very same thing.” (A111)  Thus, when we speak of cognitions as containing concepts that are law-like, it is the categories of understanding which spells out exactly what the laws are.  Causation, substance, singularity, plurality, etc. are all necessary laws that govern our understanding of the perceptual world.  Thus, if we add this bit to the formal argument laid our above, we get the following conclusion:

27. Concepts operate with law-like necessity.
28. Law-like necessity is best represented by the categories.
29. Concepts are best represented by the categories. (27,28)

I’ve tried to be as faithful to the formal construction of this argument as possible by sticking as closely as possible to the original text.  That said, the <A> deduction argument seems to be weak in spots and overburdened with what Kant wants to show.  He has a long meandering argument meant to bring together apprehension, reproduction, and recognition, and even if he is successful, it is not all conclusive that memory and the ability to recall those memories are exhaustive of the conditions of the understanding necessary to explain how we understand and organize the external world internally.  And beyond that, he simply asserts the categories are the law-like concepts he has in mind without actually arguing for them.  I’m pretty sure if Kant’s ghost were next to me right now, he’d probably say that he already made those arguments in the last chapter, but I found those a bit lacking as well.  With that said, it is time to push onward to the <B> deduction to see if he fares any better.

To be continued…

Back to The Clue to the Pure Concepts                                                 Forward to Part 2 of the Deduction

  1. spinoza1111 said:

    Brilliant, absolutely brilliant…and why I’m glad to be too old to be a graduate student in philosophy (I applied to Princeton in 2000, they bounced me, no hard feelings on my side.)

    This is because your exactitude in re-creating the flow of the argument is exactly what a philosophical community, consisting not only of tyros but also of colleagues (who need to get on the same page as the rest of the community) is what we need in place of what I’ll call the “vanity rehash” in which a philosopher like Strawson has such an axe to grind that he distorts Kant by ignoring critical issues (such as the thickness of apperception in the 1781 edition versus that of the 1787 edition) and failing to ensure that a proper presentation has been made.

    Hate to say it, but anyone who proposes to speak on Kant needs to create your non-vain rehash, let us say just to annoy, as a Power Point presentation.

    You’ve gone through every word and ended up with a large collection of admonishments as a resource. I think this is what one needs to do with any difficult philosopher until we get to the next step which is critique, which may or may not be as fecund as was Strawson’s, or Kripke’s of the analytic and synthetic aPrioris.

    Since your version of the two “chapters from Hell” is so complete as far as I can see the next step is figuring what parts of the text are original, and representative of Kant’s thought circa 1781, and other parts circa 1787. For example, a view of apperception (sensation to perception) as binary and atomic, involving either “I am having a perception” or nothing (no signal) is “1781” whereas an account of apperception as potentially much “thicker” involving a Proustian-thorough recollection of *les temps perdu” is groundable only on 1787.

    But note that I haven’t argued for the superiority of 1787: note the coincidence here that the two editions of the Critique coincide with the two versions of the United States’ Constitution, the 1781 Articles of Confederation and the 1787 Constitution. In my country (USA) the Tea Party, the Sons of Liberty and other buffoons argue for the superiority of our first constitution, the Articles of Confederation, whereas people with a clue or two and men of wealth and taste like me (well, taste) (nyuk) (nyuk) argue for the superiority of our Constitution as signed in 1787, especially as enhanced by the “Reconstruction Amendments” (Thirteen through Fifteen) which solved the li’l ole Problem pointed out by Taney that we’d failed to give non-whites any rights. Oops. Dang. Hate when that happens.

    The effect of events in the United States on Kant as well as the question of the reverse effect is a fascinating question which I can’t answer here, so I shall make an end.

    Arguing the superiority of the 2nd Edition is the next step, not a relatively minor question probably of interest only to American philosophers.

    • Bill Liktor said:

      Wow, thanks for the kind words. This section is definitely taking all my mental powers to keep from going mad. It’s hard at times because (as you have pointed out) Kant was developing a new system here, which unfortunately has the side-effect of being opaque in places. This opaqueness exists in spots in the B version as well. That said, I agree that the only real way to know a philosopher is by analyzing every sentence and trying to organize what they say into as clear as possible formal arguments that are faithful to their thoughts. I agree that people like Strawson tend to push their own ideas more than anything, but I think they are assuming their readers are already knowledgeable in Kant (though I could be wrong there). I’m working on the B deduction now and will have some notes posted be the end of the week. I’m glad you’re enjoying them 🙂

      • spinoza1111 said:

        Check p 613 of the Guyer/Moore translation (the Cambridge University Press paperback). There’s a sentence of ** 150 words ** tucked away in that obscure section (the Critique of All Speculative Theology) which I had to diagram to understand. I call it The Whopper: my apology for depositing this monster in your comments but I needed to give you a quick idea of its size:

        “The absolute totality of the series of these conditions in the derivations of their members is an idea which of course can never come about fully in the empirical use of reason, but nevertheless serves as a rule for the way in which we ought to proceed in regard to them: namely that in the explanation of given appearances (in a regress or ascent) we ought to proceed *as if* the series were in itself infinite, i.e., proceed *in indefinitum*, but where reason itself is considered as the determining cause (in the case of freedom), hence in the case of practical principles, we should proceed as if we did not have before us an object of sense but one of pure understanding, where the conditions can no longer be posited in the series of appearances, but are posited outside it, and the series of states can be regarded *as if* it began absolutely (through an intelligible cause); all this proves that the cosmological ideas are nothing but regulative principles, and are far from positing, as it were constitutively, an actual totality in such series.”

        In the above Whopper, Kant in an almost anguished way, reminiscent of Beethoven’s late quartets, tries to show the distinction between what Stephan Körner (The Philosophy of Mathematics) calls “Platonism” (logicism) and ** intuitionism ** as applied to the contemplation or construction of infinity.

        Intuitionism was developed by Brouwer, Heyting et al. ** based on Kant ** so the tragedy of Kant is that he lacked a language for expressing what he knew but provided the preconditions for the development of that language! Kant is trying to tell us, like a returning spaceman who’s seen what the astronaut of 2001 sees at the end, that while we cannot contemplate a finished infinity, we can “contemplate” the recursive or otherwise rule that generates the infinity.

        We cannot contemplate the last number (or the smallest real number s such that 0<s p) or the existence of a finished infinity as opposed to a construction rule. Their (continental European) education stressed Kant and they constructed Intuitionist mathematical philosophy on a groundwork painfully laid by a philosopher who lacked the logic and language they, Brouwer and Heyting, developed!

        With what I consider to be a tragic grandeur (see the sentence diagram of The Whopper I shall shortly blog) Kant gave Kantians their language without himself knowing that language. Like Moses, or Simon Bolivar, Kant never made it to the promised land.

  2. spinoza1111 said:

    I don’t think Strawson assumed his readers knew Kant. Quite the opposite because Strawson, who was supposed to teach Kant, wanted to do his own thing. Like in my old field of computer science when I saw that a very early mobile phone tool (1979) was “compiling” Z-80 instructions. Oughta called the guy “Strawman” because he seems not to have included anything about transcendental apperception as opposed to empirical app (what I call “thick” as opposed to “thin” where more than one step is required to get from sensation to intuition (concept).

    Or Strawman could be like me, seeing guys like you with better memory more willing to painstakingly learn Kant by heart in order to recall specifics. This disheartens us because we’re spoiled brats who before Oxford or Penn or Princeton we were the smartest person in the room, so we get creative. In computer science we write a brilliant compiler that does exactly what the user wanted…and makes coffee and orders pizza …. you get my drift?

    In philosophy we “renarrate” what Kant said. But as a faculty I soon learned that not everybody goes to uni to learn pure truth especially after universal coeducation … they come male and female, to get that non-negotiable (according to Dick (wad) Cheney) middle class life. Therefore I have to watch out for excess creativity. Call me out at any time on this issue for I gave up memorizing Kant when I decided that Kant didn’t know what he was talking about or what he believed owing to the imprecision of his language. I think that there’s a Kant out there with a *telos*, a purpose,who can be predicted like Heisenberg’s cat and all we can do is come up with a reliable automaton Kant.

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