Copyright © 1998, Allan Randall

  In Defence of Transcendental Idealism

A Reconstruction of Kant's Transcendental Deduction of the Categories (B Edition)
Allan F. Randall
Dept. of Philosophy, York University
Toronto, Ontario, Canada,


It is thought by some that Kant's idealism makes the physical world a mental phenomenon. However, Kant's system was not fundamentally mentalist. True, he thought that physical objects as physical objects were mental in character, but this does not mean they are merely in our heads, nor that they have no objective existence in a reality outside of us. This is because their ultimate reality can be logico-mathematical in nature and completely nonmental, while their physical objecthood remains a matter of mind. I will explain how this is so by reconstructing Kant's transcendental deduction of the categories, from the Critique of Pure Reason (B edition). Although not the force that it once was, I believe that some kind of transcendental idealism is the only way of thinking that makes sense in this age of quantum theory. I will develop the deduction in a somewhat more modern context than that of Kant, bringing in modern ideas in logic, mathematics and physics.  Thus, I do not consider the particular set of categories that Kant chooses to be fundamental, preferring to ground things in a more modern notion of the foundations of logic, such as that found in recursion theory (Kant's particular categories may or may not then flow out of this more modern foundation). I will therefore tend to prefer Kant's lesser-used term "logical functions" over his more frequently used Aristotelian term "categories" (Kant himself uses the terms interchangeably). I  close by suggesting that Kant's grounding of physical law in the synthetic unity of consciousness (apperception) can perhaps be viewed as an early version of the modern cosmological anthropic principle.

I. Introduction

In the Critique of Pure Reason [CPR], Kant attempts a "Transcendental Deduction" of the "pure concepts of the understanding", or the "categories", which he argues are the necessary preconditions for the possibility of objects of experience [CPR 120-175]. These categories are logical "functions" which are capable of bringing together into a unity more than one preexisting representation, whether they be "intuitions" or "concepts".

An intuition is that which is presupposed in any experience, but is preconceptual. Intuition is the innate "hard-wiring" through which all sensory data must be filtered before it can be conceptualized in the understanding. An intuition is "pure" insofar as it is detached from all empirical content. In the "Transcendental Aesthetic", Kant argues that the a priori pure forms underlying all sensory intuition are space and time [CPR 65-91]. Space underlies our intuition of "outer sense", while time underlies our intuition of "inner sense". In order to perceive an object in the world, or even conceive of one in imagination, we must presuppose an infinite, singular, 3-D Euclidean space. Time is an even more basic intuition, since it underlies any kind of cognition at all, even those in which we introspect, looking inward at ourselves, ignoring the outer world. Even such an inward sense of ourselves must presuppose a notion of an infinite progressing continuum of moments in time.

A pure intuition has had all empirical content stripped away, but it has also been stripped of conceptual content, that aspect of it which is conceptualized in the understanding. Concepts for Kant go beyond intuition. They are broader in scope. We have innate intuitional filters through which we see the world, yet through the understanding, we can conceive of objects which are never, and perhaps can never, be directly experienced. For instance, we cannot experience, even in imagination, objects moving in a 4-D space, since we are limited to 3-D intuition filters, which always present things to our consciousness in terms of 3-D Euclidean space. This is true even when we just imagine the object and the space in our minds, with our eyes shut, reclining in an armchair. Our intuition is simply limited to 3-D space. Yet, due to some remarkable feature or other of the human capacity for understanding, we can strip this intuitional restriction away, and generalize our 3-D experience, by reasoning about it, and come to a conceptualization of an object moving in 4-D space. The set of all cognizable or thinkable objects is therefore a superset of the set of all perceivable objects. In what has come to be known as the "Metaphysical Deduction", Kant argues that his "logical functions", which he calls the "categories" after Aristotle, are the necessary a priori precondition for all objects of cognition, in general. [CPR 102-113]

However, the Metaphysical Deduction says nothing about the categories being a necessary precondition for all objects of experience. It is always possible that once we have generalized, for instance, our notion of 3-D space to the more abstract conceptualization of a 4-D space, having successfully stripped away all (or most) of the empirical and intuitional content, that we have in fact stripped away that which makes the object of experience what it is. That is, it is possible that there is something about our cognizing of an object in experience that is completely left out of any purely conceptual generalization of it. If so, then it is also possible that we might be capable of perceiving the object without any need for the categories. Certainly, it seems that we can have immediate perception of objects without actually explicitly formalizing them in terms of logical functions [CPR 123-125], and although the Metaphysical Deduction argues that to form conceptualizations of objects requires the categories, it does not tell us that experience of objects does. This is the purpose of the "Transcendental Deduction" of the categories, wherein Kant argues that the categories are the necessary a priori condition of all objects of experience. The argument is "transcendental" because it starts with what is immediately experienced and argues for a necessary precondition of that experience. The Transcendental Deduction ties together the Transcendental Aesthetic (which shows that the pure forms of intuition are the necessary precondition for experience) and the Metaphysical Deduction (which shows that the categories are the necessary precondition for objects of cognition). The Transcendental Deduction attempts to show that the categories are also the necessary precondition for any object of experience whatever.

I will outline the Transcendental Deduction, and attempt a reconstruction of its basic argument structure, but placed somewhat more in the context of twentieth century thought. Thus, I do not consider the particular set of categories that Kant chooses to be fundamental, preferring to ground things in a more modern notion of the foundations of logic, such as that found in recursion theory. Kant's particular categories may or may not then flow out of this more modern foundation. In either case, I do not think that Kant's argument loses any of its force when updated in this manner. So as not to bias things towards Kant's particular category set, I will tend to prefer Kant's lesser-used term "logical functions" over his more frequently used Aristotelian term "categories".

II. The Role and Purpose of the Transcendental Deduction

Just as space and time are pure intuitions, logical functions are pure concepts, with no empirical content. A logical function brings together lower level intuitions or concepts, whether pure or impure, into a new concept. If it has empirical content, it is an impure concept; if not, it is a pure concept. This building up is the process of synthesis, which underlies all human cognition. To build an object up in this way is to generate something new. But if we take such a synthesized concept and break it down, or analyze it, we do not create any new knowledge. Everything that flows out of an analysis of a concept is already there in the concept to begin with.

Conceptualization can only be brought about through synthesis, and synthesis can only be performed via our innate intuitional filters. Yet somehow, the understanding can generalize the results of synthesis into pure concepts of the understanding, by recognizing what is and is not empirical and intuitional, and stripping this off.

In the Metaphysical Deduction, Kant concludes that the logical functions or categories are what underlies this capacity for conceptualization. But in the "Transcendental Deduction" of the categories, he wants to show more than this; he argues that not only are the categories presupposed in the cognition of any object of thought, but they are also necessarily presupposed in any object of experience whatsoever. This is a crucial step beyond the Metaphysical Deduction, which does not require that every object of experience be grounded in the categories. The Metaphysical Deduction strips away what is contributed by experience and the intuition filters, to leave us with pure concepts. But this does not mean that an unconceptualized immediate experience of an object need be necessarily grounded in the categories.

Objects may ... appear to us without their being under the necessity of being related to the functions of understanding. ... Thus a difficulty ... is here presented, namely, how subjective conditions of thought can have objective validity, that is, can furnish conditions of the possibility of all knowledge of objects. ... Everything might be in such confusion that, for instance, in the series of appearances nothing presented itself which might yield a rule of synthesis and so answer to the concept of cause and effect. This concept would then be altogether empty, null, and meaningless. But since intuition stands in no need whatsoever of the functions of thought, appearances would none the less present objects to our intuition. If we thought ... that experience continually presents examples of such regularity among appearances and so affords abundant opportunity of abstracting the concept of cause, ... we should be overlooking the fact that the concept of cause can never arise in this manner. It must either be grounded completely a priori in the understanding, or must be entirely given up as a mere phantom of the brain. ... Appearances do indeed present cases from which a rule can be obtained according to which something usually happens, but they never prove the sequence to be necessary. [CPR 123-125]
When I see a cat, I can recognize it as a cat, and proceed to analyze the concepts involved, perhaps purifying them to a large extent, stripping away the empirical and intuitional components. But on the other hand, I certainly do not need to do this. When I see a cat fall out of a tree, I can conceptualize it as obeying a law of gravity, but again there is no necessity of this in the appearance itself, not even in all the appearances of falling objects I've ever encountered in my life can this necessity be found.

So is the unconceptualized raw perception of the falling cat somehow subject to the categories, in the same way my more abstract and rarefied concepts of "cat" and "gravity" were? It is this point, the grounding of all objects of experience whatsoever in the logic of the categories, that is the aim of the Transcendental Deduction. The last part of the above quote is an obvious reference to Hume [1739], who showed that one can never derive causal necessity from empirical observation. Causal necessity must therefore arise as an a priori concept in the brain. Yet causal necessity is a fundamental feature of physics. The law of gravity says the cat must fall, not just that it could fall, or that other cats in the past have fallen. So a prime motivator for the Transcendental Deduction is Kant's desire to justify the laws of physics in terms of the concepts of the understanding, since they cannot be justified from appearances alone.

Since for Kant physical objects are transcendentally ideal, it is not surprising that the Transcendental Deduction will turn out to be crucial for making a strong case for transcendental idealism, already argued for in the Transcendental Aesthetic, which argues that our mental representations do not conform to external objects in the world, but rather that empirical objects conform to our mental representations. This is an extremely counter-intuitive notion to most people, since it sounds as if objects are somehow created out of our mental representations, and are thus merely illusory or wholly mental. Thus it might seem that objects in the world are somehow created by the very act of our thinking about them. Yet this is not really Kant's view (although he may have allowed that God might have such an ability). Kant seems to believe that objects can, in a sense, be mental constructions without being merely illusory and wholly in the mind. How this can possibly be the case can only really be appreciated once the Transcendental Deduction has been understood.

III. Synthesis and Analysis

Although our main subject is the Transcendental Deduction, we will also need to understand the basics of both the Transcendental Aesthetic and the Metaphysical Deduction. We will start by looking at just what "synthesis" is. While the synthetic versus analytic distinction is crucial to Kant's whole system, it is important to realize that they are not wholly separate activities. Synthesis is the more basic cognitive function. Any kind of thinking at all involves synthesis, the bringing together of different representations. Analysis, as itself a kind of thinking, must of course be carried out through synthesis, and hence relies in the process on our innate intuition. The point to the Metaphysical Deduction is that conceptual representations can be detached from their intuitive and empirical components. Analysis uses synthesis to breakdown what synthesis has already constructed. That is why Kant says that only synthesis generates something new.

Figure 1 illustrates the general principle of synthesis (as described by Kant in many places, but see in particular [CPR 259]). Synthesis combines a logical function, call it F(), with some other representation, call it D. D is now conceptualized in terms of F(), although this may not be at all obvious to the perceiver if the conceptualization is not pure, but is still tainted by an empirical component.

Fig. 1. Synthesis performed in the mind via intuition.

At the moment, it is a bit of a mystery exactly what this "D" is. Perhaps if looked at carefully, it turns out to consist of yet another lower-level mental representation, and so is itself the application of a function, and would be better called E(D), rather than just D. But then we still have some kind of lowest-level object D to contend with. Just what is this D we find at the end of our chain of analysis, as we analyze a concept down from F(E(D)) to {F(),E(D)} to {F(),E(),D}? What is "D" ? It would seem that it cannot be yet another mental representation, or we will end up with an infinite regress of representations. So perhaps it is the object out there in the world that is acting on us, causing us to have the perception in the first place.

If transcendental idealism is correct, however, such an empirical object must conform to our representations, rather than our representations conforming to the object. So yes, D is an object, but somehow we must define it in terms of the representations it was analyzed out of, rather than the other way around. This is the most contentious part of Kant's whole system. Surely it would make more sense, says the realist, just to accept that D is somehow ultimately a "thing-in-itself", a physical object, in the world, and go from there. But Kant insists that we cannot know anything but representations, so how can we possibly believe that we are perceiving a thing-in-itself, a "noumenon"? Perhaps we are, but perhaps not. We can but take the object as given, in terms of mental representations.

One might think that this is equivalent to suggesting that the mind somehow creates empirical objects out of its own imagination. Synthesis churns away, and at the lowest level "produces" the very matter out of which it synthesized its contents in the first place. Yet this seems paradoxical. How can the act of synthesis generate its own raw material? To see why this absurdity is not in fact a necessary consequence of transcendental idealism is the primary purpose of this essay, and is an issue we will tackle later on when we look at the Transcendental Deduction of the logical functions in more detail. For now, we will leave the issue unresolved as a major puzzle.

The raw "formal" concept, F(), is itself not an "objective" concept, since it has no object. F() by itself may be the completely general notion of "cat", for instance, but is not as such applied to any actual object. In order for there to be an object of cognition, F() must be applied to some object, such as D. D is the object being cognized, which may be itself an analyzable appearance, or a lower level object.

Without synthesis, we cannot use concepts at all. This is because, for humans, general concepts are always thought via some kind of particular instantiation involving synthesis with empirical data (although this may be imagined data, and the synthesis thus performed in imagination). So even purely analytic judgments are always thought via some kind of synthesis, by imagining or even actually generating some kind of empirical experience. When I prove to myself that the shortest distance between any two points is a straight line, it seems obviously a priori and universal. Yet how did I prove it? I certainly did not draw every possible pair of points and then draw every possible path between them and measure their distances! No, instead I either imagined or actually drew a particular set of points and a particular line and then proceeded to reason about the resulting empirical objects. Without the empirical object, my general forms or concepts are useless: "In the absence of such [an empirical] object, it [the formal concept] has no meaning and is completely lacking in content, though it may still contain the logical function which is required for making a concept out of any data that may be presented." [CPR 259]

This process of synthesis, as depicted in figure 1, is achieved in and through the cognitive faculty called "imagination", which always operates through some kind of intuition filter. Formal concepts, which cannot even be thought on their own, are like logical or mathematical functions, which require some kind of data to be realized as anything concrete. The function F() is merely an abstraction. To actually think about F(), we need to talk in terms of its application to some kind of data, as in F(x). Even to think about the concept (i.e., function) completely in general, we can still only do this with respect to some domain of empirical objects that can be synthesized with the concept, as in F(x), x:{o1, o2, ...}. Kant's conception of this melds very naturally with modern notions of recursive functions (i.e., computation), and so I will tend to talk in those terms. Synthesis, in fact, is very like computation in that it can only be understood as a process of combining things, not as something static on its own.

Figure 2 shows the way the intuition filters work to repeatedly filter out first the empirical component and then the intuitional component from incoming sensory data, D. D (and keep in mind we are remaining sceptical as to what D "really" is at this point) is synthesized with the empirical concept E() to generate the initial experience of a cone-shaped hat. At this point, we have not necessarily analyzed the experience or abstracted from it; we have just done whatever minimum amount of cognizing must take place to have an experience. We have a raw unanalyzed experience of a hat. The "hat" object, then, is one member of the set of all possible objects of experience. E(D) is an objective empirical representation--objective because it has a determined object, and empirical because that object has an empirical component. We will call this kind of cognition "empirical synthesis" because it does not filter out the empirical component of the experience.

E() is an impure empirical concept, not a pure concept, because it depends on empirical elements of its incoming data. The resulting perception, E(D), is next passed to the pure intuition filter, utilizing the pure intuitive concept F() and yielding F(E(D)). F() is a "higher-level" concept than E(). Its synthesis with the data strips away all dependence on the empirical elements of D, but does not strip away the intuitive components. In figure 2, this further conceptualization, or generalization, of E(D) yields an immediate perception of an imaginary 3-D cone in our minds. The intuition filter is considered pure in this case only because the resulting cone we hold in our minds is sufficiently free of dependence on the empirical object. This will not necessarily hold of all mental images of cones. Just because the synthesis occurs in imagination does not guarantee that it is pure. One can imagine a cone in one's mind without actually drawing one on paper or looking at a cone-shaped physical object, but that mental cone might still be dependent on the empirical data, or our memory of past empirical data. It could be coloured blue, for instance.

Fig. 2: Repeated filtering out of the synthetic components of experience.

Note that F(E(D)) is still, of course, an experience with an empirical component. When we talk of "filtering out" the empirical component, we do not mean that the experience thus generated has no empirical component whatsoever. That would be absurd, of course. All experience has an empirical component. The intuition filter removes all trace of dependence on D, by treating the empirical object before the imagination as if it were free of D. Not that it ever can be literally experienced without being attached to some particular empirical object. In figure 2, F(E(D)) is called an "objective intuitive representation". The "object" here is abstract, and detached from experience, but it is still dependent on intuition, and thus is bound up in presuppositions about 3ÐD Euclidean space and uni-dimensional time.

The notion of a cone, while it does not depend on experience, does depend on our intuition of space and time. Any truths that we might formulate about a geometric cone, while they may be a priori, are only necessary from the point of view of thinking beings with intuition filters of the same nature as ours. The geometric cone is a member, not of the set of all objects of experience, but of the larger set of all objects that can in principle be intuited by human (or human-like) cognizers. They may literally not be directly experiencable at all. We are still not talking, however, about the even larger set of all conceivable objects that can be grasped by human understanding. We are still restricting ourselves to objects that can be thought of as being in space and time. As such they are "world objects". This set is bigger than the set of actually experiencable objects, since it is possible to imagine that there are objects in space and time that are far too complex to ever actually construct in one's imagination. Yet we can understand that they are possible objects. A 1000-sided polygon cannot be directly experienced as a 1000-sided polygon, in the way a triangle can be experienced as a triangle, since the 1000-sided polygon is too complex to construct in the imagination. But that does not detract from the dependence of this too-complex object on human intuition filters.

If, however, we were to further detach our experience from human intuition as well, we could run our representation through yet another filter. Just as pure intuition was required to completely filter out the empirical component, a pure concept of the understanding will allow us to filter out both the empirical and the intuitional component, leaving us only with what flows directly from the concepts themselves. If for instance we generalize our objective intuitive representation of the geometric cone into an imaginary 4-D cone, we have generalized beyond our capacity to intuit, but not beyond our capacity to conceptualize. This 4-D cone, as detached from intuition, is no longer a member of the set of all possible world objects, but of the larger set of all possible objects of cognition whatsoever. World objects can also be so conceptualized, of course, and so are a subset of the set of cognizable objects. The difference is that world objects necessarily are conceived as existing in space and time, something that is dependent on our innate cognitive capacities, as explained in the Transcendental Aesthetic.

So, although we noted earlier that "all knowledge begins with experience" (seeing that nothing can be cognized except as an experience), we see now that "it does not follow that it all arises out of experience," [CPR 41] since our intuition and conceptual filters allow us to filter out the empirical and intuitional components. The cognitive filtering that detaches the object from the pure forms of intuition is called "analysis". It is contrasted with "synthesis", even though it is itself a kind of synthesis, because it allows us to treat the object of our experience as if it were a more general object not subject to the innate restrictions of our cognitive machinery. Pure analysis is just that kind of synthesis that allows us to break down a synthesized representation in such a way that we can see its pure conceptual form. The resulting "objective conceptual representation", is therefore depicted in figure 2 in functional notation, stripped of its visual content (of course, an actual complete functional description of a cone would be much more complex than what is depicted in the figure).

Note that the way we have presented the cognitive machinery, the very act of synthesis already presumes logical functions, or concepts (although they are not yet necessarily pure concepts). The grounding of experience in our capacity for conceptualization, and thus ultimately in the pure concepts of the understanding, is the main point of the Transcendental Deduction. The Metaphysical Deduction only tells us that these pure logical functions apply to all objects that we can think of through the understanding. Given only the Metaphysical Deduction, it might always be possible that there are objects we can experience that cannot be thought of conceptually. Recall that E(D) is what we immediately experience, not D itself, nor E() itself. To isolate E() from D is a feat of the understanding, an act of conceptual analysis. But so long as we are dealing with an unanalyzed experience, how can we be sure it is analyzable into an E() and a D? Perhaps there is some kind of experience that cannot even be thought of as synthesized like this. "Appearances", says Kant, "can certainly be given in intuition independently of functions of the understanding." [CPR 124]. So E(D) does not on its own provide us with any knowledge of E() at all. Until we analyze E(D) down into E() and D, an act of the understanding, our unanalyzed perception is just of an object sitting before us.

So why does Kant think E() is even involved in unanalyzed perception? Perhaps Kant is wrong and logical functions can be used to abstract from immediate experience, but they are not necessarily presupposed in the lower level unanalyzed perception at all. For even if we manage to decompose some experiences into function and data, how do we know that all objects of experience can be so analyzed? As we saw earlier, Kant wishes very much to show that this is so, in order to ground physical law in the a priori. The goal of the Transcendental Deduction, distinct from that of the Metaphysical Deduction, is to show that the pure concepts of the understanding, the categories, are the a priori necessary preconditions for all objects of experience.

IV. The Transcendental Deduction of the Logical Functions

Intuition Is Subject To The Categories

We know from the Transcendental Aesthetic that everything has a temporal element. Space is secondary to time in the sense that space is required only for an intuition of outer things, while time is required for any intuition at all. So for now we will ignore space, and concentrate on time. Might inner sense, all by itself, be sufficient to account for all the possible objects of cognition? According to Kant, no, since time by itself is like space a singular thing, not a general concept. The logical functions are required to produce objective cognitions. These are applied in the imagination through synthesis. But this process of synthesis takes time, of course. Since it is by its nature the transformation of one representation into another, the notion of progressing moments of time is clearly presupposed in it.. So anything experienced must have a temporal quality. This explains why time is the pure form of inner sense, since to perform synthesis in the imagination, even without any external sensory input, requires a notion of time.

Yet one cannot apply time in this fashion without imagining something that is undergoing the transformation. The very intuition of time implies the possibility of objects being transformed. So our sense of outer sense must be employed in order to apply our intuition of inner sense in any experience. "All experience does indeed contain, in addition to the intuition of the senses through which something is given, a concept of an object as being thereby given, that is to say, as appearing. Concepts of objects in general thus underlie all empirical knowledge as its a priori conditions." [CPR 126]

All experience, then, involves an intuition of space and time, the application of which requires some kind of operation that transforms the objective representations through time. If there were no such operations, there could be no application of the intuition of space and time, and no experience. These operations are just the logical functions we have been talking about it, and "they relate of necessity and a priori to objects of experience, for the reason that only by means of them can any object whatsoever of experience be thought."

The Synthetic Unity of Apperception

We have seen that the logical functions are required for application of our pure intuitions, and for perception of objects, and we have seen how this occurs through synthesis. But there is a remaining puzzle here that Kant takes very seriously, and ultimately has serious consequences for transcendental idealism. This is the question of the unity of synthesis. Now you might think this is a silly thing to worry about. "Okay, look," you say, "I've got representation A and representation B. I combine them and get representation C. That's synthesis, by definition. Why is there any mystery as to how these things get united? Synthesis is the uniting of various perceptions together. No mystery."

But think again. There are many different possible syntheses. Altogether, the space of possible mental representations is huge. What privileges some of the combinations to get tried and not others? Remember the falling cat? Given transcendental idealism, we must define the empirical cat object in terms of our continually combining, and recombining mental representations. The "law of gravity" seems to constrain these representations to combine and recombine in particular ways. Why? If the cat really was an illusion in my head, anything at all might happen. And there is absolutely nothing about the appearances themselves that seem to indicate that certain kinds of combinations of representations should be preferred, even mandated. This is why the unity of the act of synthesis in imagination is so important, because it has a particular structure, tied to the laws of physics. And these laws, as lawful, are a feature of appearances as applications of the understanding, and not as appearances, per se. So explaining why particular combinations of representations become united in synthesis, while others do not, is crucial to understanding how physics can be properly grounded in the a priori (if indeed it can be).

Kant's answer is that these representations are united in synthesis according to the nature of our self-consciousness. Consider what is required to have a synthesized experience of an object in the first place. Obviously, we need some kind of at least low level consciousness, some awareness of the object, or we have no experience or representation to begin with. Imagine two different possible temporal streams of experiences. We will drop the functional notation we were using earlier, so as not to presume too much, and just consider that we have a stream of successive raw experiences.

Suppose that the mental function Q() is a concept shared by both myself and Socrates. Now Socrates and I are different, separate persons; we have distinct personal identities. It would be impossible, for instance, for me to literally turn into Socrates at the moment he was sentenced to death, since that would by definition no longer be my consciousness. It would be the consciousness of Socrates. A particular mental experience does not take place isolated in time; it is connected by memory to other mental experiences that together are united into a personal identity. At least this is so for human beings. It might not be so for a crayfish or an ant, in which case those creatures, while conscious, are not self-conscious. The moment one experience gives way to another, from the perspective of the crayfish, you might as well have a completely different individual. Perhaps we as rational observers of the crayfish can come up with other reasons to unite the crayfish's experience into a single individual persisting through time, but the crayfish itself is not capable of doing this. It has no sense of itself. It has immediate experience of objects, but no experience of itself. It has no personal identity. (If someone would like to argue that a crayfish does have some rudimentary sense of self, I will not take issue with them; the crayfish is only meant as an illustrative example--perhaps the crayfish has a tiny window of self-consciousness that lasts only a short while.)

Humans, of course, are different. Persons who are future me's are persons who remember being me, and persons who are past me's are persons whom I remember being. I would propose that this follows from the very definition of what we mean by "person". So it is an analytic truth that any arbitrary person cannot become Socrates at the moment he was sentenced to death. It follows from our definitions of what a person is, and what Socrates is. Even if I had brain surgery, and through some high technology, had my memories replaced with precisely those of Socrates and was then transported back in time, disguised as Socrates and put in his place, still one could not say that I had become Socrates, for at the moment of the brain surgery, my self-identity ceases to exist, and that of Socrates is put in its place.

While I cannot experience the full experience, call it S, that Socrates had when he was sentenced, I can share with Socrates the concept Q(), since we are both rational beings. Perhaps Q() is the concept of "injustice", which Socrates was applying to S in a synthetic act of judgment on his incoming sensory data. As a fellow rational being, I can certainly share this concept with Socrates, but I can never experience the particular experience of injustice he felt when he judged his situation to be unjust by combining Q() with S, thereby experiencing Q(S).

Now assume that Socrates' experience at the trial proceeds according to the first sequence of experiences above: D E F G. What ties these experiences together? Why not substitute your own experience sitting here reading these word right now, call it N, for F? Is the resulting D E N G a possible sequence of experiences? Of course not. Again, this is an analytic truth. Even if you imagine some advanced technology swapping your brain with Socrates' at just the right moment so as to drop your N experience into the sequence, while artificially maintaining any empirical input so as to keep N intact, and then swapping it out again, still D E N G would not be an experienced sequence of events. No amount of high-tech shenanigans attempting to conjoin these experiences in space and time can possible really make them into a unitary sequence of experiences. For what determines that these experiences belong in this particular chain, related in this funny way to one another , is the self-identity and hence self-consciousness of the person having the experience. This is an analytic truth that flows from our concept of personal identity (another concept Socrates and I may share even though we cannot share our experience of it). Now what about the second sequence of representations? Could this be possible?

This would require Socrates to experience his sentencing in a different order. This is, of course, as impossible as my turning into Socrates. Socrates after the sentencing remembers being the Socrates who was sentenced, who remembers being the Socrates before sentencing. This is determined by Socrates' own sense of personal identity, which is determined by his self-consciousness, his internal model of himself. My consciousness can no more becomes Socrates' consciousness, than Socrates' consciousness after sentencing can become something that took place before the sentencing. But this, again, is an analytic truth that flows from our definitions and concepts of personal identity, constrained by our states of consciousness (and whatever it is that produces them; Kant does not try to give a complete account of how consciousness itself is generated). Any consciousness that has such a concept of its own personal identity, that so ties itself together into a distinct conscious being through such sequences of experience, is a self-conscious being. Kant calls this "apperception", as opposed to mere "perception". A crayfish may well be conscious, as it undoubtedly has some kind of perception of the food it catches, but it probably does not have "apperception"; it is not self-conscious. It has no sense of itself as a thing separate from its environment and persisting through time.

The Synthetic Unity of Objects of Experience

The nature of an object is likewise of something that persists through time and has an identity separate from other things around it. If we take only our actual experiences as experienced then all we have is an experience. In order to separate out an object D as the object of experience, we must be able to in some sense to recognize the D as separate from the the remainder of the experience. Otherwise, all we have is a single unitary experience (which is probably a fiction, anyway). This means that some kind of cognitive faculty that performs such a function is required for the cognition of any objects of experience whatsoever. Experience D is transformed into E according to some kind of function that preserves personal identity, which is likewise transformed into F, et cetera. In order to have a self-conscious being, then, we need to have such a sequence of transformations. That is why time is the pure intuition of inner sense. Our intuition of time is simply an abstract expression of the necessary structure of self-consciousness as something that ties experiences into a progressive sequence. And the functions that achieve this transforming action are, again, the logical functions or categories.

For the manifold representations, which are given in an intuition, would not be one and all my representations, if they did not all belong to one self-consciousness. As my representations (even if I am not conscious of them as such) they must conform to the condition under which alone they can stand together in one universal self-consciousness, because otherwise they would not all without exception belong to me. [CPR 153]
Summary of the Argument

To sum the argument up in Kant's own words, "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." [CPR 160] But it is just the logical functions that perform this kind of uniting operation. So the "manifold in a given intuition is necessarily subject to the categories." [CPR 160] Yet to have a perceived object maintain its identity likewise relies on the identity of the perceiver. So we need something like the categories, or logical functions, to have a unitary intuitive experience of any object in space and time. "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." [CPR 170]

In other words, to explain the structure we see in our objects of experience--i.e., the lawfulness of nature--we must invoke the unity of apperception, which is also required for the unity of intuition and understanding alike.

All synthesis, therefore, even that which renders perception possible, is subject to the categories; and since experience is knowledge by means of connected perceptions, the categories are conditions of the possibility of experience, and are therefore valid a priori for all objects of experience. [CPR 171]
So What Have We Accomplished?

We have deduced, from the nature of our self-conscious experience, that there is a necessary faculty of the mind that operates on experience so as to separate out an object. This necessary function of the mind is required for self-consciousness, which separates out the self as such an object. To see a hat and recognize it as a hat requires separating out the hat from the rest of its environment according to the concept "hat". By synthesizing a judgment and getting E(D), we separate D out from the background of other incoming data, and recognize it as an object. Yet we cannot help but do this. To imagine experiencing E(D) as merely a unitary experience without an object and concept is actually quite absurd. All judgments and all experience--cognition in general--has this quality of combining sensory data together with concepts. Our previous attempts to imagine "raw experience" with absolutely no application of concepts at all has turned out to be a fiction.

So whatever it is that gives the particular combination of representations that accompanies the falling cat its lawful structure does not "lie in the objects, and cannot be borrowed from them ... On the contrary, it is an affair of the understanding alone." [CPR 154] So then, we ask yet again, what is this object? Is it an illusion or dream? No. It is that which is united together by a sequence of synthetic acts of judgment through time, and these in turn are determined as belonging together in that particular order and form because of the very nature of self-consciousness, and one's sense of self-identity. Empirical objects get their unity wholly through your unity.

IV. Transcendental Idealism

So we have determined that, given a self-conscious perceiver, all perception presupposes logical concepts, and in the perception of objects, the identity of the object is tied to our own self-consciousness. This is the key to making transcendental idealism work. Recall that our basic problem with transcendental idealism was figuring out how the objects that we perceive can in some sense exist in a world out there, apart from our minds, and at the same time be determined by our mental representations, rather than our mental representations being determined by them. Looking back at figure 2, recall that the transcendental method (encompassing the Transcendental Aesthetic, and the Metaphysical and Transcendental Deductions), has lead us from immediate experience to a broader realm of possible world objects and an even broader realm of conceptually possible objects. These broader realms can be transcendentally deduced, and yet are not themselves directly experienced.

Now let us ask why it is that most people find idealism so counter-intuitive. If all we directly experience are mental representations, then why would we even be so predisposed in the first place to thinking that they must be "out there" independent of our minds? For most, the pull of naive realism lies in the "law-governed" nature of empirical objects. It is the fact that they seem governed by law that makes it seem implausible that they are merely illusory. When we hold a ball in front of us and drop it, it always falls. Such is not the case in dreams, where what laws there are can be randomly broken at a moment's notice. The transcendental method provides us with reason to see that there may be laws governing our objects of experience even if they are defined solely in terms of mental representations. Note that Kant's idealism does not claim that objects are identical to mental representations, but rather simply that they conform to them, rather than the other way around. The objects are determined by the representations, rather than the objects determining the representations.

Since the logical functions are implicit in any object of experience at all, this means objects of experience are subject to logic. One cannot, for instance, experience a square circle. But, as empirical objects of experience, they are also subject to the unity of apperception. Just as we unite ourselves through time by our faculty for self-recognition, we unite the objects we recognize through time by the same faculty. For what makes the cup of hemlock, from the point of view of Socrates, the same object after drinking as before? Why, only the unity of his own self-consciousness through time, of course. Just as D cannot possibly come in sequence after F, for Socrates, due to his own self-identity, so the empty just-drunk cup cannot possibly come before the full not-yet-drunk cup, for Socrates. For either the experiences or the empirical objects to fall in a different order would be impossible, analytically, just by virtue of Socrates' self-consciousness.

"Now see here," pipes up the realist, "all this means is that the cup's external properties and purely physical unity is consistent with Socrates' personal unity. But the cup's unity could still just as well be determining Socrates' unity as the other way around. You've really said nothing other than to restate the rather absurd creed of transcendental idealism."

Well, okay then, what if we try to generalize Socrates' experience without preferencing his own subjective awareness of himself? What if we decide that that is an overly anthropocentric view of Socrates' world, and we can surely view him and his environment in a more objective light. Well, then, there is no reason any more to think of Socrates' world as something apart from the entire realm of conceptually possible objects (some of which may be worlds and some of which may not). In this case, there is no reason to give any necessity to the sequence D E(D) F(E(D)) G(F(E(D))). We might as well drop in someone else's experience, or something that is not an experience. We have no reason to view Socrates himself as a thing within this huge concept-space. Neither is there any reason to view the cup as such a thing. We could just as well decide that the cup full of hemlock is but a 3-D projection of a 16.6254-dimensional fractal object which in the next moment of "time" will become the paper you hold in your hands now. This may sound bizarre, but what is to stop us analytically from defining our objects however we like? As long as we have produced something conceptually sound, without contradiction like a square circle, the realm of cognizable object is truly immense. Unless we restrict our analysis of concept-space to possible worlds containing possible perceivers, it is hard to see how we can talk about possible objects of experience at all. But once we do this, we must define such objects in terms of the self-identity of the perceiver. The extent to which they are physical objects maintaining their identity in a three-dimensional world is the extent to which we as the observers of the object are self-conscious beings maintaining our identities through time. The identity of the empirical object as an object with 3 spatial dimensions persisting through repeated transformations in uni-dimensional time is directly tied to the requirements of our own self-consciousness to experience itself as persisting via repeated transformation through uni-dimensional time. The former depends on our innate outer sense, the latter our innate inner sense.

So the cup of hemlock, as an empirical object persisting through time, is completely defined in terms of the mental representations in the self-consciousness of Socrates. The empirical object conforms to the mental representations, and not the other way around. Or at least, this is how it has to be if we are to have any hope of grounding physics in the a priori. One can still, without contradiction, take the realist's position that there is some thing-in-itself, some "noumenon", that really is the cup. This is a possible idea to have, and is not contradictory. Yet if some such noumenon, rather than the synthetic unity of apperception, is responsible for the unity of the cup, then physics will be forever beyond our ability to conceptualize. Only if the object of perception can be embedded in the set of possible world objects, likewise embedded in the set of possible conceptual objects, and only if our own personal placement within this whole is what determines the structure of this unity, can physics be understood. Otherwise, it will be forever beyond our grasp. Kant's argument does not prove the realist wrong, but it does give us reason to believe transcendental idealism might not be so outlandish after all, and it certainly gives us reason to hope that it had better be true if we have any hope of grounding physics in the a priori.

If you are still thinking it is a little fishy to talk about the representations determining the cup, because the cup surely has a lawful existence of its own, consider this. The cup of hemlock can still be generalized into the broader scope of conceptually possible objects (even though in the process it loses its identity as a physical object), so it need not be (although it still could be) a mere illusion in the mind. The cup as a concept still exists outside any individual person's mind. It resides not in a particular mind, but in the whole concept space that is transcendentally available through analysis to any rational being. But it does not reside in this huge concept space as a physical object apart from your self-consciousness. Only by defining the "object" as a connected set of representations that cling together distinct from other representations can we say we have an object at all. But the only way to preference the particular way of doing this that yields the cup of hemlock is to do it, not analytically, but synthetically, in terms of a self-conscious being's identity in a world. Without the synthetic component, the cup is not a coherent object; but still its existence need not reside solely in the observer's mind, but can be understood analytically, minus object-hood, as quite apart from the mind.

Since, as an empirical object, the cup is subject to logic and to what is logically possible given the requirements of a unitary self-consciousness, it may well obey all kinds of "laws" that we can't just change by an act of will. For can we change the nature of our own self-consciousness through an act of will? No. We have a model of ourselves that plucks us out of the environment as an object, just as we have a model of the cup that does the same for it. We see ourselves through our cognitive filters, as we see the cup. Both self and cup get their unity through this subjective criterion. We see ourselves "only as we appear to ourselves, not as we are in ourselves." [CPR 166] The cup's unity and my unity are one unity. And it is the constraints placed on both these objects of experience by the unity of apperception that determines the laws of physics as we know them.

Although Kant never got so far as to actually embed the laws of physics in the a priori of the transcendental realm, it was his dream to do so. Today that dream is being pursued in the field of quantum cosmology by those advocating the "anthropic principle", which embeds our world in an ensemble of possible worlds, determined by the logical requirements for the possibility for conscious life.

V. Conclusion and Future Work

I have tried to develop Kant's argument here apart from the actual set of pure concepts of the understanding, or categories, that he proposes, because I think what is really important, and correct, about Kant's system is his transcendental deduction of the logical functions, not necessarily the particular set of functions, or categories, that he chooses. In my view, modern symbolic logic gives us a more precise set of primitive logical functions, from which any object of cognition can be built. I am not saying that Kant's breakdown of the categories is wrong or metaphysically irrelevant; rather I am saying that I would prefer to develop his system without presuming his particular function set, and see where it gets me. Perhaps the same old Kantian categories will pop right out, or perhaps the function set will end up being somewhat different.

Today, logic and mathematics have been shown to have (insofar as they are analytic rather than synthetic) a common logico-mathematical base, which is realized in recursion theory, the most elegant formulation of which (in my view) is the lambda-calculus of Alonzo Church. Most if not all determinate concepts can be reduced to expressions in this calculus. It is an extremely simple and elegant system, consisting of basically two features: (i) the ability to built larger and larger structures out of a small number of simple primitive components, and (ii) the ability to repeatedly substitute certain "forms" in these structures for other forms. This latter feature is called "substitution" or "generalization", and is a very general formulation of abstraction or mechanism. It also includes within it a kind of time, since one form is transformed into another, and a kind of causality, since given the laws of logic, one form must necessarily lead to another.

The lambda-calculus is roughly equivalent to the traditional functional notation in which we write F(D), except that F() and D are not fundamentally different kinds of things in the lambda-calculus. The concept that is combined with the data to produce the new synthesized representation is not necessarily a different sort of thing than the representation it transforms. However, it is being applied on a different level. F(D) brings D under the category F, which is not the same as bringing F under the category D(). However, it nonetheless is possible to do the reverse and compute D(F) instead of F(D), since function and data are not fundamentally different kinds of things.

It is generally believed in the fields of metalogic and information science, although it has never been proven, that this simple mechanism can account for anything thinkable, at least anything that is thinkable in precise and logical terms. This claim of maximal expressiveness for recursive functions is called the "Church-Turing Thesis".

In Kant's terminology, the lambda-calculus is the a priori necessary precondition for all objects of thought. Remember that this simple formalism can be used to express, with respect to their analytic content, but not necessarily their synthetic content, anything that human beings have yet been able to dream up. And if the human mind can itself ultimately be understood conceptually (perhaps through the efforts of cognitive scientists), then any proposition with synthetic content can also be expressed in the lambda-calculus, but only by expressing the self-consciousness of the observer in the calculus, and arbitrarily deciding to take up the point of view of this self-conscious being. For only by taking on its viewpoint can the synthetic unity of objects of its experience even be considered. Without such a choice of viewpoint, the objects may exist outside the being's mind, but they do not so exist as unitary objects.

The complex structures we build up in the lambda-calculus could be considered as abstractions from our intuition of objects in space. The lambda-calculus transformation rule could be considered as an abstraction from our intuition of things changing in time. Thus, these two fundamental building blocks from which all things in modern science, mathematics and logic can be constructed correspond directly to Kant's fundamental categories of (i) "quantity" (the infinity of possible structures) [CPR 171] and (ii) causation (the transformation of these structures given a rule) [CPR 172].

If you doubt that such a simple logical formalism could be so powerful, keep in mind that the lambda-calculus, as simple as it is, is a complete computer programming language, and so could in principle be made to simulate the running of the entire universe, at least to whatever extent that its running is conceptualizable by human beings. (Kant himself seems to consider the existence of objects, at the very least, as outside the conceptual realm--as noumenal. God, perhaps, has a unique noumenal skill for some kind of nonhuman "generative" synthesis. These kinds of remarks by Kant, in my view, weaken his transcendental idealism.)

In Quantum Phenomenology [Randall 1997], I give a kind of transcendental deduction of the lambda-calculus, tying it in with the anthropic principle from quantum cosmology, which is not too un-Kantian, although to draw further parallels would go beyond my current understanding of Kant's system, which I have not yet mastered. I mention the lambda-calculus here only to introduce the reader briefly to the modern notion of the foundations of logic, and suggest parallels with Kant's system. Whether my own ideas concerning the anthropic principle and logic are ultimately in harmony with Kant's system is a possibility for future investigation, but something which I have not yet sufficiently explored.

It seems clear, though, that the modern anthropic principle has at least some general features very much in common with Kant's system. Both attempt to ground physics in the a priori by making the centrepiece of physics something that most scientists in the twentieth century (in spite of quantum mechanics) have been loathe to take into consideration: the self-consciousness of the observer. Yet Kant's Transcendental Deduction makes it difficult to imagine any other possible way of explaining physics coherently at all. Either we ground the lawfulness of physics in the synthetic unity of apperception, or physics will be an endless chasing after unknowable noumena. Many (perhaps most) modern advocates of the anthropic principle would whole-heartedly agree with Kant's belief that "the principle of apperception is the highest principle in the whole sphere of human knowledge." [CPR 154]


Immanuel Kant (1781). Critique of Pure Reason (2nd. Ed.), Norman Kemp Smith (Trans.)., 1781, 1787, 1985, 1996. [Cited as "CPR pp".]

David Hume (1739). A Treatise of Human Nature.,1739, 1740, 1969.

Allan F. Randall (1997). Quantum Phenomenology., Dept. of Philosophy, York University, Toronto, 1997.

Acknowledgement: without the help and wisdom of Robert Hanna, this paper could not have been written.
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