[This is a graduate seminar paper from fall, 1993. --mh]

Problems from Kant

by Michael Huemer

1  The Kantian philosophy

The Critique of Pure Reason is unified by a single line of argument involving just two or three central ideas, which, in spite of a certain complexity and obscurity in its development, can be fairly summed up as follows: Kant poses the question, "How is synthetic, a priori knowledge possible?" And he answers: Synthetic a priori cognitions express conditions on the possibility of experience. As such, he argues, we can know that they are valid for the realm of appearances but not for things as they are in themselves.

This argument makes use of three special, philosophical notions: first, "synthetic, a priori knowledge"; second, "conditions on the possibility of experience"; and third, the distinction between "appearances" and "things in themselves". I aim to explicate these notions herein, by way of understanding the general idea in Kant. Of course, I will have to neglect the considerable number of details, elaborations, and subpoints in the labyrinthine path the Critique traces, but I think this general, essential examination of the work will be more valuable for understanding Kant than a detailed examination of just one tiny piece of it would.

2  The problem of the synthetic, a priori

The notion of synthetic, a priori knowledge is the clearest of the trio. A priori knowledge is that which is known not through experience.

A synthetic proposition, according to Kant, is one in which the concept of the predicate is outside the concept of the subject (B10-11).(1) This is opposed to analytic propositions, which are true by definition. Analytic truths(2) are also sometimes characterized as those which are based on the law of identity (B10), or contradiction (§2(b)), in the sense that their denials are self-contradictory.

In philosophy, it has always been customary to regard analytic propositions as being in a sense empty and only describing our concepts; whereas only synthetic propositions are really substantive, new knowledge. Kant also takes this point of view:

Thus it is evident: 1. that through analytic judgements our knowledge is not in any way extended, and that the concept which I already have is merely set forth and made intelligible to me ... (at A8)

And thus Kant's problem seems to be how we can obtain substantive knowledge independent of experience.

Kant's examples of this type of knowledge include the law of causality, arithmetic, and geometry.

What is not so clear to me is why this sort of knowledge is supposed to be a problem. In other words, where Kant wonders, "How is synthetic, a priori knowledge possible?" I wonder why shouldn't it be? Presumably some answer to my question is presupposed by Kant's; that is, in order to wonder how it is possible that p, you first must have in mind some sort of reason for expecting that ¬p. Unfortunately, Kant has little to say about this, apparently taking the obviousness of the problem he has in mind for granted. He protests vigorously on the difficulty of the supposed problem in the Prolegomena:

... [A] satisfactory answer to this one question requires a much more persistent, profound, and painstaking reflection than the most diffuse work on metaphysics, which on its first appearance promised immortal fame to its author. And every intelligent reader, when he carefully reflects what this problem requires, must at first be struck with its difficulty, and would regard it as insoluble and even impossible did there not actually exist pure synthetical cognitions a priori. (§5, p. 24)

But, to the disappointment of his evidently less intelligent readers, Kant fails to explicate the source of this great difficulty.

In several passages he insists on the impossibility of objective and a priori knowledge, but these passages, rather than explaining the reason for this impossibility, do little more than restate that it is impossible:

If intuition must conform to the constitution of the objects, I do not see how we could know anything of the latter a priori... (Bxvii)
It would be quite otherwise if the senses were so constituted as to represent objects as they are in themselves... The space of the geometer would be considered a mere fiction, and it would not be credited with objective validity because we cannot see how things must of necessity agree with an image of them which we make spontaneously and previous to our acquaintance with them. (§13, remark I, pp. 34-5)
If our intuition were of such a nature as to represent things as they are in themselves, there would not be any intuition a priori, but intuition would always be empirical. For I can only know what is contained in the object in itself if it is present and given to me. It is indeed even then incomprehensible how the intuition of a present thing should make me know this thing as it is in itself, as its properties cannot migrate into my faculty of representation. But even granting this possibility, an intuition of that sort would not take place a priori, that is, before the object were presented to me; for without this latter fact no ground of a relation between my representation and the object can be imagined, unless it depend upon a direct implantation. (§9, pp. 29-30)

This last passage comes closest to making an argument, which I think is most charitably read like this:


Knowledge requires a kind of correspondence between a representation and the properties of an object.


This correspondence cannot be merely fortuitous, or due to chance.


The properties of things-in-themselves are independent of us.


So the requisite correspondence cannot come about by our representations affecting the objects' properties. (from 3)


So it must come about by the objects' properties affecting the representations. (allegedly from 1, 2, + 4)


And in order for objects to influence our representations, we must be acquainted with them; i.e., we must have experience of them.

I think many non-Kantian, empiricist philosophers would make this sort of argument if they were sufficiently articulate. My doubts about the argument concern the derivation of (5) from (2+4). The assumption is that the only ways for a correspondence between representation and world to come about are (a) pure chance, or (b) causal interaction between object and representation. While this is superficially plausible, to see that it is false we need only consider any knowledge of the future. For instance, I know that the sun will rise tomorrow. Now my belief is not caused by its object (since the object is in the future); nor, presumably, will my belief cause the sun to rise. But neither is the correspondence merely fortuitous. What makes it more than chance is no causal connection between the belief and the fact but a purely epistemic relation; that is, I have a rational justification for believing that the sun will rise tomorrow (based on inductive evidence), and that is all that is required. That in this case the justification is empirical does not matter. Analogously, I know that 2+2=4. Presumably, my belief does not cause the mathematical relation, nor is it caused by the abstract objects. But neither is it a matter of mere chance, because my belief is brought about by genuine understanding of the abstract objects, and is rationally justified.

A second, less impressive reason why Kant might have regarded synthetic, a priori knowledge as problematic is that ever since the enlightenment, because of the development of the new science, philosophers have rushed to get on the bandwagon of empiricism. From Kant's time up until our own, it has been pretty much just taken for granted that all knowledge -- or at least, all real knowledge -- must be based on experience. Armchair reasoning has been devalued to the point where philosophers regard the detection of the presence or absence of contradictions as the sole function of reason. Now if you have that presupposition, then it is obvious that you are going to regard synthetic, a priori knowledge as a problem. But then the solution of the problem is as easy as rejecting the false presupposition.

I think we can fairly conclude, then, that Kant's problem is far less difficult and compelling than he makes it out to be.

3  CPE's: four interpretations

When Kant claims that the synthetic a priori represents conditions on the possibility of experience, there are at least four ways we might conceivably interpret "conditions on the possibility of experience" (CPE's):


A CPE is something that must be true in order for there to be any experience -- a sort of anthropic principle. For instance, it is a condition on the possibility of experience in general that consciousness exist. If consciousness didn't exist, there couldn't be any experience.


A CPE is something that must be true of an object in order that we experience it. For instance, in order for me to experience an object, it must be within my backward light cone (because the speed of light is the fastest any information can travel).


A CPE is something that we must experience as being true. For instance, for the man who is wearing green glasses, everything must be experienced as green.


A CPE is something that must be true of experiences. I can't think of any very good examples of this, but some philosophers have claimed that all experiences must be self-intimating (i.e., it is not possible to have the experience without knowing one has it).

(1) is probably the most natural reading of the phrase "condition on the possibility of experience", but (3) is probably more consistent with what Kant says about these things.

4  Appearance vs. thing-in-itself: four interpretations

There are likewise at least four conceivable interpretations of the famous distinction between appearances and things in themselves:


Appearances and things-in-themselves occupy two separate and distinct realms, related as California is related to New York, so that there is no object that is both an 'appearance' and a 'thing in itself'.


Appearances are how objects seem to be, whereas things in themselves are how the objects actually are. E.g., the far away tower may appear to be round when actually it is square.


Things in themselves are objects, and appearances are the ideas in us that the objects cause. E.g., there is a distinction between a yellow station wagon and a visual experience of a yellow station wagon, where the latter is caused by the former.


Things as they are in themselves are the intrinsic properties of objects, whereas appearances are only relational properties that objects have, sc., in relation to us.

(1) is the most naive interpretation and almost certainly wrong. The way Kant frequently talks about objects as they appear and then those same objects as they are in themselves indicates that he intended a distinction between two aspects of objects -- e.g.:

Since, however, in the relation of the given object to the subject, such properties depend upon the mode of intuition of the subject, this object as appearance is to be distinguished from itself as object in itself. (B69; emphasis Kant's)

So here one and the same object is spoken of as appearance and then 'in itself'.

And (2), though most obviously suggested by the terminology, is probably also not what Kant meant by appearances versus things in themselves:

When I say that the intuition of outer objects and the self-intuition of the mind alike represent the objects and the mind, in space and time, as they affect our senses, that is, as they appear, I do not mean to say that these objects are a mere illusion... I am not saying that bodies merely seem to be outside me, or that my soul only seems to be given in my self-consciousness. (B69; emphasis Kant's)

That's a pretty clear denial of interpretation (2).

The third interpretation, however, in which things in themselves are the cause of appearances, has a good deal of textual support. The passage above shows Kant taking "as they [objects] affect our senses" to be equivalent to "as they appear", just as he does repeatedly in other places:

[A]ll conceptions, like those of the senses, which come to us without our choice enable us to know the objects only as they affect us, while what they are in themselves remains unknown to us.(3)
I, on the contrary, say that things as objects of our senses existing outside us are given, but we know nothing of what they may be in themselves, knowing only their appearances, that is, the representations which they cause in us by affecting our senses. (§13, remark II, p. 36)

On this conception, appearances are simply the effects that things in themselves have on our minds. It's true that this sits poorly with Kant's later claim that the category of causation cannot be applied to things in themselves. It also makes his claim that we cannot know our own consciousness "in itself" strange, since the putative reason we could not know external objects in themselves was that we only knew their effects on our own consciousness. We must now suppose that it is possible to indeed know the effects that things have on our minds without yet knowing what goes on in our minds. We must then suppose that mental events -- which we do not know -- produce effects on consciousness which we do know, and that these effects are distinct from any mental events.

The existence of these contradictions I do not think warrants overriding the "he said what he meant" principle of exegesis, especially in the absence of any other understandable interpretation of the "thing-in-itself vs. appearance" distinction.

The fourth interpretation is almost equally well-supported. In elaborating on why he is not making mere illusions of our perceptions, Kant explains:

The predicates of the appearance can be ascribed to the object itself, in relation to our sense ... That which, while inseparable from the representation of the object, is not to be met with in the object in itself, but always in its relation to the subject, is appearance. (B70, footnote a)
Now a thing in itself cannot be known through mere relations; and we may therefore conclude that since outer sense gives us nothing but mere relations, this sense can contain in its representation only the relation of an object to the subject, and not the inner properties of the object in itself. (B67)

These passages suggest that the "in itself" aspect of objects is their intrinsic, internal properties, as opposed to their merely relational properties.

This interpretation is just about consistent with the previous one, if we look at the relational properties in question as being causal properties. There is a slight difference, which we may suppose Kant overlooked, viz., that in the previous interpretation, appearances are mental representations in us (which are effected by objects); whereas in this interpretation, appearances are objects, considered under the aspect of their relational properties (sc. powers to cause effects in us).

5  Kantian arguments

I think we have pretty well determined what Kant meant by "appearances" and "things in themselves" above. Things in themselves are just objects, under the aspect of their intrinsic properties. These objects can produce certain effects in us, which are their appearances. Now in order to settle what conditions on the possibility of experience (CPE's) are, and hence what Kant's theory of synthetic a priori knowledge is, we must consider the arguments that Kant gives. In general, in order to see what a claim means, it is a good idea to look at the argument for it, or any argument in which it appears, and try to interpret the claim so that the argument makes sense. CPE's and synthetic a priori knowledge appear in three arguments:


The claim that items of synthetic a priori knowledge are CPE's is supposed to explain how the propositions can be known a priori.


That the synthetic a priori are CPE's is also supposed to guarantee their validity for the realm of appearances, but


That synthetic a priori knowledge are CPE's deprives them of application to things in themselves.

5.1  First argument

Take the first argument. I have to admit that I have difficulty understanding why CPE's would be a priori on any interpretation of "CPE's". Kant more or less just asserts that he has explained the a prioricity of certain items of knowledge:

For we can a priori and prior to all given objects have a knowledge of those conditions on which alone experience of them is possible, but never of the laws to which things may in themselves be subject, without reference to possible experience. (§17, pp. 44-5)
Therefore in one way only can my intuition anticipate the actuality of the object, and be a cognition a priori, namely: if my intuition contains nothing but the form of sensibility... For that objects of sense can only be intuited according to this form of sensibility I can know a priori. (§9, p. 30; emphasis Kant's)

I cannot see why this would be known a priori. In order to know how it is possible to 'intuit' things, isn't it necessary to have some experience, on which to base one's claims about the nature of 'intuition'? Doesn't the knowledge of what form of sensibility we have depend on experience? It may be only an introspective experience (though I may perhaps wonder, even then, how we could be sure that the means by which we had so far had intuitions were the only ones possible) but experience nonetheless. Or if it is possible to know a priori how intuition or experience works, then we must ask whether this knowledge be itself analytic or synthetic. If it is analytic, then only analytic consequences can be derived from it. And if it is synthetic, then we must wonder how is it possible? for Kant has then only pushed his question back one stage: we can have synthetic a priori knowledge of external objects, he claims, because we have certain synthetic a priori knowledge of the conditions under which experience is possible.

Furthermore, even if the major premise were knowable a priori, in order to deduce the truth of the CPE's we would have to know that experiences exist. In other words, we can use the following sort of argument:

X is a precondition on the possibility of experience.
Experience exists.
Therefore, X.

or perhaps:

In order for us to experience an object, it must have property P.
We experience X.
Therefore, X has P.

where "X" or "X has P" is the putative item of synthetic, a priori knowledge. But surely the minor premise -- the existence of experiences -- is an empirical fact. How else do I know that there are experiences, except by having some?

I am afraid we must conclude that examination of this argument sheds no light on the nature of CPE's, inasmuch as no interpretation of CPE's makes the argument valid.

5.2  Second & third argument

We turn now to the pair of arguments which assures us that synthetic, a priori principles will hold good for the realm of appearances, or possible experience, but not for the realm of things in themselves.

I don't think my first proposed interpretation of CPE's -- as requirements for experience in general to exist -- could be right. Besides that it doesn't have any support in the text, if it were right, then synthetic a priori truths would hold good in general, without qualification, and would not be referred specially to appearances. For example, I said that the existence of consciousness is a condition on the possibility of experience in this sense. Since there is experience, there is consciousness. But that fact isn't a fact about 'the realm of appearances' in any interesting sense. It's just a fact about the world.

Now suppose that CPE's must be true of objects that we experience, in order that we experience them. Still, why would this mean that they weren't really true of the objects 'in themselves'? Wouldn't it just mean that we were assured that the CPE's were valid for a certain subset of the things-in-themselves, namely, the ones of which we have experience? Well, this interpretation of CPE's might fit with the interpretation of 'appearances' as relational properties; perhaps the conditions things have to satisfy in order to be experienced by us are just some relational properties. But it remains a mystery why we should conclude -- as Kant does -- that all knowledge is of mere appearances. If the CPE's that are represented in synthetic, a priori knowledge are some relational properties, and if things-in-themselves are the intrinsic properties of objects, doesn't that just mean that synthetic, a priori knowledge is not about things in themselves, whereas perhaps other kinds of knowledge still are about things in themselves?

For example, when Kant argues that space is not an independently existing entity but a mere 'form of sensibility,' I can see how it follows that our knowledge of geometry (as knowledge of space) does not pertain to 'things in themselves,' but I do not see how it follows that our knowledge of other things -- even granting that we must represent them in space -- does not represent things in themselves. Kant says that

... nothing intuited in space is a thing in itself, that space is not a form inhering in things in themselves as their intrinsic property, that objects in themselves are quite unknown to us, and that what we call outer objects are nothing but mere representations of our sensibility, the form of which is space. (B45)

I accuse Kant of confusing the form of representation with its object: Assuming that space is merely our means of representing objects, and that it has no independent existence, it should not be thought for that reason that space is the object of our representations, or that the things we represent by means of it do not have independent existence. Even assuming that spatial characteristics are merely relational properties, still, they are not the only properties that we perceive, so it would be a hasty generalization to say that we can only know relational properties of objects. But that assumption is too generous. When an object affects our sensibility in some manner, the referent of the perceptual experience is not the effect it produces; nor is it, even, the causal power; the referent of an experience is the property -- the intrinsic property, that is -- by which the object has the power to produce its effect in us. For this reason, the conclusion that space is a form of sensibility inhering in us does not imply that the properties it enables us to cognize inhere in us, or only exist relative to us.

Let us consider the third interpretation of CPE's, as things that we must experience as true. Now this interpretation would fit with the interpretation of 'appearances' as things that merely seem to be true: that is, if synthetic, a priori principles are only CPE's in this sense, then we can be assured that they will always appear to be true, but we can never be assured they really are true. Fortunately, however, I think this interpretation is ruled out by Kant's above-quoted protestations that he does not mean to reduce our sense perceptions to mere illusion.

Finally, consider the interpretation under which CPE's must be true of experiences. This fits with the reading of 'appearances' as mental states, in us, that external objects produce: That is, if we can interpret synthetic, a priori truths as describing conditions that must hold true of our experiences, and if we also interpret appearances as a sort of experience, then we know the synthetic a priori truths apply to appearances but not to things in themselves. When Kant states his thesis of the unknowability of the thing in itself, about half the time he says that we can only know appearances, that is, the effects (or representations) that objects produce in us; and the other half the time he says we can only know the objects as appearances. In the former case, the objects of our representations would be themselves mental states; in the latter, they would be external things, known by their relational properties. While this distinction may seem overly subtle, its neglect is a potential source of error.

The former interpretation is philosophically (but not exegetically) untenable. First, although we must (in the case of perception) know objects by means of their effects on us, to conclude that these effects therefore are the objects of our knowledge, that they are what we know about, would simply be a confusion. Rather, the effects constitute the knowledge, whose object (referent) is the thing that causes them. Second, if Kant really meant appearances to be only effects in us, as distinguished from external objects that cause them, then appearance vs. thing in itself would not be a distinction between two aspects of a single thing -- as he usually portrays it. It would just be a distinction between two separate things. Third, it's pretty clear that the principles Kant concerns himself with -- as "Every event has a cause," "The shortest distance between two points is a straight line," and "7 + 5 = 12" -- do not say anything about experiences. They are propositions about causes & effects, lines, numbers, et cetera, not about mental states. How, then, they could possibly be interpreted as conditions that must be true of experience would be entirely obscure.

6  Conclusions from these excursions

It seems Kant was prey to a certain ambiguity in his understanding of "appearances," regarding them sometimes as representations in us and sometimes as objects, considered in respect of their relations to us; and corresponding with this was his indecision concerning whether conditions on the possibility of experience were properties of experiences or of things experienced. This ambiguity, I believe, is symptomatic of a more serious problem in the Kantian philosophy. Kant's fundamental problem, owing to which there is so much obscurity in the notions of "appearances", "things in themselves", and the like, is that he tries both to preserve the truth in an ordinary sense of our synthetic, a priori knowledge, so that we are entitled to go on thinking and saying these geometrical propositions and so on, and at the same time to deny their correspondence with reality (things in themselves) -- a plan which, I submit, is impossible by its nature. Now if he were to stick with a single meaning of "appearance" then the nature of his difficulty would be obvious. Thus, if he said that synthetic a priori 'knowledge' was derived from conditions that only applied to our representations but not to the world, then it would immediately emerge that such judgements are not knowledge at all, because not true (not corresponding with reality). On the other hand, if he said simply that synthetic a priori knowledge was derived from conditions that apply to objects we experience, then it would emerge that such judgements were true of things as they are in themselves, albeit perhaps only a limited number of things in themselves (viz. the ones that we have experience of). I think we are meant to interpret CPE's, in the explanation of how synthetic a priori knowledge is possible, as conditions objects have to satisfy to be experienced; but when, immediately after, Kant explains why we cannot know the thing in itself, we should interpret CPE's as conditions our experience alone has to satisfy.

Now I believe that the correct position -- which is the naive and most obvious one which I see no reason to abandon -- is to admit that there is synthetic a priori knowledge (for besides Kant's there are many examples of such items of knowledge that could be listed) but interpret it as being a body of perfectly objective knowledge. Where Kant boggles over the possibility of such a thing, I nonchalantly accept the reality of what he says can't even be conceived:

But if we understand by it [the term "noumenon"] an object of a non-sensible intuition, we thereby presuppose a special mode of intuition, namely, the intellectual, which is not that which we possess, and of which we cannot comprehend even the possibility. (B307; emphasis Kant's)

So far am I from being unable to comprehend the possibility of this faculty, I believe I am acquainted with the operations of intellectual intuition all the time, sc. in every a priori cognition. Why this should be so incomprehensible I do not think Kant ever satisfactorily explained. It is good to reflect, therefore, that the problem Kant hoped to solve by transcendental idealism may never have existed.


1. All page references beginning with "A" or "B" refer to Kemp Smith's translation of the Critique of Pure Reason. References beginning with "§" refer to the sections and pages in the Prolegomena to any Future Metaphysics (Indianapolis: Bobbs-Merrill, 1950).

2. It seems our attention is restricted to true propositions for the purposes of this distinction.

3. Foundations of the Metaphysics of Morals, section 3, under "Of the interest attaching to the ideas of morality".