Kant actually argues that there is empirical knowledge in an obscure and little noticed passage at the close of the Transcendental Aesthetic's conclusions from the metaphysical and transcendental expositions concerning space.(3) The passage is devoted to proving that space is the only thing given in outer intuition that can be known a priori. For first, whereas there are synthetic a priori principles concerning space (those of geometry), there are no synthetic a priori principles concerning color, sound, warmth, or any of the other components of our outer intuitions. Even more significantly, none of these other components can be anticipated in advance of experience.
This second point is backed up by a number of specific examples, some alluding to themes standardly employed by empiricists when arguing for the necessity of some prior reference to experience for knowledge. We are told that different people can experience colors, tastes, and so on differently, so that the color of a rose can appear differently to every eye. If the color of a rose can appear differently to every eye, then presumably it can appear differently to the same eye at different times as well, so that this color can only be known a posteriori. We are told further that the taste of a wine is a function of the particular constitution of the senses of the subject who tastes it. Presumably, it too will therefore change with that subject's diet, state of health, age, and so forth, so that again it can only be known subsequent to actually tasting the wine. Finally, and most convincingly, we are told that the quality of a taste or color is incommunicable in advance of experience, so that those deprived of the particular "organization" involved in producing these sensations cannot have them; for example, those who have been blind since birth can have no conceptions of color, and those who have never eaten pineapple can have no conception of its taste.
Of course, Kant did suppose that there is something about sensations like those of color and taste that we can anticipate in advance: that they will exhibit a degree or intensive magnitude that can be continually diminished toward nothingness.(4)Even so, we still need experience to tell us, first, what particular degree or intensive magnitude any given sensation has, and second, what kind of quality bears this degree. "The quality of sensation (for example, color, taste, and so on) is always merely empirical and can never be represented a priori," Kant writes.(5) Though colors might be known a priori to be such that they can all be diminished through infinitely fine gradations to black, or tastes to insipidity, or sounds to silence, what particular degree of saturation or brightness or vivacity these sensible qualities exhibit is still something that only experience can tell us.
What holds of the qualities and the intensive magnitudes of sensible qualities also holds of their locations. Space and time may be a priori, but it is only through experience that we know what sensible quality is to be found at any given place or time. After all, to say that the quality and the particular degree of intensity of a sensation cannot be anticipated is just to say that what sensible qualities are located at what future times is something that only experience can reveal to us. Moreover, to say that no one who has not first tasted pineapple can know this sensation a priori is to say that the sensible contents of certain regions of space (those occupied by pineapples) can only be known a posterior).
Yet while Kant might so far appear to have left experience in charge of determining most of our knowledge (all that involves sensible qualities), his subsequent treatment of a priori forms and categories appears to severely delimit its role. Kant's treatment of reasoning from cause to effect is a paradigm example of this. Seeing someone undermine the foundations of a house, I can anticipate that it will collapse. In this case, I only need to rely upon experience to inform me of certain initial conditions (like the existence of an excavation), and I can proceed to deduce effects in an apparently a priori fashion, and so anticipate even the sensible content of a future experience. Empiricists have traditionally responded to these sorts of cases by claiming that it is only through prior experience that one learns causal rules, such as the rule that unsupported heavy bodies fall down, and that as these rules are discovered only by induction, they are subject to continued confirmation by experience. However, Kant is widely reputed to have refuted empirical approaches to causal reasoning, and to have established the a priori validity of certain causal laws, such as the laws of Newtonian physics.
Despite this reputation, however, Kant did not entirely reject the empirical approach to causal reasoning, and the scope that he took a priori laws and principles to play in natural science, at least in his work in the 1780s, is a carefully restricted and nuanced one. Consider, for example, the following remark:
We are accustomed to say of many items of knowledge that have been
derived from experiential sources that we are capable of acquiring
them a priori, because we do not derive them immediately from
experience, but from a general rule, even though we have derived this
general rule itself from experience. Thus, one says of a person who
has undermined the foundation of his house that he could have known a
priori that it would collapse, that is, that he did not have to wait for
experience to show that it would actually collapse. But he could not
know this completely a priori. For that bodies are heavy, and thus that
they must fall when their support is removed, had to have been taught
to him previously by experience.(6)
This passage comes from the B edition Preface to the Critique of Pure Reason, written in 1787--two years after Kant had claimed, in his Metaphysical Foundations of Natural Science, that universal gravitation, including the attraction of undermined foundation stones to the earth below them, can be assumed a priori. The two texts are not necessarily contradictory, for even if gravitation can be assumed a priori, there might be other forces, about which we can only learn empirically, that mitigate, cancel, or even reverse its effects. Smoke rises, and undermining the foundations of a house will not cause it to collapse if its structure is rigid enough. Yet this passage from the B Preface serves to show that the Kant of the canonical critical text, the B Critique, took there to be a degree of empirical determination in our reasoning about some purportedly universal cause and effect relations.(7) Just how much of a degree is a question I now turn to address.
Kant's reputation as an opponent of empirical approaches to causal reasoning is grounded in his own claims to have offered an answer to the "attack" (Angriff) on a priori causal inference classically launched by Hume.(8) It is surprisingly difficult, however, to find a precise statement of what it is about Hume's account of causality that Kant considered himself to have corrected. Hume's name is not even mentioned in the central Kantian text on causality, the Second Analogy.(9) Moreover, Kant's most prominent description of what he refers to as "Hume's problem" concerning causality, that offered in the Preface to the Prolegomena, contains no contrasting account of his own "solution" (Auflosung) to that problem.(10) While the Prolegomena's later treatment of the concept of causality does go some way toward applying the "solution" to the "problem,"(11) Kant's most detailed and direct engagement with Hume's position is actually to be found in a rather obscure and infrequently read corner at the back of the Critique, an appendix to the second section of the first chapter of the Doctrine of Method.(12) In what follows, I will refer to this passage as the "Polemic," after its section title. As this passage is both important and little read, its major points are paraphrased here.
Kant begins the Polemic by remarking that Hume was the most ingenious and effective of all the sceptics, and that it is therefore worthwhile to examine his arguments and expose his errors. He proceeds to observe that Hume attacked the notion of a synthetic a priori judgment. It is only through experience? Hume charged, that we can affirm something of an object that is not analytically contained in its concept. In making this charge, Hume is supposed to have erroneously treated the synthetic a priori claims of pure understanding as being of a piece with those of pure reason, even though the procedure used by the two faculties to arrive at their claims is quite different. Pure understanding is able to connect something synthetically, and yet a priori, to the concept of an object because it proceeds by grounding all of its claims in considerations of what is required for any object to be experienced by beings like us. Pure reason, in contrast, seeks to describe objects that go beyond the bounds of any possible experience. Hume's ignorance of the special resources pure understanding has to call upon led him to suppose that all synthetic a priori laws and principles, whether originating from reason or from the understanding, are equally illegitimate, and that they are all in fact only contingent claims, masquerading as necessary truths.
Continuing, Kant describes just how this Humean error manifests itself in the paradigm case of a synthetic a priori principle, that concerning the connection of cause and effect. Hume rightly observed, Kant says, that we are unable, a priori, to connect one thing with another entirely distinct thing, and say that because the one exists, the other must also. It is only experience that teaches us laws of cause and effect, laws, that is, that tell us that because this particular thing exists now, that other particular thing must exist subsequently to it. Kant is doubtless thinking here of Hume's powerful point that no one, upon witnessing a cause for the first time, can tell a priori what its effect will be, just from contemplating that cause. Adam, on seeing water for the first time, could not know a priori that it would not support the weight of a human body were one to stand on it. That bread nourishes while grass and earth do not, that fire burns, and countless other things are learned only from experiencing that such causes do in fact have such effects. Were we left to try and ascertain these facts a priori, we would have absolutely no basis upon which to proceed, and could not consider the most prodigious cause-effect correlations to be any less likely than any other. For all we can tell a priori, the falling of a pebble might extinguish the sun, or the wish of a human being control the orbits of the planets.
The examples I have just been giving are all Hume's, but Kant offers one of his own in the Polemic: That sunlight should melt wax and yet harden clay, he observes, is not something that anyone could tell in advance, simply by analyzing the concepts of sunlight, wax, and clay. "Only experience could teach us such a law," Kant writes.(13)
Kant proceeds to observe, however, that just because reason cannot go beyond the bounds of experience to tell us something about what effect a previously unknown cause will have (or, for that matter, what cause a previously unknown effect must have had), that does not mean that the understanding is unable to tell us anything about causes or effects prior to experience. A highly significant passage is:
We saw in the Transcendental Logic that, though we can never go
immediately beyond the content of a concept that has been given to us,
we can still know, completely a priori, the law of its connection with
other things. (It is just that we know this in relation to a third thing,
namely possible experience, though nonetheless still a priori.) When,
therefore, previously hard wax melts, I can know a priori that
something had to have preceded (such as the warmth of the sun) upon
which this event follows in accord with a constant law. However,
without experience I certainly could not discover either the cause from
the effect or the effect from the cause; I could not, a priori and without
learning from experience, know this determinately.(14)
While Hume was right that I cannot, prior to experience, tell what the effect of a given cause will be, or what the cause of a given effect must have been, I can know, prior to experience, that there must be some cause, and I can know, prior to experience, that whatever this cause might be, whenever it occurs, it must be followed by the effect.(15) Transcendental logic, by examining the conditions for the possibility of any experience whatsoever, is able to demonstrate that everything that happens has to have been preceded by some other event, and that this other event is one upon which the subsequent event "follows in accord with a constant law." (More precisely put, transcendental logic is able to demonstrate that it is a law that whatever happens must belong to a type or class of event, that it must be preceded by some other event that likewise belongs to a type of class of event, and that all the members of the latter class must be followed by members of the former class.) Though I may not be able to determine what this antecedent event is, I can be assured a priori that it must exist. This is a point that is seconded in the general proof of the three Analogies, and again in the Prolegomena, where Kant remarks that it is characteristic of the Analogies that they do not allow us to determine anything about what exists, but merely to affirm the necessity of a "relation" of some unknown thing to a given thing.(16)
"From the contingency of our determination in accord with the law Hume falsely inferred the contingency of the law itself," Kant concludes in the Polemic. That is, from the fact that it is only through experience that we can discover what the cause of a given effect is, Hume falsely inferred that the very existence of a cause, and the "necessity" of the succession of the effect upon every occurrence of this cause, is likewise empirical. The law, that is, the causal principle, tells us a priori that any given event must have a cause, and that this cause must be of a type that is always followed by events like the one we are considering. When we follow this law, and look for the cause of any given event, our discovery is made only empirically. However, the law itself, which promises us that there must be such a thing, is known a priori.
What does the Polemic teach us about Kant's position on Hume's critique of a priori causal reasoning? There are two major components to Hume's critique.(17) The first is an attack on the notion that it is possible to infer previously unobserved causes or effects a priori, just from inspection of their given effects or causes, without even an appeal to analogous cases experienced in the past.(18) The second is his attendant attack on the notion that we have knowledge of a force or power in causes in virtue of which they are enabled to make their effects come about, so that we can infer previously unseen effects from given causes by a kind of deduction from this force or power, and previously unseen causes from given effects by inferring what kind of force or power would have been required to bring them about.(19) This brief survey of Kant's Auseinandersetzung with Hume in the Polemic has shown that he is not concerned to reply to either of these points.
Kant accepts the justice of Hume's charge that it is impossible to deduce previously unseen effects from their given causes, or previously unseen causes from their given effects. This is a point that is not just made in the Polemic, but in the Anticipations, the Second Analogy, and the Prolegomena as well.(20) And, like Hume, Kant conceives of causes in terms of succession in time rather than in terms of efficacious power. This is a point that is also made elsewhere in the Critique, in the definition of the schema of the concept of cause in the schematism chapter and the phenomena and noumena chapter, in the statement of the principle of the Second Analogy, and in certain remarks that Kant makes about the impossibility of knowing fundamental forces in the Anfangsgrunde.(21) The differences Kant takes himself to have with Hume focus just on the manner in which this succession in time is conceived. Kant conceives the succession as necessary--succession "in accord with a constant law"--though this necessity is not underwritten by the demonstrated existence of any discernible force or power in the cause, but by certain considerations internal to Kant's Transcendental Logic and articulated in the Second Analogy. Kant charged, however, that Hume took causes to be types of events that are merely shown to us by experience to be followed by their effects, so that the connection between causes and their effects is only inductively warranted and therefore can never be necessary or strictly universal.(22) This is the only respect in which Hume got things wrong, as far as the Polemic is concerned. The other mayor passages where Kant discusses Hume merely repeat this point.(23)
There are therefore important respects in which Kant remains an empiricist about causal reasoning. The discovery of any specific causal rule, such as the rule that sunshine melts wax, will depend upon experience, though it will have an a priori component. We are assured a priori that every event will prove to have a cause and that this cause will be necessarily connected to the effect, in the sense that it will be a type of event that, whenever it occurs, will have to be followed by the effect. Yet because we are merely assured by the technicalities of Kant's Transcendental Logic that this is the case, without having any real insight into why (we have no knowledge of the forces or powers in causes that make their effects come about), we still need experience to discover what the cause is, and to confirm that we have correctly identified it. Thus, all our causal rules will be, as Kant puts it, "impure" a priori rules.(24) They will have an empirical component that has to do with the identification of the type of event that causes (that is, constantly precedes) an empirically given effect, and an a priori component that promises the necessity of the connection between the true cause, whatever it is, and its effect (but that does not promise that we have ever correctly identified the true cause).(25)
Kant occasionally refers to the a priori component of a specific causal rule as the "exponent" of that rule.(26) Klaus Reich notes that, as Kant would have found it explained in the work of Kastner, Klugel, or Euler, an exponent is not a number indicating the degree of a power, but a feature of the Euclidean doctrine of proportion.(27) The exponent is the number by which the first member of a proportion must be multiplied in order to yield the second. It is thus not exactly analogous to the a priori component of a causal rule, since that component does not allow us to determine the nature of an unknown cause from the nature of its given effect, but just to determine the necessity of its existence.(28) However, like an exponent, the a priori component of a causal rule holds between two variables, one of which must first be "given" somehow before the other can be determined, and when the one is given, it allows us to determine something (albeit bare existence) about the other.
There is another venue in which a priori reasoning threatens to creep into Kant's philosophy and steal away the prerogatives of experience. The appendix to the Critique's Transcendental Dialectic, entitled, "The Regulative Employment of the Ideas of Pure Reason," contains a strikingly idealistic argument. Kant there declares that the parsimony of fundamental natural causes and genera is not merely an assumption we should employ as a guide to scientific research, but something we can know a priori to be a true or objectively valid feature of the world.(29) "Reason does not here beg but command," as he puts it, that the understanding find the greatest unity of causes and species in its investigations of nature.(30) Furthermore, it would be ludicrous, he claims, to command that the understanding treat the various causes and genera in nature as systematically unified under more general ones, if there might be no such unity. For in that case, reason would be commanding the understanding to produce what it itself recognizes to be a possibly distorted picture of nature. And that would be contrary to the very essence of,reason. In what follows I refer to this as the wishful-thinking argument.
In the process of giving the wishful-thinking argument, Kant stresses that we should not imagine that the unity of nature is something that reason merely proposes as a hypothesis, and erjoins the understanding to seek. For if it were a hypothesis, it would permit of disconfirmation, whereas no degree of failure to discover unity will ever lead us to abandon the supposition that it does exist. Kant illustrates this point with a pair of examples, one drawn from psychology, the other from chemistry.(31) He also appeals to the tacit practice of modern scientists and the explicit theses of scholastic ontology.(32) The demand for the unity of nature is supposed to grow out of the very essence of reason, so that it could only be abandoned if reason itself were abandoned, and along with it, "all coherent use of the understanding, and any sufficient criterion of empirical truth."(33) Since failure to discover unity is not, therefore, countenanceable, Kant writes that the unity of nature cannot be "merely subjectively and logically necessary (as method), but must be objectively necessary."(34)
Kant himself seems to have been ambivalent about the wishful-thinking argument and to have elsewhere inclined to the more moderate conclusion that the principle of parsimony is merely regulative.(35) Whatever one might think of his wishful-thinking argument for the a priori validity of the principle of parsimony, all that that principle tells us is that nature must be (or ought to be) unified, not how. Finding the common mark that unifies a variety of empirically given species under a genus is still left as a problem for the understanding to resolve, as is finding the general law, of which a variety of empirically discovered causal rules are all expressions.
Admittedly, there are certain very general principles (such as the causal principle itself) that are derived completely a priori in the Analytic of Principles. However Kant is pessimistic about our ability to proceed from the top down, deriving general laws from these principles, and specific causal rules from the general laws:
Pure understanding is not able, through mere categories, to ascribe any
other a priori laws to appearances than those that touch on a nature in
general, as law-likeness of appearances in space and time. Specific
laws, since they concern empirically determined appearances, cannot
be completely derived from those touching on a nature in general,
although they do all stand under them. Experience is required to get any
sort of knowledge of specific laws, though only those touching on a
nature in general can give us a priori instruction concerning experience in
general, or what can be known as an object of experience in general.(36)
This is why, in the very section where Kant argues for an objectively valid (or perhaps merely regulative) "transcendental" principle of parsimony, he also devotes considerable energy to articulating the operation of a hypothetical or "logical" use of this principle.(37) Kant describes how, proceeding from the bottom up, this "logical" use groups specific types of event together in a genus and takes a generalized version of the specific causal rule holding for one of them to be a law holding analogously for all. If this law in fact proves to hold for all the species that are seen to fall under the genus, it is used in the prediction of further phenomena. As long as the predictions prove correct, the law is relied upon, but failure requires that we revise either the law or our choice of the common mark defining the genus. The law is therefore only inductively valid and open to disconfirmation by subsequent experience.(38)
Specific causal rules are inductive and open to disconfirmation by subsequent experience in much the same sense. We merely suppose, based on the experience of constant conjunctions, that a certain type of event is the true cause of a given event. Should subsequent experience ever reveal the effect to occur without its supposed cause, or the cause without its effect, we will reject the rule as mistaken and look elsewhere for the true cause. Yet in the case of causal rules, we are assured a priori that there must indeed always be a cause of any given event and that true causes can never fail to be followed by their effects. We rely on experience just to tell us what this cause is, not to give us a measure of the likelihood of its existence or of its being followed by the effect. For Kant the question is whether general laws have a similar a priori "exponent" or whether we must rely on induction to inform us, not merely of the nature of the general cause, but of its very existence and of the degree of its reliability.
Kant's problems arise because, if general laws are taken to have an a priori "exponent" it cannot be for the same reasons that established the necessary existence and necessary precedence of specific causes in the Second Analogy. The Second Analogy claims that, as a matter of transcendental logic, every event must be preceded by some other event upon which it follows in accord with a rule. While this result needs to hold at a certain level of generality, between types of events rather than just tokens, the argument of the Second Analogy does not require that this generality be carried on up to the highest levels. I can think that sunshine is the cause of the melting of wax without having to have any beliefs about the effects of the causes of heat in general on any fusible body whatsoever.
Kant needs a "transcendental" principle of uniformity to supply the warrant that the Second Analogy is not suited to establish. The transcendental principle guarantees that there will in fact be more generic laws under which specific causal rules can be discovered to be unified, just as the Second Analogy guarantees that there will always be types of cause upon which any given type of event can be found to regularly follow. In doing so, the principle underwrites our inductive or "logical" search for such laws, assuring us that, however total our failure to discover enduringly valid general laws may be, there are indeed such laws out there to be found. Kant's problems are with how the principle should be supposed to provide this assurance by establishing the objective validity of the uniformity of nature and parsimony of causes, as the wishful-thinking argument would have it, or by establishing merely the necessity for researchers with minds like ours to adopt a certain approach to scientific inquiry. Investigating how (or whether) Kant resolves this issue is beyond the scope of this article. I want instead to draw a more immediate conclusion about Kant's empiricism.
If what I have said here and in section II above is correct, then Kant does not need to bring empirically established causal rules under more general laws and these in turn under the universal causal principle in order to explain, through incorporation in a deductive system from a priori first principles, how causal rules that are only established empirically could have the necessity and strict universality that he claims any rule labeled as "causal" must incorporate. There is no such need because the Second Analogy's proof that every type of event is preceded by some other type of event upon which it follows in accord with a rule is not merely the proof of a universal principle, but a proof of the presence of an a priori "exponent" in each and every specific causal rule that may be discovered. What is empirical in these rules is just the identification of the cause; its existence and its necessary precedence, and hence its "dignity" as a cause, are guaranteed a priori by the exponent.
Insofar as there is a transition problem in Kant's philosophy of science, therefore, it is not a problem posed by the need to get down to the specific level in order to provide specific rules with an a priori warrant they supposedly lack; it is rather a problem posed by Kant's hankering to get up to the intermediate level, and explain what it is that allows us to suppose that the a priori warrant carried by specific rules remains with them after they have been generalized and applied to a range of merely analogous phenomena. Depending on how anxious Kant is to get up to this level, he takes the principle of uniformity to be either objectively true and established by "transcendental" considerations (such as the wishful-thinking argument), or a merely methodological or heuristic principle that might guide research, but cannot actually dictate the form of the world.(39)
It might nonetheless be objected that Kant does not always approach this transition problem from the bottom up, as he does in the appendix, when he enjoins the discovery of laws by generalization from specific rules. Some general laws, such as the laws of Newtonian mechanics considered in the Anfangsgrunde, are derived from the top down, by being shown to be instances of pure a priori principles. These laws do not need an exponent in order to underwrite their claims to describe a necessary and strictly universal connection between generic causes and their effects; their pure a priori origins do that job.(40) Moreover, it might be thought that Kant took even laws that are originally discovered inductively, such as Kepler's laws of planetary motion, to obtain their authority, not from an exponent established by such dubious means as the wishful-thinking argument, but by being subsequently shown to be special cases of pure a priori principles or by being systematized in some other way.(41)
However, these objections would only challenge the account I have presented here if it were supposed that Kant envisioned the possibility of a purely "top down" science.(42) If he took induction to be even as little as an essential first step to the discovery of general laws, then he granted that experience is required for the discovery of specific uniformities in nature. And if he took some general laws to be deducible purely a priori, but took the deduction to be possible only at a high level of generality, and to fail before specific causal rules could be derived, or if he took it to be possible only in a special and limited field (such as cosmology) but not in all, then again he granted that there are uniformities in nature that can only be discovered empirically. I take it that, whatever he may have thought in his final years, the Kant of the 1780's took the general laws of the Anfangsgrunde to be limited in all of the ways I have just mentioned.(43) Kant says as much in the Anfangsgrunde and at the end of the Deduction,(44) and it is an inevitable consequence of his scientific methodology in the Anfangsgrunde. Further demonstration of this point, however? would be too much of a digression here and therefore has been put off until the last section (VI).
In the previous section, I remarked that Kant's position on the role of induction in formulating general laws poses a problem for him. We can call this the general-law problem: Given that particular causal rules must be inferred from empirical investigation of what events regularly precede what other events, how is it that these rules should have turned out to be as systematically analogous as they in fact are? Why is it that the set of "common marks" defining a species should so often turn out to share some marks in common with other species, permitting us to define a genus? Even more surprisingly, why is it that the causal rules holding for each species should so often be analogous to one another, so that they can all be seen to be applications of a common, general law to the individuals in that genus?
There is another, more primitive and fundamental version of this question that is already posed by the degree to which induction is involved just in the formulation of specific causal rules. We can call this the causal-rule problem: Given that particular causal rules must be inferred from empirical investigation of what events regularly precede what other events, how is it that these events should have turned out to be as regular as they need to be in order for us to discover any causes in nature? Why should it not have turned out that our experience is in such disorder that no one thing could ever be found to regularly precede any other, and no casual rules ever be formulated?
Kant was sensitive to both of these questions.(45) Yet he devoted most of his attention--the two introductions to and the teleology of the Critique of Judgment, following upon the Appendix to the Dialectic--to responding to the first of them. In contrast, he barely touched on the second question in his published work--and did so only in a single text--the A Deduction--that was subsequently withdrawn. In this he has been followed by the majority of commentators, who have focused almost exclusively on his worries about the unification of specific rules under general laws, rather than the conformity of particular types of events to specific rules.
I propose instead to concentrate on the second question, both because I consider Kant's answer to the first to have been well worked-out,(46) but also because I consider it to be less of a problem. As has already been shown, the Critique of Pure Reason does not just demonstrate the existence of general, synthetic a priori principles, such as the principles of the necessary existence of causes and the conservation of matter, but also provides an a priori "exponent" for each and every specific causal rule--something that warrants our belief in the necessity of the connection between that specific cause and its effect. While Kant consistently maintained that the very possibility of experience depends, not just on this, but on bridging the gap between general and specific levels with a systematic account of the laws of nature, it is hard to follow him at all sympathetically in this view.(47) Kant's own account in the Second Analogy would appear to entail that, in the words of Philip Kitcher, "Those who are quite ignorant of Newtonian mechanics, to say nothing of Kant's foundational derivations of its principles, can, nonetheless, be justified in claiming that the boat has moved downstream."(48) The inquiry into the ground and extent of systematic unity in nature is an "add-on"--an entirely extraneous worry that does not have to be solved as a part of the explanation of the critical account of knowledge. The inquiry into the ground and extent of the conformity of the intuited manifold to rules, in contrast, goes to its very heart.
Let us review the nature of the latter, causal-rule problem. According to Kant, every event must be of a type that is preceded by some other event in accord with a rule. Yet while this is something I must assume a priori, only experience can reveal what this other event is. In accord with the schema of the concept of cause, I look for this other event by trying to identify something that can be supposed to always be followed by the effect I am considering, and I take this (provisionally on continued confirmation by subsequent experience) to be the cause.(49) However, since the sensible quality and the intensive magnitude of experience is precisely what cannot be anticipated in advance,(50) it is at least possible that my experience might reveal no such thing to me. I might find all sorts of types of antecedent events, but none that appear to regularly precede the type I am considering.(51)
In fact, however, our experience does reveal regular antecedents to us--moreover, it does so in all the cases we can describe. Appearances do not simply "crowd in upon the soul" but exhibit a rule-governed order in their manner of occurrence. At first sight, this ought to appear extraordinary. Why should things that are as distinct and apparently unrelated to one another as the variety of events we discover in nature always proceed in a certain order? There is, after all, no obvious contradiction in these events occurring independently of one another.
Kant refers to this extraordinary phenomenon as the affinity (Affinitat) of nature.(52) This is a term that has been widely misunderstood, so two explanatory comments are in order.
First, the term is employed by Kant in two senses, whether he is using the Latin (Affinitat) or the Teutonic (Verwandschaft) form. In its more frequent, colloquial usage, "affinity" means family resemblance or similarity.(53) However, in the chemistry of Kant's day, the term had a special sense. "Affinity" was the name for the selective tendency of certain materials to combine with certain other materials. This usage, unlike the colloquial one, does not imply membership in a common genus or similarity.(54) The chemical elements with an "affinity" for one another can be quite distinct. The chemical use of "affinity" was widely current in Kant's day--so much so that it is even to be found in the title of a dreadfully saccharine romance by Goethe (Die Wahlverwandtschaften).
Kant introduces the term "affinity" into his discussions of the general-law problem as well as into his discussion of the causal-rule problem. Though the term is the same, its sense is not in the two different contexts. When he speaks in connection with systematic unity in nature, Kant's references to "affinity" are meant in the colloquial sense. The "affinity" of the Critique of Judgment and the Appendix to the Dialectic has to do with family resemblance or similarity of species and of specific rules insofar as they fall under a genus or general law. When he speaks in connection with the question of the conformity of the manifold to rules, however, Kant's references to "affinity" are meant in the chemical sense.(55) As noted in section II above, Kant follows Hume in claiming that we have no knowledge of causes as things with a faculty or power in virtue of which they are enabled to bring about their effects. A cause is just what regularly (that is, "in accord with a rule") happens before the effect, not what makes the effect happen. In principle, anything may regularly precede anything else. Thus, a cause and its effect are analogous to chemical substances that regularly combine with one another and never with anything else. In both cases we are dealing with two distinct things that have a prima facie inexplicable "affinity" that leads them to go together--in the latter case to combine, in the former to follow regularly.
This leads to a second point about the proper interpretation of the term "affinity": As used by Kant, "affinity" (in either sense) refers to a relation between things at the same ontological level: different events, different chemical elements, different cognitive faculties, different species, and different causal rules are all spoken of as having an affinity with one another. Affinity does not hold between levels--the empirically given manifold does not have an affinity for the exponent of the causal rule, and specific causal rules do not have an affinity for general laws. The elements of the manifold have an affinity for (tendency to regularly precede or follow) one another, and specific causal rules have an affinity with (similarity to) one another--albeit under a law. Affinity is not, therefore, the solution to the problem of why the manifold conforms to our need to discover causes in nature. It is simply another name for the problem. Given that events do have affinities for one another, that is, are regular in the ways they need to be in order for us to identify causes, what is the ground of this extraordinary fact?
I remarked above that Kant waffles between conflicting positions when discussing the general-law problem. On the one hand, he wants to take parsimony to be an objective feature that reason (or, in the Critique of Judgement, reflective judgement) imposes on nature; on the other he wants to take it to be a merely regulative maxim that must be assumed as a guide to scientific investigation, but that cannot be taken to be necessarily true of nature. A similar conflict surfaces in his account of the ground of the affinity of the manifold. On the one hand, he regards this affinity as too extraordinary to be a product of mere chance, and too important to be grounded in the nature of the objects that affect us and thereby revealed only through experience.(56) He therefore tries to give it an a priori foundation by explaining it as a consequence of the unity of apperception.(57) This line of thinking leads him to go on to make certain strongly idealist claims about the role of understanding in legislating laws to nature, claims that are reminiscent of his comments about a similar role for reason in the Appendix to the Dialectic.(58)
However, there are also powerful considerations inducing Kant to retreat from these claims. If we impose affinity on the manifold, then we ought to be able to know in advance what form it will take, just as, if we impose spatiotemporal order on the manifold, we ought to be able to know the structural features of space, and hence the axioms of geometry, in advance. Thus, upon having a given sensation, we ought to be able to tell, even in advance of experience, what other sensations must have an affinity (in the quasi-chemical rather than the family-resemblance sense) with it and so must succeed or must have preceded it. In that case, however, inferences from causes to effects or effects to causes would not be a posterior). Given a single event, we ought to be able to deduce all its causal ancestors and the entire chain of its effects a priori, without having to consult experience, and this is not something Kant accepted, even in the A Deduction.(59)
Kant had a second, more general reason to refrain from explaining how affinity is made possible--one that applies not just to idealist accounts that seek to ground affinity in the cognitive constitution of the subject, but to realist ones that would seek to ground it in the nature of affecting objects such as God or things in themselves. This reason arises from his position on causality. According to Kant, we have no coherent concept of faculties, powers, or forces that make things happen. All that it can mean for one thing to cause another is that things of that type precede those of the other type in accord with a constant law. Thus, to explain the phenomenon of affinity by saying that there must be something--be it the action of affecting objects or the will of God or the activity of the subject--that makes events happen in a regular sequence reduces to saying that there must be something that precedes our experiences of affinity in accord with a constant law. The only way we can know that affecting objects or God or we ourselves cause affinity, therefore, is by discovering through experience that one or other of these things always precedes the occurrence of cases of affinity. Yet, even supposing that an experience of such objects were possible, far from explaining how affinity is possible, such experience would merely constitute another instance of it.
These considerations should have been no less present for Kant when he wrote the first edition of the Critique, in apparent innocence of the charges of unqualified idealism that his work later raised, than when he wrote the second, and was deeply concerned to distance himself from those charges.(60) In light of both considerations, we ought to wonder just how idealistically Kant intended his remarks on affinity and the laws of nature in the A Deduction to be taken.
Unfortunately, this is a very difficult question to answer, because the central texts are ambiguous. Kant argues for the necessity of affinity by means of a reductio ad absurdum that makes a crucial appeal to the notion that we could not be conscious of appearances unless they are in affinity with one another.
Were it the case that perceptions were not associable, there would be a
collection of perceptions, and even an entire form of sensory
experience, in which much empirical consciousness was to be found in my
mind, but in separation and without belonging to a consciousness of
myself. But that is impossible. For only insofar as I count all perceptions
as belonging to one consciousness (of original apperception) is it
possible for me to say of any of them that I am conscious of them.(61)
From this it immediately follows that, insofar as we are conscious of it, the parts of the manifold must have an affinity with one another.
We can find [the ground of] this affinity nowhere other than in the
principle of the unity of apperception concerning all cognition that might
pertain to me. According to this, all appearances, must so come to be in
the mind, or so be apprehended as to accord with the unity of
How is it, exactly, that we should take this necessary conformity of appearances with the demands of apperception to be effected? Is productive imagination supposed to impose affinity on the manifold? Or is Kant's point just that we are so constituted as to be unable to notice matters that have no affinity with the rest of our experience, so that even though these matters may have occurred in inner or outer sense, they cannot ever make it into consciousness?(63) Or again--a sort of medium between the two extremes just considered--is the idea rather that any item that we are conscious of must be imagined to have some form of affinity with the causal nexus, provided merely that this hypothesis is consistent with experience and subject to revision should experience prove contrary to it?
In all of these cases we end up being able to say that affinity is a necessary feature of the events of our experience, but in the third case it is necessary only that affinity be hypothesized, not that it be demonstrated, and in both the second and third cases the necessity is something of a sham. In the second case it is not necessary that the elements of the manifold have an affinity for one another, but just that those events of which we are conscious have such an affinity, and it remains a fortuitous circumstance that our consciousness should be as rich and extensive as it is (that is, that there should be as much affinity between elements of the manifold of inner and outer sense, and hence as much content to our consciousness as there in fact is). In the third case it is fortuitous that our hypotheses should be as successful as they are--that we should by and large be able to identify certain types of events as regular antecedents of other types of events, and not be forced to continually revise our hypotheses in light of recalcitrant experience or have recourse to occult and empirically unverifiable antecedents like fate or the will of God in order to give some semblance of regularity to events. In the first case, however, it is empirical experience that ends up being a sham, since it is hard to see how specific causal rules would need to be empirically discovered, as the A Deduction does still claim that they do, if affinity were imposed by the mind.(64)
A similar obscurity infects Kant's remarks concerning laws of nature. When he says, in the A Deduction, that "nature regulates itself according to our subjective ground of apperception, and even depends on it for its law-governed features," that "the order and regularity in appearances that we call nature we ourselves introduce, and we would not have been able to find them there had we not, or had the nature of our minds not originally put them there," and that "the understanding is the source of the laws of nature," it is unclear whether he means to imply that the understanding legislates specific causal regularities, like the regular precedence of sunshine to the melting of wax, or whether he only means to say that it dictates certain universal principles, such as "every event some cause" and "same cause same effect," and thereby supplies the a priori exponents for specific causal rules.(65)
In the light of all of this obscurity, it is imperative that we turn to Kant's own, considered restatement of these issues in the B Deduction for illumination. Admittedly, the question of the ground of the affinity of the manifold is not mentioned in B, and the term "affinity" does not even occur in the B Deduction, though there is a corresponding, briefer, and much more rigorously empiricist discussion of the laws of nature.(66) This very absence of attention to the issue is illuminating. If you do not have an answer to a question you will not ask it, but will rather talk about other issues that you can resolve. The fact that Kant's preferred approach to the problem of affinity in the B Deduction seems to have been to drop the whole issue implies that he had no answer to give. This in turn implies that he had rejected any attempt to ground affinity in the activity of the subject and developed a certain willingness to consider affinity to be merely a brute fact that cannot be further explained. If not purely fortuitous, it is grounded on nothing more than our inability to be conscious of what lacks affinity (in which case it is the extent of our consciousness that is fortuitous). Interestingly, in his later work Kant expresses a parallel willingness to answer the general-law problem by claiming that, objectively considered, the affinity of specific causal rules is also fortuitous--a "favor" that nature does for us--and something that we can only be regulatively enjoined to seek.(67)
Writing about Kant's views on affinity, Henry Allison once claimed that "whereas Hume regards [the orderliness in experience] as a fact to be wondered at, Kant treats it as a necessity to be explained."(68) If what I have said here is correct, however, there is no difference between Hume and Kant on this issue. Kant has no coherent, nontrivial explanation for the necessity of affinity, and in the end he, like Hume, appears to have reconciled himself to simply wondering at the brute fact that it exists.
In the second of the three remarks appended to Part I of the Prolegomena, Kant compared himself to Locke, who had denied that we know the secondary or tertiary qualities (that is, the forces and powers) of things, but had never been charged with being an idealist for all that. Then he went on to complain bitterly that he himself should have been charged with being an unqualified idealist even though he merely went one step further and took the primary qualities of objects to also belong only to their appearances. He had no more denied that things in themselves exist than had Locke, he protested. What should he have done, he wondered, in order to successfully avoid all charges of idealism? Should he have taken space and time to be features of things in themselves and have given the palm to the true idealists, who could then appeal to the antinomies to demonstrate the incoherence of the notion of an external world?
One can imagine a ready empiricist answer to this complaint: restrict space and time to appearances, if you must, but get rid of the apparatus of a priori forms and categories, in virtue of which the subject constitutes reality, and admit that what we know is not determined by us, but by something that exists independently of us. If you want to be considered a representational realist, like Locke, then be an empiricist, like Locke, and do not take the subject to be the engineer of experience.
Though Kant never abandoned his views on the existence of a priori forms and categories, he nonetheless had strong empiricist credentials. Rather than take experience to be engineered by the subject, he took the qualities, the intensive magnitudes, the causal relations,(69) and the general laws of objects all to be determined by experience, which will not be imposed upon by the subject in these matters, but rather legislates to it. On occasion, when dealing with the quasi-chemical "affinity" of the elements of the manifold in the A Deduction, or the family resemblance of causal rules and species in the Dialectic and the "First Introduction," Kant said things that might have threatened to deprive experience of its authority, and vest that authority instead in the productive imagination, the reason, or the reflective judgment of the subject. The A Deduction, however, is too obscure for us really to be sure about this (and was in any case withdrawn), and the other remarks contradict positions Kant took within a few lines or pages of having made them.
Is this empiricism enough to absolve Kant of the charge of unqualified idealism? In one sense, it might be objected that the one issue has no bearing on the other. The notion that a posterior) experience implies realism and that a priori experience implies idealism is based on a tacit causal argument: that effects that we cannot anticipate in advance must have external causes, whereas effects that can be known a priori must be due to our own nature. This causal argument is one that Kant, were he consistent, would have to reject as a piece of nonsense, for it turns on a notion of causes as things that make their effects happen or bring them about, rather than as things that regularly precede them in time. (This must be the case since things in themselves are not in space or time, and so cannot intelligibly be supposed to regularly precede our a posterior) experiences, and insofar as we have any experience of ourselves, this self is known as a subset of our experiences--those of "inner" sense--and not as something that regularly precedes the a priori component of all of our experiences in time.(70))
Nonetheless, Kant was unable to resist the temptation to at least think of the a priori component of experience as due to the subject. This was something that he could quite consistently do, since he claimed that, though we can only know causes insofar as we schematize them as regular antecedents in time, there is a notion of timelessly exercised power contained in the unschematized intellectual category of cause that we can nonetheless think as a matter of sheer speculation.(71) By similar argument, we ought to be able to at least think the a posterior) component of experience to be due to the agency of mind-independent, external objects. Particularly in an ad hominem context, where Kant is responding to those who assume a license to infer the existence of such external objects from the a posteriori character of experience, he is entitled to claim that, by their very argument, he is no more of an idealist than they, for he, too, supposes that what appears is a posteriori.(72)
Appendix. Here I argue that Kant's method of top-down derivation of a priori laws in the Anfangsgrunde is limited in its power and its scope. While some general laws can be discovered by the method, iterated applications cannot uncover more and more specific causal rules. What is more, those laws that can be discovered can only be used to explain phenomena in the near-ideal science of cosmology, the only science that treats bodies moving just under the influence of those forces that can be demonstrated a priori.
To substantiate these charges, I want to first summarize Kant's methodology in the Anfangsgrunde and then to look at how it is executed.
The most general metaphysical principles, for Kant, are those established by the Critique's Analytic of Principles. They specify the conditions for the possibility of an experience of an object in general. Yet precisely because they tell us what holds for any object of sensory experience in general, they cannot tell us anything about what exists in particular. Consequently, more specific a priori laws even laws that are more specific just in the sense that they tell us about a certain, general kind of object-cannot be directly deduced from these principles.
Kant adopts an elaborate procedure in order to establish more specific a priori laws. He first considers the concept of a specific kind of object, and then he proceeds to try to isolate the conditions of the possibility of the experience of an object satisfying that concept.(73) In effect, therefore, he repeats the kind of project he carried out in the Analytic of Principles in order to demonstrate general metaphysical principles like the principles of the endurance of substances and the necessity of causes. It is just that whereas the earlier project was carried out by considering what conditions space, time, and the categories place on the possibility of our experience of any sort of object whatsoever, the later considers what conditions must be satisfied in order for our experience of an object of a certain kind to be possible.
Kant's method in the Anfangsgrunde, however, has a further wrinkle. If the project that has been articulated so far is to tell us something that is not merely analytically contained in the general metaphysical principles already established by the Analytic, then everything will turn on the added information supplied by the more specific concept. What justifies us, then, in introducing this further detail?
When Kant first remarks on the necessity of appeal to a specific concept, he notes that the specific concept is obtained from experience.(74) Yet that will hardly do. If we must rely on experience to teach us about the specific details on which the derivation turns, then the conclusions of the derivation cannot be a priori. They will be subject to verification by future experience and will hold only so long as the world continues to appear as it does now.
We might try to get around this consequence by saying that our investigation is just into what an object satisfying a more specific concept would have to be like (what principles it would have to satisfy) were it to exist. This would seem to be something we could say a priori. However, Kant regards the arbitrary postulation of specific concepts as totally illegitimate. His general position is that the real possibility of an object cannot be inferred from the fact that its concept can be thought without contradiction.(75) Accordingly, before a specific concept can be admitted, even hypothetically, it must be proven that an object satisfying that concept could possibly be experienced. This is why, after first noting that specific concepts are obtained from experience, Kant goes on to remark that this empirical origin is incompatible with an a priori enterprise, and that we must rather show that an object satisfying the specific concept can be constructed (that is, that the features specified in the concept permit of being presented in pure intuition and in accord with the conditions of the possibility of experience).(76)
It is this aspect of Kant's method in the Anfangsgrunde that eventually limits its power and scope. He takes it that the only way to proceed to formulate more specific a priori principles is to represent objects, not as they in fact are, but as they would have to be, through the conditions of their possibility, were they to exist. Accordingly, specific metaphysical principles, no matter how specific they may become, will never be able to do more than describe conditions of the possibility of objects, and hence a range of possible worlds. As the method is iterated for more and more specific concepts, the realm of possibility becomes broader and broader, and worlds increasingly unlike our own in their specific detail are constructed as possibilities. Already at a very early stage, the existence of certain kinds of motion (such as that due to so-called absolute repulsion) and certain kinds of matter (such as the ether) are shown to be in principle indemonstrable of our world. At this point the chances of deducing more and more specific laws of motion in our world crash. Let us turn to consider exactly how this happens.
Kant opens the Anfangsgrunde by considering a pair of empirical concepts that effectively divide the world of possible objects between them: the concepts of an object of inner sense and an object of outer sense in general. However, as he proceeds, the twin demands of his metaphysics and his methodology--specifically the demand, grounded in the First Analogy, that objects must be reidentifiable over time,(77) and his demand that the features in virtue of which objects are thought be constructible in a priori intuition--quickly work to ensure that only a subset of the objects falling under these concepts will be tractable. Kant realized that there can be no objects of inner sense; whatever exists in time can only be a state of some spatial object, and not an object in its own right.(78) This is because there can be no way to reidentify things that exist only in time no way to distinguish a repeated encounter with the same temporal object from a successive encounter with a number of distinct, but resembling objects. In effect, therefore, nothing endures in time, and everything in inner sense is in constant flux.(79) It is only spatial experiences that can satisfy the First Analogy, and thus the study of purely temporal experiences (psychology) can never be more than a history of empirical occurrences, not a study of objects that have any a priori features beyond those already accounted for in the Analytic.(80)
Granting, however, that spatial objects are reidentifiable, these objects must now, insofar as they are the subject matter for a priori principles, be thought in virtue of features that can be represented or constructed in pure intuition (that is, in virtue of spatial or spatiotemporal features). For this purpose, bare location in space is not enough. An object that has no other feature than location in space (for example, a mathematical point) cannot be reidentified from one moment to the next, unless we make the further, empirically false supposition that the universe is static. In a universe of moving point-objects, there is nothing to distinguish between one object and another, especially when one seeks to establish which point has followed which trajectory after a collision.
Point-objects that have sensible qualities in addition to location like minima visibilia with contrasting colors or stars with differing spectral profiles, would have some marks that (assuming they are relatively constant for individual minima and sufficiently various for different ones) might allow some degree of individuation and reidentification. Yet since sensible qualities cannot be constructed a priori in pure intuition, sensible point-objects could only be the subject matter for specific a priori principles with reference to their motions. The latter can be represented or "constructed" as points traveling with a certain speed along lines in space. Though even here the points and lines in question have to be tacitly ascribed contrasting sensible qualities in order to be individuated and identified over time, the nature of these sensible qualities has no bearing on the motion, and so the empirical element can be disregarded.
A wider scope for the possibility of specific a priori principles (though at the same time a narrower field of possible objects of those principles) is gained if the spatial objects we consider are supposed to have extension, namely, shape and size, as well as location, that is, if they are taken to be bodies rather than just points. (In what follows, I will use the term "body" to refer just to objects that are taken to have some extension in space.) If the shapes and sizes of individual bodies are sufficiently permanent, and those of different ones sufficiently various, then they, too, can provide for the possibility of at least some degree of individuation and reidentification. Of course, the varying shapes and sizes of bodies cannot be perceived by us unless they also exhibit contrasting sensible qualities. Again, as long as these sensible qualities contrast, it does not matter what they are, so this empirical element, while it must be present, plays no further role and can be dropped out of consideration.
There is one further thing that cannot be dropped out of consideration, however, and it is revealed by further examination of the conditions of the possibility of the experience of bodies. If bodies were to possess sensible qualities, but not resist the motion of other bodies, so that their sensible qualities could be compressed into nothingness by surrounding bodies--in effect, penetrated and annihilated--then bodies would not be permanent, and the First Analogy would be violated. Accordingly, any bodies conceived as the ultimate subjects in an a priori science must be conceived to prevent the motion of other bodies into the space they occupy.(81) This is a much more essential feature of the possibility of the experience of bodies than the possession of sensible qualities, and moreover, it is mathematically constructible (by representing an approaching body as having its motion slowed and stopped, or abruptly stopped, or turned back).
Another way to put this point is to say that bodies must exert a repulsive force, but all that this expression means is that, as a matter of constant law, the motion of other bodies into the space occupied by a given body is impeded and prevented. The words "resistance," "impenetrability," or "repulsive force" do not describe any power whose workings we have come to understand but merely name certain regularities that we can assume a priori to take place in the motions we construct.(82)
Once repulsive forces are postulated, attractive ones must be as well--otherwise there would be nothing to prevent the matter in the universe from expanding to infinity, and, if the strength of a repulsive force can be supposed to diminish as it extends over a larger and larger volume,(83) at infinity the force would evaporate, and matter would again be annihilated, contrary to the First Analogy.(84)
By this point, Kant has established two fundamental a priori principles governing all motions of bodies: that any body that moves in such a way as to compress another body will have its motion impeded, and that all bodies will move toward one another, so far as is consistent with the first principle. Now let us turn to look at what having to rely on the mathematical construction of merely possible objects does to the possibility of going on to derive any more specific laws. These merely possible objects are all motions or changes of motion. Repulsive and attractive forces are represented by the deceleration and acceleration of motions,(85) and bodies are just volumes at the surface of which the motions of other bodies begin to be impeded.
While motion is constructible in pure intuition, it is also an empirical concept.(86) Motion is empirical because it involves the notion of one and the same body being in adjacent places at successive times. Hence it presupposes some way of establishing that the body that is now here is the same one that was there earlier, and this once again drives us back to having to appeal to empirically observable marks, like sensible qualities, as the only evident resource for making judgments of identity over time. Sensible qualities, however, cannot be anticipated in advance, as was noted in section I above.
Of course, because motion is mathematically constructible, we know that it is really possible. We can therefore take it for granted that there can be moving objects, that are individuated somehow, and we can proceed to consider how these possible objects can or must be represented without having to rely on anything learned only empirically about what it is that in fact allows us to reidentify moving bodies from one moment to the next. We can draw lines on paper to represent possible motions without having to worry about whether the actually moving objects, like the lines, are black or whether their extensions, like the paper, are white, or whether the sensible qualities of the actually moving objects will have any bearing on our results.
However, this method of generating the specific a priori result that all bodies must exercise repulsive and attractive forces is not without consequences. Since "the movable" can only be identified empirically, the speed and direction of motion of any actually existing body can only be known empirically. This is why Kant's phoronomy does not allow us to determine the existence of a single motion in nature, but has as its "sole principle" a thesis concerning the manner in which the (empirically given) motion of a body may be represented as a composite of two or more motions.(87) (In effect, the Phoronomy is devoted to defining an exponent.)
The implications of the empirical status of motion reach beyond the phoronomy chapter. Because the speed and direction of motion can only be determined empirically, we can only know a priori that the motion of compressing bodies will be impeded, not how it will be impeded--whether it will be stopped dead at the point of contact by an overwhelming (in effect, infinite or, as Kant puts it, "absolute") repulsive force, or whether the repulsive force will only gradually approach infinity as the body is compressed to a point--and if the latter, with what rate the force will approach infinity per unit of decrease in volume.(88) The coefficient of resistance (the strength of the repulsive force field) of any given body can therefore only be determined by experience.(89) Because different bodies might be found to have different coefficients of resistance, it becomes an empirical question whether there might not be specifically different kinds of matter, varying in their characteristic repulsive force, and if so how many such kinds there might be.(90) Thus, not only must the speed and direction of motion be an empirical matter for Kant, so must the number of kinds of bodies.(91)
The necessity hereby created for recourse to experience to resolve physical questions rises to the most fundamental levels. If it is an empirical question whether there are specifically different kinds of matter, and if so how many, then the corpuscularian hypothesis that matter is uniform, and varies only in shape and size, cannot be affirmed or denied a priori.(92) Moreover, since an empty space is indistinguishable from a space occupied by a body with a repulsive force that only begins to become noticeable as the body is compressed to a point,(93) and an absolutely hard atom is indistinguishable from a body with a force that very quickly approaches infinity after the least compression occurs, it follows that the corpuscularian hypotheses of absolutely hard atoms and absolutely empty space must be no more than possibilities--and empirically unverifiable (though not thereby incoherent) ones at that. However, what is hypothetical in one direction is hypothetical in the other as well. It is equally the case that the whole question of whether a physics of bodies with varying degrees of repulsive force is to be preferred to atomistic physics ends up being an empirical one.(94)
There is, however, another direction in which the Anfangsgrunde seeks to go to establish a priori laws: by means of an account of mass, inertia, and collision, leading to a deterministic account of motion. To see what success might be achieved by this account, a preliminary consideration of the attractive force is required. On this score, the same point that has just been made about repulsive force can be made about attractive force: because the speed and direction of motion can only be determined by experience, the strength of an attractive force field can only be measured by experience (by, say, measuring how a standard mass, placed at a point in the field of operation of an attractive force, is accelerated--in effect, putting it on a balance(95)). Admittedly, since he has already identified variations in the field strength of repulsive force with variations in the kind of matter, Kant must take it to be true by definition that every kind of matter exerts the same attractive force.(96) However, it remains open to him to take empirically observed variations in the strength of the attractive force field possessed by various bodies to be due to the quantity of that kind of matter contained within the volume of the body.(97) He then proceeds, in his mechanics chapter, to set up rules for how to represent the combination of motions resulting from collision that depend crucially on this notion of quantity of matter. This chapter almost seems to hold out the promise that, if only we could ascertain the masses and trajectories of all the bodies in the universe, we could proceed to deduce all motions a priori, from the laws of inertia and collision.
Kant's mechanics, however, cannot sustain such a result. The problem is not just that his mechanics is not incorporated with his dynamics, and so fails to take account of phenomena such as retardation of motion due to the drag of gravitational forces or collisions with bodies that are not "absolutely" impenetrable. Even on its own terms, the picture that has so far been presented of forces and their operation is an idealized one: of single bodies in empty space having their volumes fixed solely by the balance of their attractive and repulsive forces (under such conditions all bodies would tend to be spherical), and of pairs of bodies moving through empty space and colliding. On earth, however, bodies exhibit other mathematically constructible characteristics in addition to volume, motion, and quantity of matter: varying shapes, cohesion (resistance of parts to separation), rigidity (resistance to relative motions of parts), brittleness (rigidity combined with a tendency for parts that have once been moved relatively to one another to lose all cohesion), resiliency, pliability and "spring" (tendency of parts to return to their original positions after deformation or to hold their new positions, and tendency of masses to resume their original volume after compression), fluidity and viscosity (cohesion with low or intermediate rigidity), adhesion or friction (resistance of adjacent, but distinct kinds of material to separation or relative motion), and chemical "affinities" (tendencies of distinct kinds of material to intermix).
All of these phenomena can be considered to be various manifestations of cohesion, and Kant sometimes speaks as if cohesion can be taken to be merely a "derivative" (abgeleitet) force.(98) His chief reason for assuming this is that cohesion is not sufficiently universal. Though all bodies cohere (or adhere), they do not adhere to all other bodies and, as the case of brittleness shows, may not even cohere to themselves in certain circumstances.(99) However, Kant is only able to offer conjectures about how cohesion might be explained. Sometimes, he speculates that its various effects might be due to the way bodies are compressed and deformed, and the way their motions are affected in the real world, by the repulsive and attractive forces of surrounding bodies. To this end, however, he feels compelled to postulate the existence of a special kind of material, the ether, the repulsive force of which greatly outweighs its attraction, and which can pervade all the space in the universe and produce the effects of cohesion in regions where gravitational forces are strong.(100) However, the actual existence of any kind of material can only be known by experience, and thus, Kant is constrained to admit that the existence of the ether is a mere hypothesis and that nothing can be known a priori about the causes of cohesion.(101)
It is for this reason that Kant maintains that chemistry is merely an empirical study(102)--and thereby that the lion's share of the forces responsible for physical phenomena on earth are intractable by the a prioristic methods of the Anfangsgrunde. While Kant might have changed his mind about this in his last years, his final attempts to escape the need to rely on experience in order to do chemistry were not crowned with success, and it is hard to see how they could have been. The specific forces of cohesion cannot be known without first determining the specific motions of specific bodies. Yet to determine the specific motion of a specific body requires that that body be reidentified over time. The only way to reidentify a body over time is by reference to its sensible qualities. And sensible qualities are a posterior). The only way Kant could provide an a priori foundation for chemistry is by giving up his position on the essentially empirical status of motion, and with that the a posterior) status of sensible qualities.
To sum up, the general laws of the Anfangsgrunde define only the broadest features of nature, and the method of the Anfangsgrunde does not hold out the hope for much progress in deriving yet more specific ones. The Phoronomy and the Mechanics do not determine the existence of a single motion in nature but only provide rules for the mathematical construction of motions, in the first case, and the (idealized) deduction of consequent motions from antecedent (empirically given) motions, in the second.(103) The Dynamics only tells us that all bodies must exert repulsive and attractive forces; it does not tell us how strong these forces are, whether the proportion of the one to the other can vary in different kinds of body, and if so, how many such different kinds of body there might actually be in nature. These dynamical results turn back and infect the purportedly a priori mechanical deductions as well: Since the actual motions of bodies will be influenced by the gravitational forces of all the other bodies in the universe, and the actual collisions of bodies will be influenced by repulsive forces (leading to rebound), by repulsive forces in combination with attractive (leading to vibration and heating),(104) and by derivative (though possibly original) forces such as viscosity and brittleness (leading to loss of quantity of motion and shattering), and since none of these forces can be known, in their particular degrees, a priori, the deductive rules of the mechanics chapter are mere idealizations, which might be more or less approximated by massive bodies moving in relatively empty spaces at vast distances from one another (as in the heavens), but which are of limited application on earth.
The locations, the motions, the field strengths of the fundamental forces and with them the kinds and quantities of matter, the very existence, number and activity of derivative forces, and even the manner of interaction of different force fields are for Kant all empirical matters, and that means that the scope for a priori principles in the study of nature is going to be a very small and, more importantly, a very sketchy one. (1) These efforts quickly established Kant's reputation as a foe of empiricism. Already in his own lifetime, C. G. Selle labeled Kant's philosophy purist. See Christian Gottlieb Selle, Grundsatze der reinen Philosophie (Berlin: Christian Friedrich Himburg, 1788), 3. The theme was taken up by Carl Christian Erhard Schmid, "Einige Bemerkungen uber den Empirismus und Purismus in der Philosophie; durch die Grundsatze der reinen Philosophie von Herrn Selle veranlabt," appended to his Worterbuch zum leichteren Gebrauch der Kantischen Schriften, 3d ed. (Jena: Croker, 1798). Schmid proposed to defend Kant's "purism" against Selle's empiricist attack.
(2) In English, I am aware of only five substantial prior treatments of the issue of affinity: Henry E. Allison, "Transcendental Affinity," in Proceedings of the Third International Kant Congress, ed. Lewis White Beck (Dordrecht: Reidel, 1972), 203-11; Lewis White Beck, "Kant on the Uniformity of Nature," Synthese 47 (1981): 449-64; Robert E. Butts, "The Methodological Structure of Kant's Metaphysics of Science," in Kant's Philosophy of Physical Science, ed. Robert E. Butts (Dordrecht: Reidel, 1986) 163-99, esp. 179-87; Richard E. Aquila, Matter in Mind (Bloomington: Indiana University Press, 1989),82-106, following upon "Matter, Form, and Imaginative Association in Sensory Intuition, " in New Essays on Kant, ed. Bernard den Ouden (New York: Peter Lang, 1987), 73-105; and Paul Guyer, "Reason and Reflective Judgment: Kant on the Significance of Systematicity," Nous 24 (1990): 17-43. The only substantial discussion of the notion of the exponent of a rule that I am aware of is Klaus Reich, The Completeness of Kant's Table of Judgments, trans. Jane Kneller and Mark Losonsky (Stanford: Stanford University Press, 1992), 7-80.
(3) Immanuel Kant, Critique of Pure Reason, A28-30/B44-5, ed. Raymund Schmidt (Hamburg: Meiner, 1956); references are to pagination in the first (A) and second (B) German editions. All translations are my own.
(4) A166 -- 9/B20--11. The classic study of this topic is Anneliese Maier, Kants Qualitatskategorien, vol. 65 of Kant-Studien Erganzangsheft (Berlin: Pan-Verlag, 1930).
(7) For more on this, see A171-2/B212-13, A206-7/B253, A766/B794.
(8) See Immanuel Kant, Prolegomena zu einer jeden kunitigen Metaphysik, die als Wissenschaft wird auftreten konnen, ed. Benno Erdmann, in vol. 4 of Kants Gesammelte Schriften (Berlin: Reimer, 1911), 257:11-262:11, 310:20 313:16, B5, B19-20, A764-8/B792-6. The reference to an "attack" by Hume on the concept of causality is from Prolegomena, 257:14. All translations from the Prolegomena are my own.
(10) Prolegomena, 257:11-261:25. The reference to "die Auflosung des Humischen Problems" is from 260:35-6.
(11) Prolegomena, 310:20-313:25.
(13) A766/B794. Hume's examples are to be found in his Enquiries Concerning Human Understanding and Concerning the Principles of Morals (hereafter, EMU), 3d ea., ed. Peter H. Nidditch (Oxford: Clarendon Press, 1978), 27, 28, 164.
(15) Causes and effects must therefore belong to types or classes of events, at least in principle. This observation has also been made by Michael Friedman, "Causal Laws and the Foundations of Natural Science," in The Cambridge Companion to Kant, ed. Paul Guyer (Cambridge: Cambridge University Press, 1992), 17-1, who has employed it to powerful effect to attack the distinction, long popular among Kant commentators, between "every event some cause" and "same cause same effect" versions of the causal principle.
(16) A178/B220-1; Prolegomena, 309:23-310:10.
(17) Hume's attack on induction is of course not an attack on a prioristic causal reasoning at all, but an attack on a rival empiricist account of how causal reasoning takes place.
(18) EHU, sec. 4, part 1, 27-32.
(19) EHU, sec. 7, part 1, 63-9.
(20) A171/B213, A206-7/B252; Prolegomena 257:20-32. In the last named passage, Kant is admittedly describing Hume's position, but he describes Hume's proof of that position as "incontestable" (unwidersprechlich, 257:27), and when he later goes on to criticize Hume for drawing a "hasty and incorrect" conclusion (258.-10), it is only because Hume extended this incontestable point to affirm an inability of the understanding to think necessary connections in general (258:5). The point being hinted at here is the same one the Polemic makes explicit: the understanding can at least affirm, on the basis of certain technicalities of transcendental logic, that, in general, every event is preceded by some other event upon which it follows in accord with a rule; it just cannot ascertain a priori what this antecedent event is. The necessary connection to some other thing is given a priori, but nothing is learned thereby about what this other thing is.
(21) In the schematism chapter Kant writes: "The schema of the effect and the cause of a thing in general is the real that, whenever it is given is always followed by some other thing. It consists, therefore, in the succession of the manifold, insofar as it is subject to a rule" (A144/B183). Note the absence of any reference to a power in the cause to bring the effect about and the focus instead on mere constancy of temporal succession. The point about the importance of succession in time for rendering the concept of cause intelligible is nowhere as clearly made as it is in the phenomena and noumena chapter, where Kant writes: "Were I to leave out of the concept of cause the time, in which something follows upon something else in accord with a rule, then I would find nothing more in the pure category than that a "cause" would be something from which one would be allowed to conclude the existence of something else, and in that case, not only would cause and effect not be distinct from one another, I would have no idea what the features are in virtue of which this concept would apply to any object, because the ability to draw these sorts of conclusions about the existence of something else would depend on conditions [that is, knowledge of powers] of which I know nothing" (A243/B301). The principle of the Second Analogy--the claim that the whole argument is directed to establish--is stated in A as being, "Everything that happens (begins to be) presupposes something else upon which it follows in accord with a rule" (A189). Here again, the emphasis is entirely on constant or rule-governed succession in time, and-there is no reference to a notion of force or power as being in any way part of what is being proved. While the B principle, "All alterations take place in accord with the law of the connection of cause and effect" (B232), is not as clear, the "law" that it mentions is arguably the law that states that no event is a cause unless, whenever it occurs, it is followed by its effect. These positive claims about what (schematized) causes are, are complemented by Kant's negative claims in the Anfangsgrunde about the unknowability of fundamental forces. See Metaphysische Anfangsgrunde der Naturwissenschaft, ed. Alois Hofler, in vol. 4 of Kants Gesammelte Schriften (Berlin: Reimer, 1911), 534:20-6, 513:2-4,, (all translations from the Anfangsgrunde are my own) and compare A206-7/B252, where the point is made that, insofar as forces are knowable, it is only empirically, through reference to regularities in the succession of observed events. It might be objected that in these passages, Kant is merely concerned to make a claim about the fundamental forces of dynamics rather than about the nature of causation in general. However, since, as the Preface to the Anfangsgrunde shows, Kant was pessimistic about the possibility of raising any other discipline to the level of a "science," if the fundamental forces of dynamics prove to be unknowable, those that are studied by other disciplines are hardly likely to be any more transparent. There is, however, one passage where Kant appears to say more about causes than just that they are types of events that are always followed by certain other types of events. This passage is A91/B124, where Kant claims "that the effect does not merely come after its cause, but is posited through it and follows out of it" ("da [beta] die Wirkung nicht blo [beta] zu der Ursache hinzukomme, sondern durch dieselbe gesetzt sei, und aus ihr erfolge"). Either this was not intended as it sounds (which is hard to imagine given the emphasis and nature of the contrast), or Kant was confused about his own position. There is no way this claim can be maintained consistently with the passage cited above from the phenomena and noumena chapter, and there is nowhere in the Second Analogy where Kant manages to "answer" Hume by proving that causes must be conceived to contain forces or powers that make effects come about, as opposed to being antecedent events that are always followed in time by a certain other type of event.
(22) This is not the place to consider whether this charge against Hume will really stand up to scrutiny. However, for an outstanding treatment of Hume's account of causality--and a much-needed corrective to the naive and caricatured versions of Hume's account propagated by so many Kant scholars--see Fred Wilson, "Hume's Defence of Causal Inference," Dialogue 12 (1983): 661-94. (23) Those passages are B5, where Kant faults Hume for being unable to preserve necessity in the connection between cause and effect, and a strict universality of causal rules; B19-20, which again takes the necessity of the connection between a cause and its effect to be at the crux of Hume's mistake; A91/B123-4, where Kant charges that appeals to experience can never establish the true necessity to the connection between cause and effect; the introduction to the Prolegomena, already discussed in note 20 above; and [subsections] 27-30 of the Prolegomena, which focus on "removing Hume's doubt" precisely concerning the principle of the necessity of the connection between causes and their effects.
(24) B2-3. Compare with Friedman, "Causal Laws," 174-5, who also maintains that specific causal rules are mixed-and impurely a priori. However, Friedman seems to take it that particular causal rules are first established by induction and then have necessity subsequently attached to them by being subsumed under transcendental principles, so that there is at least a two-stage process involved (Friedman, 178, 180, 185). This does not fit well with the argument of the Second Analogy, which claims that necessary connection needs to be taken as axiomatic as a condition of localizing events in time in effect, that there can be no purely inductive first stage (A196/B241). See also Henry Allison, "Causality and Causal Laws in Kant," in Kant and Contemporary Epistemology, ed. Paolo Parrini (Dordrecht: Kluwer, 1994), 291-307, esp. 301-302; and Philip Kitcher, "The Unity of Science and the Unity of Nature," in the same volume, 25072, esp. 258.
(25) This is also why Kant claims in the Critique of Judgment that specific causal rules are contingent, and that we can fail to see their necessity. It is not contingent that every type of event has some type of cause, but it is a contingent matter whether we have correctly identified this cause. While the true cause is necessarily followed by its effect, we have no a priori insight into why and so cannot deduce the identity of the true cause but must instead rely upon experience to inform us. See Immanuel Kant, Kritik der Urtheilskraft, ed. Wilhelm Windelband, in vol. 5 of Kants Gesammelte Schriften (Berlin: Reimer, 1913), 183:14-28. All translations are my own.
(26) For references to the exponent of a rule, see A159/B198, A216/B263, A331/B387, and A414/B441.
(27) Reich, Kant's Table of Judgments, 76; 128, n. 23.
(31) A650/B678 and A652-3/B680-1. The example drawn from psychology is an especially powerful one, given that elsewhere (Anfangsgrunde 471:11-37) Kant remarks that psychological phenomena can only be studied "historically," not predictively, since even specific empirical rules cannot be reliably formulated or tested where psychological phenomena are concerned. That we should hold there to be unity among the psychic forces in the face of such clear evidence of our inability to take even the first step toward articulating it is a true testament to the fact that "reason does not here beg but command."
(34) A648/B677; see also A661/B689.
(35) A305-306/B362-3; A666-8/B694-6; A680/B708; Critique of Judgment, 180:14-17, 184:10-15, 185:35-186:7; Immanuel Kant, "First Introduction to the Critique of Judgment," ed. Gerhard Lehmann, in vol. 20 of Kants Gesammelte Schriften (Berlin: De Gruyter, 1942), 214:8-14, 219:9-11. All translations are my own. Nonetheless, a variant on the wishful-thinking argument-which might be called the unlikely accident argument-continues to be found in the "First Introduction," 210:10-19, and the wishful-thinking argument itself is repeated there at 215: 14-17.
(36) B165. See also A680/B708; Critique of Judgment, 184: 10-15; "First Introduction to the Critique of Judgment," 214:8-14, 219:011.
(39) For a third version of the nature of the transition problem in Kant, see Michael Friedman, Kant and the Exact Sciences (Cambridge: Harvard, 1992), 256-7. While Kant may well have come to perceive this third sort of gap in his system in his later years, I question whether it is serious or whether he should have been bothered by it. For more on this, see section VI, below.
(40) See Friedman, "Causal Laws," 181-6, for more detail.
(41) For an example of an argument along the former line see Friedman, "Causal Laws," 175-80. For one along the latter line, see Kitcher, "Unity of Science," 259-62.
(42) This is suggested by Friedman, "Causal Laws," 186.
(43) See Butts, "Kant's Metaphysics of Science," 171, 175-6, and compare Friedman, "Causal Laws," 185-6, who presents a much more optimistic picture of the possibilities for the progress of a prioristic science following the methodology of the Anfangsgrunde. (Since he does not recognize exponents, but rather takes the a priori component of specific causal laws to arise from their being subsumed under general ones, Friedman has no choice if he wishes to preserve Kant's claims that all causal laws are indeed necessary.)
(44) Anfangsgrunde, 470-1, 473, 518:25-31, 534:15-30; B165.
(45) For the first, see Critique of Judgment, 185:23-34, and "First Introduction," 203:4-12, 209:8-19, 213:8-15. For the second, see A89-91/B122-3.
(46) Butts, "Kant's Metaphysics of Science," 180-7.
(47) The claim is made most notoriously by the wishful-thinking argument, A650-4/B678-82, but see also Critique of Judgment, 179:31-180:5, 183:28-184:2, 185:19-22; "First Introduction," 203:12-21, 209:20-30. Guyer, "Reason and Reflective Judgment," 19, implicitly suggests that Kant might have been worried that a failure to discover systematic unity in nature would break the unity of apperception, in effect inducing a kind of multiple personality disorder in those who are unable to fit all of their experiences under a single law and a single genus. Kant may have had this worry at the back of his mind, and his occasional retreats from a merely regulative understanding of the principle of uniformity may have been due to it. However, if this was so, his worry was misplaced. At its most extreme, the unity of apperception might be taken to demand that all experiences be fitted together in a single representation, but this single representation is the representation of a world, not a system. The form of the world, insofar as it is known by us, is not generic subsumption (that is really a purely intellectual form that might apply to a noumenal world but that could only be demanded of the sensible world we experience through an "amphiboly"), but spatiotemporal arrangement. An aggregate of individuals is still an aggregate, and not a world, even if those individuals can be grouped into species, the species into genera, and so on up to a highest genus. The aggregate, whether hierarchically organized or not, only becomes a world for us when the individuals it contains are located relative to one another in space and time. As the Third Analogy teaches, this happens through their being seen to stand in relations of thoroughgoing reciprocal causal interaction to one another. For this purpose, however, a plethora of specific causal rules, linking all the events and objects in the world with one another in a tangled web of cries-crossing, multifarious reciprocal causal relations, will serve just as well as a hierarchical system of laws.
(48) Kitcher, "Unity of Science," 258.
(50) See section I above.
(51) Kant is explicit in recognizing this possibility at A89-91/B122-3, A111, A112, and A121-2. (52) A113, A122. At least it is plausible to read him in this way. Kant also makes certain remarks that indicate that he might have taken there to be two kinds of affinity, "empirical" affinity, which consists in the fact that different appearances are associable in virtue of resemblance, contiguity, and regular succession (the sort of phenomenon I have been discussing), and a higher, "transcendental" affinity that makes the empirical possible by ensuring that all events, however disparate, will belong to the unity of apperception and so will be such that we can compare them with one another (A113-14, A123). The question I am worried about here, however, is that of how it is that the manifold exhibits such a high degree of so-called empirical affinity. If Kant was not in fact concerned with this question in the A Deduction, but was instead aiming to exhibit the role of "productive imagination" in effecting some dark, "transcendental" affinity that serves to bring appearances together so that we can associate them, then what follows is that he nowhere discussed what I have referred to as the causal-rule problem. In that case, the conclusion that I will go on to draw in this section--that Kant takes so-called empirical affinity to be a brute fact that has no transcendental ground and that is rather a "favor" that nature does for us--will be even more inevitable. Before leaping to that conclusion, however, it is proper to consider whether the A Deduction might not in fact have been designed to explain "empirical" affinity. That is what I proceed to do.
(53) Jacob and Wilhelm Grimm, Deutsches Worterbuch (Leipzig: S. Horzel, 1956), s.v. Verwandschaft, includes "gemeinsame Abstammung, Zugehorigkeit zu einer Familie im ethnologischen und naturwissenschaftlichen Sinn, Ahalichkeit, Ubereinstimmung im Eigenschaften und Wesenart, Wechselwirkung." The use of Affinitat to stand for relation through marriage (Heiratsverwandschaft, Schwagerschaft; compare Theodor Heinsius, Volkthumliches Worterbuch der Deutschen Sprache [Hanover: Hanschen Hofbuchhandlung, 1818]), also mentioned by Grimm as a sense of Verwandschaft, is probably derivative. Kant himself defines Verwandschaft as "die Vereinigung aus der Abstammung des Mannigfaltigen von einem Grunde" in Anthropologie in pragmatischer Hinsicht, ed. Oswald Kulpe, in vol. 7 of Kants Gesammelte Schriften (Berlin: Reimer, 1917), 177:26-7. All translations are my own. The major German dictionary of Kant's day, Adelung's Grammatisch-Kritisches Worterbuch, does not contain entries for either Affinitat or Verwandschaft.
(54) Grimm, s.v. Verwandschaft, cites Liebig, chem. Briefe 35 as remarking "ganz dem gewohnlichen Sprachgebrauch und der Bedeutung des Wortes entgegen, hat man die chemische Kraft V[erwandschaft], Affinitat gennant." Among the "chemical forces" in question are affinitas aggregationis, affinitas compositionis, and (most relevant for the topic of this paper) attractio electiva. Kant discusses this chemical use of Verwandschaft in Anthropology, 177:19-29 and n., instancing sensibility and understanding as two powers of the soul that have this special sort of affinity for one another, and that produce entirely new compounds that combine their two features. This is not the same sense of Verwandschaft discussed in the Anthropology's previous paragraph.
(55) Even though this is in no way conclusive, some further evidence that Kant used the term "affinity" in the two distinct senses I have identified can be gleaned from the Kant dictionary authored by Kant's disciple, Schmid (Carl Christian Erhard Schmid, Worterbuch zum leichteren Gebrauch der Kantischen Schriften [Jena: Croker, 1798]). The entry for "affinity" expounds the two senses in the reverse order to that I have just given, and with a decidedly idealistic gloss: "Affinitat. Verwandschaft der Erscheinungen bedeutet (1) den durchgangigen, regelmabigen Zusammenhang derselben, als den objectiven Grund, wodurch eine regelmabige Begleitung und Folge (Association) ihrer Vorstellungen moglich wird, dab z.B. der Zinober immer roth und specifisch schwer erscheinet. Da die Erscheinungen selbst nur Vorstellungen sind, und der Grund ihrer Verknupfung nur im Gemuthe liegen kann: so ist jene Affinitat eine Folge theirs der Einbildungskraft, die alle Erscheinungen so apprehendirt, dab Einheit des mannigfaltigen empirischen Bewubtseyns in einem einzigen entspringen kann, worinnen alles zusammenhangt, theils der Categorien, als verschiedener Aeusserungen und Formen unsres Selbstbewubtseyns. Sie heibt a) empirisch, sofern sie wahrgenommen wird; b) transcendental sofern man ihr eine Nothwendigkeit a priori beylegt. Diese macht jene moglich und ist ein nothwendiges Erfordernib einer Natur. Crit. I. 100. 113. ff. 122. der ersten Ausg. (2) soviel als Continuitat, Statigkeit z.B. dab alle Dinge, ihre Eigenschaften und Krafte stufenweise von einer Species zur anderen ubergehen, als hochst mannigfaltig und zugleich als hochst gleichartig von der Vernunft gedacht werden mussen. Crit. I. 685. 688."
(56) A121-2, A112.
(57) A113-14, A122-3.
(58) A114, A125-7. Compare A650 4/B678-82, A656/B684, A660/B688.
(60) Indeed, his sensitivity to the first of the two considerations I have mentioned is made explicit in the last lines of A127.
(62) A122; see also A113.
(63) This appears to be implied by B156n.
(64) A127. (65) A114, A125, A127. Here, however, there is at least one text, the last few lines of A127, that clearly rejects the first alternative.
(66) B165, cited above.
(67) Critique of Judgment, 184:16-21.
(68) Allison, "Transcendental Affinity," 204.
(69) Though not the necessity of these relations.
(70) That I should be only a subset of my experiences is what lies behind Kant's description of self consciousness as "paradoxical" at B152-3.
(71) A2401, 242-3/B300-1. It is this sense of "intelligible causality" that lies at the basis of freedom and Kant's ethics, and, though it has not been pertinent to consider it in this article, it plays a huge role in Kant's philosophy as a whole.
(72) I am indebted to Brigitte Sassen for critical comments on earlier versions of this paper, and for instruction on the early reception of Kant's philosophy.
(73) Anfangsgrunde, 469-70.
(74) Anfangsgrunde, 470:2-3.
(75) This general position is repeated in this context at Anfangsgrunde, 470:19-20.
(76) Anfangsgrunde, 470:2-3, 470:23-6.
(77) The role of this demand is most evident at Anfangsgrunde, 509-10, but this argument is implicit throughout.
(78) Kant later made this explicit in B: "All our inner perceptions are such that we must determine the time over which they last, or the time at which they occur, by taking it from that which is presented to us as altering in [enduring] outer things" (B156). See also B291-4.
(80) Anfangsgrunde, 471.
(81) This is contested by Gordon Brittan, "Kant's Two Grand Hypotheses," in Kant's Philosophy of Physical Science, ed. Robert E. Butts (Dordrecht: Reidel, 1986), 61-94, esp. 84. Brittan claims that Kant regarded repulsive force as a merely possible predicate of body. Yet while it may be merely possible that a body exert an absolute as opposed to some sort of relative repulsive force (that is, a repulsive force that stops approach in an instant, as opposed to slowing it over a distance, and that will not allow the least compression of the body to occur), that a body exert some sort of repulsive force or other is entailed by the application of the First Analogy to the construction of the concept of a spatially extended object.
(82) Anfangsgrunde, 513-14, esp. 514:2-7. Repulsive force therefore allows of being constructed and Kant never says otherwise, despite an opinion currently popular among a number of commentators (see Brittan, "Kant's Two Grand Hypotheses," 84-90, and the sources cited there). To construct a repulsive force is just to represent the motion of a second body as a composite of two opposed motions in accord with the procedure set out in Kant's phoronomy. The one motion is the motion of the body considered on its own; the other is the motion due to the repulsive force of the repelling body. Since there is nothing else to repulsive force than this regular effect on motion, there is no mystery to its construction.
The contrary view seems to be based on four texts (all of which actually say different things): Anfangsgrunde, 534:20-36 and related texts such as 513:2-4, 502:25-6, and 524:29-36; Anfangsgrunde, 521-2; Anfangsgrunde 517-18; and Anfangsgrunde 525:7-12.
In the first set of texts, Kant's point is not that the activity of repulsive forces does not admit of being constructed, but that how a body is able to retard or repel another, and change its motion in ways we can construct, does not in turn admit of being constructed. All that we know is that bodies repel, not why.
The second text addresses a problem with the representation of the operation of repulsive forces within the volume of a body. This problem is created, not because of any difficulty with constructing repulsive forces, but because of Kant's extraneous commitment to the infinite divisibility of matter (Anfangsgrunde, 503-505). We tend to think of the repulsive force as radiating outwards from a point to the surface of the body, and acting there on contact. Yet Kant's position on infinite divisibility led him to want to claim that every point within the volume is in fact a center of repulsive force. This is a feature of matter that does not easily lend itself to construction when one considers cases of rarefaction and condensation (we tend to want to conceive of the number of centers of repulsive force as staying constant and either moving away from one another in a void, or being more tightly compacted to squeeze out a void, and this is not true if repulsive force always operates from every point within a body, even after rarefaction or prior to condensation). Kant's proposed solution to this problem is to represent the repulsive force as acting over an infinitesimally small sphere around each point within the volume of a body (see Anfangsgrunde, 520-1 as well as 521-2). Thus, there is not a single point where the body is within a larger sphere where it acts, but body is rather taken to be at every point within the sphere of its repulsive force. When rarefaction or condensation occurs, we are not to represent the infinitesimally small spheres of force around each point as increasing or decreasing in size, but to simply attribute a proportionally lesser or greater quantity of repulsive force to all of the points within the increased or diminished volume of the body. Here, far from saying that the activity of repulsive force cannot be constructed, Kant is saying that it can be--is point is just that the construction is awkward and unnatural and is not as easy to conceive as the expansion or contraction of spheres around points.
The third text does not say that repulsive (or attractive) forces cannot be constructed, but that Kant himself felt unable to provide a general formula or procedure for calculating how the repulsive and attractive forces can combine in a given body to determine its size and shape. Kant had given an account of how two different motions are to be represented as combined in a single body in the phoronomy chapter, and he was to go on to apply this account to represent how the motions of two different bodies will be combined and distributed after collision in the mechanics chapter. However, when it came to the task of providing a general formula for calculating the point where a given attractive force, continuously diminishing in strength with the square of the distance, cancels the influence of a given repulsive force, continuously diminishing in strength with the volume (that is, the place where the surface of a body is located), he felt simply unable to manage the mathematics involved. This was a problem that he (quite rightly) felt could be assigned to someone with more training in mathematics, and it certainly has no bearing on his claim that we can construct the concept of a repulsive force or an attractive force in isolation. (For what it is worth, the problem might be resolved by representing the attractive force as a field emanating from the center of mass of the body, at every point of which vectors representing the strength and direction of the force at that point could be drawn. Note that Kant may have been precluded from even starting this story if he lacked an appropriate vector concept, as Brittan, "Kant's Two Grand Hypotheses," 86n., has suggested. The repulsive force would have to be represented as a series of potential vector fields, varying with volume in the way discussed in the previous paragraph. [It would be simpler, though less true to what Kant takes to be the necessary facts of the case, to also represent the repulsive force as a field of vectors, diminishing in intensity with distance from a central point.] Since the attractive force decreases with the square of the distance whereas the repulsive force decreases with the volume, there is only one distance at which the vectors describing the attractive force are of the same length as the vectors describing the repulsive force would be, were the body compressed within that volume. The surface of the body must enclose that volume.)
The final text mentions a further problem: that the coefficient of repulsion--the specific degree of repulsive force characterizing any given kind of material--needs to be determined empirically and cannot be anticipated a priori. This is a profound point that will be explored in more detail below, but it has no bearing on the issue of whether or not repulsive forces can be constructed. The forces can well be constructed. What is more, each different coefficient of repulsion can be constructed simply by representing the compressing body as being turned back sooner in its approach. Thus, it is possible to construct repulsive forces that would allow huge quantities of matter to be compressed to very small volumes before exerting the smallest resistance; it is possible to construct repulsive forces that would allow very small quantities of matter to exercise great resistance to the smallest compression, and it is possible to construct all the infinitely many variants in between. The problem is just that there is no way to construct which of these infinitely many different kinds of possible force must people the actual world.
(83) Anfangsgrunde, 501.
(84) Anfangsgrunde, 508-509.
(85) Anfangsgrunde, 514:2-7.
(86) A41/B58, B155n
(87) Anfangsgrunde, 495:5-10.
(88) Anfangsgrunde, 524:3-4, 533:36-534:5.
(89) There are two quite distinct notions of the strength of a repulsive force in Kant. According to one, the strength of a repulsive force is a function of the volume of a body and increases as a body's volume is decreased. However, Kant also takes it that the rate at which a repulsive force increases with decreases in volume could vary for different kinds of body, so that some bodies might have stronger repulsive forces, not because they have been compressed, but because similar quantities of those bodies contained in similar volumes exert a greater resistance to compression than do other kinds of body. I will use the expression field strength" to distinguish this second kind of strength from the first, but I do not mean anything more by the term "field" than what has just been said. The modern concept of a field is one that is only dimly present in Kant's work (as, for example, at Anfangsgrunde, 520-1 and 521-2). (90) A661/B689.
(91) Anfangsgrunde, 525:7-10, 525:20-1. It may, however, be a regulative principle (that of affinity or continuity of species) that we must assume there to be, somewhere in nature, a kind of body with each and every kind of repulsive force. See A658-61/B686-9.
(92) Anfangsgrunde, 524:10-17.
(93) Anfangsgrunde, 535:7-10.
(94) This last point is explicitly acknowledged by Kant at Anfangsgrunde, 524:40-525:7, though he nonetheless regarded the hypothesis of atoms and void as one to be shunned--chiefly because it involves the concept of void, which he regarded as empty and fictitious ("der absoluten Undurchdringlichkeit" at Anfangsgrunde 525:14 should probably read "des leeren Raumes," but see also 524:13-14 and 532:11-13), but also because absolute hardness is an "occult quality" that cannot be described by a law of the approach and retreat of bodies (See Anfangsgrunde, 533:21-4: motion resulting from the collision of absolutely hard bodies would not be continuous, but abrupt and, in effect, magical, as there would be no reason why collision should result in one kind of motion of the colliding bodies rather than another.).
(95) Anfangsgrunde, 541:11-26 suggests this.
(96) Anfangsgrunde, 509:7-11. Since the attractive force is inferred as necessary to prevent the unlimited extension of bodies under the influence of the repulsive force, if the field strength of the repulsive force is to be said to vary for different kinds of body, what it is said to vary with reference to must be the attractive force, which for that reason must be supposed to be the same in all bodies.
(97) This is merely a matter of definition. "Kind" of matter, for Kant, just means "field strength of the repulsive force of a given body," and "quantity" just means "field strength of the attractive force of a given body." Kant could just as well have taken the attractive force to vary with reference to the repulsive, hence taken different kinds of bodies to be characterized by different specific gravities, and variations in the repulsive force exercised by different samples of the "same" body to be due to the quantity of that kind of matter compressed into that volume. The facts are not thereby changed, merely the labels attached to them.
(98) Anfangsgrunde, 526:33-5.
(99) Anfangsgrunde, 526:20-5, 526:27-33. This is not a very persuasive reason, unless, like Kant, one is antecedently convinced of the transcendental objectivity of the principle of the parsimony of forces.
(100) Anfangsgrunde, 563:39-564:5, 534:5-11.
(101) Anfangsgrunde, 534:12-13, 518:25-31.
(102) Anfangsgrunde, 470-1.
(103) I pass over comment on the phenomenology chapter, which was written merely to provide an explanation of how it could be possible to accept the results of Newton's bucket experiment without having to invoke absolute space, that is, to explain how it is possible to have true motions that are nevertheless not absolute motions.
(104) Anfangsgrunde, 522:24-38.
Correspondence to: Department of Philosophy, The University of Western Ontario, London, Ontario, Canada, N6A 3K7.
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|Publication:||The Review of Metaphysics|
|Date:||Mar 1, 1997|
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