is “space” a concept? kant, durkheim, and french neo-kantianism

Journal of the History of the Behavioral Sciences: Vol. 32(4) 441 -455 October I996 Q 1996 John Wiley & Sons, Inc. CCC 0022-5061/96/040441- I5

IS “SPACE” A CONCEPT? KANT, DURKHEIM, AND FRENCH NEO-KANTIANISM

TERRY F. GODLOVE, JR.

The concept of space is a singular representation embracing all things within itself; it is not an abstract common concept containing them under itself. For what you speak of as several places are only parts of the same boundless space related to one another by a fixed position. And you can only conceive to yourself a cubic foot if it be bounded in all directions by the space which surrounds it.

Immanuel Kant, Inaugural Dissertation.‘

According to Kant, all humans share a basic form of spatial representation-space is an “a priori intuition.” Durkheim felt that Kant’s a priori stance blocked the kind of empirical inquiry that would show human spatial representation to be, on the contrary, quite diverse. Durkheim’s claim raises the issues in intellectual history and philosophy addressed in this paper. First, the paper traces Durkheim’s reading of Kant through the nineteenth- century French neo-Kantians Renouvier and Hamelin. Second, it argues that Kant’s and Durkheim’s projects are not, after all, genuine competitors. The result is to reassert the sharp distinction between epistemological and sociologicdl approaches to spatial representation that Durkheim and others tried to collapse. 0 1996 John Wiley & Sons, Inc.

In the Critique of Pure Reason (1781) and earlier, in the Inaugural Dissertation (1770), Kant famously argues that space is not a concept in the usual sense. Rather, it is an a priori, “pure intuition,” which, along with time, “is represented as an infinite given magnitude.” Part of what Kant means by “infinite given magnitude” is that the parts of space can only be thought as in “the one all-embracing space.” With “common concepts,” the situation is re- versed: They admit of subspecies without end, the more specific concepts constituting parts of the extension under the given concept. Whereas the parts of a concept fall under it, the representation of space contains “an infinite number of representations within itself.”2

I shall return in a moment to Kant’s distinction between pure intuitions and concepts. As has been ably documented by Albert0 Coffa, Michael Friedman, and others, it suffered mightily at the hands of the great nineteenth- and early twentieth-century advances in geometry, logic, and physics. By the turn of the twentieth century, even most neo-Kantians agreed that the master had been wrong to deny space and time conceptual content, wrong to remove them from the sphere of empirical investigation.’ At about the same time, Emile Durkheim and Marcel Mauss co-authored what is arguably the first self-conscious essay in the sociology of knowledge, “De quelques forms primitives de classification: contribution B 1’6tude des reprksentations collectives” (1903): They argued that the contents of our fundamental concepts, including space and time, are owed to the nature of the local social arrangements. Thus, the idea of a sociology of concepts and the availability of space and time as concepts came more or less together. This was no coincidence. In the Introduction to the Elemental Forms of Religious Life (1912)? Durkheim tells us that, by overthrowing Kant’s denial of

TERRY F. GODLOVE, JR. received his Ph.D. from the University of Chicago in 1984. He is currently Associate Professor of Philosophy and Chair at Hofstra University in Hempstead, New York, 11550- 1090.

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442 TERRY E GODLOVE, JR.

conceptual content to space and time, his late friend Octave Hamelin had made it possible for him to take them as objects for his new social science.

Durkheim’s assessment invites the two questions I shall pursue in this paper. The first-How did Durkheim come to view Kant as a threat?-is one of intellectual history, and its answer lies with the interpretation of Kant’s philosophy that Durkheim took over from Hamelin and from the great French neo-Kantian philosopher Charles Renouvier.6 The second question is philosophical: Was Durkheim right to view Kant as a genuine competi- tor? Because I think Kant’s arguments for the intuitive content of space and time are still worth taking seriously today, I will also comment briefly on a third question: From a generally Kantian point of view, what are we to make of sociological accounts of our representations of space and time? That is, whether Kant likes it or not, the sociology of space and time is now an ongoing scholarly industry; what place should it have on a broadly Kantian map of human knowledge?

The issues in Kant interpretation I shall be treating are familiar. But I hope there will be value in arranging them in such a way as to make explicit their historical and substantive relevance to a formative moment in the social sciences. To make matters more practicable I will focus exclusively on space. Before asking how Durkheim came to view Kant as a threat we must clarify Kant’s views themselves; in particular, his refusal to see space as a “common concept.”

I. KANT ON CONCEPTS AND SPATIAL REPRESENTATION

At first glance, Kant does indeed seem to present an obstacle to Durkheim’s project. In the Elemental Forms (Introduction, $II), Durkheim claims that recent fieldwork shows that human beings hold a variety of alternative concepts of space, and that the content of these notions follow from the form of local social organization. To take Durkheim’s best-known example:

Among the Zuiii . . . the pueblo contains seven quarters. . . . Now their space also contains seven quarters, and each of these seven quarters of the world is in intimate connection with a quarter of the pueblo, that is to say with a group of clans. . . . Over the course of history, the number of basic clans has varied, and the number of regions has varied in the same way. Thus, spatial organization was modeled on social organization and replicates it. (24-25)

By seeming contrast, Kant holds that space is not a concept at all. Thus, Durkheim seems to have reasoned that, if Kant is right, he must be wrong. Whether there is a genuine opposition here depends of course on what Kant means when he denies space conceptual status.

In the Critique, Kant argues for the thesis that space is an a priori or pure intuition in section $4, the “Metaphysical Exposition of the Concept of Space” (A24/B39-A25/B40). In the fourth numbered paragraph, Kant remarks that the representation of space is singular, and unlike a concept, contains “an infinite number of representations within itself” (A25/B40). How is this supposed to set off the representation of space from a general concept? The crucial point is that Kant regards the extension of a concept as a bounded space or “sphere” (A72/B97) and not as the class of individuals to which the concept applies. Among other recent commentators, Manley Thompson and Michael Friedman have brought this point to the forefront of current discussion. As Thompson puts it,

Whatever is contained under a given concept is contained under subspecies of that concept, and the extension or spheres of the more specific concepts constitute spatial parts

IS “SPACE’ A CONCEPT? KANT, DURKHEIM, AND FRENCH NEO-KANTIANISM 443

of the extension of the given concept. There is no absolutely lowest species just as there is no absolutely smallest space, and the individuals falling under a concept are then like points in space. They have no extension and cannot constitute parts of space?

The point is that, by regarding concepts as extensions or spheres, the relation of an individual to its species is not that of part to whole-it is rather that of a point, a mere limit, to a space that includes it.8 In this sense, individuals fall under concepts; by contrast, spaces are parts of the including space, and so fall within it.

Kant provides an example in his so-called “Vienna” series of lectures on logic, tran- scribed during the period when the Critique of Pure Reason was being prepared for publica- tion:

E.g., all beings on earth are organized or not organized. The organized ones are plants or animals. Logical division is nothing other than taking apart the sphaera of a concept. This dividing is something other than taking apart. In the case of division, I distinguish the manifold under the concept, i.e., the sphaera. In the case of taking apart, I analyze the concept. I do not analyze the concept in itself [in division], but rather I only divide the sphaera, the lower concepts, insofar as they are contained under the universal.’

Thus, we may divided the extension of “earthly beings” into its parts, “organized” or “not organized,” and then treat the species “plants” and “animals” as parts of the genus “organized earthly animals.” There is, as Thompson and Friedman note, no absolutely lowest species1° (in the next paragraph, Kant offers moving “either on the earth, or in the air, or in water” as parts of the genus “animals that move”). Whereas individuals (a particular flying animal) and species (flying animals) are contained under a genus (animals that move), only the species are parts of the genus.

By contrast, the individual (e.g., that bird) is related to its species (flying animals) as is a point to the space that includes it. Kant’s account stands opposed to more recent views, according to which a concept’s extension is a class of individuals. A Kantian epistemology has to resist this view, because it wants to count as individuals only what can be given to us through the forms of sensible intuition, space and time. And here, at length, we come to the reason that space cannot be a concept. We have seen that a concept’s extension is a bounded space, composed of a limitless number of species and subspecies under it; however, in the Critique (the third numbered paragraph of the Metaphysical Exposition), Kant claims that we run into immediate difficulties in trying to specify the extension of the “concept” space:

Space is not a discursive or, as we say, general concept of relations of things in general, but a pure intuition. For, in the first place, we can represent to ourselves only a single space; and if we speak of diverse spaces [vielen Raumen], we mean thereby only parts of one and the same unique space [alleinigen Raumes]. Secondly, these parts cannot precede the single all-embracing space [einigen allbefassenden Raume], as being, as it were, constituents out of which it can be composed; on the contrary, they can be thought only as in it. Space is essentially singular; the manifold in it, and hence the general concept of spaces, depends solely on limitations. Hence it follows that an a priori, and not an empirical, intuition underlies all concepts of space. (A24-25B39)

The relation between “diverse spaces” and “the single all-embracing space” is that of part to whole, and insofar they may appear to stand in the relation of species to genus. What blocks this conclusion is the fact that we cannot (so the claim) piece together the concept of “the single all-embracing space” from these parts, because the representation of it makes possible the thought of its parts.


Kant’s clearest expression of this point is perhaps found in the quote from the Inaugural Dissertation (1770) with which I began: “What you speak of as several places are only parts of the same boundless space related to one another by a fixed position. And you can only conceive to yourself a cubic foot if it be bounded in all directions by the space which surrounds it.” In these passages Kant is apparently expressing a fact about our experience of space; namely, that places are given in one space in the sense that the thought of a particular space carries with it the represention of its having been cut from “the space which surrounds it.” The force of these passages from the Critique and the Dissertation is to give the representation of space a priority over the thought of its parts that does not obtain in the case of general concepts. Whereas general concepts are constructed from parts under them, space is nonconceptual, a “pure intuition” in that spaces (and so objects in space), can only be conceived as in the “one all-embracing space.”

If our focus were exclusively on Kant’s doctrine, we ought now to further prosecute the grounds of this alleged priority-that is, why should we concede a priority to our representation of the “same unique space” over those of individual spaces? Even granting the plausibility of Kant’s claim that space must be experienced as unique and boundless, Kant’s defenders must still meet a variety of naturalistically motivated (and other) objections. Thus, the evolutionary epistemologist will want to know why any consideration advanced thus far establishes Kant’s conclusion that space is an a priori intuition. Having evolved thus far, might we not further evolve into creatures who are able to assemble spaces together without presupposing a representation of the whole?”

On the questions of how Kant thought of the alleged priority of space over spaces and of the plausibility of the claim, the literature reflects two main alternatives, each with compelling textual and analytical bases. One, pursued lately by Hintikka, Friedman, and others, emphasizes Kant’s limited (by our standards) conception of geometry and his (again) impov- erished logic; the other, favored for example by Thompson, Parsons, and Melnick, appeals to the unavoidable place of the knowing subject, to the “phenomenological” necessity of being located in and having to turn and move through space over time (in the course of experience). I will take up aspects of this debate in sections three and four of this paper, though only to clarify some of the points at issue. For now, we have seen enough of Kant’s denial of conceptual status to space to ask why Durkheim found it so threatening.

11. HOW DID DURKHEIM COME TO REGARD KANT’S VIEW OF SPACE AS A THREAT?

Durkheim apparently found Kant’s views threatening because he thought they undercut the possibility of an empirical inquiry into what he saw as the diversity of spatial representation-and so the sort of sociological program that Durkheim wished to inaugurate. Durkheim never says as much in the Elemental Forms, but this attitude is implied by what he does say. For example, after rejecting Kant’s “a priori” view, Durkheim remarks that, “besides, there are cases where this social character [of spatial representation] is made manifest” (24). Thus, Durkheim sees his sociological (empirical) account of spatial representation as incompatible with Kant’s theory.

Once Durkheim had determined that Kant’s views on space were a threat to his project, he apparently felt he could not proceed absent a compelling reply to them. He found them in the work of the neo-Kantian Renouvier (1 8 15 - 1903) and in that of his Renouvierist contemporary Hamelin (1856- 1907). The extent of Durkheim’s intellectual debt to Renouvier and Hamelin has been well documented by others.I2 Although Renouvier goes unmentioned in the Elemental Forms, a hallmark of his philosophy was the insistence that Kant had been

IS “SPACE” A CONCEPT? KANT, DURKHEIM, AND FRENCH NEO-KANTIANISM 445

wrong to deny that space and time are general concepts. Given Durkheim’s deep familiarity with Renouvier’s ~ystern,’~ his influence at this point can hardly be doubted. In the case of Hamelin, Durkheim provides two references, the first in a footnote:

I call time and space categories because there is no difference between the role these notions play in the intellectual life and that which falls to notions of kind and cause. (See on this point Hamelin, Essai sur les e‘le‘ments principaux de la repre‘sentation [ 1907].’4 ( 2 1-22)

And a page later:

As Hamelin has shown, space is not the vague and indeterminate medium that Kant imagined. If purely and absolutely homogeneous, it would be of no use and would offer nothing for us to hold on to. Spatial representation essentially consists in a primary coordination of niven sense exDerience. But this coordination would be imDossible if the parts of spaccwere qualitathely equivalent, if they really were mutualli interchangeable. (23)

These are breathless passages and a sustained response is probably out of place. (Taken philosophically, they are obviously unsatisfactory. The first argues from fiat;I5 the second takes Kantian space as a “medium” apparently implying independent reality.)16 We probably do best to see Durkheim as pausing simply to announce telling criticisms of Kant in the spirit of one who has mastered the philosophical issues with Hamelin’s help, but who cannot now be distracted from the pursuit of larger game. He provides the references to Hamelin for the benefit of the reader who wishes to attain a like mastery on his or her own time.

But in fact there is no evidence in the Elemental Forms or elsewhere in Durkheim’s writings (as far as I know) that his assessment of Kant as a threat went beyond the rather preliminary thought recounted above; that is, that his own empirical and Kant’s a priori approach to spatial representation could not both be sustained. In particular, Durkheim gives us no reason to think that he appreciated the details of Kant’s view as presented in Section I, and so no reason to think that he measured his own project against them. What is clear is that Durkheim believed that Hamelin had already answered Kant on technical, purely philosophical grounds, and, in so doing, has shown that our underlying representation of space is not an a priori intuition but rather a general concept-just the result that Durkheim felt he needed.

I shall argue in the next section that Hamelin’s (and Renouvier’s) criticisms of Kant are instructive but unpersuasive. Durkheim’s appeal to Hamelin fails. However, I shall argue in the final section that Durkheim was wrong to see Kant as a threat-more broadly, that he misunderstood the relationship between the classical tradition in epistemology and the emerging social sciences. Durkheim’s project is safe from Kantian attack, we might say, in spite of his defense of it: His unsuccessful appeal to Hamelin against Kant is unnecessary, off the point. To see that Kant is no enemy of Durkheim’s we must consider in greater depth Kant’s reasons for giving priority to the representation of space over that of its parts. Since Renouvier and Hamelin took themselves to be disputing precisely this point, we will return to Kant’s arguments by way of their criticisms.

111. RENOUVIER AND HAMELIN ON KANT ON SPATIAL REPRESENTATION

When one follows up on Durkheim’s reference to Hamelin’s Ele‘ments principaux, one is directed back to Renouvier’s Truite‘ de logique ge‘ne‘rule et de logique formelle (1875).


There, says Hamelin, “Renouvier explains why he does not separate time and space from other concepts” (90).

Renouvier’s argument is a clever attempt to use Kant against himself. After noting Kant’s segregation of space and time, the “forms of receptivity,” from both pure and empirical concepts, Renouvier writes: “However, if we observe that these forms are constructed in representation in the manner of all other relations, by thesis, antithesis and synthesis . . . we will find it convenient not to separate them” (209). Renouvier is apparently appealing to Kant’s own account of how he derived the third member in each of the four divisions of the Table of Categories, Kant remarks that, “the third category in each class always arises from the combination of the second category with the first” (B 1 lo). For example, under the quan- titative categories, totality is plurality considered as a unity. Though he leaves the claim un- explicated in the 1875 volume, Renouvier fills it out in an 1896 contribution to L‘Anne‘e philosophique:

The synthetic notions of determinate duration and of determinate extension are constituted respectively by a limitative notion: the instant, the point, and by an extensive notion of indeterminate interval: the indefinite time, the indefinite space [Z‘ espace vague] of confused intuition. Thus, these categories present to us a perfect analogy of forma- tion with the general categories of qualitative relation. (33 -34)

Now Kant’s qualitative categories are, in order, reality, negation, and limitation; thus, limitation is negation as applied to the real. (In the Anticipations of Perception Kant makes it explicit that he wants this formula construed in terms of sensation: A limited intensity of sensation results from applying “negation = 0” to “the real, which corresponds to sensations in general [Empfindungen iiberhaupt]” [A175/B217].) So, in Renouvier’s “perfect analogy,” the concept of a determinate (that is, limited) extension is derived from bringing a limitative notion, a point, to bear on an extensive notion, “indefinite space” (in the sense, I take it, of without limit, boundless). Putting aside questions of interpretation,” our interest must now be in what force this has against Kant’s denial of conceptual status to space.

Certainly Kant can have no objection to the concept of a determinate space, per se. In- deed, Friedman, Parsons, and others have recently cited Kant’s remark that there is “a general concept of space, which is common to both a foot and an ell alike” (A 25). The idea would then be to reserve the “general concept” for regions of space, and allow it, as Fried- man puts it, “to relate to parts of space or spaces as general concept to the instances thereof.” The general concept of space would then contrast with the use of “space” as it applies uniquely to “the same unique space,” space as a singular individual.1s What, then, of Renouvier’s claim that we form the concept of a determinate region of space by introducing limits to “vague,” boundless space? The point, of course, is that Renouvier has preserved just the priority on which Kant places all the emphasis. We should understand Renouvier’s story as about the general concept of space; it maintains a Kantian reliance on the presupposition of space considered as a unique indi~idual.’~

We are moving, as I have noted, toward recognizing that the priority of space over spaces removes whatever threat Durkheim perceived in Kant’s doctrine. But while we have noted the priority in Kant and have seen that it persists as unthematized in Renouvier, we have so far left it ungrounded. Why should we grant priority to the singular intuition over the general concept?

This issue is central to Hamelin’s concerns in Ele‘ments principaux de la repre‘sentation. The attraction of this work for Durkheim is obvious; Hamelin begins his remarks on space by observing that, “Kant’s error . . . is not to ground the reality of space solidly by placing

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it among the concepts” (84). With concepts construed empirically, this is precisely the result Durkheim felt he needed to launch his sociological inquiry. Hamelin continues:

Kant’s arguments here . . . have no merit. To say that homogeneous space has no logical extension at all, that its parts are in it but do not fall under it, is to make an inade- quate representation of it, where the interval subsists only after abstraction from limits. Now there is no more an interval without limit than a limit without interval: for it is necessary that any extension extend from here to there. . . . There must be some mark of division, however vague, to make the parts [pour y produire des parties]. (84)

In this passage, Hamelin has faithfully reproduced the Kantian formula that the parts of space are “in it,” “but do not fall under it.” But we may note that, at the same time that he is rejecting Kant’s view, he is playing by the rules of B39 (reproduced above); at least on one natural reading, he is making claims about our ability to represent space and spaces. His central claim is that, contrary to Kant, spatial intervals need not be “abstracted from” the whole. Thus, to adjudicate the issue between him and Kant we must ask ourselves whether, as Kant maintains, the thought of a region of space carries with it the representation of its being located in one boundless space, “the single all-embracing space.” If so, then Kant will have shown that, as Hamelin puts it, “the interval subsists only after abstraction from limits” (clearer would be, “from limitlessness,” but in either case we may take Hamelin to be criti- cizing the Kantian claim that we cannot represent spatial regions [intervals] until we have in- troduced the relevant limits). On this question, reflection tilts decisively in Kant’s favor; we do not know how to imagine a region of space without that region being always already im- mersed in space. So long as we confine discussion to such phenomenological claims about our representational capacities as applied to space, Kant’s footing appears solid.

In a second line of attack, Hamelin focuses on what Kant saw as the boundlessness or infinity of space:

Because space in general is somewhat abstract it appears as infinite-that is as indeterminate; and because it is a concept it could be an abstraction. The abstract necessarily appears after everything concrete: animalness for example after a particular animal. It follows that spatial determinations can no more escape this law than do other determinations; abstract space appears after every determinate extension (86).

When taken strictly as a reply to Kant, this objection fails because it begs the question in an obvious way. Hamelin is urging that the general term “animal” stands to particular animals as “space in general” stands to “determinate extensions.” But this is to assume without argument precisely what Kant denies. Kant has claimed that we represent the parts of space, and so objects in space, within one space, that is, with the accompanying representation of surrounding, contiguous space. This has the force of denying that “space” and “spaces” behave like general terms and their instances. Hamelin is simply assuming what Kant doubts.

But what fails as an objection may still serve to sharpen the broader issues. Hamelin’s comments in this second objection remain, like the first, within the theoretical confines of Kant’s third and fourth arguments in the “Metaphysical Exposition of the Concept of Space.” The claims are of a broadly phenomenological sort, describing (in Kant’s case) or disputing (in Hamelin’s) our basic experience of space as a single, boundless individual. I have already recorded my own feeling that, when the debate is conducted in these terms, Kant carries the day. But a new set of issues comes into play when we try to make Kant’s phenomenological claims support conclusions about the nature of the physical world. Granting the B39 point against Renouvier and Hamelin-that we must represent space as boundless, and so as a


pure intuition and not as a general concept-the question then arises whether this fact describes more than our experience. This is just to ask again what grounds the priority that Kant documents we give to space over the general concept of spaces; we are now asking whether that grounding is extraphenomenological.

As I noted in section I, the literature has long reflected a deep division among those who answer in the affirmative. Some argue that Kant meant to ground the priority of space over spaces in the possibility of geometry; such persons read the third and fourth arguments of the Metaphysical Exposition prospectively, in the light of the following Transcendental Exposition of the Concept of Space. Others place the emphasis on the possibility of experience (understood in the Kantian sense of a subject making empirical judgments about objects around her); they read the third and fourth arguments retrospectively, in the light of the preceding first and second.20 This is a live issue in current Kant-studies, and there is of course no question of resolving it here.21 However, we must clarify several points in order to assess Durkheim’s reaction to Kant.

Crucially for Durkheim, Renouvier and Hamelin adopt neither the prospective nor the retrospective reading of Kant’s thesis of the representational priority of space over spaces. Instead, they treat the claim as self-standing. Because Durkheim cites Hamelin, his case is the one most immediately relevant. In the two sections of the Elkments principaux following the one we have been considering (titled “Les espaces non-euclideans” and “Les espaces B plus de trois dimensions”), Hamelin discusses the mathematical and geometrical views of Couturat, Delboeuf, Gauss, Helmholtz, Lechalas, Poincark, and Riemann, views which were (are) widely held to have rendered Kant’s philosophy of space of merely historical interest, but without so much us mentioning their connection to Kant. Clearly, Hamelin felt that he had already assessed Kant’s philosophy of space independently of his views on geometry.

Neither do we find a reference in Hamelin to the first or second argument of the Meta- physical Exposition. In the first, Kant writes that

Space is not an empirical concept which has been derived from outer experiences. For in order that certain sensations be referred to something outside me (that is, to something in another region of space from that in which I find myself), and similarly, in order that I may be able to represent them as outside and alongside one another, and accordingly as not only different but as in different places, the representation of space must be presupposed. The representation of space cannot, therefore, be empirically ob- tained from the relations of outer appearance. On the contrary, this outer experience is itself possible at all only through that representation. (A23B38)

This passage has of course been read by many different critics in many different moods. Here I wish only to echo those commentators who have pointed out that it does contain a natural answer to our question, viz., why must we accord priority to the singular intuition space over the general concept of spaces? Its answer is that in representing regions of space or the objects in them, I must presuppose that they lie at some distance from me. The presupposition of distance from me applies as much to delimited regions of space (instances of the general concept “space”) as it does to objects, so long as all are supposed to be “outside me.” (Even the delimiting cut must be outside me, over there.) I shall return to this point in concluding.

For the moment, let us note only that Durkheim, taking his Kant through Renouvier and Hamelin, had access to neither of these construals of Kant’s doctrine. Writing in 1912, Durkheim surveyed a philosophical landscape from which Kant’s distinction between concepts and forms of intuition had been all but banished. Most technically inclined philosophers of this period felt that the job had been accomplished by advances in geometry,

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physics, and logic so revolutionary as to have been unforeseeable in Kant’s day.22 I have been suggesting that, in Durkheim’s case, the job was accomplished through a one-sided treatment of Kant’s arguments in the “Metaphysical Exposition of the Concept of Space.”

This brief survey of Renouvier’s and of Hamelin’s case against Kant will have to suffice for our present purposes. (I hasten to add that the Traitt de Eogique and Eltments principaux are large works, each containing much of independent interest. My treatment has been selec- tive in the e~treme.)’~ To sum up, it appears to me that neither Renouvier nor Hamelin jeop- ardize Parsons’ recent judgment that Kant’s central phenomenological claims about space are “on the whole sound.”24 These claims include the priority of space over objects (we experience objects as in space, and for that reason we cannot construct the concept of space from relations between objects), and the singularity and boundlessness of space as experienced. If Durkheim is right that these results pose a threat to sociological inquiry into the form of human spatial representation, his appeal to Hamelin (and, tacitly, to Renouvier) will be in vain. At the same time, we recognize that this leaves unaddressed the deeper and philosophically most pressing issue, namely, the ground of the phenomenological priority of space over spaces.

IV. GENUINE COMPETITORS?

In this section I want to set out a way of seeing Kant’s and Durkheim’s projects as complementary rather than as the competitors Durkheim took them to be. My strategy will be the indirect one of first examining a bit of recent work in the sociology of knowledge and then moving back toward Durkheim.

The contemporary French sociologist Mona Ozouf has written influentially, and in a Durkheimian spirit, on the cognitive dimensions of the French revolution. In a recent collec- tion of essays on Durkheim, the historian Lynn Hunt remarks that Ozouf demonstrates that the social changes wrought by the revolution “transformed French . . . notions of space and time,” that they provided, “a new sense of space and time.”25 In particular, says Hunt, Ozouf shows that

The revolutionaries sought to repress all spatial reminders of the Catholic past. Festival itineraries either avoided the religious processional routes of the past or showed off new symbolic representations that purposely over-shadowed those reminders. On occasion, the festivals included the ceremonial burning of royalist and Catholic symbols. In their design of the festivals, the revolutionaries usually favored large open spaces. Open spaces had no memories associated with them and thus were well-suited for the expression of new values.26

Now if we read these lines in the context of our discussion thus far-a discussion of criticisms of Kant’s insistence that space is not a general concept - they would invite something like the following Kant-friendly response:

When Ozouf and Hunt write that “open spaces had no memories associated with them,” they aren’t really talking about spaces at all. They really mean that that open field or those gardens or that public square is free of unwanted associations. And when they write that, “the revolutionaries sought to repress all spatial reminders of the Catholic past,” they really mean that they tried to avoid the streets, buildings and the like the sight of which reminded them of the Catholic past. In short, when Ozouf and Hunt seem to be writing about space or spaces, they are really writing about objects in space. Indeed, if they wish their remarks to be true of the world outside us, they must be writing about objects in space.

450 TERRY F. GODLQVE, JR.

I say that Ozouf and Hunt would invite this response if they were writing in the philosophical context I have been developing. But Ozouf is a sociologist and Hunt is a historian-and in this context, the Kantian reply is badly out of place. It is dull and wooden and perhaps even patronizing. It calls to mind someone who insists on explaining the humor in an obvious joke. For of course Ozouf and Hunt intend us to interpret them as talking about objects in space and not about space or spaces per se. It is just obvious to all concerned that the streets and plazas and cathedrals of Paris-rather than the space or spaces-carry the unwanted associations and reminders. It is so obvious that we wouldn’t ordinarily point it out.

What does merit pointing out-what isn’t so obvious-is what supports our decision to take Ozouf and Hunt to be talking about objects in space rather than about space. In making this decision, we are thereby making Ozouf’s and Hunt’s remarks out to be true or at least plausible, whereas were we to interpret them as referring to space or spaces we would be portraying them as highly paradoxical. As Quine, and after him Davidson, Dennett, Put- nam, and others keep emphasizing, charity is ubiquitous in linguistic interpretation.

To return to Durkheim: Must we extend the same sort of interpretive charity to him? The following passage occurs just after he has announced that Hamelin has overthrown Kant’s view that space is an a priori intuition:

Besides, there are cases where th[e] social character [of spatial representation] is made manifest. There are societies in Australia and North America where space is conceived in the form of an immense circle, because the camp has a circular form: and this spatial circle is divided up exactly like the tribal circle, and is in its image. There are as many regions distinguished as there are clans in the tribe, and it is the place occupied by the clans inside the encampment which has determined the orientation of these regions. Each region is de- fined by the totem of the clan to which it is assigned. Among the Zufii, for example, the pueblo contains seven quarters. . . . Now their space also contains seven quarters, and each of these seven quarters of the world is in intimate connection with a quarter of the pueblo, that is to say with a group of clans. . . . Over the course of history, the number of basic clans has varied, and the number of regions has varied in the same wa . Thus, spatial organization was modeled on social organization and replicates it. (24-25) *7

This passage has been widely and productively read in the same empirical spirit as the one from Hunt - indeed, if our interests are strictly sociological or anthropological, any other reading would be unnatural. So considered, Durkheim is writing, as were Hunt and Ozouf, about objects in space. He is writing about people, the physical organization of their community, and how that organization governs their acquisition and use of the general concept of space. Interpretive charity prevails here too: Although in the more than eighty years since Durkheim published the Elemental Forms our knowledge of the peoples about whom Durkheim is writing has changed a great deal (indeed, the book’s ethnography is notoriously bad), we ignore these differences and take his and our beliefs to be about the same peoples.

So one way to view the Kantian and the sociological projects as complementary is by dissolving the potential or apparent tension on the sociological side. In this spirit, we have pointed out that Ozouf and Hunt, and, in one influential mood at least, Durkheim himself, may be fairly understood as really talking not about space but about objects in space.

At the same time, Durkheim flatly says he is opposing Kant in these pages. And, since we have seen that the position he sets up to criticize is at least recognizably Kantian-recall that he takes Kant to be committed to space as a “vague and indeterminate medium,” as “purely and absolutely homogeneous”-it would be patronizing in the other direction, and simply false, to say that he doesn’t also intend to be taken as talking about the single individual space (as distinct from the general concept).’’ Now when we accept Durkheim’s invita-

IS “SPACE A CONCEPT? KANT, DURKHEIM, AND FRENCH NEO-KANTIANISM 45 1

tion to inquire philosophically into the form of spatial representation characteristic of a particular community of persons, we find we must employ a form of charity very different from the one we have already encountered. Thus, in reading Durkheim’s account of the Zuiii, we imagine one of them orienting herself in the world- turning, perhaps, without changing position. Looking left and right, she now moves forward and shifts her attention toward what is out of sight, perhaps in imagination only, perhaps as accompanied by physical gesture. This activity sets the context, the “field,” we might say, into which she now introduces cuts suffi- cient to yield seven regions each of which will accept the general concept, “space.” The field itself as a singular individual must be presupposed, which is just to say that each delimiting cut must be placed at some distance from where she finds herself.

The question of charity arises when I acknowledge that, in so arguing, I have exported to this person what I know to be true of myself. That is, my conclusions are based on my imaginative construction of what I take to be possible for her in orienting herself in the world. I take it that we orient ourselves alike, and that, as a consequence, her cognitive com- merce too must be with objects and spaces located at some distance from where she finds herself. This judgment should not be seen as empirically motivated; it is not based, for example, on a Quinean appreciation that we are similar enough sorts of animals, equipped with similar enough sorts of sensory and cognitive apparatus. The judgment cannot be made or tested in the light of experience, because it claims that space is a condition of experience. And in fact I am taking neither myself nor this person as objects in the world, but rather am acknowledging a condition that makes it possible for creatures like me to confront a world at all. If I am pressed as to how I know she is like me, I can only answer that likeness in respect of spatial orientation is a condition for making sense of whatever empirical differences we may have-including cultural (or other) differences in our ways of representing the parts of space. If this is charity, it is of a primitive form indeed.29

Thus, when we approach Durkheim’s work in the philosophically weighty sense that he intended, it is neither dull nor wooden to advance the Kantian claim that the variation in social organization he describes must have taken place in one continuous space. (A further claim would be that the fact that we can meaningfully disagree with Durkheim on this point shows that it is not an analytic a priori truth that the general concept of space presupposes the a priori intuition.) From the Kantian point of view, Durkheim is offering to explain how people come to think differently about the parts of space, about how they acquire and apply the general concept of it. This is, after all, the most natural way to read Durkheim’s comments on the ZuAi, notwithstanding Durkheim’s stated belief that they cut against Kant. Here then is another sense in which Kant’s and Durkheim’s projects are not competitors. Kant’s theory of space as a pure intuition issues in the derivative notion of parts of space, which, in turn, is one place where Durkheim’s sociological theory finds natural application (and is one place where Durkheim actually applies it). The two are thus seen as complementary, whether we take the sociologist as interested in the human representation either of objects in space or of the parts of space itself.

I have faulted Durkheim twice-first, for thinking that Hamelin and, though he goes unnamed, Renouvier, had overturned Kant’s denial of conceptual status to space; second, and more important, for concluding that his and Kant’s projects were genuine competitors. But though my remarks have been largely critical, it has been as much a part of my project here to see the Elemental Forms’ concern with how we orient ourselves in space as preserv- ing contact with Kant’s motivating insight in the Critique’s “Metaphysical Exposition of the Concept of Space.” Focussing narrowly on the doctrine of space, we might summarize by saying that what became obscured between Kant and Durkheim was the distinction between


space as the field of possible (outer) experience and the culturally bound ways in which that field gets divided up. More generally, what was lost was the philosophical standpoint from which this distinction can be made plausible. That is the standpoint of one who recognizes his unavoidable conformity to rules while conforming to them; in the present case, one who recognizes the absurdity in claiming the right to cognize an object in space not located at some distance from where he finds himself. This, as I have noted, is not advanced as an empirical claim, though it purports to offer a background against which to locate the various empirically motivated ways we humans have come to represent the parts of space.

Retreating to a still broader level of generality, our theme has been the breakdown of Kant’s doctrine of space as a form of outer intuition. Recent work on this theme has mainly focused on the relevance of the mathematical and physical developments of the nineteenth and early twentieth century on scientifically minded philosophers, and has emphasized the lingering importance of Kant for, among others, the logical positivists. These authors - recent, positivist, and nineteenth century alike-take Kant’s commitment to the a priority of Euclidean geometry as a premise for his view that physical space, space as intuited, is Eu- clidean.

But Kant’s philosophy of space was eroded by a second stream of nineteenth-century thought, one tracing its source to the German Idealists. This tradition places the emphasis on Kant’s phenomenological claim in the Metaphysical Exposition that we can only individuate regions of space by their location in the one boundless space. Rather than taking Kant’s Eu- clidean allegiance as a premise for this conclusion, its members take the phenomenological claim as self-standing-thus, Renouvier and Hamelin. But when taken as self-standing, the claim is unconvincing; we want to know why the singular intuition must precede the general concept. It is as a member of this tradition that, in the Elemental Forms, Durkheim con- cludes that Kant has “merely repeated the question in slightly different terms” (494). Durkheim responded by dramatically changing the terms of the discussion, from the individual to the social, a brilliant move and one formative for a range of those disciplines that came to be known as the social sciences.30 As I have been urging for the last several para- graphs, Durkheim was deeply right to see Kant’s theory of space as an a priori intuition as tied to an individualistic conception of epistemology. Whether he correctly perceived its bankruptcy is another matter. I have tried to sketch-alongside these two critical tradi- tions -a third position which remains genuinely Kantian and which promises peaceful co- existence with Durkheim’s sociological programme. To establish its philosophical cogency and textual credentials would of course be a much larger ~ndertaking.~~

NOTES

1. Immanuel Kant, Inaugural Dissertation, David Walford and Ralf Meerbote, Trans. and Ed., Kant’s Theoreti- cal Philosophy, 1755-1 770 (New York: Cambridge University Press, 1992), p. 396 [2:402]. Bracketed references will throughout refer to the Akademie pages.

2. Kant, Critique of Pure Reason, A25B40; citations will be to the Kemp-Smith translation (New York St. Mar- tin’s, 1963), with some modifications, and will henceforth appear in the text.

3. But neither were Becker, Carnap, Helmholtz, Husserl, Poincarb, and Weyl willing to endorse a thoroughgoing empiricism. Friedman details the variety of ways in which they tried to show that empirical physics presupposes Kant’s conception of space rather than either supports or refutes it; see, “Camap and Weyl on the Foundations of Geometry and Relativity Theory,” Erkenntnis 42 (1995): 247 -260.

4. Emile Durkheim and Marcel Mauss, “De quelques forms primitives de classification: contribution h I’btude des reprisentations collectives” L‘AnnCe sociologique, 6 (1903): 1 -72; Rodney Needham, Trans., Primitive Classi- fication (Chicago: University of Chicago Press, 1963); chapter 3 treats space, four time.

Durkheim, Elemental Forms of Religious Life; citations will be to the Joseph Ward Swain translation (New York: Humanities Press, 1965), and will henceforth appear in the text. I have occasionally modified Swain’s transla-

5.

IS “SPACE” A CONCEPT? KANT, DURKHEIM, AND FRENCH NEO-KANTIANISM 453

tion from the French, Les formes klCmentaire de la vie religieuse: Le systPm totemique en Australie (Paris: F. Alcan, 1912). I have also benefitted from the new translation by Karen E. Fields (New York: Free Press, 1995). 6. My aim here is limited in several respects. First, I follow only the explicit footnote trail leading from the

Elemental Forms to Hamelin to Renouvier, leaving out Durkheim’s-and Durkheim’s and Mauss’s-related work. Second, I make no attempt to characterize the broader currents of nineteenth-century French neo-Kan- tianism; of particular importance would, of course, be the views of Durkheim’s teacher, Emile Boutroux. Fi- nally, I am ignoring the prevailing institutional climate which, according to Phillipe Besnard, encouraged Durkheim and his circle-composed mostly of disaffected agrkgks in philosophy-to adopt a critical stance toward the philosophical tradition. Besnard emphasizes the need “for sociology, in order to legitimate its scien- tific credentials, to progressively carve out its own field by taking over material originating in other disciplines” (“The ‘AnnBe Sociologique’ Team,” in Besnard, Ed., The Sociological Domain: The Durkheimiuns and the Founding of French Sociology (New York: Cambridge University Press, 1983), p. 15. In this connection, see also the contribution of John Brooks to this volume. For an excellent discussion of the influence of Renouvier and Hamelin on Durkheim and Mauss, see Steven Collins, “Categories, Concepts or Predicaments? Remarks on Mauss’s use of Philosophical Terminology,” in Michael Carrithers, Steven Collins, and Steven Lukes, Eds., The Category of the Person: Anthropology, Philosophy, History (New York: Cambridge University Press, 1985), pp. 46-82. 7. Manley Thompson, “Unity, Plurality, and Totality as Kantian Categories,” The Monist 72/2 (April 1989):170. 8. “Now in space there is nothing real which can be simple; points, which are the only simple things in space, are

merely limits, not themselves anything that can as parts serve to constitute space” (B419; cf. A169-70D211 [cited in Thompson, 186, n.101).

Kant, Lectures on Logic, J. Michael Young, Ed. and Trans. (New York: Cambridge University Press, 1992). p. 366. For discussion of the issues surrounding the dating of the Vienna Logic and for further references, see Young’s, “Translator’s Introduction,” pp. xxv -xxvi. 10. Citing A654-56/B682-84 in support, Friedman also makes this point in Ch. 1 of his, Kant and the Exact Sci- ences (Cambridge, MA: Harvard University Press, 1992), p. 67 (a revised version of, “Kant’s Theory of Geometry,” Philosophical Review 94 [1985]: 455-506). 11. Charles Parsons imagines this objection in “The Transcendental Aesthetic,” in Paul Guyer, Ed., The Cambridge Companion to Kant (New York Cambridge University Press, 1992), pp. 72-3. 12. For discussion and further references, see Steven Lukes, Emile Durkheim His Life and Work: A Historical and Critical Study (New York: Penguin, 1973), pp. 54ff., 435ff; S. G. Stedman Jones, “Charles Renouvier and Emile Durkheim: ‘Les Regles de la Methode Sociologique,’ ” Sociological Perspectives 38 (1995): 27-40; DBnes NBmedi and W. S. F. Pickering, “Durkheim’s Friendship with the Philosopher Octave Hamelin: Together with Translations of Two Items by Durkheim,” British Journal of Sociology 46/1 (1995): 107-25; and Ivan Strenski, “Durkheim, Hamelin and the ‘French Hegel,”’ Historical Reflections 16/2-3 (1989):

13. Lukes reports Durkheim’s advice to a colleague thus: “If you wish to mature your thought, devote yourself to the study of a great master; take a system apart, laying bare its innermost secrets. That is what I did and my educa- tor was Renouvier” (Emile Durkheim, p. 54). 14. I will be quoting from the second edition of Hamelin’s Essai sur les Cle‘ments principaun de la reprdsentation (Paris: F. Alcan, 1925); citations will appear in the text. For help with the French I thank David Booth; responsibil- ity for any remaining errors is mine. 15. I have not been able to find this point in Hamelin; but compare Renouvier, Trait6 de logique gknCrule et de logique formelle:

9.

135-70.

The intuitive character that knowledge takes on in relation to sensible objects-that is to say, to the phenom- ena manifesting all the conditions of space and time-introduces no more of a difference between size and duration, on the one hand, and all the other notions, on the other hand, than there is, for example, between a cause and a number, between a number and a quality. (2nd ed. [Paris, 18751, three vols., p. 209; all references will be to vol. I11 and will appear in the text)

16. The argument, if it is one, is difficult to parse. The phrases “vague and indeterminate” and “purely and absolutely homogeneous” recall the priority Kant gives to the representation of space as “boundless” and “all-embracing.” Taken as such, it is true that it gives us nothing “to hold on to,” in the sense that we are representing space as whole (as without parts). But we have seen that Kant recognizes our ability to introduce “cuts”-han- dles, to preserve Durkheim’s imagery. In the second half of the passage, Durkheim is apparently attributing to Kant the view that regions of space are in themselves “qualitatively equivalent.” The worry then seems to be over how I am to individuate objects which appear to exist in different regions of space if spaces are “mutually interchangeable.” But this again misses Kant’s insistence on the priority of the representation of space as boundless. Whatever I cognize as outside me must be located in a single, unique space-only then can the orientation of the parts of space or the objects in those parts be fixed as differently located. I return to this point in my conclusion.


17. For example, the appeal to a “confused intuition” of “vague space” seems to invite the rejoinder-conge- nial to either a Kantian or a relational account of spatial representation-that we do not intuit space as an individual at all. Further, it is not clear how we are to understand the relation Renouvier intends between points and space; in particular, whether (against Kant) we are to take points as having extension and so as able to constitute parts of space; if so, then “constitute” rests uneasily with “limit” (how to introduce a limitation into what has not yet been constituted?). But without extension it is not clear how to spell our their limitative role. 18. Friedman, Kant and the Exact Sciences, p. 69. Parsons notes that this is the distinction Kant “ought” to make, and documents Kant’s (at least) terminological inconstancy from the Dissertation through the two editions of the Critique (“The Transcendental Aesthetic,” p. 94). 19. I pass over Renouvier’s highly implausible treatment of (what we are now calling) the general concept of space as on par with Kant’s pure categories. Kant would surely view the privileged status that Renouvier accords l’espace vague as an invitation to reassert the Critique’s basic claim that, whereas categories are “concepts of an object in general” (B128), we individuate those objects by their spatiotemporal location. 20. References to the former tradition of interpretation will be found in Parsons, “The Transcendental Aesthetic,” pp. 97-98 notes 36, 38 and 41; to the latter, in Robert Pippin, Kant’s Theory of Form: An Essay on the Critique of Pure Reason (New Haven: Yale University Press, 1982), p. 55, n. 4. 21. Currently, the prominent discussants are far from consensus. Consider, for example, the concluding sentence of the third argument in Metaphysical Exposition (A25D39; quoted up to this point in section I). After making his whole-before-parts claim, Kant adds:

So too geometrical principles, that, for example, in a triangle two sides together are greater than the third, can never be derived from the general concepts of line and triangle, but only from intuition, and this indeed a priori, with apodeictic certainly.

Of this sentence, Friedman comments, “In the end, therefore, Kant’s claim of priority for the singular intuition space rests on our knowledge of geometry” (Kant and the Exact Sciences, p. 70). Pippin’s rather different assessment is that, “Kant gratuitously adds a remark about the possibility of geometrical judgments which obviously be- longs in the Transcendental Expositions” (Kant’s Theory ofForm, p. 64). 22. For the details of this story, see, Coffa, The Semantic Tradition From Kant to Carnap to the Vienna Station (New York: Cambridge University Press, 1991), and Friedman, Foundations of Space-Time Theories: Relativistic Physics and Philosophy of Science (Princeton: Princeton University Press, 1983). 23. For example, Hamelin denies Kant’s appeal to incongruent counterparts. In a series of writings from 1768 to 1786 (but not in the Critique) Kant claims that we cannot distinguish on purely conceptual grounds between objects that are mirror image reflections of one another, for example, left and right hands or spirals. On the contrary, says Hamelin,

The qualitative character presented by a screw turning to the left is to us as much conceptual as the red color- ing or the warmth presented by a body. And we are supported in our opinion by the fact that these qualities combine with others in the constitution of species-certain snails, to recall Kant’s own examples, spiraling to the right and others to the left; beans twisting to the right around a pole, while hops adopt the opposite direction. (85)

I pass over this issue because Hamelin nowhere engages or even mentions Kant’s reason for claiming otherwise; namely, that we require a prior representation of space in which to orient the snails or beans or hops. Up to date references to this ongoing debate may be found in Parsons, “The Transcendental Aesthetic,” pp. 93-94n.20, 9511.27, 96n.28 and n.29. 24. Parsons, “The Transcendental Aesthetic,” 72. 25. “The Sacred and the French Revolution,” in Jeffrey C. Alexander, Ed., Durkheimian Sociology: Cultural Stud- ies (New York: Cambridge University Press, 1988), pp. 29, 30. Hunt is commenting on Ozouf, La F3te rivolution- naire 1789-1799 (Paris: Gallimard, 1976), pp. 280-90. 26. Hunt, “The Sacred and the French Revolution,” p. 29. 27. I have omitted Durkheim’s footnotes to his ethnographic sources; for references, see Fields’ translation, pp. 11-12. 28. Charity again: As I noted above, space is not a “medium” for Kant in any sense that implies independent reality, but we discount that error in light of the context. That is, Durkheim describes a Kantian-enough view so as to make it unreasonable to dismiss his claim to be opposing Kant as itself unreasonable. 29. Readers determined to find a point of genuine opposition between Kant and Durkheim may look to 54 of the Conclusion to the Elemental Forms. After remarking that the individual, “is situated at a determined point in space,” Durkheim continues: “However, all these [spatial] relations are strictly personal for the individual who recognizes them, and consequently the notion of them which he may have can in no case go beyond his own narrow horizon” (489). Here the Kantian project may seem sharply opposed, that is, as aiming precisely to “go beyond,” to tease ob-

IS “SPACE A CONCEPT? KANT, DURKHEIM, AND FRENCH NEO-KANTIANISM 455

jectivity out of the conditions for one’s own “narrow horizon.” But it seems to me more than charitable to think that Durkheim appreciated this point. 30. Compare this passage from Robert Brandom, commenting on John McDowell:

I want to claim that the mistake is to begin with to individualize the space of reasons. The complaint I want to make about McDowell’s discussion is that he makes nothing of the essential social articulation of that space. . . . He says the thought is that we ought to be able to achieve flawless standings in the space of reasons by our own resources, without needing the world to do us any favors; but for all he says here or elsewhere, this us could be each of us, individually or by ourselves, rather than all of us collectively. But this difference makes all the difference.

Without wanting to push the analogy too far, the passage does neatly capture Durkheim’s attitude toward Kant, at least the Durkheim I am describing. (“Knowledge and the Social Articulation of the Space of Reasons,” Philosophy and Phenomenological Research 65/4 [December 19951: 102 [author’s emphasis]; commenting on McDowell’s, “Knowledge and the Internal,” same journal, 877-891 .) 31. For helpful comments and suggestions on several drafts of this paper, I thank John Brooks, Warren Frisina, Bob Holland, Leon Pearl, Warren Schmaus, and my colleagues in the Hofstra University Philosophy Department.

is “space” a concept? kant, durkheim, and french neo-kantianism

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