Glouberman.kant's Diversity Theory a Dissenting View (Article)

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Kant's Diversity Theory: A Dissenting ViewAuthor(s): Mark GloubermanSource: History of Philosophy Quarterly, Vol. 7, No. 4 (Oct., 1990), pp. 461-474Published by: University of Illinois Press on behalf of North American Philosophical PublicationsStable URL: http://www.jstor.org/stable/27743953 .Accessed: 03/11/2013 14:45

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History of Philosophy Quarterly Volume 7, Number 4, October 1990

KANT'S DIVERSITY THEORY: A DISSENTING VIEW

Mark Glouberman

I. No Breakthrough

CONSENSUS

reigns among interpreters that a crucial "strategic move Kant made" in the drive to the critical position was his development

of a "theory of the radical diversity of [sense and intellect]."1 But the theory of sense/intellect diversity, even if correct, is no unprecedented Kantian

discovery; no Kantian 'breakthrough'.2 In endorsing diversity, Kant does

not do justice at long last, after a century of Cartesian bumbling, to the structure of cognitive awareness. Rather, he reverts to a position his

modern predecessors rejected. Specifically, he opposes a reduction to which

the Cartesians were, as a condition of solidifying the emerging scientific

worldview, committed.

IL A Consequence of the Usual Interpretation

On the consensual construal, Kant is first among the moderns to appreciate the root diversity of the receptive and the organisational functions in cogni tion. If so, the earlier, Cartesian, conceptualisation of experience competes

with Kant's in name only. That view, for obliterating an essential difference

between the functions, stands to the Kantian as the position ascribing distrib

utivity of addition over multiplication?[a + (be)] = [(a + b)(a + c)]?stands to standard arithmetic.

This runs afoul of Kant's declared opinion. Kant contrasts the critical

doctrine, transcendental idealism, with transcendental realism. And the

latter he explicitly identifies as the position espoused by those who deny diversity.

The clash between the contrastlessness that the interpretation implies, and the contrast that Kant asserts, would only seem harmless to those who

independently regard (what is identified as Kant's position) with favour. And, in the event, the consensual position's advocates are independently committed to (what they take to be) a broadly Kantian view. As a result, any treatment of experience worthy of the name gets filtered by them

through a Kantian lens?a mode of handling guaranteeing that no pre


462 HISTORY OF PHILOSOPHY QUARTERLY

Kantian position will be portrayed as standing in any relation of genuine theoretical opposition to Kant's.

III. Reduction

The debate between Kant and the pre-Kantians is a fairly standard reduction debate. The various mathematical positions taken on the ratio

nal/irrational duality supply a helpful parallel.

From the time the irrationality of /2T was, much to the horror of the

Pythagoreans, discovered,3 the radical irreducibility of irrationals to ratio nals was generally held. Some twenty-five centuries later, however, Rich

ard Dedekind explained how, by the device of the Dedekind Cut, to 'construct' irrationals out of rationals.4 So a "mathematical ontology" ad

mitting only the rationals is sufficient for netting the irrationals.

Now the earlier theorists in the mathematical case deny reducibility. In the philosophical case, the opposite is, I maintain, true. This merely indicates that the philosophical reduction debate, like many such debates, is ongoing. The early moderns actively deny a yet earlier, pre-modern, thesis of diversity. Kant, in opposing them, is therefore effecting a mediated reversion to a form of the pre-modern position. Indeed, I shall myself attempt to restart the debate by importing some recent materials.

IV Two Factors vs. One Factor

Confronting us is an historical case in which a one-factor view (the view

of the Cartesians, the anti-diversity view) is replaced by a two-factor one

(Kant's, the diversity view). Also, proponents of the former claim that the two-factor view is reducible to the one-factor one.

Analytical readers of the classical modern texts, due to a common feature of their training, are poorly equipped to see the matter this way. I allude to the fact that analysts, as inheritors of the modern tradition, do not

usually extend their gaze back farther than Descartes, modern

philosophy's official patriarch. But the Meditations certainly does not

spring up in a vacuum. Descartes is striving, by and through the work, to

supplant an entrenched, though increasingly beleaguered and weary, scho

lastic worldview.

Kant is opposing the pre-Kantians. It by no means follows from this that his view lacks recognisable positive antecedents. For the pre-Kantian

moderns were also, in their time, oppositionists. In the event, those iden

tified by Kant as denying diversity are, in turn, combatting a broadly Aristotelian worldview.

Elaborated slightly, my claim is that Kant's diversity theory reflects a


KANTS DIVERSITY THEORY 463

constitutive feature of an Aristotelian view. And once we identify that

feature, we will ipso facto see the Platonic slant of the Cartesian position.

Formally, the contrast drawn pits a one-factor against a two-factor

account. To what, now, does a Platonist intone a "1" to the Aristotelian's

"2"? An Aristotelian maintains that both matter and form are metaphysi cally fundamental factors; the Platonist holds that form alone has basic status. As this indicates, I see Kant's diversity theory as a denial, trans

posed into an epistemological register, of a broadly Platonic position on basic metaphysical constitution.

V Fundamental Duality

Some will claim that even if the contrast between a Platonic and an Aristotelian view on the matter/form duality has Kantian reverberations, these are distant from Kant's sensibility/understanding duality. Before

working out my thesis, let me outflank the objection by looking at an influential analytic reading of Kant.

The substantive part of PF. Strawson's commentary on Kant's first

Critique commences thus:

The duality of intuitions and concepts is...one form or aspect of a duality which must be recognised in any philosophy which is seriously concerned with human

knowledge, its objects or its expression and communication.5

Contemporary philosophers of analytic bent will feel comfortable with Strawson's use of the duality: the duality counts for them as an un

hypothetical starting point. However, as a matter of Kant-interpretation, a mistake has been made already.

Suppose we came upon a document beginning with the following cate

gorical declaration:

The duality of form and matter is a duality that must be recognised in any philosophy that is seriously concerned with the objects of human knowledge.

These words, formatted ? la Strawson, echo the position in Aristotle's

Metaphysics. But the status assigned to the fonn/matter (henceforth: F/M) duality is scarcely regarded by the Stagirite as uncontroversial. For him to treat it as axiomatic would be to invite a charge of question-begging from

members of the audience. In the event, Aristotle argues for the basic status of the F/M-duality?most particularly against his Platonic mentors.

That the concepl/instance duality?Strawson's logicised version of the

sense/Intellect duality?can be advanced as axiomatic in Strawson's frame

of reference does not mean that it enjoys axiomatic standing in Kant's.

Strawson's "axiom" of interpretation is affiliated to modern, Fregean, logic. But Kant's use of the concept/intuition duality is embedded in a rather different matrix of historical facts.6 It remains to link the concept/intuition duality with the F/M-duality, thereby showing that historical difference to be philosophically relevant. The issue at present is, however, more



restricted. Can any sense can be made in Fregean terms of the idea of a

rapprochement between concepts and instances? Either way, Strawson, as

a Kantian interpreter rather than one who uses Kantian texts for his own

purposes, is in trouble. If the affirmative, Strawson himself, for operating with the duality as though it were irreducible, would be begging the

question against Kant's opponents. If the negative, then the interpretative pertinence of the Fregean duality would be impugned. For, as explained, Kant's self-representation leaves no doubt that he regards the critical stand as genuinely contrastive.

VI. More F

The pre-Kantian denial of diversity has here been identified with the Platonic denial that the F/M-duality is basic. To show how this last emerges in the Cartesian context, let me transfer to expressly scientific terms.

What kind of science did Descartes encounter in his intellectual minor

ity? (1) Pre-modern, Aristotelian, science?"natural philosophy" might be better?is fundamentally qualitative. (2) In this treatment of nature, there is a multiplication of categories of being and an associated explosion in

principles of explanation.

Consider (1). Why, for the Aristotelian, is the treatment of nature qual itative? A metaphysical answer is given: the forms of things exercise their effects via the matter which they in-form. In (pure) geometry, circularity is exact, formulae like "A = nr2" satisfied. But the fact that the geometrical form (F) is, in the physical realm, exemplified in matter (M) compromises the exactitude. Similarly, a machine design may, from an engineering point of

view, be perfect. But the actual machine, fashioned in steel, will suffer from all manner of (non-design) flaws and failings: rusting, metal fatigue. Because of the contribution of the extra-formal element, the precision characteristic of

the formal level is upset on the level of concrete particularity.

What about (2)? Even if the formal precision were not compromised by the material element, the multiplicity of irreducible forms would still

generate a multiplicity of laws clashing with the requirements of system. The resulting science, even if quantitative and exact, would correspond to

Chinese idiograms, which must be learned individually.

Multiplicity anathema to system properly so-called, and inexactitude anathema to science as we regard it, are thus characteristics of the Aris

totelian treatment of nature. And, as (1) and (2) indicate, the deviation from our view is linked with the F/M-duality.

How would a proponent of the nascent modern science react, a proponent who saw the success of modern science as hostage to the provision of an

alternative metaphysical foundation? In all likelihood, such a one would

challenge the F/M-duality.

This, in a nutshell, is what transpired. The genesis-fable of modern



science has Aristotelianism collapsing with the simultaneous thud of the balls dropped by Galileo onto the Pisan piazza. Even if the experiment was

performed, the balls are most unlikely to have impacted at one time. The real point concerns the way a difference in time of impact (including a null

difference) is explained, viz. by citing more factors of the same sort. A pebble does not "naturally" fall more slowly than a boulder. Rather, variable frictional forces and variable air currents produce an overall effect on the one different from that produced on the other.

Where an Aristotelian natural philosopher, committed to the F/M-dual ity, sees the F-confounding influence of M, Galilean eyes perceive the effect of more factors of the sort Aristotelians assign to the F-compartment. Similarly, for the Galilean, heavenly motion does not differ in kind from terrestrial. Rather, the various forces acting on a planetary object, re

solved, yield curvilinear motion. In both cases, M, as an independent factor, is eliminated. Formally put: F+M is mapped onto F.

Did the actual progress of science require more than that more F be identified? Wouldn't showing a pre-modern that what he or she took as a

metaphysically grounded deviation from formal explicability is receptive to formal analysis of an unsuspected kind provide the impetus to closer observation? As the case may be, the mapping of F+M onto the F-part of itself supplies an abstract basis sustaining the changed approach, sustain

ing it, that is, despite the myriad cases where the "more" resisted disclosure

by the (crude) experimental means that were available.

The pre-modern-to-modern move is from a two-factor (F and M) to a

one-factor (F) conception. Descartes's identification of matter with (pure) extension is a salient philosophical expression of the move. This, to put it

crudely, brings Platonic formality down to earth.

A last point here concerns the term "rational." Platonists and Aristote lians both agreed that matter is an irrationaliser.7 Because Aristotle

regarded matter as metaphysically basic, it would have been dogmatic for him to hold that the world was rationally penetrable.8 Modern science, in

principio, took the Platonic side; and this came to metaphysical expression in the banishment of matter, i.e. that which in principle blocked the mind from achieving a transparent grasp of the world, from the basic level.

VIL A Generic Issue

The two major elements of our story are: the F/M-duality; the Kantian

sense/intellect duality. The latter, I hold, is an epistemological relative of the former. But without appreciating the generic character of the issue, the

spirit of much of Kant's discussion, and the detailed content of some, will not be understood aright. Note for example that one of the functions of the Aristotelian M-component is to individuate particulars sharing the same form. Similarly, on Strawson's representation of the concept/intuition dis



tinction, space is represented as doing individuative work for Kant. There is however a great difference between the Aristotelian citation of M in the

mentioned capacity and the Strawsonian citation of space. The Aristotelian

analysis is concentrated on particulars as a type; Strawson's focusses on

particulars as particulars. Aristotle is asking whether there is more than F to the type particular thing. Strawson is asking how instances of that

type, i.e. concrete particulars, are distinguished from other instances. The

first of these questions belongs to general ontology; the second, to the

theory of reference. In the sequel, my discussion will focus entirely on the

type-question. As will emerge, much of what Kant says about space con

cerns this matter.

I propose now to introduce some modern materials to revivify the generic debate between Kant and the others: to make something in current terms of the anti-Kantian thesis that the duality of data and organisation is not basic.

VIII. Modern Materials for the Reduction of M

For the Aristotelian, the applicability of mathematics to the world is an article of hope or faith, not of knowledge. Descartes's identification of

matter with extension functions as a direct repudiation. Prima facie, a

strong defense of the Cartesian view would consist in showing that what the Aristotelians account material is itself simply (more) form. Develop

ments in fractal geometry can be enlisted to cobble up something that fills this bill,9 fractal mathematics operating on the F/M-duality much as the Dedekind construction works on the rational/irrational duality.

The fractal case supplies two exploitable ideas. The first is that of a fractional dimension; for instance, a non-Euclidean geometrical object whose dimension lies between 1 and 2. The second is that of an informa tional bonus. Combined, these ideas can be used to breathe new life into the dispute between Kant and his predecessors, the Leibnizeans especially, on the matter of the synthetic a priori. Before applying CPR, let me first sketch the mathematical case.

The Koch ("snowflake") curve is a regular fractal. To construct a sample,

begin with an equilateral triangle with sides of unit length. Using as the base the middle third of each side, another such triangle is drawn out

wards, and the base erased. After the first step?three additional triangles have been constructed, one on each side of the original?we have a polygon

(the outline of a Magen David) whose perimeter relates to the perimeter of the original in the ratio 4:3. Each subsequent construction extends the

pattern. The perimeter of the figure tends, as can easily be seen, to increase

without limit. At the third step, the perimeter is 16/9 (i.e. 42/32) units, at the fourth 43/33, and so on. The end result is a regular polygon of finite area with an infinite perimeter.

What is the dimensionality of the curve's perimeter? If we envisage the



perimeter at, say, 5 steps along, we get a very spiky line. As the construction

continues?keeping in mind that the perimeter's length tends to infinity? the spikes come arbitrarily close to each other. At the limit, they are

adjacent?"touching": the perimeter has a breadth. According to fractal

theorists, the dimensionality of the Koch curve's perimeter is log 4/iog 3, a value between 1 and 2. (Mutatis mutandis, we can generate surfaces whose

dimensionality computes out between 2 and 3.) As mentioned anent the Dedekind treatment of irrationals, we thus have here an infinitary reduc tion: in the case of the Koch, a reduction of items of n-dimensionality (2>n>l) to items of 1-dimensionality.

As for the other pertinent feature of fractals, let us construe "informa tion" as follows. The more points on a curve we have determined, the more

information we have about the curve. Suppose we begin with a compass

whose ends are separated by 1 unit. Starting at the vertex of the original equilateral triangle, we can, by swinging the compass until it contacts the

perimeter of the polygon, fix 3 points: the vertices. But suppose now we switch to a compass separation of 1/3 units. The information given by the same process is 12. That is, as the unit is decreased by 3, the information increases by 4. Fineness of measurement thus, in such a case, carries an

informational bonus.

This, in general, is a fact about natural objects. Such objects being irregular?fuzzy, bumpy?greater refinement in measuring units (in effect,

higher resolution) yields proportionately more information. If information

(x) is plotted against fineness of investigative grid (y), x's value increases more quickly than y 's.

We can return to the philosophical issue. Let me discuss Kant's position in reverse, beginning from his applied, "metaphysical," discussion and

moving thence to the core "transcendental" treatment in the Critique.

IX. Kant in Defense of Mathematical Physics

Kant, in a fashion echoing commonsense, denies the reducibility of matter to form. He opposes the counterintutive Cartesian equation of matter and extension. Thus, in the 1786 Metaphysical Foundations of Natural Science, Kant asserts that "[b]y the proof of the infinite divisibility of space, that of matter has not by a long way been proved."10 But Kant is

by no means an opponent of the scientific revolution. He also states that

"a doctrine of nature will contain only so much science as there is applied mathematics in it."

The tension here is palpable. While applauding the revolution, Kant

rejects precisely that move initially perceived as pivotal. He admits that the "matter" of empirical knowledge is ineluctably extra-formal. But in face of the criticism of the Cartesian view with which this admission tradition

ally consorts, the Kantian project is to secure the early gains against the



critics. Expressed in our terms of discussion, the aim is to revert to the more natural Aristotelian position about F/M without opening science to a principled threat of irrationality.11

With respect to the basic science, physics, Kant holds, for reasons I will

display later, that there is nothing in the notion of force?the notion that

distinguishes physics from geometry?that stands in the way of the appli cation of the formally specified features of space or extension.

To prepare the ground for the preceding claim, Kant argues in the Foundations that, so far as the requirements of physics go, the common

sensical notion of a 3-dimensional spatial occupant can be eliminated in favour of the notion of a force, which, though it has 3-dimensional effects, is not itself 3-dimensional. In the event, Kant's argument for the elimina tion begs the question.12 And, if you think about it for a moment, how could the admission of Ms irreducibility?which is what the denial that force is a geometrical notion amounts to?be compatible with the Cartesian result? If the physical world involves more than can be expressed in F-terms, how could it fail to be the case that our information gathering activities, as natural scientists, are fundamentally open-ended from the standpoint of F?

The fractal example supplies us with a basis for mediating between the

Cartesians, on that point where their position was, for the reasons Kant

felt, implausible, and Kant, whose own position, for granting F/M-irreduc

ibility, turns dogmatic on the issue of the foundations of science.13 The fractal case vouchsafes a reasoned basis for equating "information addi

tional to that available on some level" with "more F"

Consider again the issue of whether the contours of natural objects can

formally be captured otherwise than approximatively. In Euclidean terms, approximations are the most we get. But the fractal geometer supplies non-Euclidean formal structures that capture exactly (or at any rate in

principle capture better, and that suffices for here) what slips through the Euclidean net. Thus, while the Koch is pure form?i.e., a formal specifica

tion, unlike the specification of a machine by means of the engineering blueprint, exhausts its character?the curve's outlines are, relative to

Euclidean formality, uncapturable. Like the material in which a machine

design is exemplified, the fractal outline or perimeter is, relative to Euclid ean formal structure, something additional.

Let me put this more abstractly. If an item of spatial dimensionality n can be constructed entirely out of items of dimensionality m, where m


any concretised m -structure will have characteristics which, from the

standpoint of a pure m-structural specification, are alien. In effect, the

functional effects associated by the Aristotelian with the material element are reduplicated without any material element being irreducibly present.

As this indicates, the fractal idea supplies a basis for mediating between the warring parties. While agreeing with the Platonists on the mappability of F+M onto F, we do not relinquish the functional reality of M. So neither side gets exactly what it wants.

X. The Modern Positions and an Overlooked Possibility

Kant, defending the diversity theory, charges that Leibniz, having "sought for all representations of objects, even the empirical, in the [intel lect]," "left to the senses nothing but the despicable task of confusing and

distorting the representations of the former."14 Aided by the preceding materials, we can hack out a sort of via media.15

Let me, to begin, chart the two modern positions. They, and the relations between them, can be fixed by reference to a pair of parameters: (i) attitude towards the F/M-duality; (ii) line taken on rationality (= R).

The Cartesians held that the (pre-modern) view of the world as closed to

principled rational penetration (as typified by the feeling that mathemat ical representability, or purely formal treatment, where it proves possible, is fortuitous) was due to failure to appreciate that F+M can be mapped onto

F. Undischarged -R (irrationality) in the pre-modern view is a residue of unreduced M. Thus?the Cartesians held?once the mapping is accom

plished, the spectre of -R would, in principle anyway, be driven off.

The Kantian position is that the Aristotelians are right about F/M. But, by arguments I cannot enter into here, Kant claims that "enough F?* is

guaranteed to underwrite the rationality (R) of science.

Suppose now that, with the Cartesians, we grant that F+M can be mapped onto F IT DOESNT follow that -R HAS been overcome. The elimination of M is its elimination at the basic level. M is not banished; it is, as indicated, reduced. But why can't the defining functional characteristic of M, viz. F-un

anticipatability, survive? Its survival is compatible with the logic of the reduction. By the same token, the Dedekind treatment of irrationals does not eliminate them. Dedekind shows that a numerical basis consisting exclusively of rationals suffices for representing the continuum.

The fractal case provides a better illustration of the fateful, overlooked, possibility. Because of the reduction of dimension n>m to dimension m, the items of dimension n are not (relative to items of dimension m) amalgams or composites of form and matter: they are entirely form, viz. m. But the



information at level n may still be greater than that of the lower level. There may still be unanticipatability.

"More information," as used here, is a predictive extension of the earlier

use, and thus separates previously undistinguished cases where informa

tion in hand has predictive value from cases where it does not. Previously, the information we had about some curve was simply identified with the number of points on the curve we had determined. So determining addi tional points ipso facto gives us more information. Now, the question is whether the information we have at some stage enables us to determine in advance what further investigation will reveal. If, given the information I have about some curve, I can determine what is the case at some higher level of resolution, then, in the present use, I have as much information at the lower level as at the higher. This will be the case when the higher resolution merely duplicates, more finely, the characteristics of the lower.

A regular fractal, e.g., the Koch, has this feature. The ratio, in this case

4/3, remains constant. So if I magnify any section of the curve I get a

duplicate of the structure of any section visible with lesser magnification.

This is pertinent to Kant. The key to Kant's metaphysical account lies in the following fact. In attempting to establish the principled possibility of a mathematical physics, Kant directly links the treatment of physical extendedness in terms of force or resistance to the claim that the structural characteristics of the whole are duplicated by those of the parts. In the extended sense of "more information," there is, so far as space goes, no more

information in the one than in the other. This is implicit in the claims (all from A25/B39) that "if we speak of diverse spaces, we mean thereby only parts of one and the same space;" "parts [of space]...can only be thought as

in it"; "the manifold in [space]...depends solely on [the introduction of] limitations." The macro- and micro-structures of space are uniform. Now, as indicated earlier, Kant's claim is that though forces?the essential addition taking us from geometry to physics?have spatial effects, i.e., resistance or impenetrability, they are not themselves spatial. That is, they themselves lack (3-dimensional) spatial structure. So, he maintains, their "internal" characteristics, whatever they may be, do not obstruct the very kind of mathematical treatment as applies to empty space.

XL Kants Argument Criticised

The argument, though nimble and imaginative, will not however work. The problem is not that there may be sub-spatial levels (cp. Boscovitchian

"point-particles") on which spatial levels supervene. That problem is raised from a standpoint alien to Kant's. The problem of record, an internal one, is that Kant's claim is not even true of space. If extended objects of dimension n> m can be constructed out of extended objects of dimension

m?so all the items here are extended?then, for the case of space, i.e., n=3, there may be "parts" which are not "limitations" in Kant's sense. (By "a



limitation of space" Kant means a dimensionally similar, i.e., 3-dimen

sional, sub-part, and the (extended) sub-parts in this case are dimension

ally dissimilar.) Consequently, it is invalid to conclude that because forces are not themselves 3-dimensional spatial occupants, a 3-dimensional for

malism (Euclidean geometry) can apply unhindered. The truth of Kant's

specification of forces as lacking the dimensionality of space and its limi tations is quite compatible with forces' being extended: they may have

fractional extensions i, where 0


that the non-dimensionality of forces suffices to ensure the applicability of a uniform and homogeneous mathematics to the materiate world is no

better than the assumption that the dimensionality of the perimeter of any curve must be 1.

As I said, this, mutatis mutandis, counts as much against the Cartesians as against Kant. Leibniz, for instance, would see the failure of mathemat ical representation as a sign that the mapping has not been accomplished completely. But, even given complete mapping, irrationality can survive.

These asseverations supply wherewithal to make something new of the Kantian synthetic a priori.Leibnizean disciples, stung by Kant's charge of

dogmatism, claimed that their man did not ignore the idea?and hence that Kant could not justly plume himself for being, first among the mod erns, "critical." The discussion indeed implies that Leibniz's non-Kantian

position concerning M may be defensible without commitment to the

implausible thesis that all truth is analytic. More F may be more F that, relative to the initial F, is quite "synthetic," i.e., inextractable by anything entitled to the label "analysis." But while the availability of more F?F all the way down?is established by abstract reasoning, what F there is is only determinable a posteriori. In a sentence: F necessarily, but no particular Fis necessary. If this makes Leibniz more "critical," it also however makes

him less 'rationalistic'.

XII. Conclusion

The pre-Kantians reject diversity. If Kant's assertion of diversity is right, that is not because the very idea of a reduction is absurd. Indeed, even if the reduction is granted, that falls short of justifying important claims which the pre-Kantians argued the reduction precisely in order to be able to sustain.

Kant's anti-reductive position is epistemologically expressed. This sug

gests that Kant's cognition-theoretic presentation may well be a reflection

of independently held views about the world, not unlike the way Aristotle's

hylomorphic epistemology reacts to the idea that objects are F impressed on M.20 Plainly, the suggestion is subversive relative to modern philosophy. If the various distinctions among subjective capacities package indepen dent views about the structure of the world, then the kind of reflexive examination undertaken by the founding practitioners?examination in

tended to determine the nature of knowledge, its possibility and limits?is

up to its neck in prior commitments.

I linked the doctrine of transcendental idealism to the theory of diversity. Does the assignment of the concept/intuition duality to general ontology enable us to make better sense of Kant's transcendental idealism? From

the general ontological standpoint, the duality means that the world's recalcitrance to being known is always a live possibility. Under the circum



stances, Kant's thesis that the world is, qua rationally penetrable, depen dent upon our form-inducing activities is pretty well what we would expect from one who wished, short of taking the Cartesian line, to break what was

perceived as the underlying realist-irrationalist bond.21

The University of British Columbia

Received December 13, 1989

NOTES

1. Jonathan Bennett, Kant's Dialectic (Cambridge: Cambridge University Press, 1974), p. 16. Bennett is quoting Lewis White Beck, Early German Philoso

phy. 2. Bennett, loc. cit.

3. The story is that members of the Pythagorean school were sworn to secrecy about the finding. Hippasus of Metapontum, so the story continues, was put to

death by the gods for, as it were, spilling the beans.

4. Qua reduction, the construction is not unproblematic, philosophically speak ing. It is an infinitary reduction. In general, when one reduces As to Bs by a method that requires an infinite number of operations on As, one might deny that a

reduction worthy of the name is effected. Consider Leibniz's account of contingent truth. Compatibly with the praedicatum inest subjecto principle. Leibniz deals with

contingency by means of the idea of infinite analysis. In the contingent case, the

predicate concept is embedded infinitely deep in the subject concept. 5. Strawson, The Bounds of Sense (London: Methuen, 1966), p. 47.

6. What does Strawson's duality have to do with the scientific ferment? This considerable interpretative narrowing of the original topic may also be a consider able distorting.

7. See my "Matter and Rationality" Apeiron, vol. 11, 1977.

8. Compare R. G. Collingwood, The Idea of Nature (Oxford: Clarendon Press,

1945), pp. 95-6: "Aristotle...had said that matter, i.e., the element of unintelligibil ity, was the source of the accidental element in nature; and it was not until

Aristotelian cosmology was swept clean away that scientists could begin to take nature seriously."

9. For a non-technical introduction, see Rudy Rucker, Mind Tools (Boston: Houghton Mifflin, 1987).

10. P 50, in the translation by James Ellington (Indianapolis and New York:

Bobbs-Merrill, 1970). Next quotation: p. 7.

11. If Kant could succeed, he would strengthen the case of modern science, since

the principled defense of the latter would not oblige so radical a departure from commonsense. However, Kant's success seems to require acquiescence in transcen

dental idealism, which is surely a most uncommonsensical view. As they say: what

you gain on the roundabouts you lose on the swings. 12. I have critically anatomised the argument in "Matter and Rationality," op.

cit., p. 28.

13. Since I have just asserted that Kant's argument begs the question, why do I

say that he is dogmatic? Why not simply say that he is wrong? The suggestion is that he sought an argument that would give him the result he wanted. That is a

kind of dogmatism. Of course, I am not suggesting that Kant recognised the

argument's invalidity.



14. Critique of Pure Reason A27Q/B332. I use the translation by Norman Kemp Smith (London: Macmillan, 1933). The echo of the claim that the Cartesian recharacterises what counts, for the pre-modern, as the F-confounding influence of

M, should be heard. Note how, pace Beck, Bennett & Co., Kant ascribes a bona fide position to Leibniz here. Kant does not say that Leibniz's assignment of the

"despicable" task to the senses is a function of his failure to appreciate diversity. 15. Isn't the conscription of the recent mathematical development flagrantly

anachronistic? It isn't. The M/F-reduction is precisely what the historical figures are debating. The fractal case is clearly pertinent to the debate.

16. Compare: the constructibility of the Koch curve out of Euclidean elements does not make the fractal object a Euclidean object. Since the dimensionality of the Koch's perimeter lies between 1 and 2, the curve is non-Euclidean.

17. And, of course, even if forces do not have fractional extensions, but are, as

Kant holds, non-dimensional, it remains possible that the extended expressions of force are expressions in fractional dimensions. This is equally damaging to Kant.

18. The neglect is explicable (though not justificable) dialectically. For if the Aristotelians linked -R to M, then the banishment of M is sure to look like the

recovery of R. Historically, it is not surprising that the second option was over

looked. Had there been awareness of the option, it is unlikely that the reduction would have been undertaken.

19. It is a fact about the natural numbers that, for instance, the location of the G?del numbers of the truths of arithmetic expressible in first-order language cannot be anticipated, there being no recursive definition thereof. Kant was quoted above as claiming that there is only as much science as applied mathematics. If the structure of things, in some physical respect, corresponds to that of the G?del numbers (cp. the ordering of flower petals or leaves accords with the Fibonacci

series) then the mathematical describability of physical reality goes along with -R. The (desperate, perhaps not fully intelligible) alternative is to say that some

features of the numbers do not belong to mathematics proper. Compare Heinz R.

Pagels' idea of a problem in computation which can be dealt with only by a

non-Turing machine. Pagels (The Dreams of Reason [New York: Simon and Shuster, 1988], pp. 306-7) reports Richard Feynman's suggestion that such a computer could simulate the correlations of quantum mechanics.

20. Consider the Kantian claim that the human subject, fundamentally passive in one aspect, the receptive aspect, of his or her cognitive functioning, is impressed by objects. The very idea of the subject's taking an impression as a piece of wax

takes the imprint of a signet ring, corresponds to the Aristotelian account. Analytic philosophers are likely to see in Kantian receptivity nothing more than an acknowl

edgement of the causal element in perceptual contact with the world. This is, again, a case in which modern concerns occlude earlier meanings.

21. This paper was written during my tenure as a Canada Research Fellow at The University of British Columbia. I am grateful to the Social Sciences and Humanities Research Council of Canada. Thanks also to Professor Verena Huber

Dyson, for help with a technicality or two, and to Professor Gordon Brittan, who commented on an earlier version of the paper delivered at the November 1989

meeting of the Northwest Conference on Philosophy, Lewis and Clark College, Portland, Oregon.


Article Contentsp. [461]p. 462p. 463p. 464p. 465p. 466p. 467p. 468p. 469p. 470p. 471p. 472p. 473p. 474

Issue Table of ContentsHistory of Philosophy Quarterly, Vol. 7, No. 4 (Oct., 1990), pp. 367-492Volume InformationFront MatterThe Generation of Form in Aristotle [pp. 367-390]The Many Appetites of Thomas Hobbes [pp. 391-407]How's and Why's: Causation Un-Locked [pp. 409-429]Berkeley's Argument for Other Minds [pp. 431-440]A Critique of Kantian Arguments against Emotions as Moral Motives [pp. 441-459]Kant's Diversity Theory: A Dissenting View [pp. 461-474]Proof and Sanction in Mill's Utilitarianism [pp. 475-487]Back Matter

Glouberman.kant's Diversity Theory a Dissenting View (Article)

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