COLLAPSE IV
Being and Slime:
The Mathematics of Protoplasm
in Lorenz Oken’s ‘Physio-Philosophy’
Iain Hamilton Grant
It is a daring act of reason to set humanity free and to abstract the shock
of the objective world; yet the venture cannot miscarry, since man becomes
greater to the degree he knows himself and his strength.
Schelling1
A philosophy or ethics without a philosophy of nature is a non-thing, a
bare contradiction, like a flower without a stem.
Oken2
1. Introduction: The Non-Thing or, On the Forms
Occurring in Contemporary Philosophy
The fate of post-Kantian philosophy depends on
whether the ‘shock of the objective world’ can be overcome
by self-knowledge, on the actuality of the ‘shock of the
actual’.3 A seismic chain runs through transcendentalism’s subjugation of earthquakes to epistemology, a
vulcanism poignantly articulated in the objections of
the cosmologist Johann Heinrich Lambert to Kant’s
relegation of time to an a priori form of inner intuition:
‘If changes are real, then time is real […] If time is unreal, then no
change can be real’.4 This is the shock of physics shattering the
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COLLAPSE IV
insularity of transcendental subjectivity, demonstrating the
stakes of the modal investigation of epistemogenesis with
which the transcendental philosophy attempted to replace
ontology.123 4
Schelling’s account of transcendentalism as a ‘daring
act of reason’ clearly articulates the substitution of ethics
for ontology that lies at its core. The accuracy of this
diagnosis is certainly revealed in transcendental philosophy’s restriction of reality to the scope of possible intuition,
1. Schelling, Of the I as the Principle of Philosophy, in Schellings sämmtliche Werke, ed. K.F.A.
Schelling (Stuttgart and Augsburg: J.G. Cotta’scher Verlag, 1856-1861), 14 vols,
cited as SW 1-14. Here SW 1: 157.
2. Lorenz Oken, Elements of Physiophilosophy, Alfred Tulk’s translation, which I have
occasionally modified, of Oken’s Lehrbuch der Naturphilosophie, 3 vols (Jena: Friedrich
Frommann, 1809, 1810, 1811, 3rd edition, Zürich 1843). References throughout will
be to Elements followed by the section numbers common both to Tulk’s work and
the recent republication of the Lehrbuch as volume 2 of the newly published Okens
gesammelte Werke, ed. Thomas Bach, Olaf Breidbach and Dietrich von Engelhardt
(Weimar: Hermann Böhlhaus Nachfolger, 2007). On Oken, see Michael T. Ghiselin,
‘Lorenz Oken’, in Thomas Bach and Olaf Breidbach, eds., Naturphilosophie nach
Schelling. (Schellingiana 17) (Stuttgart-Bad Canstatt: Frommann Holzboog, 2005),
433-57; Olaf Breidbach and Michael T. Ghiselin, ‘Lorenz Oken’s Naturphilosophie in
Jena, Paris and London’, in History and Philosophy of the Life Sciences 24 (2002), 219-47;
and Olaf Breidbach, Hans-Joachim Fliedner and Klaus Ries, eds. Lorenz Oken. Ein
politischer Naturphilosoph (Weimar: Hermann Böhlhaus Nachfolger, 2001).
3. Novalis, Heinrich von Ofterdingen, as cited by Hegel in the Rezensionen aus den
Jahrbüchern für wissenschaftliche Kritik in Georg Wilhelm Friedrich Hegel. Werke ed. Eva
Moldenhauer und Karl Markus Michel (Frankfurt am Main: Suhrkamp, 1979),
vol.11: 215. Interestingly, Hegel is here discussing the relation between actuality and
freedom.
4. Lambert, Letter to Kant of October 13th 1770 in Kants gesammelte Schriften (Berlin:
Königliche Preussische Akademie der Wissenschaften, 1902ff), cited Ak. Here Ak.X:
107 (italics in original). Lambert is responding to § 14 of On the Form and Principles of
the Sensible and Intelligible World, where Kant argued that ‘although time, posited in
itself and absolutely, would be an imaginary being […], it is a condition, extending to
infinity, of intuitive representation for all possible objects of the senses’ (Ak.II: 401;
1992a: 395). Kant echoes Lambert’s question and his response in the first Critique:
‘Time is certainly something real, namely, the real form of inner intuition’ (A36-6/
B53-4).
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Grant – Being and Slime / Todosch – Drawings
but its terms are more overtly displayed in the unstable
dualism of teleology and mechanism in the third Critique.
The dualism is unstable, because despite appearances, it
is not only a dispute about natural causality (although this
is certainly part of it), but outlines the procedure whereby
physical grounds are reduced to the inscrutable abjecta of
reason’s ultimately moral actualisation. This procedure
consists in (a) maintaining the phenomenal indifference of
moral and natural purposes in keeping with the constraints
placed by the first Critique on theoretical reason; while (b)
extending the authority of practical over theoretical reason,
in keeping with the second Critique; and thereby (c) rejecting
ontology for an ethicised phenomenology. It should be
noted, moreover, that the logical form of this procedure is
self-reinforcing: (a) + (b) = (c) = (a) + (b). We shall call it
the ethical process.
The claim of this paper is that this ethical process is
as untenable as it is ubiquitous. It is point (c) that makes
it recognisably ubiquitous, although usually (not always)
without the string of reasons (a) and (b) that establish it.
It is untenable because reason must now affirm ethical
grounding as the absence of grounds, or the absence of grounds
as ethical grounding. The ethical process is the principal
element of the philosophy of what Oken, above, calls the
‘bare contradiction, the non-thing’.
In the equation of ‘bare contradiction’ and ‘non-thing’,
it is clear that Oken considers logical forms to entail
ontological consequences: that a bare contradiction is a
non-thing. This is in complete contradiction to the verdict
of Hegel’s Philosophy of Nature, where he dismisses Oken
as practising a ‘mere formalism’ comprising nothing but
‘assertions’ common to ‘the philosophy of nature of his
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time’.5 In contrast, what the geological Naturphilosoph Henrik
Steffens called Oken’s ‘hard, insurmountable realism’6
consists, in part, in a realism with regard to grounds. The
core philosophical problem to which Oken’s Naturphilosophie is addressed is consequently to determine ‘how
something derived its existence from nothing’.7 As will
become apparent, the ‘nothing’ from which ‘somethings’
always derive their existence is the mathematical nothing,
the zero. Thus, Oken’s ‘generative history of the world’8
consists entirely in demonstrating the repeated ontological
consequences of what he calls, emphasising this generative
operation, the mathes-is issuing from Zero. Thus, the formal
reason of an existent is = the real ground of existence = 0.
The question is whether the zero is always the same, i.e.
whether 0 is always = 0, or whether, for instance, in the
domain of biology, the 0 is slimy.
The story is often told that the immediate post-Kantian reaction consists in the ‘organicist turn’, with Goethe,
Schelling and the Naturphilosophen cited as evidence. While
it is certainly true that the post-Kantian philosophers and
naturalists attempted to resolve Kant’s dualism by way
of organic or self-organizing causality, this story remains
5. Hegel, Philosophy of Nature, trans A.V. Miller (Oxford: Oxford University Press,
1970) §346, Zusatz. There are moments in the Elements, notably its first section, that
seem to ratify Hegel’s assessment: ‘Philosophy, as the science which embraces the
principles of the universe or world, is only a logical, which may perhaps conduct
us to the real, conception.’ Hegel ignores countervailing propositions: ‘what holds
good of mathematical principles must also hold good of the principles of nature’
(Elements 67).
6. Henrik Steffens, Schriften alt und neu Vol.1. (Breslau 1821: 81), cited in Hinrich
Knittermeyer Schelling und die romantische Schule (München: Ernst Reinhardt, 1928),
192.
7. Elements, 10.
8. Ibid.,11.
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COLLAPSE IV
philosophically inadequate. In brief, the reasons for the
insufficiency of this story are (i) that it segregates philosophy
from nature, making the former merely the corollary of the
latter; and (ii) that by making the naturalisation of teleology
versus cognitively insuperable intentionality (the problem
of ‘access’) into the only significant problem to which the
Idealists contribute, it (iii) leaves the problem of the forms
of realism pursued in the long aftermath of Kantianism,
entirely unaddressed. This essay will therefore take Oken’s
Mathesis as a particular case study in the pursuit of a postKantian realism reducible neither to dogmatism nor to the
ethical process, a pursuit that remains as insistent today as
it did two hundred years ago.
2. Physio-Philosophy as the System of the Generation
of the World
The Elements of Physio-Philosophy (Lehrbuch der Naturphilosophie) is a summative work that synthesises Oken’s previous
researches. Since his Preface to the Lehrbuch provides a retrospective of this works, and since, like most of the Naturphilosophen, Oken remains as scorned as he is ignored, we will
introduce the main points of Oken’s system through his
own bibliographical commentary.
Oken’s first work, the Outline of Nature Philosophy, Theory
of the Senses and the Animal Classification based Thereupon (1802),
sets out from the thesis that ‘the animal classes are virtually
nothing else than a representation of the sense-organs’, a
position by which, he states, he ‘still abides’ in the Elements
(xi). This is notable both in its attempt to infer a system
from physiological particulars, a realism that will survive,
just as it is inverted, in the Elements; and in the structural role
it allots to the theory of recapitulation, further developed
and exemplified in this gloss of the theory as propounded
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Grant – Being and Slime / Todosch – Drawings
in On the Significance of the Cranial Bone (1807):
[…] the head is nothing other than a vertebral column […] [just
as] the maxillae are nothing else but repetitions of arms and
feet, the teeth being their nails […]9
This ‘vertebral theory of the skull’, over the discovery
of which Oken disputed with Goethe,10 not only ‘supposed
a community between the human skull and that of the
lower vertebrates’, but extended beyond the organic into
the mineral, geological and cosmogenic domains, carrying
the ‘law of serial repetition […] to ludicrous lengths’ in
Oken, according to some.11 While such a law must lose in
determinacy what it gains in extent, the principle behind
it is simple: that no product of nature arises in isolation
from all other products, each being dependent on others,
‘tak[ing] its starting-point from below’, as Oken notes.12
How far below, however, must research plunge in order to
locate the basal, serially repeated element? Writing retrospectively in 1846, this is what the neurophysiologist Jacob
Henlé called the ‘genetic method’, which had as its goal ‘to
identify the simple type of a given structure and to trace
its progressive elaboration’.13 Where the genetic researcher
is in possession of the fully elaborated organ, the task is
9. Elements, xii.
10. As notably discussed by Hegel in his Philosophy of Nature, §354 Zusatz: ‘Oken,
to whom Goethe had communicated the treatise [On Morphology 1785], paraded its
ideas as his own in a programme he wrote on the subject, and so gained the credit
for them.’
11. Edwin Clarke and L.S. Jacyna, Nineteenth Century Origins of Neuroscientific Concepts
(Berkeley: University of California Press, 1987), 42.
12. Elements, zxiii.
13. Cited in Clark and Jacyna (1987), 21, 43.
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COLLAPSE IV
simplified; insofar as the basal element of any living organisation is to be encountered within the domain of the biotic,
the task becomes simpler still: to find the basal type of all
life.
However, if in principle there are no independent
products in nature, then the prospect of an end to the genetic
typing of any natural product is not to be found in the part,
but rather in the whole. Oken’s next work will accordingly
transform the search for nature’s basal elements into the
search for ‘the nature of nature’,14 or metaphysics.
Combining the results of the Outline and Significance,
Oken’s On the Universe as a Continuation of the Sensory System
(1808) argued ‘that the Organism is nothing other than a
combination of all the Universe’s activities within a single
individual body’ and that ‘World and Organism are one
in kind, and do not stand merely in harmony with each
other’.15 The last clause here indicates an important thesis
regarding the theory of recapitulation, which does not
assert that there merely exists a contingent ‘harmony’ or
phenomenal similarity between parallel series (e.g. worldgeneration and speciation) that remain of fundamentally
different natural orders, but rather that all of nature is
involved in the generation of any part of it. Moreover, as
evinced by the work’s title, Oken is no longer concerned,
as he was the Outline, to derive merely formal devices from
physiological givens, but rather to assert that this structure
is really instantiated in the universe as such. Accordingly,
Oken extended his systematising attention to the elements
of physics in First Ideas towards a Theory of Light, Darkness,
Colour and Heat (1808), where each of these phenomena
14. Novalis, Werke 2: Die Christenheit oder Europa und andere philosophische Schriften, ed.
Rolf Toman (Köln: Könemann, 1996), 440.
15. Elements, xii.
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are derived from tensions, antagonisms and motions in the
aether, constituting a ‘primitive field theory’,16 and in the
Natural System of Ores (1809), where mineral particulars are
considered for the first time.
While the resultant dynamics fulfilled the post-Kantian brief for physics established especially by Franz von
Baader’s Ideas On Rigidity and Fluidity (1792), Apolph Karl
August von Eschenmayer’s Propositions from the Metaphysics of
Nature applied to Chemical and Medical Objects and Attempt to
Derive the Laws of Magnetism A Priori from the Propositions of the
Metaphysics of Nature (both 1797), Oken had also to integrate
the phenomena of life into this universal physics. While it
is only in the Elements that this is achieved, Oken’s contribution towards it – the theory of ‘primal slime’ or protoplasm
– was first advanced in On Generation (1805), which argued
[…] that all organic beings originate from […] the infusorial
mass, or the protoplasm [Urschleim] from whence all larger
organisms fashion themselves or are evolved. Their production
is therefore nothing else than a regular agglomeration of […]
mucus vesicles or points [Schleimpunkte], which first form
themselves by their union or combination into particular
species.17
Since naturephilosophy is to be ‘the generative
history of the world’,18 rather than that of biological
individuals alone, the Elements undertakes to synthesise
the sensory, cosmogonic, geological, embryological and
16. Pierce C. Mullen, ‘The romantic as scientist: Lorenz Oken’, Studies in Romanticism
16 (1977): 381-99, 388.
17. Elements, xi-xii.
18. Ibid., 11.
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philosophical systems into a single, self-recapitulating series.
The question arises as to how primary the ‘primal slime’ is.
Written prior to the cosmogonic synthesis of Of the Universe,
Oken’s programme in On Generation has not yet undertaken
the transition to from the physics to the metaphysics of
nature. Thus, as briefly digested as the Elements is vast
(numbering 3652 propositions), Oken describes its project
as finally
[...] bring[ing] these different doctrines into mutual connexion,
and to show, forsooth, that the Mineral, Vegetable and Animal
classes are not to be arbitrarily arranged in accordance with
single or isolated characters, but to be based upon the cardinal
organs or anatomical systems, from which a firmly established
number of classes must of necessity result; moreover, that each
of these classes commences or takes its starting-point from
below, and consequently that all of them pass parallel to each
other.19
Yet even here Oken holds out a physicalist solution to
the genetic problem, noting that a parallelism between the
classes make it possible ‘to prove that they by no means
form a single ascending series’.20 Although the primacy of
primal slime may thus yet be safeguarded, how the Elements’
project is to be achieved is set out in the opening sections
of the work, which introduce the naturephilosophical terms
of reference. Amongst the most important of these is the
actual and logical priority of natural ground:
Naturephilosophy is the first, philosophy of mind, the second:
the former, therefore, is the ground and foundation of the latter,
19. Elements, xiii.
20. Ibid.
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for nature is antecedent to the human mind. […] Without
naturephilosophy, therefore, there is no philosophy of mind,
any more than a flower is present without a stem, or an edifice
without a foundation.21
Moreover, since naturephilosophy ‘has to show how,
and in accordance indeed with what laws, the material took
its origin’, it follows that history forms a single temporal
series from the development of matter to particular natures
to mind. The formal reason = real ground of existence
consists in the various solutions to the problem of ‘how
something derived its existence from nothing’.22
The other element, then, is Zero, the nothing, and it
is introduced in the Elements for the first time as paralleling
the Urschleim in biology. In what sense, however, ‘parallel’?
Are the biological and the mathematical parallel and thus
independent, or does everything depend on ‘what is below
it’? The problem of the relative and mobile primacies
attaching to the various basal types running throughout
Oken’s system is that Zero is the equilibrium point in
Oken’s polar philosophy of nature, and is so dominant
that it led Steffens to describe Oken’s ‘insurmountable
realism’ as complemented only by an ‘ideal element’ that
is ‘entirely negative’, a view Knittermeyer endorses.23 The
basal Zero – ‘Oken’s most pervasive principle’ – states that
‘all development proceeds along the same path by adding
elements to an original nothingness’, a law that ‘holds
for human ontogeny, the historical sequence of species,
21. Elements 15-16, t.m.
22. Ibid., 10.
23. Schelling und die romantische Schule (op.cit.), 192.
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Grant – Being and Slime / Todosch – Drawings
the evolution of the earth itself’.24 This account certainly
follows from the irreversible priority Oken attaches to
Nature over Mind; but the problem remains: either the Zero
is the merely formal element Hegel accused Oken’s naturephilosophy as consisting in, in which case ‘The universe’ is
not ‘the reality of mathematics’;25 or ‘existence derives from
nothing’ and Slime is not primal. The Okenian solution to
the genetic problem therefore consists in a struggle between
Nothing and Slime.
3. Zero or Slime? The Elements of the Elements
and the Groundedness of the Ground
The Elements outlines its system in sections 18-21 of its
‘Introduction’. The ‘generative history of the world’ divides
into three parts:
1. Mathesis (of the whole),
from which stem (a) Hylogeny and (b) Theogony, or the
generative philosophy of matter and mind;
2. Ontology (of the singular),
which follows the generation of nature from Mathesis, and from
which stem (a) Cosmogony and (b) Stoichogeny; and
3. Biology (of the whole in the singular),
which recapitulates the generation of Hylogeny, Theogony and
Ontology in embryogenesis.
Mathesis – the actions of mathematics, ‘the only true,
24. Stephen Jay Gould, Ontogeny and Phylogeny (Cambridge MA: Bellknap Harvard,
1977), 44, 40.
25. Elements 2.
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the primary, the universal science’26 – subdivides in turn
into the theories of material totalities or Hylogeny, a ‘rather
primitive field-theory’27 comprising aether, light and heat;
and of immaterial totalities or Pneumatogeny, a Theogony
comprising God and Nothing. Ontology divides into
Cosmogony, or the emergence of the cosmic bodies, and
Stoichogeny, or how the heavenly bodies ‘divide themselves
further […] into the elements’. Biology, concerned with
‘the whole in singulars [which] is the living or Organic […]
divides into Organogeny, Phytosophy and Zoosophy’.28
Two things concerning Oken’s conception of Biology
are immediately apparent. The first is that it is no longer
predicated, as was Oken’s procedure in the Outline (1802),
on a particular kind of being whose contours are given in
nature, but rather on a particular stage in the development
of structural complexity involving God, Nothing and Matter,
or mathematics, singulars and substance; that is, the whole
of nature. Since the whole is the self-division of God,
Nothing and Matter, and the singular is the elemental,
hylogenetic singular attained and actualised through these
divisions; and since further it is articulated primarily
by mathematics, then the true object of Biology is the
mathematics of these self-divisions as actualised in living
somethings. This is the fork in Biological science that leads
to the theory of the Primal Slime (Urschleim) and its manifestation in Slime Points (Schleimpunkte). The theory of slime
which forms the oozing ground of Oken’s ‘physio-philosophy’ is ultimately therefore a ‘mathematics endowed with
26. Ibid., 24-5
27. Mullen (1977) Loc.cit.
28. Elements, 21.
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substance’,29 or the product of the mathetic-ontogenetic
process; the biogenetic process then ‘takes its starting point’
from the ‘infusorial mass’ or ‘primal slime’ below, which it
divides into the innumerable ‘mucus vesicles [Schleimpunkte]’
that are the ‘primal constituent parts of [this] organic mass’.
The production of complex singulars (individuals) consists
therefore in the ‘agglomeration of infusoria’ up to the
level of species.30 Biology is therefore the science of the
production of individuals that has as its basis the science of
the production of wholes.
Secondly, if the system that supports this account of
the organic is a true system, that is, if the philosophy of
nature is not merely a reflection upon nature, but rather
‘the generative history of the world’,31 a world that articulates
‘mathematical propositions’ as much as it generates ‘natural
things’,32 then it follows that Biology is no isolated science
of abstracted particulars, but rather concerns the developmental singularities by which the mathematicising cosmos
is actualised. Hence Oken’s insistence that
Natural History is not a closed department of human
knowledge, but presupposes numerous other sciences, such
as Anatomy, Physiology, Chemistry and Physics, with even
Medicine, Geography and History.33
Biology becomes the science it must when and only
when the totality of the sciences – of wholes, singulars,
29. Ibid., 26.
30. Ibid.,xii.
31. Ibid., 11.
32. Ibid., 30.
33. Ibid., xiv.
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and singulars-in-wholes – recovers the entirety of science
as such. This means that Biology recapitulates Mathesis,
just as Oken’s categories suggest: of the Whole, and of
the Whole in the Singular. The one science of the whole is
mathematics, the language of ontogenesis. From this second
perspective, Oken derives what many, including Hegel,
deride as the ‘empty formalism’ of his system, a formalism
articulated around an irreducibly ontogenetic element: the
‘oscillating Zero’, or God: ‘God is = + 0 –’.34 The problem
of the relation between the multiplicity of sciences and the
‘universal science’ arises starkly: either there is one universal
science to which all others are reducible, or Mathesis, the
theory of the whole, has no claim to universality, and does
not therefore articulate ontogeny. In short: what is the relation
between the Primal Slime and the Zero? Oken’s proposed solution
is: mathematics is the universal science that generates, interconnects, and necessitates all the others. The ‘wavering
Zero’ is the generative core of being and slime.
The problem of priority is a problem for a metaphysically realist natural history precisely because the theory of
recapitulation, considered causally, abolishes linear time.
Whenever there arise claims to priority (the primal Zero
34.Elements, 99. Knittermeyer puts Oken’s case economically and concisely: ‘God
is the father, the generator, but himself ungenerated, transformed into the plus
and the minus and yet always remains himself as the existent nothing [das wesende
Nichts]. God is the son who goes forth from the father into finitude, and he is the
mind that takes finitude back, in turn, to the origin and reproduces the “mental
bond” with the generating origin. As the first, this divine acting is the ‘primary rest
[Urruhe]’, the “wavering and resting point in the universe”, the “never appearing
and yet ubiquitously present”. As the second he is eternal ponentiation and hence,
corresponding to the number series 1 + 2 + … + n, the creator of the temporal series.
As the third, however, God is he who takes back the finite [being] released into the
restless time effecting motion and life, into the whole and binds it into him in all-filling
space. The formless oscillation of life here receives form and integument. The divine
brings itself closer to appearing and therefore materiality.’ (Hinrich Knittermeyer,
Schelling und die romantische Schule. München: Ernst Reinhardt, 1928, 189).
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or the Primal Slime), Oken appears to equivocate. Having
noted therefore the priority of the philosophy of nature
over that of mind in section 15; along with the ontogenetic
dependency of the latter on the former (‘nature is antecedent
to mind’) in section 16; section 17 concludes not with this
serial genetic dependency, but with a ‘parallelism’ between
the two. One section later, however, the parallelism is
extended to the relative priorities of the one over the other.
Thus:
It will be shown in the sequel that the mental is antecedent to
nature. Naturephilosophy must, therefore, commence from the
mind.35
Which, then, does come first – Zero or Slime? Around
what axis is the topology of nature and mind spinning?
Does mathematics remain the ‘primary science’, or is a
mathematical realism usurped by a realism concerning
natural history? The relation of system and history remains
at the core of the metaphysics of natural history; especially
as this project was renewed in Prigogine and Stengers new
‘physiophilosophical’ alliance.36 What is seldom noted is
that this entails a natural history of metaphysics that extends
beyond the steady accumulation of form that characterises Hegelian history of philosophy. The natural history
of metaphysics is a physics of metaphysics, a science of the
grounds of metaphysics in nature, or a physics of ideation
as such. Although sounding more redolent of hard-nosed
contemporary eliminativists than of post-Kantian idealists,
this recognition was core to Naturphilosophen such as
35. Elements, 18.
36. Ilya Prigogine and Isabelle Stengers, Order out of Chaos (New York: Bantam, 1984),
translation of La nouvelle alliance (Paris: Gallimard, 1979).
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Schelling, who characterised philosophy as ‘the natural
history of mind’37 and Troxler, who defines metaphysics as
the physics (Naturlehre) of human knowledge.38 If nature is
necessary to generate mind, as sections 15 and 16 note,
then mind is necessary to the abstract recapitulation of
natural production in reflection, or to the recapitulation of
the mathetic whole in the biological singular. Yet Oken’s
system extends beyond reflection on natural production,
since ontogenesis depends on Mathesis. The Platonic
kinship is unmistakable:39 mathematics, or the Idea, are not
simply nominal or formal processes, but rather ontogenetic.
Just as the Phaedo argues40 that it is because of the form of
Beauty that beautiful things exist, so Oken argues that it is
because of Mathesis that things exist, or because of Nothing
(= 0) that there are beings. That Oken inverts the causal
or physical dependency of mind on nature does indeed
stem from his characterisation of Mathesis as hylogeny and
theogony , which gives direction to the system, towards the
production of animals capable of Mathesis and therefore,
famously, of man:
Man is the summit, the crown of nature’s development, and
must comprehend everything that has preceded him [while]
man is a complex of all that surrounds him, namely, of element,
mineral, plant and animal.41
37. F.W.J. Schelling, Ideas for a Philosophy of Nature (Cambridge: Cambridge University
Press, 1988), 30; SW 2: 39.
38. Ignaz Paul Vital Troxler, Naturlehre des menschlichen Erkennens oder Metaphysik
(Hamburg: Meiner [1828] 1998).
39. As Mullen (1977: 388) notes, ‘In form and to some extent in substance [the
Elements] closely resembles Plato’s Timaeus.’
40. Phaedo, 100d.
41. Elements, 12, 98.
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At the very point where thinking slime affords nature
linearity, however, at the crown of its development from
elements to animals, directionality reverses. Mathesis
as theogony is concerned with the immaterial whole;
yet what is the ‘immaterial’? Merely ‘that which is nothing
in relation to the material’,42 just as ‘God is = + 0 –’43 or ‘the
eternal is the nothing of nature’.44 The ‘immaterial’ is the
zero of material, its generative ground, just as God is that of
nature, since nothing iterated is the becoming of something.
Thus the sense in which ‘something derives its existence
from nothing’45 now becomes ‘very clear’. Just as
numbers have not issued forth from zero as if they had
previously resided therein, but the zero has emerged out of
itself […], and then it was a finite zero, a number46
so something emerges not ‘out of’ but rather from the acts
of the nothing’s self-extensions: ‘Zero is […] the primary act
[and] numbers are [its] repetitions’.47 Thus another primary
whose ‘positing and negating are called realisation [which]
is a process of extension taking place in the Idea’.48 And
this positing and negating takes place, equally, in the ‘highest,
most exalted art […] of war’,49 reducing everything to
42. Elements, 8.
43. Ibid., 99.
44. Ibid., 44.
45. Ibid., 10.
46. Ibid., 37.
47. Ibid., 55, 57.
48. Ibid., 48, 38.
49. Ibid., 3652.
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nothing after the Napoleonic model. The nothing initiates
a ceaseless imitatio nihil amidst the extended multiplicities
formed of the infinite repetition of the primary act, while
existence resists the sink at its core.
At first sight far from satisfactory, all this wavering
Nothing leaves an ontological queasiness in place of
any principle of sufficient reason. It pervades Oken’s
system, with its martial apex. For what kind of
biologist does war supercede life as the system’s goal?
That the complexifications of Primal Slime here cede to the
destruction of war demonstrates that the cosmos worships
the Nothing-God. The culmination of Biology is the
destruction of individuals, which is held in check so long as
there remains something. Kant tells us, reassuringly enough,
that reality can never sink to zero; but Oken’s mehylotheogony
supplants all Being with increase and decrease, each limitless.
The fragile hold of beings is secured by Slime alone – all
that ontology can hope for is Slime potentiated and negated
into and out of all things. The question thus arises is this:
is the Urschleim – or, ontically speaking, the Schleimpunkte –
negable, reducible, as well as ‘potentiable’? The prospect
of the contingency of all beings issues directly from this as it
were gravitational distortion of the local spacetime of their
generation.
The question would hold no terror were the passage
from mathetic metheology to ontology secured, e.g. by a
causal or a linear-progressive process; but it is not. The
whole is not left behind by history, by the accumulation
of causes from whence emerges time; rather, it returns in
Biology. Oken’s Biology is not therefore testimony to the
final discovery of a ‘Newton of the blade of grass’, of an
organicism to save us from the ravages of nature, but
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only the repetition of the None-All in every generated
particular.
All directionality, whether in ideation or cosmogeny,
in embryogenesis, hylogeny, temporalisation or primary
Mathesis, is withdrawn in favour of the polar model that
determines the ‘primitive field theory’ Oken constructs
around the tensions, antitheses and motions of the aether
in the First Ideas for a Theory of Light, and which inherits and
extends the galvanic process Ritter discovered to ‘constantly
accompany the animal kingdom’ into the mineral, chemical
and mathetic domains along the lines suggested by the
magnetic schema, in which the zero is not primitive, but
first and last in, and the principle of, all the extensions of
its force.50 Oken’s mutiplicity of primaries – act, slime, rest,
etc. – are primary relative both to the lower nothing from
which, at ontogenetic root, they issue, and to the ‘higher
zeros’ that counteract them which they in turn give rise:
rest, war, act.
The polar metaphysics of nature, therefore, collapses
the axis of higher and lower, antecendence and succession,
into a field theory of polar dependency: ‘The world is God
rotating’ or ‘a rotating globe of matter’.51 Natural history is
always therefore relative to the mathetic zero from which its
50. The schema owes its most definitive account to Karl August Eschenmayer’s
Attempt to Deduce the Laws of Magnetic Phenomena a priori from the Propositions of Metaphysics
(1797), and to Schelling’s reworking of it in his Exposition of my System of Philosophy
(1801). For Eschenmayer, see Jörg Jantzen, ‘Adolph Karl August von Eschenmayer’,
in Bach and Breidbach, eds., op.cit., 153-79 and Gilles Châtelet, Les enjeux du mobile.
Mathématique, physique et philosophie (Paris: Seuil, 1993), esp. 137-9. On Schelling’s
transformation of the magnetic schema in his so-called Identity philosophy, see Iain
Hamilton Grant, Philosophies of Nature after Schelling (London: Continuum, 2006), 15882, and ‘The physics of the world soul’, in Judith Norman and Alistair Welchman,
eds. The New Schelling (London: Continuum, 2004), 128-50.
51. Elements 142, 161.
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objects issue, and the frame of reference is always generated
after the field that is its object. The ultimate significance
of sections 15, 16 and 18 of the Elements is therefore that
the priority of nature with respect to mind generates a
nothing in nature from which naturephilosophy begins.
Ironically, Oken’s post-Kantian solutions make Lambert’s
physico-critical intervention redundant by realising the full
consequences of self-effecting processes: the elimination of history
in nature: ‘Time is the infinite succession of numbers or the
mathematical nothings’.52 We turn now to Oken’s solutions
to his polar take on the genetic problem.
4. Okenian Solutions, and …
Oken’s solution to the genetic problem is not what
Henlé’s ‘student of the nervous system’ might have hoped
for. Rather than identifying the ‘basal element’ of neurogenetic recapitulation, Oken resolves individuation into the
whole. Schematically:
(1) Mathesis→ Ontogenesis → Biogenesis → the production
of the whole in the singular → Mathesis potentiated.
(2) The consequence of this is that the causal series
that ties time to change is sacrificed for a codependency relation, a reciprocity, between the elements
recapitulating the basic scheme of the whole in a
singular. ‘The law of causality is a law of polarity’,
not of time.53 Time, Oken continues, is accordingly
‘only repetition, and thus also a suppression of
52. Elements 72.
53. Ibid., 79.
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COLLAPSE IV
[…] positions’.54 Because the whole is expressed at
the apexes of individuation (Ideation and War),
Okenian ontogenesis produces irreducibly local
maps, while ‘pneumatogenesis’ has primally and
then derivatively multiplied them. Potentiation is
potentiation of the whole in its individuation, as
Schelling would later note of the involutive-evolutive process.55
(3) If, logically, mathematics is the expression of the
whole in the individual; and if, theogonically,
‘God = + 0 – is before and after all things’, then
modally, only the nothing is necessary. Here,
then, we derive the central lesson of Oken’s
system of nature: the contingency of all beings,
so the ‘principle of sufficient reason’ is satisfied
by nothing potentiated. Precisely in consequence
of this, mathematics or mehylogeny does not so
much supplant nature as generate it: by taking on
the project of the ‘natural history of metaphysics’,
Oken’s slimy Platonic naturephilosophy has
mathetic functions accreting numbers and organs,
indifferently: ‘all development’, as Gould notes
of Oken’s system, ‘begins with a primal zero and
progresses to complexity by the successive addition
of organs in a determined sequence’.56 The zero
accretes by self-extension in the forms of mineral,
chemical, plant and animal organs.57
54. Ibid., 74.
55. See Schelling’s Stuttgart Private Lectures (1810; SW VIII), in Thomas Pfau, ed.
Idealism and the Endgame of Theory: Three Essays by Schelling (Albany NY: SUNY, 1994).
56. Gould, op.cit., 40.
57. Elements, 867.
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(4) If, as we have seen, recapitulation becomes, by
virtue of (2), above, if not aionic (although Oken
occasionally makes precisely this point: ‘Zero
must be endlessly self-positing, for in every
respect it is indefinite or unlimited, eternal’),58 then
certainly achronic. It forms the logic of Idea in the
hylogenetic → biogenetic process, and as such is
the repeated intercession of the eternal into time,
or its negation.
(5) Even anthropogenesis, so often criticised as
the ‘anti-copernican’ core of the post-Kantian
‘restoration’, accordingly suffers. No sooner is man
declared the ‘highest’, insofar as it is through man
that nature achieves Ideation and thus reproduces
Mathesis, than war erupts because ‘the Nothing is
higher than the highest’: ‘the Zero, the highest’.59
Oken therefore demonstrates that anthropogenesis
culminates neither in the humanism of finitude nor
in the ontolotheological eschatology, but rather
ceaselessly repeats the mathetic mehylotheogony of the
cosmogonic process:
In the process of destruction, the finite being seeks
to become the universe itself [because] man is a
complex of all that surrounds him.60
58. Elements 53.
59. Ibid., 40.
60. Ibid., 91, 98.
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COLLAPSE IV
5. … Post-Okenian Problems.
The continuance of Being is a continuous positing of the
Eternal, or of nothing, a ceaseless process of becoming real in
that which is not. There exists nothing but nothing, nothing
but the Eternal, and all individual existence is only a fallacious
existence. All individual things are monads, nothings, which
have, however, become determined.61
We have noted that the Okenian number series are
primary, and issue from a primary Zero, ‘the one essence
of all things, the 0, the highest identity’.62 Disregarding for
the moment the metaphysics of polar time, the Zero is, if
not primitive, then ultimate, insofar as everything resolves
into it. Oken invests considerable effort in the elaboration
of zero.
Firstly, it is twofold: intensive or ideal, and extensive
or real. Yet these two remain indifferent: ‘the real and the
ideal are no more different than ice and water; both […] are
essentially one and the same’.63 This is where the repeatedly
claimed similarity of Oken’s Zero and Schelling’s reformulated law of Identity are apparent:64 that identity is the
61. Ibid., 58.
62. Ibid., 40.
63. Ibid., 36.
64. This tendency starts with Oken’s translator, Tulk: ‘the present work stands alone
in Germany, as being the most practical application upon a systematic scale of the
principles advanced by Schelling, more especially in the Mathesis and Ontology’
(Elements vi). More recently, Joseph L. Esposito, in Schelling’s Idealism and the Philosophy
of Nature (Lewisburg: Bucknell University Press, 1977, 143) repeats the point:
‘Essentially Oken’s system is the same as Schelling’s, but with specific scientific
disciplines superimposed on it, so that it became at once a picture of the World
System and a proposal for how to study it. […] Mathesis is the condition of Schelling’s
Absolute Identity, wherein the first differentiation occurs’. See also Wolfgang Förster,
‘Schelling als Theoretiker der Dialektik der Natur’, in Hans Jörg Sandkühler, ed.,
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COLLAPSE IV
ground of differentiation, and that no differentia, insofar as
they are different, are identical.
Secondly, the susceptibility of Zero to ‘infinitely
numerous forms’65 invites speculation as to the other forms
it has in fact assumed: apart from Eschenmayer’s magnetic
schema, therefore, Kant’s account of the eliminative
actions of negative magnitudes, or the ontological problem
of negative numbers, pinion around zeros, as does the
‘minimax’ of zero sum games, or the empty set from which
Russell and Whitehead, on the one hand, and Badiou
on the other, draw such diverse ontological conclusions.
Finally, and perhaps decisively, the ungenerated and
ungenerable, non-phenomenal attributes of the Platonic
Idea make it into the zero of the physical world, a series
of problems best explored in the Parmenides. The actual
and potential permutability of zero into many formal
schemas brings Oken’s theorizing out of the domain of
the ‘number mysticism’ of which he has been routinely
accused66 to demonstrate the ontological vitality of the
problem of the relation of number, being and animal.67 The
question Badiou raises against Deleuze of the separability
of mathematics and ontology, on the one hand, from nature
on the other, is, as is topologically appropriate, twisted in
Oken. On the one hand, Mathesis, ontology and biology form
Natur und geschichtlicher Prozess. Studien zur Naturphilosophie F.W.J. Schellings. (Frankfurt
am Main: Suhrkamp, 1984), 188, and Ghiselin, loc. cit. , 439.
65. Elements 40.
66. Ghiselin, loc.cit., 440.
67. See Alain Badiou, ‘Deleuze, The Fold: Leibniz and the Baroque’, in Constantine
Boundas and Dorothea Olkowski, eds., Deleuze and the Theater of Philosophy (New York:
Routledge, 1997), 51-69 and my discussion of it in relation to these problems, in
Philosophies of Nature after Schelling, 8ff.
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distinct domains that are all, on the other, articulated by their
respective and interrelated zeros. In other words, each
series takes its starting point from its predecessor, so that
Mathesis entails ontology entails biology. The problem of
the independent dependence of series one on the other is in
effect the problem solved by the generation of nature itself,
insofar as it recapitulates these series in all its products. On
Oken’s evidence, then, number is inseparable from animal
precisely because animals are the numbers of nature:68 ‘life’, he
writes, ‘is a mathematical problem’.69 Mathesis, ontology
and biology are equally inseparable, therefore, because the
series are not statically taxonomic, but actually genetic. It is
the genetic element in Oken that indicates a resolution to the contemporary problem.
Thirdly, the Ideal and Real forms correspond to the
Zero in a state of intensity and extensity in number series.
‘The latter’, writes Oken, ‘is only expanded intensity, the
former, extensity concentrated in the point’.70 It is this
latter differentiation that provides Oken with the means to
formulate the issuing forth of something out of the nothing
by way of the latter’s repetition rather than its expulsion of
a latent content.
The Zero thus provides a genuine solution to the
problem of sufficient reason: nothing is the reason why there
are beings, or is the ungrounding of primary ground from
which grounds emerge. This thesis is rich in implications:
firstly, since the determination of nothing occurs only in
68. I owe this point to lengthy and unforgettable conversations with my colleague
Sean Watson.
69. Elements, 104.
70. Ibid., 37.
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COLLAPSE IV
the process of extension and concentration, and since it is
susceptible to ‘infinitely numerous forms’, it grounds the
contingency of all beings, although it ought not to be omitted
that it grounds this contingency of singulars. Secondly, if all
things have one essence (= 0; Elements 40), then in what
sense are all things really diverse? If merely formally (as Oken
in fact argues), then ontology – the actual generation of
singulars – cannot fulfill its function, and the All remains =
0; if essentially, then the Zero ceases to be the primitive = the
highest in all things, and the All is not = 0. The problem this
poses can thus be summatively stated: is the Zero capable
of real generation? Since Oken answers that ‘naturephilosophy is the generative history’ or ‘the science of the genesis
of the world’,71 the formal and essential ‘generations’ of zero
must be essentially indifferent while formally different. If,
however, all difference is formal difference, and the Zero is
always the generating (potentiable and negable) element,
then it must either be concluded that formal difference is
essentially indifferent or that formal differentiation is the
generation of an additional mode not given in the alternatives.
This, indeed, is Oken’s solution: ‘positing and negating the
Eternal is called realisation’.72
What does the contingency of all beings therefore
entail? That the formal differentiation and essential indifference of the generations of zeros never attain to fixity,
whether of species, phyla or morphology. Indeed, this is
guaranteed by the endlessly rotating axes of theogonic
and hylogenic nature,73 just as it is by Oken’s ‘singular to
71. Ibid., 11, 66.
72. Ibid., 40.
73. cf. Elements 142, 161.
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whole’ transformation of the genetic problem. Accordingly,
Oken’s is a universal morphogenesis, which earned his
work credit from D’Arcy Thompson74 and E.S. Russell,75
amongst others. Okenian ontology does not therefore so
much chart whole entities, but rather singulars, both in the
sense of cosmogony, or the generation of the one universe –
‘there can be only one nature’;76 and of stoichogeny, or the
generation of the elements and organs that accrete to the
various formally differentiated singulars. Ceaselessly oscillating
around the zeros from which they issue and the complexes
they recapitulate, depending on the extensity of the zeros’
generations, the emergent material forms are not so much
limited geometries as they are limited acts.
Taking these points together, it becomes evident that
what the contingency conferred upon beings by Oken’s
principle of sufficient reason consists in is the consequence
of the contingency of dynamics. On this account, biology is
the science of the contingent dynamics of the primal slime,
oscillating between the achievement of Ideation and mineral
inertia. Indeed, the polar field thus generated by biology
involves rocks as much as Ideas, as much as the biological
singular involves the osseous and the nervous systems;
all biological systems, however, are evolved from the slimy,
74. D’Arcy Thompson cites Oken twice by name in On Growth and Form [1917]. Ed &
abridged by J.T. Bonner. (Cambridge: Cambridge University Press, 1966), and gives
the following, Okenian account of morphology: ‘Morphology is not only a study
of material things and of the forms of material things, but has its dynamical aspect,
under which we deal with the interpretation, in terms of force, of the operations of
Energy’, 14.
75. E.S.Russell, in Form and Function: a Contribution to the History of Animal Morphology
(London: John Murray, 1916), 90, thus describes Oken as’a careful student of
embryology’. The most recent exponent of the positive view of Okenian morphology
is Stephen J. Gould, op. cit.
76. Elements, 166.
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COLLAPSE IV
protoplasmic mass whose contingencies are involved in them.
To return to the problem of the separability of mathematics
and nature, we must now pose it the other way round: is a
slime-free matheme possible? Morphology, with its principle of
sufficient reason, argues not.
6. Conclusion: The Rotations of the Before
and the After
With Schelling, we argued at the beginning of this
essay that the ethical process is possible only if the ‘shock of
the objective world’ can be abstracted away. One means
of achieving this is by insisting on the separability of
mathematics and nature, and by insisting on the ‘impossibility’ of a philosophy of nature, as does Badiou.77 Another
means of achieving this is by insisting on the insuperability
of the nominal frameworks of self-conscious, finite reason.
Since the latter is a subdivision of the former, however,
there is no difference in kind, but only in degree, between
these two means of abstracting the world.
Oken’s insistence, by contrast, on the material world of
nature as forming the generative basis not only of natural
individuation, but also of the thought-series that can only
arise on their basis in turn, suggests that one more entailment
might flow from his principle of sufficient reason: the order
of priority of nature and mind. With this order, the shock
of conjoint time and change by which Lambert forced the
progressive splintering of the system of transcendental
philosophy, is reintroduced: if there is an order of priority,
how can it be grounded given the ceaseless rotation of Matter
and God? To resolve this merely formally, by arguing that
77. Badiou, loc.cit., 64.
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Matter is the zero of God, just as God is the zero of Matter,
is not to resolve the problem at all, but to avoid it, since
Mathesis consists precisely in the formal differentiation of
Matter and God – of hylogeny and theogony – from which
ontogenesis flows. Further, we have already noted Oken’s
inversion of his initially stated order of priority: ‘nature
first, mind second’78 becomes ‘mind first, nature second’.79
Since we must concede that Oken’s dynamics admit of no
transcendent or transcendental axes, therefore, the grounds
of the before and the after must be established by other
means.
Ultimately, as Oken repeatedly argues, the task of
naturephilosophy is ‘to show how […] the Material took its
origin; and therefore, how something derived its existence
from nothing’.80 By now we recognise this as Oken’s
trademark, polar procedure: matter and nothing are
conjointly the first focus of the systematic task of generating
nature in thought. Thought, in other words, involves matter
and nothing, i.e., the whole (Mathesis). Indeed, philosophy
and war are the latest of the zero’s accretions, the former
consisting always in ‘the repetition of the origin of the
world’,81 while the latter, through the ‘process of destruction’,
seeks to reestablish the essential identity of everything82 in
the zero that must necessarily remain. Each involves the
entire universe and its generation; the first as universal
repetition, the second as universal equation. War reveals
the ground, and philosophy repeats its generations, up to
78. Elements, 15-16.
79. Ibid., 18.
80. Ibid., 10.
81. Ibid., 2.
82. Ibid., 91.
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Grant – Being and Slime / Todosch – Drawings
and including its own generation in nature. Because ground
supersedes its repetition, which precedes its revelation,
an order of priority can be established in thought. Hence
Oken: ‘Time is the act of numbering; numbering is
thinking; thinking is time’.83
This is not to argue that time exists only in thought, in the
Kantian manner, but rather that, as Oken notes, thinking is
time. This is because
Time itself is only repetition […] The vicissitude of things is in
fact time; if there be no change, there is also no time.84
In other words, because the grounding of existents
consists in the repetition of zero, this grounding extends to
Ideation, to philosophy. Philosophy is the formal repetition
of cosmogony, while war is its essential repetition. Because
Ideation is not itself the ground of time (Kant), but time
that of Ideation, the grounding of existents in nothing
establishes the a priority of nature with respect to mind,
but without segregating mind from any part of nature or
Mathesis. The principle of sufficient reason therefore states:
something emerges from nothing, and this process is inviolable.
Oken’s natural history of metaphysics therefore indicates
that naturephilosophy is not simply a means, but the necessary
means by which post-Kantian philosophy escapes the trap
that the ethical process sets for it: the primacy of nature
extends even to those slimy neural accretions to the primal
Zero that make metaphysics possible.
83. Elements, 75.
84. Ibid., 74.
321