Nietzsche’s Brave New World of Force
Thoughts on Nietzsche’s 1873 ‘Time Atom Theory’ Fragment & on
the Influence of Boscovich on Nietzsche
KEITH ANSELL PEARSON
http://www.warwick.ac.uk/philosophy/pli ... _pli_9.pdfBoscovich & Natural Philosophy
Boscovich’s A Theory of Natural Philosophy was first published in Latin
in 1758 with a revised and enlarged edition published in 1763 (this was the
‘Venetian’ edition Nietzsche read).15 The work consists of 558 ‘articles’
and is divided into three main parts: an introductory part 1, part II on
‘application of the theory to mechanics’, part III on ‘application of the
theory to physics’, an appendix on the soul and God, and six further
supplements including two on ‘space and time’. In his ‘synopsis’ of the
text Boscovich presents an outline of the chief articles of the work,
pointing out the relation of his theory to Newton and Leibniz, what it
shares with them, where it departs from them and how it attempts to chart
new ground. His system offers a ‘midway’ between those of Leibniz and
Newton and has both much in common with them and much that is
different. He holds it to be simpler than either and so marvellously suitable
for ‘deriving all general properties of bodies, and certain of the special
properties also, by means of the most rigorous demonstrations’ (p. 19, part
1). With Leibniz it shares the idea that matter is composed of simple nonextended primary elements, and with Newton it shares the idea of the
universe as composed of mutual forces that vary as the distances of the
points from one another vary. There are two kinds of forces, attractive and
repulsive.16 The contention is that any particle of matter is connected with
every other particle no matter how great the distance between them, so
that with a change in the position of one the factors determining the motion
of all the rest will be altered. A departure is made from Newton who held
that his indivisible and extended atoms touched on another; a departure is
made from Leibniz who thought there was no void and that non-extended
points were at rest.
In essence, Boscovich’s work offers a specific theory of forces built
from what today one might call a philosophy of nature founded on the
principles of a ‘critical rationalism’. Matter is conceived in terms of
simple, non-extended and indivisible points that are separated from one
another:
…that each of these points has a property of inertia, and in addition
a mutual active force depending on the distance in such a way that,
if the distance is given, both the magnitude and the direction of this
force are given; but if the distance is altered, so also is the force
altered; and if the distance is diminished indefinitely, the force is
repulsive, & in fact also increases indefinitely; whilst if the distance
is increased the force will be diminished, vanish, be changed to an
attractive force that first of all increases, then decreases, vanishes,
is again turned into a repulsive force, and so on many times over;
until at greater distances it finally becomes an attractive force that
decreases approximately in the inverse ratio of the squares of the
distances. (p. 10)
Two key ideas presented in the book, but not elaborated upon in the
synopsis, include ‘compenetration’ and the ‘Law of Continuity (a law
Boscovich insists is unassailable). There can be no perfect rest anywhere
in nature, and neither can there be at all times any perfect analogy between
time and space. For Boscovich the advantage of his conception of matter -
simplicity, indivisibility, and non-extension - is that it does away with the
ideas of a passage from a continuous vacuum to a continuous matter
through any sudden change or leaps in nature. From this he adduces the
conclusion: ‘nothing infinite is found actually existing: the only thing
possible that remains is a series of finite things produced indefinitely’ (p.
12). By doing away with the idea of an actual infinity in existing things,
notes Boscovich, ‘truly countless difficulties can be got rid of’ (p. 46).17
As Peter Poellner has pointed out, Boscovich’s forces are actualised
accelerations or propensities of accelerations.18 The corpuscular doctrine
of matter - the conception of matter as made up of extended and rigid
particles moving about in empty space and interacting through pressure
and impact - has to be abandoned on account of it being internally
inconsistent. It implies that the particles of matter are accelerated
instantaneously and discontinuously by finite increments upon impact. This
discontinuous change of velocity violates for Boscovich the law of
continuity and entails that a system of interacting particles can be in two
different states at one and the same ‘instant’ of time. Such a state also
requires an infinite force. Poellner summarizes the technical details of
Boscovich’s own position as follows:
Boscovich concludes that change does not take place instantaneously
and discontinuously upon contact between moving particles, but rather
continuously, on account of a repulsive force acting asymptotically as the
distance between them decreases. Since the magnitude of this repulsive
force approaches infinity with diminishing distance, it makes direct contact
between the elements impossible. Hence the ultimate constituents of
matter must be assumed to be perfectly simple and at some distance from
each other, for they must be indivisible in principle…The upshot of
Boscovich’s theory of matter is that matter consists of unextended point
centres surrounded by fields of “force”.19
Boscovich insists that his ‘forces’ are nothing mysterious and that they
contain a ‘readily intelligible mechanism’. The difficulty we have thinking
of them in terms of non-extended points arises from our inability to
perceive them by the senses. It is thus necessary to build up a more
adequate conception of matter through a process of reasoning (throughout
the text Boscovich negotiates a position in relation to induction and
champions the rights of deduction; on the use made of induction in the
book see p. 30). This attack on the senses is what Nietzsche will comment
on around 1884-5 as one of the most significant aspects of Boscovich (it
means for him, as we shall see, giving up on materialistic atomism). This
attack on sensualist epistemology has been a principal feature of modern
philosophy of science since Descartes, and the attempt to go beyond
perception plays a crucial role in more contemporary attempts to ‘think
beyond the human condition’ (one of the best examples of this being the
work of Bergson).20
Now Boscovich is fully aware that this conception of matter is not
novel or peculiar to him. He mentions Leibniz’s monads as coming close
to his notion of indivisible and non-extended points. However, he argues
that Leibniz remained a Zenonist (articles 138 & 139, p. 59).21 In order to
escape the snares of Zeno’s paradoxes it is necessary to give up the idea of
continuous extension (such extension cannot be generated from things
without extent):
Those arguments that some of the Leibnizian circle put forward are
of no use for the purpose of connecting indivisibility & nonextension
of the elements with continuous extension of the masses
formed from them … Those who say that monads cannot be
compenetrated, because they are by nature impenetrable, by no
means remove the difficulty. For, if they are both by nature
impenetrable, & also at the same time have to make up a
continuum, i.e., have to be contiguous, then at one & the same time
they are compenetrated & they are not compenetrated; & this
leads to an absurdity & proves the impossibility of entities of this
sort. For, from the idea of non-extension of any sort, & of
contiguity, it is proved by an argument instituted against the
Zenonists many centuries ago that there is bound to be
compenetration; & this argument has never been satisfactorily
answered. (article 139, p. 59)
We will return to this crucial aspect of Boscovich’s theory shortly. For
now, a further point needs noting: the primary elements of matter are not
only indivisible they are also immutable: ‘these are quite simple in
composition, of no extent, they are everywhere unchangeable, and hence
are splendidly adapted for explaining a continually recurring set of
phenomena’ (p. 16). Boscovich does allow for a principle of divisibility
but admits it only to the extent that any existing mass may be made up of
real points that are only finite, ‘although in any given mass this finite
number may be as great as you please’. For him this is to substitute
‘infinite divisibility’ with ‘infinite multiplicity’ (my emphasis).
The divergence from Leibniz centres on Boscovich’s commitment to
simplicity and homogeneity. The oppositions to Zeno can never be
answered, he claims, with regard to the issue of ‘compenetration of all
kinds with non-extended consecutive points’, and this applies with the
same force he holds to the system of Leibniz. If we admit homogeneity
among all the elements then any distinction between masses can be seen to
depend only on relative position and different combinations of these
elements. Chemical operations are an example of this, Boscovich claims,
and their analysis is beginning to show that the enormous variety of
different materials are composed of a relatively small number of elements
which can be explained in terms of an even smaller number of ultimate
constituents, perhaps just the one. If we maintain these principles of
simplicity and homogeneity then key aspects of Leibniz’s teaching,
notably, the principles of indiscernibles and sufficient reason, can no
longer prevail. The principle of sufficient reason is for Boscovich a false
one, ‘calculated to take away all idea of true freewill’. Moreover, all
possible reasons are not known to us. If we are to decide in favour of one
sufficient reason over another then it would be necessary to know
precisely what we do not know (article 93, p. 47; see also articles 94-6).
Nature is to be built up then out of the most simple principles in which
everything is shown to depend on the composition of the forces with which
the particles of matter act upon one another (on Boscovich’s departure
from Newton see the discussion on pp. 19-20, and the treatment of the law
of gravitation on p. 24).
What does Boscovich understand by ‘compenetration’? We have on his
schema a conception of matter as composed of indivisible and nonextended
points combined with the idea of a vacuum in which they are
‘scattered’ which ensures that the points are separated from one another
by definite intervals. An interval can be indefinitely increased or reduced
but can never vanish altogether, except in cases where there is
‘compenetration’ between them:
…I do not admit as possible any immediate contact between them.
On the contrary I consider that it is a certainty that, if the distance
between two points of matter should become absolutely nothing,
then the very same indivisible point of space, according to the usual
idea of it, must be occupied by both together, and we have true
compenetration in every way. Therefore indeed I do not admit the
idea of vacuum interspersed amongst matter, but I consider that
matter is interspersed in a vacuum and floats in it (pp. 20-1).
Boscovich’s ‘law of continuity’ is simply the idea that any quantity (mass)
in passing from one magnitude to another has to pass through ‘all
intermediate magnitudes of the same class’. This idea he develops in a
discussion of Maupertuis (1698-1759). The latter thought that the law of
continuity was violated by any sudden change no matter how small
(whether of a lesser or a greater degree, and where large and small are
relative terms). Thus any passage is made up of intermediate stages or
steps which Maupertuis understands as involving small additions made in
an instant of time. Boscovich argues that this should rather be interpreted
as follows: ‘single states correspond to single instants of time, but
increments or decrements only to small intervals of continuous time’ (p.
28).
Let me now address explicitly the thinking of time that is informing
Boscovich’s philosophy of nature. Boscovich is troubled by the notion of
an instant of time simply because ‘there is need of time…’. Time has a
continuous nature, however short, in order for things to happen. In the case
of water flowing from a vessel, for example, the velocity is generated not
in a single instant but within a ‘continuous interval of time’, passing
through ‘all intermediate magnitudes’. Boscovich is novel in the attempt to
think the interval. The difficulties he reaches stem from his inability to give
up on the ‘fiction of instants’.22 We end up with the curious conception of
time as made up of not simply of intervals existing between instants but as
finite intervals conceived as infinitely divisible through the interpolation of
‘other points and still others’:
There cannot be two instants…contiguous to one another; but
between one instant & another there must always intervene some
interval of continuous time divisible indefinitely. In the same way,
in any quantity which lasts for a continuous interval of time, there
must be obtained a series of magnitudes of such a kind that to each
instant of time there is its corresponding magnitude; & this
magnitude connects the one that precedes with the one that follows
it, and differs from the former by some definite magnitude (article
49, p. 33).
What a massively revealing passage this is! Its key components merit
careful unfolding. It is interesting to note that in the previous article (48)
Boscovich refers to a ‘metaphysical argument’ that he believes supports
his law of continuity and which he has addressed in his dissertation De
Lege Continuitatis. This ‘metaphysics’ draws in part on Aristotle, and
Boscovich cites Aristotle as claiming that ‘there must be a common
boundary which joins the things that precede to those that follow; and this
must therefore be indivisible for the very reason that it is a boundary’. On
Boscovich’s model, then, we have an interval of continuous time
intervening between instants. But this interval is itself indefinitely
divisible. The key question is this: if it is impossible to generate continuous
extension from non-extended points, how is to possible to generate a
conception of noninstantaneous time on the basis of indivisible boundaries
and actual instants? Is this any more an adequate resolution of the
Zenonism that Boscovich identifies as afflicting Leibniz’s theory of
monads? (articles 138 & 139, p. 59). The notion of continuous intervals of
time is designed to fill in the black holes that characterise any attempt to
arrive at a continuous extension from non-extended and indivisible points.
But Boscovich retains an attachment to the idea of the instant and the
theory of compenetration that is fully implicated in Zenonist paradoxes.
The notion of intervals is a genuine innovation in Boscovich’s work and it
plays a key role in his argument against the sense and in favour of new
modes of thinking and knowing the universe:
Intervals, which in no wise came within the scope of the senses,
were considered to be nothing; those things the ideas of which were
always excited simultaneously & conjointly, were considered as
identical, or bound up with one another by an extremely close and
necessary bond. Hence the result is that we have formed the idea of
continuous extension, the idea of impenetrability preventing further
motion only on the absolute contact of bodies; & then we have
heedlessly transferred these ideas to all things that pertain to a solid
body, and to the matter from which it is formed (pp. 66-7).
An instant is, by definition, devoid of duration (p. 197). As Boscovich
himself appreciates there is a close resemblance between the notion of
‘points’ (of position) and that of ‘instants’ (of time). The latter cannot
provide us with a thinking of duration:
…a point is not a part of a continuous line, or an instant a part of a
continuous time; but a limit & a boundary. A continuous line, or a
continuous time is understood to be generated, not by repetition of
points or instants, but by a continuous progressive motion, in which
some intervals are parts of other intervals; the points themselves, or
the instants, which are constantly progressing, are not parts of the
intervals (p. 198)
Whereas time has one progressive motion only (duration), analogous to the
single line, space has extension in three dimensions (length, breadth, and
depth). Boscovich then decides in favour of time being generated from the
instant: ‘in the threefold class of space, & in the onefold class of time, the
point and the instant will be respectively the element, from which, by its
progression, motion, space & time will be understood to be generated’ (p.
199).
15 I have used the following English translation, cited by page number: Roger Joseph
Boscovich, S.J., A Theory of Natural Philosophy, English edition from the text of the
first Venetian edition published under the personal superintendence of the author in
1763, with a short life of Boscovich, Cambridge, Mass., MIT Press 1966.
16 On this point we can note that Boscovich claims to have departed from Newton in
admitting forces that at very small distances are not positive or attractive, as Newton
supposed, but repulsive. See article 4, pp. 19-20 & article 81, p. 43.
17 Further: ‘The theory of non-extension is…convenient for eliminating from Nature all
idea of a coexistent continuum - to explain which philosophers have up till now
laboured so very hard & generally in vain. Assuming non-extension, no division of a
real entity can be carried on indefinitely; we shall not be brought to a standstill when
we seek to find out whether the number of parts that are actually distinct & separable
is finite or infinite. For if the primary elements of matter are perfectly non-extended &
indivisible points separated from one another by some definite interval, then the
number of points in any given mass must be finite; because all the distances are finite’
(article 90, p. 46).
18 Poellner, ‘Causation and Force in Nietzsche’, p. 293.
19 Ibid., pp. 293-4.
20 See, for example, H. Bergson, ‘The Perception of Change’, in The Creative Mind
(Totowa, New Jersey: Littlefield, Adams & Co, 1975), pp. 130-59, p. 132: ‘The
insufficiency of our faculties of perception - an insufficiency verified by our faculties of
conception and reasoning - is what gives birth to philosophy’.
21 For Leibniz on Zeno see Leibniz’s letter attempting to explain certain difficulties in
Bayle, in G. W. Leibniz, Philosophical Texts, trans. and edited R. S. Woolhouse & R.
Francks (Oxford, Oxford University Press, 1998), p. 201-8, p. 207, & Leibniz’s ‘New
System’ and Associated Contemporary Texts, trans. and ed. Woolhouse & Francks
(Oxford Clarendon Press 1997), p. 85, p. 120, p. 123.
22 For a deft treatment of this fiction see Milic Capek’s essay, ‘The Fiction of Instants’
in Capek, The New Aspects of Time: Its Continuity and Novelties (Dordrecht: Kluwer,
1991), pp. 43-55.