THE LAST AND THE LEAST THINGS: ATOMS AND SOUL-MONADS
The reaction against Aristotelianism had, as one of its results, a
renascence of the atomic theory of Democritus and Lucretius; and one of
the earliest adherents of the renovated doctrine was Bruno. Although
a complete presentation of the theory was not given until his later
works, the _De Minimo_ and the _Articuli adv. Mathematicos_, appeared,
yet already in the Italian dialogues there were frequent references to
it. In the _Cena_,[381] for example, it is said that in the physical
division of a finite body infinite progress is impossible, and, as
we shall afterwards find, in Bruno there is no distinction between
physical and mathematical division. Again, in the _Cena_ an animistic
atomism is suggested, which presents a curious anticipation of some of
Leibniz' characteristic views. "It is more than probable, as all things
partake of life, that many or innumerable individuals live not only
in us, but in all composite things; when anything "dies," as is said,
we must believe it to be not death, but change only; the accidental
composition or concord ceases, the things that enter into it remaining
always immortal; and this is truer of those things we call spiritual
than of those we call corporeal or material."[382] Thus every body or
organism, for all bodies are organisms to Bruno, is itself constituted
by other living beings, the atoms--living atoms--being alike the
origin and the end of all. So Leibniz wrote:--"Every living body
has a presiding entelechy, which is the soul in the animal; but the
members of this living body are full of other living beings--plants,
animals,--each of which, again, has its entelechy or presiding
soul."[383] In the _Infinito_ Bruno refers to the continuous changes of
all composite bodies as arising from the ceaseless flux of atoms out of
and into each body, even the greater "animals," the stars and planets,
sending out particles, which wander through the universe from one to
another.[384] Again, when discussing the four elements, he ascribes to
water the power of holding together the atoms of earth, or "the dry."
"If from the earth all water were to be removed, so that there remained
purely dry matter, this remainder would necessarily be an incoherent,
rare, loose substance, easy to be dispersed through the air, in the
form of innumerable discontinuous bodies; for while the air or ether
makes a continuum, that which makes a _coherent_ continuum is water or
moisture."[385] These indivisible "prime bodies," of which the worlds
are originally composed, are spoken of as flying throughout space from
world to world, in infinite movement, entering now into this, now into
that "composition."[386] Finally, in the _Spaccio_, we are reminded
that "every trifle, however worthless, is of value in the order of the
whole, the universe, for great things are composed of little, little
things of the least, and these of the individuals (or indivisibles)
or minima."[387] In its main outlines, accordingly, Bruno's atomic
theory was already formed in his mind when he wrote his earlier
philosophical works, and even some of his peculiar applications of it
had already suggested themselves. It is hardly possible, therefore,
to find any very marked development in this regard between the London
and the Frankfort periods. There is elaboration and completion rather
than development in any definite direction;[388] and, as we have seen,
the writing of the larger works, containing the developed system, was
projected in London, and even carried out to a certain extent before
Bruno left England.[389] In the _Acrotismus_, which occupies a middle
place between the two periods, the doctrine is equally in evidence,
in reference both to the atoms and to the continuous ether in which
they move. "There is a limit to the division of nature--an indivisible
something; the division of nature arrives at ultimate minimal parts,
unapproachable by human instruments. Of these minimal bodies every
sensible body is composed, and such a body, resolved into its minima,
can retain no semblance of complexity; for these are the first bodies
out of which all others are made, and which are, in the truest sense,
the matter of all things that have corporeal existence. Resolved into
these parts, stone has no look of stone, flesh of flesh, bone of bone;
in their elements, bone, stone, and flesh do not differ, but only when
formed out of these, compounded, compacted, and arranged in diverse
manners, do flesh, stone, and bone and other things become different
one from another."[390] And Bruno describes how, between the heavenly
bodies, there is a substance, "ingenerable and incorruptible, the
immeasurable air, a kind of spiritual body"--the ether.[391]
[Sidenote: Object of _De Minimo_.]
[Sidenote: Atomism a metaphysical doctrine.]
Its full extension, however, the theory receives in the _De Minimo_,
where the atom, or corporeal unity, is not the sole minimum discussed.
The full title of the work is:--"On the threefold minimum, and measure,
being the principles of the three speculative sciences and of many
practical arts." We find nowhere any distinct statement as to what
Bruno meant by the "threefold minimum," and the three speculative
sciences to which its several members refer. It was supposed that the
minima were (1) the monad or unity which is the unit of number, (2)
the point, which is the unit of the line, and (3) the atom, which is
the unit of body. But arithmetic and geometry can hardly be called
speculative sciences, and Tocco has shown that Bruno had in view the
triad of _God_, the _soul_ and the _atom_--the three kinds of simple
substance, each immortal and indestructible:--_God_ as the supreme and
most simple unity, Monad of Monads; _soul_ as that which lives in each
composite being and holds in unity the atoms which from time to time
enter into its composition; and the _atom_, the most simple of material
substances, in the sum of which, with their containing ether, the
material universe consists. Had Bruno carried out his subdivision of
the speculative sciences, he would probably have referred God, as the
substance of all reality, to a speculative theology, of Neoplatonist
type; soul as the simple substance of animate beings to metaphysics
proper; and the atoms, the substance of body, to a speculative physics,
dealing with the metaphysical presuppositions of the general theory of
nature, which was set forth in the _De Immenso_. The scheme, however,
was never fully carried out,[392] the times being not yet ripe for
the complete separation of the speculative and the experimental or
observational sciences. In referring the atomic theory to metaphysics,
Bruno showed a true instinct, for while in one sense atomism is a
scientific hypothesis capable of furnishing laws which explain the
interaction of bodies,--the corpuscular theory,--and as such has
proved its value by the brilliant developments of recent years, on the
other hand, it is also a presupposition of knowledge, a ground of the
possibility of our knowledge of body, and therefore has its place in
speculative theory, or metaphysics, in the widest sense. Both points of
view are presented in Bruno's doctrine, but that from which he starts
is the epistemological, following in this the guidance of Nicholas of
Cusa.
[Sidenote: Knowledge implies the atom.]
[Sidenote: Relativity of minimum.]
Knowledge is measurement, and all measure implies a minimum in each
kind of being. Were it possible to subdivide anything _ad infinitum_,
the half would be potentially equal to the whole, and measurement
frustrated. There must be a limit to division, an ultimate part, which
itself has no parts, and which is the _substance_ of the composition
into which it enters, the composition on the other hand being an
"_accident_" of this minimum. As it is primarily a condition of
measurement, the minimum differs in the different spheres of measure or
knowledge to which the category of quantity applies. In magnitudes of
one or two dimensions it is the point, in bodies the atom, in numbers
the monad or unity. Thus number is accident of the monad, monad is the
essence of number, as composition is accident of the atom, atom is
essence of the composite. Again, the "sensible minimum" must be far
greater than the natural or real minimum, for in so far as minimum is
qualified by sensible, it is implied that the minimum is not absolutely
such, but is a composite. The minimum of taste, touch, etc., must
possess certain qualities, by which it has relation to sense, and
these can derive only from some form of composition. In their primary
form the minima of nature must be without difference; therefore that
some are sensible, others not, must be due to some addition in the
former.[393]
Thus each species of existence, as light, moisture, vital force,[394]
has its own minimum, and the minimum is relative in this sense also,
that there are different kinds of existence not resolvable one into
another: the absolute minimum would be God, who is also the absolute
maximum. The relative minimum, accordingly, is determined either by
the thought and design of the observer, or by the species of existence
to which the subject belongs; nature has set limits, both lower and
upper, within which the individual of any species must stay, or cease
to belong to that species. Accordingly, what _one_ regards as great and
composite, _another_ may take as first and minimum: the unit of one
science may be analysed in another into further elements. "Pythagoras
in his philosophy started with the monad and numbers; Plato with atoms,
lines and surfaces; Empedocles with the four elements; the physicians
with the four humours, and so on; but the Pythagorean monad is prior to
the placed monad (the atom), Plato's matter of bodies to the qualified
bodies of Empedocles, the four simple bodies of Empedocles to the four
first combinations of these, the four humours. So to the universe
the whole solar system, the sun and all its planets, may be a simple
unit."[395]
Here Bruno suggests two principles for the classification and
systematising of the sciences, to which it would have been well had he
himself and his successors faithfully adhered. The one is, that the
modes of measurement, _i.e._ the methods and laws of the sciences,
must differ for the different kinds of existence studied: that a
biological law, for example, cannot be adopted as an explanation of
mental phenomena, nor the atomic theory account for the phenomena of
life. On the other hand there are _orders_ of existence, according to
the complexity of the subjects involved. If we regard the science which
deals with the more concrete subject as "higher," then each higher
science (_e.g._ psychology) must take for granted the principles and
results of each lower science (biology, physics, mathematics),--each
must adopt and retain a unit for itself, which it has not further to
analyse.
[Sidenote: The "minima" in the classification of sciences.]
In the same way the minima offer a ground for the distinction of the
more abstract sciences one from another. The term "individual nature"
(_atoma natura_) may, according to Bruno, have one of several uses. It
may be applied either "negatively or privatively, and if negatively,
then either accidentally or substantially." His instance of the
_accidental_ use is a voice or sound, which expands spherically, is
wholly wherever it is, _i.e._ the full content of the sound is heard,
wherever its influence extends, not a part here, a part there, although
the intensity may vary in degree. Of the _substantial_ use examples are
the spirit, which is wholly in the whole body of man, or that spirit
which is in the whole extent of the life of the earth, by whose life we
live and in which we have our being, or, above this substantial nature
or individual soul, that of the universe, and supreme above all, the
mind of minds, God, one spirit completely filling all things.[396]
The atom-nature is _privatively_ so-called, when it is the element and
substance of a magnitude which is the same in kind with it, and may
be reduced to it, and it is distinguished from the atom _negatively_
so-called, because it is not divisible, either in genus or in species,
either _per se_ or _per accidens_. Examples are, (1) in discrete
quantities:--unity to the mathematician, the universal proposition to
the logician, the syllable to the grammarian; and (2) in continuous
quantities, varying with the species of continuum:--the minimal pain,
sweetness, colour, light, triangle, circle, straight line, curve; in
duration, the instant; in place, the minimal space; in length and
breadth, the point; in body, the least and first body.
[Sidenote: Minimum as substance.]
In the second place, the atom or minimum is also a metaphysical [Greek:
pou stô]; not only is it the last result of analysis, but it is also
the permanent substance of being, and again it contains all being in
itself--it is essence of being. Thus such an individual nature "never
comes into existence by way of generation, nor passes out of it by way
of corruption or dissolution; only _per accidens_ may we say that it
now is, now is not."[397] Certain of them, however, the souls, deities,
God, are in their intrinsic nature eternal, immortal, indissoluble. Of
these it was Bruno's intention to treat at large in a _Metaphysics_ and
a _De Anima_ which he purposed to write "if God granted him time."[398]
Unfortunately, it was willed otherwise.
Nothing that becomes, changes, decays, is real (_ens_). It is by
meditating on this perpetual unity of nature, by conforming ourselves,
and preserving ourselves in likeness to it, that we come to partake in
the life of the gods, and to deserve the name of substance. That which
time, movement, fate bring to us is nought; for while they are, they
are not. "Let us then," cries Bruno, "supply the mind with material,
in the contemplation of the _minimum_, through which it may exalt
itself to the _maximum_."[399] Since the real minimum, whether atom
or soul, is immortal and indestructible, we know, as Pythagoras saw,
that there is no death, but only transition; death is a dissolution
which can occur only to the composite, for the composite is never
_substance_, but is always _adventitious_. Otherwise we should be
changing our substance every moment with the continuous influx of
atoms into our bodies. Only by the individual substance of the soul
are we that which we are; about it as a centre, which is everywhere in
its whole being (_ubique totum_), the disgregation and aggregation of
atoms takes place. According to a law of the soul-world, all bodies
and forces tend to the spherical form; God, as monad of monads, is the
perfect or infinite sphere, of which the centre is at once nowhere and
everywhere; and in Him (as in all minima, simple substances, monads)
all opposites coincide, the many and the few, finite and infinite;
therefore that which is _minimum_ is also _maximum_, or anything
between these, each is all things, the greatest and the whole.[400]
Therefore, if contemplation is to follow in the footsteps of nature, it
must begin, continue, and end with the _minimum_.[401] In other words,
the minimum in each sphere of being contains implicitly in itself the
whole reality of that sphere. The minimum is its substance, not merely
the ultimate of analysis, but the actual source, the dynamic origin of
reality, as God is implicitly the whole universe and also the source of
the universe as it actually exists. It is because the minimum is all
reality, is the _maximum_, that the knowledge of it gives us that of
the whole.
[Sidenote: Uniqueness of all things.]
[Sidenote: Sense and knowledge.]
[Sidenote: Relativity.]
[Sidenote: Judgment based upon sensation.]
In the third place the atomic theory offers an explanation of the
uniqueness of each natural existence, which Bruno's philosophical
theory already assumed. The ever moving atoms present a mechanism by
which the infinite diversity and infinite succession of change in
things may be brought about. The _appearance_ of similarity, exactness,
etc., is, as we have found, an illusion. Mathematically exact figures
or bodies--a true circle, for example--are unattainable by sense, even
if they exist in nature; but they do not exist in nature. Sense is the
primary faculty, through which the material of all others must pass,
so that what has not entered through that window of the soul cannot be
known at all. But a single point out of place on the circumference of a
circle makes it cease to be a true circle, and our sense-apprehension
is necessarily so confused and indistinct that we cannot distinguish
between the true and the false, where truth depends upon so
inappreciable a difference. Moreover sense-knowledge is relative to
the knowing subject, or to the subject's position with regard to the
object. What to the eye of one is too large is to another too small; a
sound which is pleasant to one ear is not so to another; the food which
to the hungry man tastes sweet, to the full man is nauseous; the ape to
the ape is beautiful, but to the man is of laughter-inspiring ugliness.
Hence the circumspect will not say "this has a good odour, taste,
sound, this has a beautiful appearance," but will add "to me," "now,"
"sometimes." Nothing is good or evil, pleasant or painful, beautiful or
ugly, _simply_ and _absolutely_; but the same objects in relation to
individual subjects receive from the senses contrary denominations,
as they in fact produce contrary effects. In deciding what is to be
called good or bad, honourable or base, nature and custom have been
the chief agents, and alterations have issued from the slow rise and
victory of different opinions. Among the Druids and Magi certain things
were performed publicly at sacrifices which now, even when committed in
privacy, are regarded as execrable, and are so by way of law, and in
the present condition of affairs. Philosophy, as it teaches to abstract
from particulars, to bring the nature and condition of things as far
as possible under an absolute judgment, must define differently the
useful and good in an _absolute_ sense, from the useful and good as
_contracted_ to the human species. Objectively there is no definitely
good or definitely evil, definitely true or definitely false, so that
from one point of view we may say that all things are good; from
another that all things are evil; from a third that nothing is good
or evil, as neither of the contraries is true; from a fourth that all
things are both good and evil, as each of the contraries is true.
No sense deceives or is deceived: each judges of its proper object
according to its own measure. There is no higher tribunal to which to
refer its object, nor can reason judge of colour any more than can the
ear; sensible truth does not follow any general or universal rule,
but one which is particular, mutable, and variable. In the working
of an external sense there may be different degrees of perfection or
defect, but not of truth or falsity, which consist in the reference
of the subject and predicate to one another. The faculty by which we
judge this or that to be _true_ colour or light, and distinguish from
apparent colour or light, is not in the eye. To affirm that man is an
animal, we must know both man and animal, know that animal nature is in
man, and other things which, as means or circumstances, concur directly
or indirectly in this knowledge. External sense can apprehend only one
species or image of the object; from the colour and figure to pass to
its name, its truth, its difference from other objects, belongs to a
more inward faculty. Yet the latter is always based upon sense;--a deaf
man can neither imagine nor dream of sounds which he has never heard,
nor a blind man of colours and figures which he has never seen.[402]
This digression on the relativity of knowledge, and on the different
functions of sense and reason, in which Bruno follows partly the
teaching of Lucretius, partly the Peripatetic doctrine of knowledge,
shows that even if a true or perfectly exact geometrical figure existed
in nature, none of the faculties with which we are endowed could
apprehend it, since it is not given by external sense.[403]
[Sidenote: No exactness or similarity in composites.]
But in the second place[404] reason tells us that no true circle,
or other figure, is possible in nature: for there is in nature
no similarity except in the atoms; a true circle would imply the
equality of all lines from the centre, but no two lines in nature
are entirely and in all respects equal to one another. The circle or
part of a circle which appears most perfect to us--the rainbow--is
an illusion of the senses, due to the reflection of the light of the
sun from the clouds; so the circles made by a stone falling into
water cannot be perfect, for this would mean that the stone itself
is perfectly spherical, that the water is everywhere of the same
density, that no wind is playing upon its surface. Sound is not equally
diffused owing to differences in the density and rarity of the air,
nor is the horizon ever a perfect circle, owing to differences of
clearness in different directions. Object and faculty alike are in
continuous change; all natural things are continually altering their
form or changing their position; therefore although they seem to
sense to remain fixed for a time, we know that this is impossible,
from the nature of things.[405] Whatsoever falls in the scope of
sense-perception, even the distant sphere and stars, we judge to
consist of the same elements, therefore to be subject equally to
perpetual variability and vicissitude. Thus--the atoms alone being
simple, and remaining ever the same--no composite thing can be the same
for one moment even, as each is being altered continually in all parts
and on all sides by the efflux and influx of innumerable atoms.[406]
"Hence nothing is perfectly straight, nothing perfectly circular among
composites, nothing absolutely solid but the atoms, nothing absolutely
void but the spaces between them." The facet of a diamond appears to
be a perfect plane, perfectly compact, yet in reality it is rough and
porous.[407] In matter no two lines or figures are entirely equal, nor
can the same figure be repeated twice.[408] No man is twice of the same
weight, the very instruments by which we measure and weigh things are
themselves in constant change, and the flux of atoms is never equal,
but now denser, now rarer. In general no two things are of the same
weight, length, sound, or number, nor are two motions or parts of
motion ever the same. To say that ten trees are equal to ten others is
to speak merely from a _logical_ point of view, for in fact each is
_one_ in a peculiar and special sense.[409] "Equality is only in those
things which are permanent and the same; changing bodies are unequal to
themselves at any two instants."[410] "Nothing variable or composite
consists at two moments of time wholly of the same parts and the same
order of parts, since the efflux and influx of atoms is continuous, and
therefore not even from the primary integrating parts will you be able
to name a thing as the same twice."[411]
Number itself is not an absolute, but a relative determination: it does
not touch the nature of the thing itself. Nature has no difference
of number, as we have, of odd and even, tens and hundreds; nor do
the gods, spirits, or other rational beings define the numbers and
measures of objects by the same series of terms. Both numbers and
the methods of numbering are as diverse as are the fingers, heads,
and mental equipment of the numberers. That which fits in with the
numbers of nature will therefore never fit in with our numbers. Thus
ten horses and ten men, although determined arithmetically by one and
the same number, are in nature, or physically, wholly unequal to one
another.[412]
[Sidenote: The atoms.]
[Sidenote: Time and space.]
In order that men's minds may be better disposed for the reception of
truth, it is necessary first to demolish the foundations of error;[413]
Bruno accordingly sets himself to disprove the infinite divisibility of
the continuum.[414] It was the common belief that there were no limits
set to the dividing power of either nature or art, so that, however
small a part might be arrived at, it was possible to divide it into yet
smaller parts, on the analogy of the division of a fraction into tens
of thousands of parts. Bruno denied this analogy to be justifiable,
as in the latter case we are concerned not with division but with
multiplication or addition, not with a continuum, but with discrete
quantities, and it was part of his general theory that the addition of
discretes might be carried on _ad infinitum_; the inverse process he
denied. He thus held opinions directly contrary to those of Aristotle,
with whom the mass of the universe was finite, limited by its enclosing
sphere, the parts of the universe unlimited. Aristotle had an upper but
not a lower limit; Bruno a lower but not an upper. So time and space,
which Aristotle had treated as _finite_ in duration or extent, but as
_infinitely divisible_, like the universe itself, are regarded by Bruno
as unlimited in their dimensions, but as consisting of discrete minimal
parts. "In every point of duration is beginning without end, and end
without beginning"; it is the centre of two infinities. Therefore the
whole of duration is one infinite instant, both beginning and end, as
immeasurable space is an infinite _minimum_ or centre. "The beginning
and source of all errors, both in physics and in mathematics, is the
resolution of the continuous _in infinitum_. To us it is clear that
the resolution both of nature and of true art, which does not advance
beyond nature, descends from a finite magnitude and number to the
atom, but that there is no limit to the extension of things either
in nature or in thought, except in regard to the form of particular
species. Everywhere and always we find the _minimum_, the _maximum_
nowhere and never. The _maximum_ and _minimum_, however, may in one
sense coincide, so that we know the maximum to be everywhere, since
from what has been said it is evident that the maximum consists in the
minimum and the minimum in the maximum, as in the many is the one, in
the one the many. Yet reason and nature may more readily separate the
minimum from the maximum than the maximum from the minimum. Therefore
the immeasurable universe is nothing but centre everywhere; eternity
nothing but a moment always; immeasurable body an atom; immeasurable
plane a point; immeasurable space the receptacle of a point or
atom."[415]
The chief source of error on the part of the Peripatetics was their
failure to distinguish between the minimum as a part, and the minimum a
_terminus_ or limit. Hence their idea that no combination of physical
minima would give a magnitude, since two or more would touch one
another with their whole surface, _i.e._ would coincide:--otherwise
the minimum would have parts, a part of each touching the other, and
a part not touching. On their theory it would follow that magnitudes
do not consist of parts, or at least not of elementary parts. This is
inconsistent with nature, for existing magnitudes must have been built
up out of nature's elements, and with art, for art can measure only
on the assumption of first parts. It is true that what is posited as
first part in one operation may be the last result in another, for
the _minimum_, as we have seen, is a relative conception, but _some_
first part is always assumed in any operation. And as the operation
of art is not infinite, so neither is there infinite subordination of
parts.[416] When two minima touch one another, they do not do so with
their whole body, _or any part of it_, but one with its terminus or
limit may touch several others; no body touches another with the whole
of itself or a part, but with either the whole or the part of its
_limiting_ surface. The _terminus_ of a thing is therefore no part of
it, and by implication not a minimal part. Hence there are two kinds of
_minima_ concerned--that of the touching body, or part, and the minimum
of that by which the contact is effected, the _terminus_.[417] The
atom, which is the minimal sphere, touches in the absolutely minimal
point, the smallest _terminus_. Other spheres do not touch in a point
simply, but in more than one, or in a plane circle.[418] By adding
limit to limit we never obtain a magnitude; the _terminus_ is no part,
and therefore if in contact it would touch with its whole self, so that
magnitude is not made up of _termini_, whether points, atoms, lines, or
surfaces which are termini; and this was the false ground on which the
Aristotelians denied the possibility of the atom. It remained to ask if
the _termini_ were infinite, since the atoms were not; but it was clear
that their number was determined by that of the atoms. For two limits
do not touch one another:--"They do not cohere or make a _quantum_,
but through them others in contact with one another make a _contiguum_
or _continuum_."[419] It may be added that if the parts of a divisible
body were infinite in number, the parts of the whole would be equalled
by the parts of the half, for in the infinite there can be no greater
and less. In the infinite, as we have seen above, there is no
difference between palms, digits, miles, between units and thousands,
nor in the infinite time that has elapsed are there more months than
years, more years than centuries. If any one set of these were less
than the others it would be finite, and if one finite number may be
applied to the whole, then the whole is finite.[420] The force of the
Achilles dilemma was derived from the false idea that the _minimum_ of
one kind had some relation to that of another kind, _e.g._ that of
time to that of motion, that of impulsive force to that of the motion
produced. A thing of one kind does not define or measure a thing of
another, and the duration of one does not compare in the same sense
with the duration of another. Parts of different things are only
equivocally called parts, and _minima_ are _minima_ only according to
their proper (and diverse) definitions; therefore one is not measured
by another, except in a rough way, for practical purposes.[421]
[Sidenote: The vacuum. Atoms spherical.]
As the atoms come into contact with one another, not in all points of
their surface, but in a definite number, it follows that there is a
space between them, in the interstices; it was this thought which led
Democritus to posit a vacuum.[422] The figure of the corporeal minimum
must be spherical, for any mass which has projections can always be
thought of as smaller, when these projections have been removed; and
nature itself suggests this, by the gradual rounding off of substances
through time, and the apparent roundness and smoothness of rough and
jagged bodies when the observer is at a distance.[423] Diversity of
forms of composite bodies results easily from spherical atoms, through
differences in situation and order, differing amounts of vacuum and
solid; but a simple vacuum with solid bodies is not sufficient,--there
must be a certain matter through which the latter cohere together.[424]
Although all other determinations may be abstracted from, figure at
least must be predicated of the atoms; quantity cannot be asserted of
that which is thought to be unfigured. These determinations of the
minimum, though not given to sense, may nevertheless be made object
of thought, by analogy or inference from the combinations of sensible
_minima_ in larger composites, the same forms of aggregation being
repeated in the higher which occur in the lower forms.[425]
From the consideration of mathematical figures as consisting of
_minima_, Bruno attempted both to remodel and to simplify the existing
mathematical theory, and, unfortunately fell foul of the new analytical
mathematics, the theory of rationals and of approximations, which
at that time was receiving marked extensions, and which has since
justified itself so completely by results. It is true he did not
entirely reject it, but he regarded it as merely an artifice for rough
practical measurements. The true measure is always the _minimum_,
inferred by analogy from the combinations of greater parts, which
are perceived by sense. Thus the minimal circle, after the atom
itself, consists of seven minima, the minimal triangle of three, and
the minimal square of four, and as each figure increases not by the
addition of one atom merely, but by a number determined by the original
number of atoms in the figure, it follows that no one figure is ever
equal to another. Thus the second triangle is of six minima, the second
square of nine, the second circle of nineteen. The "squaring of the
circle" is therefore impossible,[426] although it may be approximately
reached through the ultimate coincidence of arc and chord, by which
the circle becomes equal to a polygon with an infinite number of
sides.[427] This, however, is only an approximation of sense, which
fails to observe the infinitesimal differences that are caused by
the existence of a few atoms, more or less, in a figure. They are
visible to the eye of reason, which comprehends that no two figures in
nature are ever exactly equal. In exact geometry the number of one
species of figure has nothing in common with that of another. It is
clear, however, that even on his own ground Bruno was in error in this
regard; for example, the seventh triangle and the fifth square are
each composed of thirty-six minima.[428] But it is hardly necessary to
take seriously his teaching in this respect. He was wholly governed
by the belief in the infinite diversity of nature, and the absolute
incommensurability of any member of one species of beings with one
of a different species. "Since a definite minimum exists, it is not
possible either in reality or in thought for a square to be equalled
by a circle, nor even a square by a pentagon, a triangle by a square,
nor in fine any species of figure by a figure of another species; for
difference in the number of sides implies also difference in the order
and number of parts. As figures in this respect are as numbers, and
one species of number cannot be equalled by another either 'formally'
or fundamentally (_i.e._ either in idea or in fact), we can never make
an equilateral figure of any kind equal to one of another by first
parts."[429] Where this transformation is apparently carried out, as
where a cube of wax is moulded to another figure, the result is due to
the varying degrees of density in the different parts of the material;
no solid parts are added or subtracted, but the disposition and extent
of the pores or vacua are altered. But no argument can be drawn from
this rough method, for the principles of practice are different from
those of science.[430]
The latter principles are then applied boldly to geometrical science:
thus it is shown that an angle, although it may be multiplied
indefinitely, can be divided only into two parts; all its lines, it is
understood, consisting of _fila_ or rows of atoms;[431] that the circle
has not an infinite number of radii, for from the circumference to
the centre only six such lines can be drawn;[432] that not every line
can be divided into two equal parts, for the physical line or _filum_
may, naturally, consist of an odd number of atoms;[433] in any case
geometrical bisection can at best be a near approximation,--though the
two halves be apparently equal, they may really differ by many atoms.
On this basis, in the fourth and fifth books of the _De Minimo_, Bruno
offers a simplification of the geometry of Euclid. As nature itself is
the highest unification of the manifold, and the monad is the unity
and essence of all number, so we are taught to pass "from the infinite
forms and images of art to the definite forms of nature, which the
mind in harmony with nature grasps in a few forms, while the _first
mind_ has at once the potentiality and the reality of all particular
things in the (simple) monad."[434] In accordance with the method
of simplification suggested by this doctrine, Bruno sets himself to
show that the greater part of Euclid may be intuitively presented in
three complicated figures, named respectively the _Atrium Appollinis_,
_Atrium Palladis_, and _Atrium Veneris_. He hoped that by this means,
"if not always, for the most part at any rate, without further
explanation, the demonstration and the very evidence of the thing
might be presented to the senses of all, without numbers,--not after
the partial method of others, who in considering a statue take now the
foot, now the eyes, now the forehead, now other parts separately,--but
explaining all in each and each in all."[435] It is no part of the
purpose of this book to go at length into the mathematics of Bruno,
which unfortunately have not yet met with a competent exposition.
Apart from the difficulty of the matter itself, the poetical form and
setting of his theorems is an additional stumbling-block in the way of
understanding. Bruno was put to many shifts in order to give a poetical
colouring to the most prosaic of subjects.
We have gone thus fully into the detail of Bruno's atomic theory, more
so perhaps than its intrinsic value seems to demand, because this
aspect of his doctrine is the most important philosophically, and
has exercised the greatest influence upon the course of speculation.
It also provides most clearly an exemplification of the return which
was made, or thought to be made, by the Renaissance to the older
pre-Aristotelian philosophy and science. The rejection by Aristotle
and his scholastic followers of the atomic theory of Leucippus and
Democritus had been based upon the identification of space and body.
The possibility of a vacuum in the corporeal world was denied, on
the ground that discreteness was inconsistent with the continuity
which was felt to be a necessary condition of space. Accordingly, the
reintroduction of the atom was possible only in one of two ways--either
by the distinction between body and space, or by the application of
the atomic constitution of body to space itself. The former and truer
solution was not open to Bruno. His time was still too much under
the domination of Peripatetic thought for him to be able to take the
important step of critically separating these two notions. The latter
way, therefore, was that which he followed. Hence the curious attempt
to remodel mathematical theory on the basis of the atom, which we
have described above, and the reduction of mathematical certainty to
an illusion of sense. Figure is to be found only in the combinations
of atoms; and owing to the spherical form of the atom, the infinite
number of them existing in any body which is presented to sense, and
the space which lies between their surfaces, mathematical equality and
exactness are impossible. Neither straight line, therefore, nor perfect
circle are to be found in reality. Mathematics, which should be based
upon, or which presupposes, continuity, is confounded with physics,
which presupposes the analysis of body into discrete, impenetrable
atoms. Physical atomism finds its justification in the experienced
fact of resistance, which is the primary quality of body as perceived
by our senses. In mathematical space, on the other hand, we abstract
from all qualities except that of dimension only. Resistance would be
inexplicable were it possible to proceed _ad infinitum_ in dividing
matter; it implies an ultimate irreducible and indestructible unit,
whether we regard this unit as a centre of force or as an inert
substance merely.
The same influence of Aristotelian thought led Bruno to posit a subtle
matter, the Ether, as filling up the interstices between the atoms.
Space and body having been identified, it was seen that a vacuum was
inconsistent with the nature of things. The Aristotelian _plenum_ was
reintroduced in this form, that there might be some reality where the
discrete atoms were not. The bolder step of asserting the fact, and
indeed, the necessity of a vacuum as a presupposition of knowledge of
the material world, was not taken until there appeared the work of
Gassendi, by whom the final blow was given to the old conception of
body and space, and through whom the critical separation of the one
from the other was first rendered possible. It is curious that Bruno
did not think of applying to the continuous ether any geometrical
measure; had he done so, he would have understood the value of the new
theory of infinitesimals and irrationals which he opposed so strongly.
Again, had he carried out more fully the distinction which he draws
between the atom and the _terminus_ or limit, the same result would
have followed. Pure geometry is the geometry of the limit; for the
limit is not only between atom and atom, or body and body, but also
between atom and vacuum or ether. In this sense it is both continuous
and figured, the compatibility of which qualities Bruno had denied; the
continuous is measured, not by making it discrete, but by making the
number, the measure, fluid or continuous.
[Sidenote: Metaphysical atomism.]
Lasswitz has shown that there are in Bruno's theory three distinct
aspects, not, however, clearly separated one from another, of the
atomic hypothesis: they may be named severally the metaphysical, the
physical, and the critical aspects. From the metaphysical point of view
the atom is the ultimately simple, indeterminate substance of things;
its conception results from the effort to find the real substance
which is outside of, and unaffected by, the change and decay apparent
on the surface of things, but felt to be unreal. Simplicity, unity,
substance, is that which is sought, an abiding somewhat underlying
the flux of the universe, which is regarded as an illusory appearance
to sense. From this aspect it is that the identity of _minimum_ and
_maximum_, of the least with the greatest, is to be explained. Number,
plurality, and diversity no longer apply to the absolutely simple: all
are determinations of human and finite origin which are here no longer
valid. In the simple all contraries coincide, for the very reason that
it has no determinations in itself; even the highest qualities which
men would attribute to God, for example,--justice and goodness,--are
improperly predicated of him, for as in him the greatest and the least
coincide, so do goodness and evil and all other contrary qualities. In
this respect Bruno was following closely in the footsteps of Nicolaus
of Cusa.
[Sidenote: Physical Atomism.]
[Sidenote: Critical Atomism.]
From the second point of view, that of _physical_ atomism, the atom
is nothing more than a hypothesis to explain the constitution and
qualities of nature as we experience it. We seek to account for the
differences in material bodies and in their ways of acting upon one
another by the interaction of ultimate elements of which the nature
and laws may be variously interpreted. Of this point of view also
there are traces in Bruno, although for it he had least regard. He
does not attempt, for example, to apply the theory of the atoms to
explain the four elements which had come down from Aristotle. He
leaves them practically intact, and we have seen that they form a
standing difficulty in the way of a consistent theory. The earth alone
is atomic in its nature; water, air, and fire seem alike fluid and
continuous in quality, but wherein their difference from one another
consists he was unable, or did not care, to make clear. Perhaps, if
we take his view at its best, we should say that all three represent
strata, varying in density, of the one fluid and all-pervading ether.
Had he worked out this conception, which was evidently present, on
occasions, to his mind, he would have given an example of what is
meant by physical atomism. But this was left for another century to
fulfil. From the third or _critical_ point of view, which inquires
into the presuppositions or the possibility of knowledge, Bruno
may be regarded as being, to some extent, a forerunner of Kant, in
the stress he lays upon the relation of the minimum to measure or
knowledge, and in his doctrine of the relativity of the conception of
the _minimum_. The minimum, instead of a last of division, becomes a
first of composition--a ground which we must necessarily assume in
order to account for the experienced fact of composition. To know a
composite is to measure it, and measurement implies the _minimum_ or
first part, without which quantity in any form cannot be explained.
As the comparison of numbers with one another, their determination
as greater or less, is only possible on the assumption of a unit, a
common measure to which each may be referred, so the comparison of
bodies with one another, as to quantity and quality alike, demands a
corporeal minimum, to which their differences must be reduced. This
relation to knowledge carries with it the relativity of the minimum
according to the subject-matter with which the knower is for the time
being concerned. If all knowledge is of the same type, then in each
application of it--each subdivision of knowledge as a whole--there
is presupposed the corresponding minimum. That which is least in one
sphere may be greatest in another; that which is element of one science
may be that which another seeks to analyse into lesser constituents.
The celestial body, which is a highly complex combination of elements,
may be the unit of astronomical science. The phrase, which is the unit
of the rhetorician, is analysed by the logician and the grammarian into
terms and words; these are analysed by another science into syllables
and letters; these by the mathematician into lines and points. Thus
every science has its own (relative) minimum. Only one _minimum_ is
_absolutely_ so named,--God as the monad of monads. It is to be noted
that the relativity of the monad is dependent upon the origin of its
conception, in the conditions of knowledge; it is because quantity
is universal that a minimum is necessary, and it is because quantity
differs in kind, in each subject of knowledge,--because it is, in
scholastic phrase, equivocally applied in the different cases,--that
the minima differ from one another. The minimal number is no measure
of the minimal body nor of the geometrical figure, and the numbers
which are in use among men are not those which may be employed by other
and higher rational beings. Thus, even number itself is a relative
determination; ten horses, said Bruno, are not _really_ equal to ten
men, but only _conventionally_.
The ancient atomism upon which Bruno founded his theory was, at any
rate in its traditional rendering, frankly materialistic. It admitted
nothing but atoms and the void, all things else being dependent upon
the _composition_ of atoms, which itself, and all that results from
it, is merely an appearance to sense, without corresponding reality
in nature. All physical operations were explained by mechanical
arrangement and movement of the atoms. The method which was pursued
thus unscientifically, without consciousness of the extent of its
validity, modern atomic theory has followed scientifically, with full
comprehension of its bearings, and perhaps without due consideration
of its limits. Bruno tells us that he had at one time been an adherent
of Democritus' atomic theory, but on reflection had been unable to
rest satisfied with his materialistic account of the nature of things.
In this case also he showed himself unable to get rid of the ties
which bound all the thought of his time--even that thought which most
believed itself to be free.
Aristotle's distinction of form and matter in nature, of pure activity
and pure passivity, had still sufficient influence to render even in
Bruno's time a purely mechanical treatment of nature an impossibility.
The opposing school, the Neo-Platonism which attracted so many minds
of that period, because of its supposed inconsistency with Aristotle's
system, was itself an offshoot, to some extent, of that system, and
was still less scientific in its tendency. Mysticism, of which it was
partly a cause and partly an effect, lent its weight also against
any mechanical interpretation of nature. Thus even while apparently
governed by scientific aspiration, Bruno gives a teleological scheme of
the universe which renders any scientific explanation of it impossible.
Not only, as we have seen, is the ether identified with the first
substance, spirit, or soul of the universe, but also the greater and
lesser organic bodies are governed each by its individual soul, which
is somehow distinguished from the universal spirit, and within each of
these is an infinite number of smaller living bodies. In other words,
the atoms themselves are animated _virtually_, if not _actually_. This
animistic interpretation is in direct conflict with the mechanical
interpretation which science has followed, and which it must continue
to follow if it is to produce any result. Thus, motion and the changes
of composition that derive from motion are explained not by the
mechanical impact of atoms and bodies upon one another, but by the
action of the intrinsic soul in each being, which causes the motion of
the body, in accordance with its need and desire of self-preservation.
All motion, even the slightest, is thus explained by a final cause.
In the whole universe also, the constantly occurring changes and
transformations are due to a similar final cause--the need for each
thing to become _explicitly_ that which it already is _implicitly_,
_i.e._ the whole of reality. It required once more a critical
separation of the spheres of validity of the respective conceptions
of nature and spirit, such as Kant attempted, before full scope could
be given to mechanical interpretation on the one side, and teleology
restricted to the domain of spirit only on the other.