mode of thought. A writer might be excused for introducing into an
avowed work of fancy this dance of the planets, and conception of an
animated Earth. If finely executed, he might even be admired for it. No
one blames a poet for ascribing feelings, purposes, and human
propensities to flowers. Because a conception might be interesting, and
perhaps edifying, in a poem, M. Comte would have it imprinted on the
inmost texture of every human mind in ordinary prose. If the imagination
were not taught its prescribed lesson equally with the reason, where
would be Unity? "It is important that the domain of fiction should
become as _systematic_ as that of demonstration, in order that their
mutual harmony may be conformable to their respective destinations, both
equally directed towards the continual increase of _unity_, personal and
social."[26]
Nor is it enough to have created the Grand Fétiche (so he actually
proposes to call the Earth), and to be able to include it and all
concrete existence in our adoration along with the Grand Etre. It is
necessary also to extend Positivist Fetishism to purely abstract
existence; to "animate" the laws as well as the facts of nature. It is
not sufficient to have made physics sentimental, mathematics must be
made so too. This does not at first seem easy; but M. Comte finds the
means of accomplishing it. His plan is, to make Space also an object of
adoration, under the name of the Grand Milieu, and consider it as the
representative of Fatality in general. "The final _unity_ disposes us to
cultivate sympathy by developing our gratitude to whatever serves the
Grand Etre. It must dispose us to venerate the Fatality on which reposes
the whole aggregate of our existence." We should conceive this Fatality
as having a fixed seat, and that seat must be considered to be Space,
which should be conceived as possessing feeling, but not activity or
intelligence. And in our abstract speculations we should imagine all our
conceptions as located in free Space. Our images of all sorts, down to
our geometrical diagrams, and even our ciphers and algebraic symbols,
should always be figured to ourselves as written in space, and not on
paper or any other material substance. M. Comte adds that they should be
conceived as green on a white ground.
We cannot go on any longer with this. In spite of it all, the volume on
mathematics is full of profound thoughts, and will be very suggestive to
those who take up the subject after M. Comte. What deep meaning there
is, for example, in the idea that the infinitesimal calculus is a
conception analogous to the corpuscular hypothesis in physics; which
last M. Comte has always considered as a logical artifice; not an
opinion respecting matters of fact. The assimilation, as it seems to us,
throws a flood of light on both conceptions; on the physical one still
more than the mathematical. We might extract many ideas of similar,
though none perhaps of equal, suggestiveness. But mixed with these, what
pitiable _niaiseries_! One of his great points is the importance of the
"moral and intellectual properties of numbers." He cultivates a
superstitious reverence for some of them. The first three are sacred,
_les nombres sacrés_: One being the type of all Synthesis, Two of all
Combination, which he now says _is_ always binary (in his first treatise
he only said that we may usefully represent it to ourselves as being
so), and Three of all Progression, which not only requires three terms,
but as he now maintains, never ought to have any more. To these sacred
numbers all our mental operations must be made, as far as possible, to
adjust themselves. Next to them, he has a great partiality for the
number seven; for these whimsical reasons: "Composed of two progressions
followed by a synthesis, or of one progression between two couples, the
number seven, coming next after the sum of the three sacred numbers,
determines the largest group which we can distinctly imagine.
Reciprocally, it marks the limit of the divisions which we can directly
conceive in a magnitude of any kind." The number seven, therefore, must
be foisted in wherever possible, and among other things, is to be made
the basis of numeration, which is hereafter to be septimal instead of
decimal: producing all the inconvenience of a change of system, not only
without getting rid of, but greatly aggravating, the disadvantages of
the existing one. But then, he says, it is absolutely necessary that the
basis of numeration should be a prime number. All other people think it
absolutely necessary that it should not, and regard the present basis as
only objectionable in not being divisible enough. But M. Comte's puerile
predilection for prime numbers almost passes belief. His reason is that
they are the type of irreductibility: each of them is a kind of ultimate
arithmetical fact. This, to any one who knows M. Comte in his later
aspects, is amply sufficient. Nothing can exceed his delight in anything
which says to the human mind, Thus far shalt thou go and no farther. If
prime numbers are precious, doubly prime numbers are doubly so; meaning
those which are not only themselves prime numbers, but the number which
marks their place in the series of prime numbers is a prime number.
Still greater is the dignity of trebly prime numbers; when the number
marking the place of this second number is also prime. The number
thirteen fulfils these conditions: it is a prime number, it is the
seventh prime number, and seven is the fifth prime number. Accordingly
he has an outrageous partiality to the number thirteen. Though one of
the most inconvenient of all small numbers, he insists on introducing it
everywhere.
These strange conceits are connected with a highly characteristic
example of M. Comte's frenzy for regulation. He cannot bear that
anything should be left unregulated: there ought to be no such thing as
hesitation; nothing should remain arbitrary, for _l'arbitraire_ is
always favourable to egoism. Submission to artificial prescriptions is
as indispensable as to natural laws, and he boasts that under the reign
of sentiment, human life may be made equally, and even more, regular
than the courses of the stars. But the great instrument of exact
regulation for the details of life is numbers: fixed numbers, therefore,
should be introduced into all our conduct. M. Comte's first application
of this system was to the correction of his own literary style.
Complaint had been made, not undeservedly, that in his first great work,
especially in the latter part of it, the sentences and paragraphs were
long, clumsy, and involved. To correct this fault, of which he was
aware, he imposed on himself the following rules. No sentence was to
exceed two lines of his manuscript, equivalent to five of print. No
paragraph was to consist of more than seven sentences. He further
applied to his prose writing the rule of French versification which
forbids a _hiatus_(the concourse of two vowels), not allowing it to
himself even at the break between two sentences or two paragraphs; nor
did he permit himself ever to use the same word twice, either in the
same sentence or in two consecutive sentences, though belonging to
different paragraphs: with the exception of the monosyllabic
auxiliaries.[27] All this is well enough, especially the first two
precepts, and a good way of breaking through a bad habit. But M. Comte
persuaded himself that any arbitrary restriction, though in no way
emanating from, and therefore necessarily disturbing, the natural order
and proportion of the thoughts, is a benefit in itself, and tends to
improve style. If it renders composition vastly more difficult, he
rejoices at it, as tending to confine writing to superior minds.
Accordingly, in the Synthèse Subjective, he institutes the following
"plan for all compositions of importance." "Every volume really capable
of forming a distinct treatise" should consist of "seven chapters,
besides the introduction and the conclusion; and each of these should be
composed of three parts." Each third part of a chapter should be divided
into "seven sections, each composed of seven groups of sentences,
separated by the usual break of line. Normally formed, the section
offers a central group of seven sentences, preceded and followed by
three groups of five: the first section of each part reduces to three
sentences three of its groups, symmetrically placed; the last section
gives seven sentences to each of its extreme groups. These rules of
composition make prose approach to the regularity of poetry, when
combined with my previous reduction of the maximum length of a sentence
to two manuscript or five printed lines, that is, 250 letters."
"Normally constructed, great poems consist of thirteen cantos,
decomposed into parts, sections, and groups like my chapters, saving the
complete equality of the groups and of the sections." "This difference
of structure between volumes of poetry and of philosophy is more
apparent than real, for the introduction and the conclusion of a poem
should comprehend six of its thirteen cantos," leaving, therefore, the
cabalistic numeber seven for the body of the poem. And all this
regulation not being sufficiently meaningless, fantastic, and
oppressive, he invents an elaborate system for compelling each of his
sections and groups to begin with a letter of the alphabet, determined
beforehand, the letters being selected so as to compose words having
"a synthetic or sympathetic signification," and as close a relation as
possible to the section or part to which they are appropriated.
Others may laugh, but we could far rather weep at this melancholy
decadence of a great intellect. M. Comte used to reproach his early
English admirers with maintaining the "conspiracy of silence" concerning
his later performances. The reader can now judge whether such reticence
is not more than sufficiently explained by tenderness for his fame, and
a conscientious fear of bringing undeserved discredit on the noble
speculations of his early career.
M. Comte was accustomed to consider Descartes and Leibnitz as his
principal precursors, and the only great philosophers (among many
thinkers of high philosophic capacity) in modern times. It was to their
minds that he considered his own to bear the nearest resemblance. Though
we have not so lofty an opinion of any of the three as M. Comte had, we
think the assimilation just: thes were, of all recorded thinkers, the
two who bore most resemblance to M. Comte. They were like him in
earnestness, like him, though scarcely equal to him, in confidence in
themselves; they had the same extraordinary power of concatenation and
co-ordination; they enriched human knowledge with great truths and great
conceptions of method; they were, of all great scientific thinkers, the
most consistent, and for that reason often the most absurd, because they
shrank from no consequences, however contrary to common sense, to which
their premises appeared to lead. Accordingly their names have come down
to us associated with grand thoughts, with most important discoveries,
and also with some of the most extravagantly wild and ludicrously absurd
conceptions and theories which ever were solemnly propounded by
thoughtful men. "We think M. Comte as great as either of these
philosophers, and hardly more extravagant. Were we to speak our whole
mind, we should call him superior to them: though not intrinsically, yet
by the exertion of equal intellectual power in a more advanced state of
human preparation; but also in an age less tolerant of palpable
absurdities, and to which those he has committed, if not in themselves
greater, at least appear more ridiculous.
THE END.
FOOTNOTES:
[1] See the Chapter on Efficient Causes in Reid's "Essays on the Active
Powers," which is avowedly grounded on Newton's ideas.
[2] Mr Herbert Spencer, who also distinguishes between abstract and
concrete sciences, employs the terms in a different sense from that
explained above. He calls a science abstract when its truths are merely
ideal; when, like the truths of geometry, they are not exactly true of
real things--or, like the so-called law of inertia (the persistence in
direction and velocity of a motion once impressed) are "involved" in
experience but never actually seen in it, being always more or less
completely frustrated. Chemistry and biology he includes, on the
contrary, among concrete sciences, because chemical combinations and
decompositions, and the physiological action of tissues, do actually
take place (as our senses testify) in the manner in which the scientific
propositions state them to take place. We will not discuss the logical
or philological propriety of either use of the terms abstract and
concrete, in which twofold point of view very few of the numerous
acceptations of these words are entirely defensible: but of the two
distinctions M. Comte's answers to by far the deepest and most vital
difference. Mr Spencer's is open to the radical objection, that it
classifies truths not according to their subject-matter or their mutual
relations, but according to an unimportant difference in the manner in
which we come to know them. Of what consequence is it that the law of
inertia (considered as an exact truth) is not generalized from our
direct perceptions, but inferred by combining with the movements which
we see, those which we should see if it were not for the disturbing
causes? In either case we are equally certain that it _is_ an exact
truth: for every dynamical law is perfectly fulfilled even when it seems
to be counteracted. There must, we should think, be many truths in
physiology (for example) which are only known by a similar indirect
process; and Mr Spencer would hardly detach these from the body of the
science, and call them abstract and the remainder concrete.
[3] Système de Politique Positive, ii. 36.
[4] The strongest case which Mr Spencer produces of a scientifically
ascertained law, which, though belonging to a later science, was
necessary to the scientific formation of one occupying an earlier place
in M. Comte's series, is the law of the accelerating force of gravity;
which M. Comte places in Physics, but without which the Newtonian theory
of the celestial motions could not have been discovered, nor could even
now be proved. This fact, as is judiciously remarked by M. Littré, is
not valid against the plan of M. Comte's classification, but discloses a
slight error in the detail. M. Comte should not have placed the laws of
terrestrial gravity under Physics. They are part of the general theory
of gravitation, and belong to astronomy. Mr Spencer has hit one of the
weak points in M. Comte's scientific scale; weak however only because
left unguarded. Astronomy, the second of M. Comte's abstract sciences,
answers to his own definition of a concrete science. M. Comte however
was only wrong in overlooking a distinction. There _is_ an abstract
science of astronomy, namely, the theory of gravitation, which would
equally agree with and explain the facts of a totally different solar
system from the one of which our earth forms a part. The actual facts of
our own system, the dimensions, distances, velocities, temperatures,
physical constitution, &c., of the sun, earth, and planets, are properly
the subject of a concrete science, similar to natural history; but the
concrete is more inseparably united to the abstract science than in any
other case, since the few celestial facts really accessible to us are
nearly all required for discovering and proving the law of gravitation
as an universal property of bodies, and have therefore an indispensable
place in the abstract science as its fundamental data.
[5] The only point at which the general principle of the series fails in
its application, is the subdivision of Physics; and there, as the
subordination of the different branches scarcely exists, their order is
of little consequence. Thermology, indeed, is altogether an exception to
the principle of decreasing generality, heat, as Mr Spencer truly says
being as universal as gravitation. But the place of Thermology is marked
out, within certain narrow limits, by the ends of the classification,
though not by its principle. The desideratum is, that every science
should precede those which cannot be scientifically constitute or
rationally studied until it is known. It is as a means to this end, that
the arrangement of the phaenomena in the order of their dependence on
one another is important. Now, though heat is as universal a phaenomenon
as any which external nature presents, its laws do not affect, in any
manner important to us, the phaenomena of Astronomy, and operate in the
other branches of Physics only as slight modifying agencies, the
consideration of which may be postponed to a rather advanced stage. But
the phaenomena of Chemistry and Biology depend on them often for their
very existence. The ends of the classification require therefore that
Thermology should precede Chemistry and Biology, but do not demand that
it should be thrown farther back. On the other hand, those same ends, in
another point of view, require that it should be subsequent to
Astronomy, for reasons not of doctrine but of method: Astronomy being
the best school of the true art of interpreting Nature, by which
Thermology profits like other sciences, but which it was ill adapted to
originate.
[6] The philosophy of the subject is perhaps nowhere so well expressed
as in the "Système de Politique Positive" (iii. 41). "Conçu logiquement,
l'ordre suivant lequel nos principales théories accomplissent
l'évolution fondamentale résulte nécessairement de leur dépendence
mutuelle. Toutes les sciences peuvent, sans doute, être ébauchées à la
fois: leur usage pratique exige même cette culture simultanée. Mais
elle ne peut concerner que les inductions propres à chaque classe de
spéculations. Or cet essor inductif ne saurait fournir des principes
suffisants qu'envers les plus simples études. Partout ailleurs, ils ne
peuvent être établis qu'en subordonnant chaque genre d'inductions
scientifiques à l'ensemble des déductions emanées des domaines moins
compliqués, et dès-lors moins dépendants. Ainsi nos diverses théories
reposent dogmatiquement les unes sur les autres, suivant un ordre
invariable, qui doit régler historiquement leur avénement décisif, les
plus indépendantes ayant toujours dû se développer plus tôt."
[7] "Science," says Mr Spencer in his "Genesis," "while purely inductive
is purely qualitative.... All quantitative prevision is reached
deductively; induction can achieve only qualitative prevision." Now, if
we remember that the very first accurate quantitative law of physical
phaenomena ever established, the law of the accelerating force of
gravity, was discovered and proved by Galileo partly at least by
experiment; that the quantitative laws on which the whole theory of the
celestial motions is grounded, were generalized by Kepler from direct
comparison of observations; that the quantitative law of the
condensation of gases by pressure, the law of Boyle and Mariotte, was
arrived at by direct experiment; that the proportional quantities in
which every known substance combines chemically with every other, were
ascertained by innumerable experiments, from which the general law of
chemical equivalents, now the ground of the most exact quantitative
previsions, was an inductive generalization; we must conclude that Mr
Spencer has committed himself to a general proposition, which a very
slight consideration of truths perfectly known to him would have shown
to be unsustainable.
Again, in the very pamphlet in which Mr Spencer defends himself against
the supposition of being a disciple of M. Comte ("The Classification of
the Sciences," p. 37), he speaks of "M. Comte's adherent, Mr Buckle."
Now, except in the opinion common to both, that history may be made a
subject of science, the speculations of these two thinkers are not only
different, but run in different channels, M. Comte applying himself
principally to the laws of evolution common to all mankind, Mr Buckle
almost exclusively to the diversities: and it may be affirmed without
presumption, that they neither saw the same truths, nor fell into the
same errors, nor defended their opinions, either true or erroneous, by
the same arguments. Indeed, it is one of the surprising things in the
case of Mr Buckle as of Mr Spencer, that being a man of kindred genius,
of the same wide range of knowledge, and devoting himself to
speculations of the same kind, he profited so little by M. Comte.
These oversights prove nothing against the general accuracy of Mr
Spencer's acquirements. They are mere lapses of inattention, such as
thinkers who attempt speculations requiring that vast multitudes of
facts should be kept in recollection at once, can scarcely hope always
to avoid.
[8] We refer particularly to the mystical metaphysics connected with the
negative sign, imaginary quantities, infinity and infinitesimals, &c,
all cleared up and put on a rational footing in the highly philosophical
treatises of Professor De Morgan.
[9] Those who wish to see this idea followed out, are referred to "A
System of Logic, Ratiocinative and Inductive." It is not irrelevant to
state that M. Comte, soon after the publication of that work, expressed,
both in a letter (published in M. Littré's volume) and in print, his
high approval of it (especially of the Inductive part) as a real
contribution to the construction of the Positive Method. But we cannot
discover that he was indebted to it for a single idea, or that it
influenced, in the smallest particular, the course of his subsequent
speculations.
[10] The force, however, of this last consideration has been much
weakened by the progress of discovery since M. Comte left off studying
chemistry; it being now probable that most if not all substances, even
elementary, are susceptible of _allotropic_ forms; as in the case of
oxygen and ozone, the two forms of phosphorus, &c.
[11] Thus; by considering prussic acid as a compound of hydrogen and
cyanogen rather than of hydrogen and the elements of cyanogen (carbon
and nitrogen), it is assimilated to a whole class of acid compounds
between hydrogen and other substances, and a reason is thus found for
its agreeing in their acid properties.
[12] According to Sir William Hamilton, as many as six; but numerical
precision in such matters is out of the question, and it is probable
that different minds have the power in different degrees.
[13] Or, as afterwards corrected by him, the appetites and emotions, the
active capacities, and the intellectual faculties; "le coeur," "le
caractère," and "l'esprit."
[14] M. Littré, who, though a warm admirer, and accepting the position
of a disciple of M. Comte, is singularly free from his errors, makes the
equally ingenious and just remark, that Political Economy corresponds in
social science to the theory of the nutritive functions in biology,
which M. Comte, with all good physiologists, thinks it not only
permissible but a great and fundamental improvement to treat, in the
first place, separately, as the necessary basis of the higher branches
of the science: although the nutritive functions can no more be
withdrawn _in fact_ from the influence of the animal and human
attributes, than the economical phaenomena of society from that of the
political and moral.
[15] Indeed his claim to be the creator of Sociology does not extend to
this branch of the science; on the contrary, he, in a subsequent work,
expressly declares that the real founder of it was Aristotle, by whom
the theory of the conditions of social existence was carried as far
towards perfection as was possible in the absence of any theory of
Progress. Without going quite this length, we think it hardly possible
to appreciate too highly the merit of those early efforts, beyond which
little progress had been made, until a very recent period, either in
ethical or in political science.