SCIENCE (CONTINUED)--POSITIVE LOGIC
Logic, says Comte, almost in the terms of Descartes, is the sole
portion of ancient philosophy which is capable of still presenting some
appearance of utility.[83] And does even this appearance correspond to
a very solid reality?
If we distinguish, according to custom, formal logic from applied
logic, Comte in his system will find no place for the former, which
establishes _a priori_ the principles and the mechanism of reasoning.
As to the principles, which are the laws of the understanding, positive
philosophy has shown that the only way to discover them is to study
the products of the human intellect, that is to say, the development
of the sciences. And it is again from these sciences that, through
observation, the theory of reasoning must be drawn. Formal logic, as
metaphysicians have constructed it, especially develops the dialectical
faculty, that is to say, an aptitude more harmful than useful, for
proving without finding.[84] Descartes said the same, in speaking of
the syllogism, that it serves more for explaining to others the things
which we know, than to discover those which we ignore.
All the utility which we can attribute to the study of logic properly
so-called is found again more extended, more varied, more complete,
more luminous, in mathematical studies. The mechanism of reasoning
is everywhere the same. Whatever may be the phenomena which are the
objects of a science the nature of deduction and induction never
changes in them. Thus in practising these forms of reasoning in the
most simple and the most general phenomena, those whose science is most
advanced, we learn to know them with the most entire evidence, and in
all the generality of which they are capable. Nowhere is reasoning so
exact, so rigorous as in mathematics. They accustom the mind not to
feed upon false reasons, and it is in that school that men ought to
learn the theory and the practice of reasoning.
But, if the old pure logic is thus replaced by mathematics, must we
not at least preserve the general study of the processes used in the
various sciences, which is called methodology? Has not Comte himself
insisted upon the irreducibleness of the several orders of laws to
one another, and in particular to the mathematical laws? Is not the
legitimate object of logic to define the processes of investigation and
of proof particular to each of the fundamental sciences?
Comte does not think so. This applied logic does not appear to him
to be more indispensable than formal logic. In the first place, the
former, in fact, supposes the latter. It proceeds from the same
philosophical conception. In order to determine _a priori_, in a
general way, the rules of the application of the mind to its various
scientific objects, we should first have to possess a knowledge of the
laws of the mind. But, according to Comte, this knowledge can only be
obtained by the observation of the methods which the mind has indeed
followed. Moreover, no art is taught abstractedly, not even the art
of reasoning well, nor that of experimenting, of finding hypotheses,
etc. It has never been sufficient to know the rules of versification
in order to write true poetry. A deep knowledge of the rules of method
will not lead to scientific discoveries.[85] Whatever we learn of an
art, it is practice that has taught us. Nothing here can replace time,
natural disposition, and experience.
Methods then cannot be studied apart from the positive researches in
which men of learning make use of them. Even supposing that in the
far future, when the sciences are advanced, the methods and their
applications could be taught by themselves, the study would run a great
risk of yielding poor results.[86] Up to the present time all that has
been said of the method, considered in the abstract, reduces itself
to vague generalities. When, in logic, we have thoroughly established
that all our science of nature must be founded upon observation, that
we must proceed sometimes from facts to principles, sometimes from
principles to facts, and a few other similar aphorisms, we know far
less of the method than the man who has studied a single one of the
positive sciences somewhat deeply, even without any philosophical
purpose. It is thus that Eclectic philosophers have imagined to make
their psychology into a science, thinking they could understand and
practice the positive method because they had read the _Novum Organum_
and the _Discours de la Méthode_. But did not Bacon, Pascal, Descartes,
and the other great scientific leaders insist on the uselessness of
abstract considerations about method? They never separated the rules
they formulated from their application to positive research.
Comte himself, their successor and their heir, uses no other language.
In his long study of the fundamental sciences he never fails to
distinguish the contents of the science from its method, what he
calls “the scientific point of view and the logical point of view.”
But, while distinguishing them, he considers that they are correlated
and closely allied among themselves. He no more conceives method
as separated from the science which he studies, than science as
separated from its method. Both constitute one intellectual reality
seen under two aspects closely allied to one another.[87] To conclude,
traditional logic is fast disappearing. In its theoretical parts it is
superannuated like the metaphysical philosophy whence it proceeds. In
its applied parts it is barren if separated from the practice of the
sciences.
II.
There is however a positive logic, and in it we can also distinguish a
theoretical and a practical part.
The theoretical part deals with logical laws. These laws which,
finally, govern the intellectual world, are invariable, and common
not only to all time and places, but also to all subjects whatever
without any distinction even between those which Comte calls real and
chimerical. They are observed, fundamentally, even in dreams.[88]
But this universality of logical laws is not understood by him in
the sense in which the rationalist philosophers understand it. Comte
is only concerned with a permanence and continuity purely historical
in character. The mind of man, like the rest of his nature remains
identical with itself, through the diversity of epochs and situations.
It evolves without changing fundamentally “without other differences
than those of gradually developed maturity and experience.”
Ancient philosophy claimed to discover the intellectual laws by
reflection, as if the mind could think and at the same time see
itself thinking, reason and observe its reasoning Comte rejects this
introspective method, which yields no scientific results. If we apply
the method of positive investigation to the intellectual phenomena
as to all the others, two ways only are open. We can look at it from
the static point of view, that is to say, study the conditions upon
which these phenomena depend, and refer the phenomena to them as we
refer generally the function to its organ. In this sense the study
of the intellectual phenomena belongs to biology. Or else, from the
dynamic point of view, we can consider these phenomena in their
evolution, by observing the successive phases through which they pass.
And since the life of the individual is too short for this “progress”
to be appreciable, it must be studied in the life of the species. So
understood, the science of the intellectual laws comes within the
sphere of sociology.
Now, higher biology which deals with moral and intellectual phenomena,
has only just been founded by Cabanis and Gall. Comte discovered that
it could not be constituted as a science without the help of sociology.
It is then to this newly born study that the search after intellectual
laws in every way belongs.
Positive logic abstains, as we see, from speculating upon the leading
principles of knowledge, principles of identity, of contradiction
of causality, etc. These kinds of principles are not objects of
examination or of discussion. Comte upon this point is in full accord
with the Scottish school. No positive science questions its own
principles, for how can we submit the very principles of all reasoning
to criticism? Nothing is less in accordance with the positive spirit
than an attempt of this kind. It is simply metaphysical and has no
chance of success.
The intellectual laws of which the research is positive are such as
the law of the three states (which is the most general of all), or
such, for instance, as these: the human mind always makes an effort
to place its conceptions in accordance with its observations; in
every case the human mind forms the simplest hypothesis, etc. These
laws, which are derived from the nature of the human mind, and whose
action has always been felt, could only be discovered and formulated
quite recently. For biology and sociology, to which they are related,
could not be constituted before the more simple fundamental sciences
were sufficiently advanced. To reach a scientific knowledge of the
intellectual laws, to found a “positive logic,” nothing less was needed
than the long evolution whose term is marked by Comte’s philosophy.
Applied logic, or theory of method, also finds a new meaning in the
positive doctrine. Comte does not fall into the mistake which he has
criticised. He does not propose to teach an art _ex professo_, and he
will not formulate the rules which positive research must follow in
order to be productive. Here again Comte will found his doctrine upon
the intellectual evolution of humanity.
In the first place, like the sciences, the positive methods are
collective works, “the work of the species gradually developed in the
long sequence of centuries.” Comte considers as impertinent the
pretensions of some modern scientists, who pride themselves upon having
invented the comparative method in biology. As if Aristotle had not
already practised it! And Aristotle had not been the first to do so.
The processes of the positive methods do not reveal themselves all at
once, under a perfect and final form. They gradually come to light
during a long period of groping. The human mind notices the processes
which have succeeded in simple cases. It endeavours to generalize them,
and tests them in new and slightly more complex cases. It seeks for the
reason why in certain cases the end is reached, in others it is missed.
Method is thus insensibly formed by a kind of practical induction.
Its essential processes are, like the leading ideas in the sciences,
“inspirations from universal wisdom.” The office of great men--and
this is sufficient for them to earn our gratitude--is to recognise the
value and the fecundity of these inspirations, to set them at work,
and especially to endow them with an often indefinite extension by
separating them from the concrete conditions in which they were at
first manifested.
Thus positive philosophy, less ambitious than its predecessors, does
not take upon itself to legislate upon method. But neither does it
confine itself to the mere duty of making statements, that is to say
to simply register the processes made use of in the sciences. Is not
its proper function to represent in human knowledge the “universalizing
mind” which in Comte’s language is synonymous with government? He
himself calls the fifty-eighth lesson of the _Cours de philosophie
positive_ his _Discours de la Méthode_.[89] He rises above the
necessarily peculiar position which belongs to specialists, and places
himself at the central and universal point of view which is proper to
the philosopher. Thence he embraces under one point of view, the entire
hierarchy of the fundamental sciences. Out of this well-ordered whole,
he watches as they arise, first the essence of the positive method,
and then the relations of the various elements in this method to one
another.
In its essence, the positive method is one, as science is one. For it
ever tends towards the same end: the establishment of the invariable
relations which constitute the effective laws of all observable events,
“thus capable of being rationally foreseen from one another.” The
positive method proceeds to this by means of a threefold abstraction.
It first separates the practical requirements from theoretical
knowledge, to be only concerned with the latter, it seeks for the laws
of phenomena without troubling itself, at least provisionally, with
any possible applications. It also puts aside æsthetic considerations,
which ought not to intervene in scientific investigation. Finally--and
here is the condition for the very existence of science--the positive
method always carefully distinguishes between the abstract and the
concrete point of view. It studies not beings, but phenomena. Even
in the simplest cases, in astronomy for instance, no general law can
be established so long as bodies are considered in their concrete
existence. The principal phenomenon has had to be detached, so to
speak, so as to submit it alone to an abstract study, afterwards
allowing us to return successfully to the consideration of more complex
realities. This is what the ancients had known how to do in geometry;
and this is what Comte himself has done in the most complex of all
sciences, in sociology. Instead of stopping at the concrete reality of
history, he determined, by a bold abstraction, the law of the essential
movement in human society “leaving to subsequent labours the care of
bringing apparent anomalies into line with it.”[90]
In the main, these general characteristics of the positive method
bring it singularly near to the Cartesian method. Comte’s “Threefold
gradual abstraction” seems indeed to have for its end, like Descartes’
analysis, to go back to what is simplest and easiest to know, and
then to come down, by a synthetic and progressive advance, towards
the reality which is given to us in experience. The one and the other
of these methods witness, here, to an effort towards generalising the
spirit of the mathematical method. Let us never forget, writes Comte,
that the general spirit of positive philosophy was first formed by the
culture of mathematics, and that we must necessarily go back so far, in
order to know this spirit in its elementary purity. The mathematical
processes and formulæ are rarely capable of being applied to the
effective study of natural phenomena, when we wish to go beyond the
most extreme simplicity in the real conditions of the problems. But
“the true mathematical spirit, so distinct from the algebraical spirit,
with which it is too often confounded, is on the contrary, constantly
of value.”[91]
We must therefore not take too much notice of Comte’s urging and
bitterness, when he criticises the narrowness of mind and the
“imphilosophisme” of geometers.[92] Undoubtedly he never tires
of safeguarding the higher sciences against the encroachments of
mathematics, and of showing the impossibility of a philosophy founded
exclusively upon their principles. But he none the less recognises
that this science possesses the double privilege of having furnished
historically, the first model of the positive method, and of presenting
still to-day its finest and purest examples.
However, Comte, even more than Descartes, takes care not to transform
the mathematical method into a universal method by a simple
generalisation. Nothing would be more contrary to the positive spirit.
For the development of this spirit the study of mathematics is a
necessary introduction. It is, however, but an introduction. The use
which mathematics can make of deduction, on account of the extreme
simplicity of their subject produces a very false idea of the power
of our understanding, and disposes us to reason more than to observe.
Far from preparing us for the method which must be followed for the
study of the other orders of natural phenomena, the exclusive habit
of mathematics tends rather to draw us from it. In a word it is a
dangerous error to take this “initial degree of sound logical education
for the final degree.”[93]
In order to grasp the positive method in its entirety, we must not
consider only mathematics, but the whole series of the fundamental
sciences. This method, always fundamentally identical, takes particular
determinations in adapting itself to each new order of phenomena.
Each of these orders introduces, so to speak, the use of some of
the principal processes of which the method is composed, and “it is
always at their source that these notions of universal logic must
be examined. Thus the mathematical science is the one which gives
the best knowledge of the elementary conditions of positive science.
In it all the artifices of the art of reasoning, from the most
spontaneous to the most sublime are continually practised with far
more variety and fecundity than anywhere else. Astronomy then teaches
us, in its initial purity, the art of observation accompanied by that
of forming hypotheses. It shows in what the rational provision of
phenomena consists, and that science always ends in assimilation or
in combination. Physics initiate us to the theory of experimenting,
chemistry to the general art of nomenclatures, the science of organic
bodies to the theory of classifications. Biology specially makes use
of the comparative method, and finally with sociology appears the
“transcendant” process which Comte calls the historical method.[94]
Positive logic extends to all the fundamental sciences the use of the
processes at first peculiar to each one of them. Each great logical
artifice, once studied in the portion of natural philosophy which shows
its most spontaneous and most complete development, can afterwards
be applied, with the necessary modifications, to the perfecting of
the other sciences. For instance, the comparative method belongs in
the first place to biology. But, when brought back to its principle
and generalised, it becomes a precious instrument for sociology, for
physics, and even for mathematics. In every science, the method is
completed by the auxiliary use of the processes whose power and whose
sphere of action have been made known by the other sciences. By these
mutual loans, in each one of them, the positive method reaches its
maximum of production.
To be cultivated in the most rational manner possible, the sciences
must then be subject to the direction of a general system of positive
philosophy, “the common basis and the uniform combining element of all
truly scientific labours.”[95] The scientific man must at the same
time be a philosopher, since philosophy alone puts him in possession
of all the resources of positive method. For instance, this philosophy
will show the geometer that he must at least have a general knowledge
of biology and of sociology. Biology will teach him the comparative
method, of which he can make use when occasion offers, and sociology by
showing him the history of his science in the general development of
the human mind, will help him better to understand it. If the geometers
had a more philosophical mind, their science would be better taught.
The great conceptions of Descartes, of Leibnitz, of Lagrange, would be
more intelligently explained and brought to light.
If it is useful for the geometer to have studied the other fundamental
sciences, it is not less indispensable for other learned men to have
gone through the study of mathematics. As an “initial” discipline,
this science can be neglected by no one. It is the common school of
positivity for all minds. It is therefore to be regretted that the
scientific education of future physiologists should be mainly made up
of literary studies and of a few notions of physics and chemistry.
The more complex the phenomena whose laws they will have to seek,
the more necessary will it be for them to have become familiarised
in mathematics and in astronomy, with the precise idea of scientific
truth. And, as a matter of fact, until this century, the study of the
exact sciences had always been regarded as a preliminary condition
for that of the natural sciences. Buffon and Lamarck in their day
had still received this discipline. If it has been so difficult to
constitute social science, it comes, among other reasons, from the lack
of scientific education among those who, up to the present time, have
wished to study social phenomena. Where, for instance, could economists
have found the scientific idea of what constitutes natural laws,
ignoring as most of them did not only biology which was being formed
beside them, but even the sciences which had already reached a positive
state?
The exclusive cultivation of a single science is always a danger for
the intellect. Nevertheless, so long as the chief task of the positive
spirit was to disorganise the system of beliefs which constituted
theological and metaphysical philosophy, the speciality of the works
and of the methods was an inconvenience of secondary importance.
It mattered little that the discoveries of the astronomers, the
physicians, the biologists should be more or less co-ordinated and
directed by a universal positive method, so long as they did their
work and prepared the future. But, when the positive spirit had to
become organic instead of critical, when it had to substitute a new
philosophy to the one which it had overthrown, then it was obliged to
subordinate the special processes which it had made use of until then
to a single universal method. Should the “scientific anarchy” have
lasted, the progress of the positive spirit would undoubtedly have led
to the discrediting of the metaphysical régime, but without replacing
it, and consequently without having done with it. By rejecting any new
general discipline, modern scientific men would unknowingly tend to
re-establish the system which they seemed to have shattered for ever.
In a word, the triumph of the positive method, to be final, presupposes
the acceptance of the positive philosophy by all men of learning. The
old logic was bound by the narrowest ties to the metaphysical doctrines
which were then dominant. In the same way positive logic is bound up
with positive philosophy. Speaking more precisely, it is an expression
of this very philosophy.
III.
Is the general method of positive philosophy objective, or subjective,
or both at once? As we know, this question has raised passionate
discussion among positivists.[96] Outside the school it has been
solved by some historians as if Auguste Comte, at the end of his life,
had gone back to a doctrine very different from the one set forth by
him in the _Cours de philosophie positive_. It suffices, however, to
distinguish, with him, two successive points of view, to see how the
two methods, antagonistic in a certain sense, can, in another one, be
very well reconciled.
If we only consider the process followed by our mind in the explanation
of natural phenomena, that is to say the object of positive philosophy
taken in the strict sense of the word, it is true that two opposite
methods are found face to face. The subjective method goes from the
consideration of man to that of the world, the objective method goes
from the knowledge of the world to that of man. The first gives rise
to theological and metaphysical philosophy, the latter to positive
philosophy. The incompatibility of the two philosophies proceeds from
that of the methods, which is irreducible. It allows us to say: “This
will kill that.”[97] In this sense, the final establishment of the
objective method, which is completed by the foundation of sociology,
implies the exclusion, also final, of the subjective method.
But “having reached its full maturity, true philosophy should
inevitably tend to reconcile these two antagonistic methods,” wrote
Comte in 1838, in the third volume of the _Cours de philosophie
positive_, that is to say, long before the time of what has been
wrongly called his second philosophy.[98] This reconciliation will be
accomplished by means of the distinction between the special point of
view of the sciences, and the universal point of view of philosophy.
The scientific investigation of the laws of natural phenomena can
only be made by means of the objective method: Comte never varies in
his thought on this point. But these sciences are but the parts in a
greater whole, for which the subjective method alone is suitable.
Two arguments especially prove this, one belonging to the logical, the
other to the moral and the religious order.
The supreme requirement of our intellect is unity. Shall we ever reach
this unity by using the objective method in the sciences? Evidently
not. Even in each order of phenomena separately considered we do not
see how to reduce the laws which we know to a single law of a more
general character. And what are the laws known to us compared with
those which elude our search, and which perhaps may do so for ever?
Considered in its object, each one of our sciences reaches, so to
speak, to infinity, far beyond our limited horizon. If then, in order
to satisfy us, a _single_ conception of the world is necessary, we
shall never obtain such a conception from the objective point of view.
But if we change our point of view, if we refer the whole of the
sciences to man, or better, to humanity, as a centre, we shall then be
able to realise the unity which we seek. This is precisely what is made
possible by sociology, by subordinating the hierarchy of the positive
sciences to the final science of humanity.
To consider the other fundamental sciences as “indispensable
preliminaries,”[99] to represent the evolution which has brought them
forth in turn as the very history of human progress; to verify the
law of the three states in all our beliefs, and in all our knowledge;
finally, to control all scientific research from the sociological point
of view: this is what Comte understands by the conciliation of the two
methods.
The whole development of positive science from mathematics to
sociology, lies between the new use which is made of subjective method
and that which was spontaneously made of it by theological philosophy.
When theological philosophy considered the knowledge of man and that
of the world as interdependent, the instinct which animated it was a
just one. But it was imagining instead of observing. It represented
the world as filled with “causes” analogous to the will of man and
equally capricious. The new subjective method rests, on the contrary,
upon the very results of the positive sciences, brought to a synthesis
in sociology. It takes as established that the intellectual and moral
phenomena depend upon the biological laws, and that the biological laws
themselves are subordinate to the laws of the inorganic _milieu_. But,
since the “final systematisation of all these laws”[100] must always
remain impossible from the objective point of view, the new subjective
method undertakes it from the point of view of humanity as a centre.
We can thus distinguish two great periods in the intellectual advance
of humanity. During the first, the positive spirit successively applies
the scientific, that is to say objective, method, to higher and higher
orders of phenomena. The foundation of sociology marks the term of
this progress. Then the second period begins. The positive spirit
from special has become universal, from analytical synthetical. It
reacts upon the particular sciences, and henceforth makes use of the
“regenerated” subjective method, to govern the whole of them.
From the moral and religious point of view, once sociology has been
constituted, and positive philosophy has been established, the
functions proper to religion appear. The intellect recognises that its
end does not lie within itself, and that it is incapable of determining
its own rule and aim. It submits to a directing authority, which
will guide its efforts and fix their object. _To act from affection,
and to think in order to act._ But if the mind understands that it is
destined to be used in the service of humanity, it sees at the same
time that in the complete positive doctrine, which contains religion,
the objective method gives precedence to the subjective, or rather that
they mutually support each other. If we were pure intellects we should
probably always go from the world to man. But in us the intellect is
only a means. Love is the principle, action is the end; and it is to
man, finally, that our study of the world must be referred.
Towards the end of his life, Comte replaced the logic of the mind,
“especially guided by artificial signs,” by the logic of the heart
“founded upon the direct connection of the feelings.”[101] We shall not
here insist upon a conception which is closely allied to his religious
system. We will only conclude that, from the philosophical point of
view the two methods objective and subjective, in Comte’s thought,
are easily reconciled, provided that both have been “systematically
regenerated.” Now, the regeneration is obtained as soon as sociology
is founded. On the one hand, as a matter of fact, it furnishes the
sciences formed by the objective method with a principle of unity,
since henceforth they are all subordinated to the single science of
Humanity. And, on the other hand, the subjective method acquires the
positivity which it lacked, for sociology has substituted to the
arbitrary “individual subject,” the “universal subject,” that is to say
again, Humanity.
FOOTNOTES:
[83] Cours, III. 336-7.
[84] Synthèse subjective, p. 85.
[85] Cours, VI., 708.
[86] Cours, I, 32.
[87] Cours, VI, 709.
[88] Cours, V, 79.
[89] Cours, VI, 731.
[90] Cours, VI, 704.
[91] Cours, II. 324-5.
[92] Lettres à Valat, p. 93 (24 septembre, 1828).
[93] Cours, VI. 712-15.
[94] Cours, VI. 720 sq.
[95] Cours, VI. 74.
[96] See above, Introduction, pp.
[97] An allusion to a famous passage in Victor Hugo’s “Notre Dame de
Paris.”
[98] Cours, III, 210.
[99] Cours, VI. 610.
[100] Pol. pos., I. 447.
[101] Pol. pos., II. 101-2.
BOOK II
THE PHILOSOPHY OF THE SCIENCES
INTRODUCTION
The Philosophy of the Sciences is one of the leading parts of Comte’s
work. No other brings out more clearly the essential differences which
distinguish his doctrine from previous systems.
In Comte’s eyes the philosophy of the sciences is inseparable from
the philosophy of history and from the theory of progress. For the
sciences are great sociological facts and, as such, are subject, in
their evolution, to invariable laws. The method of the philosophy of
the sciences could therefore only be the positive method, ever like to
itself.
Moreover,--and this is an immediate consequence of this first
consideration,--the object of the positive philosophy of the sciences
is in no way to “explain” what the sciences themselves do not explain.
The sciences, as is well known, do not inquire into their data and
their principles. They consider them as sufficiently established by
the implicit consent of all men, or at least by the universal usage
of learned men. The geometer leaves to others the care of speculating
upon the essence of space, or upon the _a priori_ character of his
definitions. The physicist, if he form an idea of matter for himself,
unhesitatingly adopts the one which appears to be the most immediately
advantageous, that is to say, the one which is best in accordance with
what he knows of its properties and of its laws. He attributes no more
value than that of a simple hypothesis to this idea.
Up to the present the business of solving the questions which
the scientific man does not examine has belonged to the
philosopher--understand by this term the metaphysician. It is for
him to seek what matter, time, movement, space, etc., may be “in
themselves.” Whether he descends from metaphysics to the positive
sciences, or ascends from the latter to metaphysics, he always
endeavours to show that such and such a transcendental hypothesis is
more in accordance than any other with what we know to-day of the laws
of nature. In a word; the philosophy of the sciences has been, in
general, an effort to interpret scientific knowledge metaphysically.
This explanation remains in respect to such a knowledge an “extrinsic
denomination.” It explains but does not touch it.
Now, according to Comte, there are not two forms of knowledge, the
one positive and properly speaking scientific the other metaphysical
and properly called philosophical. _The whole_ of our real knowledge
in the end bears upon special or general facts. There can therefore
be no question of a philosophy which should be essentially distinct
from positive knowledge. Any attempt to explain by essences, causes,
principles or ends, is excluded by the positive method. Metaphysical
problems can no longer be set and, in this sense, when they disappear,
the philosophy of the sciences disappears with them.
But, on the other hand, as we have already seen, the positive sciences
are not self-sufficient. They need to be crowned and ordered by a
philosophy. If then a philosophy is indispensable, and if, at the same
time, this philosophy must be positive, relative like the sciences
themselves, and _homogeneous_ with them, only one solution remains
possible. The philosophy of the sciences will consist in substituting
the point of view of the whole to that of the parts. It will still be a
product of the positive spirit; but in it this spirit from special will
have become general; from particular it will have become universal.
This universal character remains common to Comte’s philosophy and to
that of his predecessors. But Comte did not understand it as they did.
For metaphysicians in general, and still for Kant, universality is the
distinctive sign of knowledge which does not come from experience,
which is therefore necessary and _a priori_. Comte, who does not know
of any _a priori_ in the Kantian sense, calls that knowledge universal
which remains relative, and which is founded upon induction, but which
regulates the other forms of knowledge in the order of generality. Thus
the principle of laws is universal. The encyclopædic laws of phenomena
are universal. The point of view of humanity is universal, because
from this point of view a synthesis of the whole of our knowledge
is possible. And, as universality is a relative thing, we conceive
universalities of different orders.
Henceforth the philosophy of the sciences is easily defined. Are we
concerned with a certain science considered by itself? The philosophy
of this science consists in embracing at a glance the whole, the
object and the method, as opposed to the special point of view of the
scientific man who follows the discovery of more or less special laws
in a branch of this science, but such a philosophy necessarily remains
imperfect and fragmentary. The philosophy of a science is only really
established in the general philosophy of the sciences, that is to say
by a view at once synthetic and single of all the sciences, in which
are co-ordinated the objects which they study, the laws which they
discover, the methods which they make use of, and the ends which they
should pursue.
It has been said that this is not a philosophy of the sciences but
simply a “synthesis of the most general results of the positive
sciences.” Comte partly accepts and partly rejects the objection. If he
is reproached with not having constructed a philosophy of the sciences
according to the old spirit, that is to say an effort at “explanation,”
which goes beyond the point of view of positive science, he grants
the objection. He considers all philosophy of this kind as out of the
question. Is it said that there is no difference between his point of
view and that of the scientific man properly so called, unless it be
that he successively goes through all the fundamental sciences? Comte
calls our attention to the fact that it is not enough to place these
sciences side by side to obtain their philosophy. A new point of view,
truly universal, although always relative, is needed. How could Comte
have distinguished otherwise, in each science, what is lasting and in
conformity with the positive spirit from what is decaying and still
bears the mark of the theological and metaphysical spirit? Could he
especially have fixed the relations which the sciences should maintain
among themselves, and could he have imposed upon them a discipline
whose principle was not to be found in any one of them?
Thus, until Auguste Comte’s time, the philosophy of the sciences had
been a metaphysical conception, joined more or less closely to the
whole of positive knowledge. Comte endeavoured to form a conception of
this whole, which should be philosophical while remaining positive. It
is this conception which is especially set forth in the three first
volumes of the _Cours de philosophie positive_. From the static point
of view it is founded upon the hierarchy of the sciences, the unity of
the method, and the homogeneity of knowledge. From the dynamic point
of view, it endeavours to show the progressive convergence of all the
sciences towards sociology, the final and universal science. With
this “guiding thread,” Comte will be able to establish in turn the
philosophy of each fundamental science, without ever losing sight of
the relation which it bears to the whole of the others.
CHAPTER I
MATHEMATICS
In the eyes of philosophers, mathematics has always occupied a
privileged place among the sciences. Plato located their object in an
intermediate region between the world of sensible phenomena and that
of intelligible realities. On the one hand mathematical objects, and
in particular the geometrical figures, appeal to the imagination as
sensible things; on the other hand, mathematical truths like ideas
and the relations between ideas, are characterised by immutable and
eternal fixity. This is why the study of mathematics is an excellent
preparation for philosophy, which is the science of ideas. While
still leaving to the mind the help of direct sensible perception, it
accustoms it to permanent truth. During the whole of antiquity the
science of mathematics, as the name indicates, was pre-eminently _the_
science. The science of physics, less sure of its object and of its
method, was hardly distinguished from philosophical speculation, and
lent itself with difficulty to the purely scientific form.
For Plato then, and for those who followed him, mathematics has
characteristics which distinguish it from the study of phenomena. In
a certain measure, it partakes of the nature of science, conceived
as bearing upon _what is_, upon the absolute reality which is
neither subject to change nor to motion. It is true that they start
from definitions and hypotheses. But, once the principles are
established, they are developed _a priori_ by a succession of necessary
demonstrations like the dialectics of ideas.
This conception offers a mixture of metaphysical and positive elements.
It implies that the object of science is reality such as it is in
itself; but, at the same time, it sees in the demonstration the
essential character of science. A long evolution, which culminates in
Comte’s doctrine, has driven the metaphysical elements out of science
while the other elements subsist in it still. Far from saying with
Plato or with his successors that there is no science of the phenomenon
or of that which passes away, Comte thinks on the contrary, that the
only object of science is phenomenal reality so far as it is subject to
laws. Science has not to search for causes or substances; it suffices
for it to determine invariable relations.
If the mathematical sciences have long been the only sciences properly
so called, and if to-day they are still more advanced than any others,
it is because the geometrical and mechanical phenomena are indeed
the simplest of all, and those which are most naturally connected
among themselves. The period during which they could be studied by
observation could therefore be very short, so short that it is even
not absurd to maintain that it never existed, and that, in this case,
rational knowledge was not preceded by the empirical establishment of
facts. But the difference between mathematics and the other sciences
none the less remains one of degree and not of kind. The Science of
Mathematics is in advance of the other sciences; but all work on common
ground. In a word, like all other sciences it is a natural science.
This endeavour to present the whole of the sciences as homogeneous,
that is to say, to avoid two distinct classes being formed of
mathematics on the one hand, and of the sciences of nature on the
other, had already been attempted before Comte. This endeavour imposed
itself, so to speak, upon modern philosophers, from the time when
Descartes sought for a universal method for science conceived as a
whole. Comte, who saw very well the defect in the Cartesian conception,
in which the ascendency of mathematics was still too much felt, did
not, however, deny that his own conception proceeded from that of
Descartes. In another form, the idea of the homogeneity of the sciences
is also found in Leibnitz and even in Kant. Does not the _Critique de
la raison pure_ show that mathematics on the one hand, and physics on
the other, equally rest upon principles which are synthetic _a priori_?
In the _Prolégomenes à toute métaphysique future_ just as the chapter
corresponding to _l’esthétique transcendentale_ is entitled “How are
pure mathematics possible _a priori_?” so the chapter corresponding to
the _Logique transcendentale_ bears as its title “How are pure physics
_possible a priori_?” On another plan Comte’s theory is parallel
to Kant’s. Here as there mathematics as well as physics rests upon
synthetic principles--“superior to experience,” says Kant--proceeding
from experience, says Comte. The latter, it is true, did not know
Kant’s theory, and, had he known it he would not have accepted it. But
the analogy of tendency subsists none the less beneath the diversity of
doctrines.
The immediate antecedent of Comte’s theory is found in d’Alembert. The
author of the _Discours préliminaire_ had said, “We will divide the
science of nature into physics and mathematics.”
II.
Every science has its origin in the art corresponding to it.
Mathematics arose out of the art of measuring magnitudes. Indeed this
art would be very rudimentary if we only practised direct measurement.
Among the magnitudes which interest us there are very few which we can
measure thus. Consequently the human mind had to seek some indirect
way of determining magnitudes.
In order to know the magnitudes which do not allow of direct
measurement, we must evidently connect them with others which are
capable of being immediately determined, and according to which we
succeed in discovering the former, by means of the relations which
exist between them and the latter. “Such is the precise object of
mathematical science in its entirety.”[102] We see immediately
how extremely vast it is. If we must insert a large number of
intermediaries between the quantities which we desire to know, and
those which we can measure immediately, the operations may become very
complicated.
Fundamentally, according to Comte, there is no question, whatever it
may be, which cannot be finally conceived as consisting in determining
one quantity by another, and consequently which does not depend
ultimately upon mathematics. It will be said that we must take into
account not only the quantity, but also the quality of the phenomena.
This objection, decisive in the eyes of Aristotle, who could not
conceive that we could legitimately [Greek: metaballein] [Greek: eis
allo genos], no longer holds good for modern thinkers. Since Descartes’
time, they have seen analysis applied to geometrical, mechanical and
physical phenomena. There is no absurdity in conceiving that what has
been done for these phenomena is possible for the others. We must be
able to represent every relation between any phenomena whatever by an
equation, allowing for the difficulty of finding this equation and of
solving it.[103] As a matter of fact, we are quickly stopped by the
complexity of the data. In the present state of the human mind there
are only two great categories of phenomena of which we regularly know
the equations: these are geometry and mechanics.
This being established, the whole of mathematical science is divided
into two parts: abstract and concrete mathematics. The one studies the
laws of geometrical and mechanical phenomena. The other is constituted
by the _calculus_, which, if we take this word in its largest sense,
applies to the most sublime combinations of transcendent analysis,
as well as to the simplest numerical operations. It is purely
“instrumental.” Fundamentally, it is nothing else than an “immense
admirable extension of natural logic to a certain order of deductions.”
This part of mathematical science is independent of the nature of the
objects which it examines, and only bears upon the numerical relations
which they present. Consequently, it may happen that the same relations
may exist among a great number of different phenomena. Notwithstanding
their extreme diversity these phenomena will be considered by the
mathematician as presenting a single analytical question, which can be
solved once for all. “Thus, for instance, the same law which reigns
between space and time when we examine the vertical fall of a body _in
vacuo_, is found again for other phenomena which present no analogy
with the former nor among themselves; for it also expresses the
relation between the area of a sphere and the length of its diameters;
it equally determines the decrease in intensity of light or of heat by
reason of the distance of the objects lighted and heated, etc.”[104]
We have no general method which serves indifferently for establishing
the equations of any natural phenomena whatever: we need special
methods for the several classes of geometrical, optical, mechanical
phenomena, etc. But, whatever may be these phenomena, once the equation
is established, the method for solving it is uniform. In this sense,
abstract mathematics is really an “_organon_.”
Geometry and mechanics, on the contrary, should be regarded as real
natural sciences, resting as the others do upon observation. But, adds
Comte, these two sciences present this peculiarity, that in the present
state of the human mind, they are already used, and will continue
to be used as methods far more than as direct doctrine. In this way
mathematics is in fact “instrumental,” not only in abstract parts, but
also in its relatively concrete parts. It is entirely used as a “tool”
by the more complicated sciences, such as astronomy and physics. It is
truly the real logic of our age.
In the philosophical study of abstract mathematics, Comte proceeds
successively from arithmetical to algebraical calculation, and from
the latter to the transcendent analysis or differential and integral
calculus. After having stated the manner in which this calculus is
presented according to Leibnitz and to Newton, he adopts that of
Lagrange, which appears to him the most satisfactory. It is true that
at the end of his life his admiration for the author of the _Mécanique
analytique_ had greatly diminished. Without here entering into the
detail of questions, we will limit ourselves to the indication of a
consideration upon the bearings of abstract mathematics, which appears
to be of capital importance to Comte. Whether it be a question of
ordinary analysis, or especially of transcendental analysis, Comte
brings out at once the extreme imperfection of our knowledge, and the
extraordinary fecundity of their applications. He can only solve a very
small part of the questions which come before us in these sciences.
However, “in the same way as in ordinary analysis we have succeeded
in utilising to an immense degree a very small amount of fundamental
knowledge upon the solution of equations, so, however little advanced
geometers may be up to the present time in the science of integrations,
they have none the less drawn, from these very few abstract notions
the solution of a multitude of questions of the first importance, in
geometry, in mechanics, in thermology, etc., etc.”[105] The reason
of this is that the least abstract knowledge naturally corresponds
to a quantity of concrete researches. The most powerful extension of
intellectual means which man has at his disposal for the knowledge
of nature consists in his rising to the conception of more and more
abstract ideas, which are nevertheless positive. When our knowledge is
abstract without being positive, it is “fictitious” or “metaphysical.”
When it is positive without being abstract, it lacks generality, and
does not become rational. But when, without ceasing to be positive, it
can reach to a high degree of abstraction, at the same time it attains
the generality, and, along the lines of its furthest extension, the
unity which are the end of science.
Hence the importance of Descartes’ fine mathematical discovery, and
also of the invention of differential and integral calculus, which
may be considered as the complement to Descartes’ fundamental idea
concerning the general analytical representation of natural phenomena.
It is only, says Comte, since the invention of the calculus, that
Descartes’ discovery has been understood and applied to the whole of
its extent. Not only does this calculus procure an “admirable facility”
for the search after the natural laws of all the phenomena; but, thanks
to their extreme generality, the differential formulæ can express each
determined phenomenon in a single equation, however varied the subjects
may be in which it is considered. Thus, a single differential equation
gives the tangents of all curves, another expresses the mathematical
law of every variety in motion, etc.
Infinitesimal analysis, especially in the conception of Leibnitz,
has therefore not only furnished a general process for the indirect
formation of equations which it would have been impossible to discover
directly, but in the eyes of the philosopher it has another and a
no less precious advantage. It has allowed us to consider, in the
mathematical study of natural phenomena, a new order of more general
laws. These laws are constantly the same for each phenomenon, in
whatever objects we study it, and only change when passing from one
phenomenon to another “where we have been able moreover, in comparing
these variations, to rise sometimes, by a still more general view, to
a _positive_ comparison between several classes of various phenomena,
according to the analogies presented by the differential expressions of
their mathematical laws.”[106] Comte cannot contemplate this immense
range of transcendent analysis without enthusiasm. He calls it “the
highest thought to which the human mind has attained up to the present
time.” The highest, because being the most profoundly abstract among
all the positive notions, this thought reduces the most comprehensive
range of concrete phenomena to rational unity.
As the consideration of analytical geometry suggested to Descartes the
idea of “universal mathematics,” which lies at the basis of his method,
so we can think that philosophical reflection upon transcendental
analysis led Comte to the idea of those “encyclopædic laws,” which hold
such an important place in his general theory of nature. For these
encyclopædic laws, analogous as they are to the differential formulæ
spoken of by Comte, are equally verifiable in orders of otherwise
irreducible phenomena, and allow us to conceive them as convergent.
III.
Geometry is the first portion of concrete mathematics. Undoubtedly the
facts with which it deals are more connected among themselves than
the facts studied by the other sciences, and this allows us easily to
deduce some of these facts once the others are given. But there is a
certain number of primary phenomena which, not being established by
any reasoning, can only be founded upon observation, and which stand as
the basis of all geometrical deductions.[107] Although very small, this
part of observation is indispensable because it is the initial one, and
never can quite vanish.
In this way, metaphysical discussions upon the origin of geometrical
definitions and space are set aside. Comte here adopts d’Alembert’s
opinion. The latter had said: “The true principles of the sciences are
simple recognised facts, which do not suppose any others, and which
consequently can neither be explained nor questioned: in geometry
they are the properties of extension as apprehended by sense. Upon
the nature of extension there are notions common to all men, a common
point at which all sects are united as it were in spite of themselves,
common and simple principles from which unawares they all start. The
philosopher will seize upon these common primitive notions to make them
the basis of the geometrical truths.”[108]
Extension is a property of bodies. But, instead of considering this
extension in the bodies themselves, we consider it in an indefinite
milieu which appears to us to contain all the bodies, of the universe
and which we call space. Let us think, for instance, of the impression
left by a body in a fluid in which it might be immersed. From the
geometrical point of view this impression can quite conveniently be
substituted to the body itself. Thus, by a very simple abstraction, we
divest matter of all its sensible properties, only to contemplate in a
certain manner its phantom, according to d’Alembert’s expression. From
that moment we can study not only the geometrical forms realised in
nature, but also all those which can be imagined. Geometry assumes a
“rational” character.
Similarly, it is by a simple abstraction of the mind that geometry
regards lines as having no thickness, and surfaces as being without
depth. It suffices to conceive the dimension to be diminished as
becoming gradually smaller and smaller until it reaches such a degree
of thinness that it can no longer fix the attention. It is thus that
we naturally acquire the “real idea” of surface, then of the line, and
then of the point. There is therefore no necessity to appeal to the _a
priori_.
Thus constituted, the object of geometry is the measurement of
extension. But since this measurement can hardly ever be directly taken
by superposition, the aim of geometry is to reduce the comparison
of all kinds of extensions, volumes, surfaces or lines to simple
comparisons of straight lines, the only ones regarded as capable of
being immediately established.”[109] The object of geometry is of
unlimited extent, for the number of different forms subject to exact
definitions is unlimited. In regarding curved lines as generated by the
movement of a point subject to a certain law, we can conceive as many
curves as laws.
The human mind, in order to cover this immense field, the extension
of which it was very late in apprehending, may pursue two different
methods. Perfect geometry would, indeed, be the one which would
demonstrate all the properties of all imaginable forms, and this can
be obtained in two ways. Either we can successively conceive each of
the forms, the triangles, the circle, the sphere, the ellipse, etc.,
and seek for the properties of each one of them. Or else we can group
together the corresponding properties of various geometrical forms,
in such a way as to study them together, and, so to speak, to know
beforehand their application to such and such a form which we have not
yet examined. “In a word,” says Comte, “the whole of geometry can be
ordered, either in relation to bodies which are being studied, or in
relation to phenomena which are to be considered.” The first plan is
that of the geometry of the ancients, or _special_ geometry; the second
is that of the geometry since Descartes, or _general_ geometry.[110]
At its origin geometry could only be special. The ancients, for
instance, studied the circle, the ellipse, the parabola, etc.,
endeavouring, in the case of each geometrical form, to add to the
number of known properties. But, if this line of advance had been
the only one which could be followed, the progress of geometry would
never have been a very rapid one. The method invented by Descartes
has transformed this science, by enabling it to become _general_,
and to abandon the individual study of geometrical forms for the
common study of their properties. This revolution has not always been
well understood. Often in teaching mathematics, its bearings are not
sufficiently shown. From the manner in which it is usually presented,
this “admirable method” would at first seem to have no other end than
the simplification of the study of conic sections or of some other
curves, always considered one by one according to the spirit of ancient
geometry. This would not be of great importance. The distinctive
character of our modern geometry consists in studying in a general way
the various questions relating to any lines or surfaces whatever by
transforming geometrical considerations and researches into analytical
considerations and researches.[111]
All geometrical ideas necessarily relate to the three universal
categories; magnitude, form, position. Magnitude already belongs to
the domain of quantity. Form can be reduced to position, since every
form can be considered as the result of the advance of a point, that
is to say of its successive positions. The problem is therefore to
bring all ideas of situation whatever back to ideas of magnitude.
How did Descartes solve it? By generalising a process which we may
say is natural to the human mind, since it comes spontaneously into
being under the stress of necessity. Indeed, if we must indicate the
situation of an object without showing it immediately, do we not refer
it to others which are known, by stating the magnitude of geometrical
elements by which we conceive the object to be connected with them?
Geographers act in the same way in their science to determine the
longitude and latitude of a place, and astronomers to determine the
right ascension and the declination of a star. These geographical and
astronomical co-ordinates fulfil the same office as the Cartesian
co-ordinates. The only difference, but it is a capital one, consists in
the fact that Descartes carried this method to the highest degree of
abstract generality thus giving it its maximum of fertility and power.
Although general geometry is infinitely superior to special geometry
it cannot, nevertheless, altogether dispense with the latter. As the
ancients did, so it will always be necessary to begin with special
geometry. For general geometry rests upon the use of calculation. But
if, as Comte has said, geometry is truly a science of facts calculation
will evidently never be able to supply us with the first knowledge
of these facts. In order to lay the foundations of a natural science
simple mathematical analysis would never suffice, nor could it give a
fresh demonstration of it, when these foundations have already been
laid. Before all things a direct study of the subject is necessary,
until the precise relations are discovered. “The application of
mathematical analysis can never begin any science whatever, since it
could never take place except when the science has been sufficiently
elaborated to establish, in relation to the phenomena under
consideration, some equations which might serve as a starting-point for
analytical work.”[112] In a word, the creation of analytical geometry
does not prevent geometry from remaining a natural science. Even when
it has become as purely rational as possible, it none the less remains
rooted in experience.
IV.
The second part of concrete mathematics (mechanics) is also one of the
natural sciences which owes its marvellous progress to analysis. Here
again we must distinguish the data which are at the basis of science,
and which are facts, from the abstract development undergone by this
science because of the simplicity of these facts and the precision
of the relations which exist between them. The distinction between
what is “really physical” and what is “purely logical”[113] is not
always an easy one. We must, however, separate facts furnished by
experience, from artificial conceptions whose object is to facilitate
the establishment of general laws of equilibrium and of motion.
Only to consider inertia in bodies is a fiction of this kind.
Physically the force of inertia does not exist. Nature nowhere shows us
bodies which are devoid of internal activity. We term those which are
not alive inorganic, but not inert. Were gravitation alone common to
all molecules, it would suffice to prevent the conception of matter as
devoid of force. Nevertheless, mechanics only considers the inertia of
bodies. Why? Because this abstraction presents many advantages for the
study, “without, moreover, offering disadvantages in the application.”
Indeed, if mechanics had to take into account the internal forces of
bodies and the variations of these forces, the complications would
immediately become such that the facts could never be submitted to
calculation. Mechanics would run the risk of losing its character as
a mathematical science. And, on the other hand, as it only considers
the movements in themselves, regardless of their mode of production, it
is always lawful for mechanics to replace, if necessary, the internal
forces by an equivalent external force” applied to the body. The
inertia of matter is therefore an abstraction, the end of which is to
secure the perfect homogeneity of mechanical science, by allowing us to
consider all moving bodies as identical in kind, and all forces as of
the same nature.
The “physical” character of this science is again evident from the
consideration of the three fundamental laws upon which it rests.[114]
The first, called Kepler’s law, is thus defined: “All movement is
naturally rectilinear and uniform; that is to say, any body subject to
the action of a single force which acts upon it instantaneously, moves
constantly in a straight line with invariable speed.” It has been said
that this law is derived from the principle of sufficient reason. The
body must continue in a straight line because there is no reason why it
should deviate from it more on one side than on the other. But, answers
Comte, how do we know that there is no reason for the body to deviate,
except precisely because we see that it does not deviate? The reasoning
“reduces itself to the repetition in abstract terms of the fact itself,
and to saying that bodies have a natural tendency to move in a straight
line, which is precisely the proposition which we have to establish.”
It is by similar arguments that the philosophers of antiquity, and
especially Aristotle, had, on the contrary been led to regard circular
motion as natural to the stars, in that it is the most perfect of all,
a conception which is only the abstract enunciation of a imperfectly
analysed phenomenon. The tendency of bodies to move in a straight line
with constant speed is known to us by experience.
The second fundamental law of mechanics, called Newton’s law,
expresses the constant equality of action and reaction. It is pretty
generally agreed to-day to consider this law as resulting from the
observation of facts. Newton himself understood it so.
Finally the third law establishes that “every movement exactly
possessed in common by all the bodies of any system does not alter
the particular movements of those different bodies in respect to each
other; but those movements continue to take place as if the whole of
the system was motionless.” This law “of the independence or of the
coexistence of movements” was formulated by Galileo. It is no more
_a priori_ than the two preceding ones. How could we be sure, if
experience did not show it to us, that a common motion communicated
to a system of bodies moving in relation to one another, would change
nothing in their particular motions? When his law was made known by
Galileo, on all hands there arose a cloud of objections, tending to
prove _a priori_ that this proposition was false and absurd. It was
only admitted later when, in order to examine it, the logical point of
view was set aside for the physical point of view. It was then seen
that experience always confirmed this law, and that, if it ceased to
operate, the whole economy of the universe would be thrown into utter
confusion. For instance, the movement of the translation of the earth
in no way affects the mechanical phenomena which take place upon the
surface or within the globe. As the law of the independence of motions
was unknown when the theory of Copernicus appeared, an objection was
put to him which was thought to be drawn from experience. He was told
that if the earth moved round the sun all the movements which take
place upon it or within it would be modified by the action. Later
on when Galileo’s law became known, the fact was explained and the
objection disappeared.
Once these three laws are established, mechanics has sufficient
foundation. Henceforth the scientific edifice can be constructed by
simple logical operations, and without any further reference to the
external world. But this purely rational development no more transforms
mechanics into an _a priori_ science than the application of analysis
deprives geometry of its character as a natural science. What proves
this, in one case as in the other, is the possibility of passing from
the abstract to the concrete and of applying the results obtained
to real cases, merely restoring the elements which science had been
compelled to set aside. If it were possible entirely to constitute the
science of mechanics according to simple analytical conceptions, we
could not imagine how such a science could ever become applicable to
the effective study of nature. What guarantees the reality of rational
mechanics is precisely its being founded upon some general facts, in a
word, upon the data of experience.
Comte could assuredly not foresee the controversies which to-day bear
upon the principles of mechanics and which have been summed up by Mr.
Poincaré in an article upon Hertz’s mechanical theories.[115] Mr.
Poincaré says that the principles of Dynamics have been stated in many
ways, but nobody sufficiently distinguished between what is definition,
what is experimental truth, and what is mathematical theorem. Mr.
Poincaré is satisfied neither with the “classical” conception of
mechanics, whose insufficiency has been shown by Hertz, nor with the
conception with which Hertz wishes to replace it. In any case it is a
high philosophical lesson to see the classical system of analytical
mechanics--a system constructed with such admirable accuracy, and
made by Laplace to arise altogether, as Comte says, out of a single
fundamental law,--to see it after a century labouring under grave
difficulties, not unconnected with the progress of physics.
Might not this be an argument in support of the theory of d’Alembert
and of Comte on the nature of concrete mathematics? Geometry and
mechanics would only differ from the other natural sciences by the
precision of the relations between the phenomena of which they treat,
by the facility which they have for dealing with these relations by
means of calculus and analysis, and, consequently, by assuming an
entirely rational and deductive form. For the extraordinary power of
the instrument should not hide from us the nature of the sciences which
make use of it. These, like the others, bear upon natural phenomena.
Only, as these phenomena are the most simple, the most general and
the most closely allied of all, these sciences are also those which
respond in the best way to the positive definition of science. They
have “very easily and very quickly replaced empirical statement by
rational prevision.” They are composed of laws and not of facts. But,
conforming in this again to the positive definition of science, they
are empirical in their origin, and they remain relative in the course
of their development.
Thus positive philosophy, having reached the full consciousness of
itself, reacts upon the conception of the sciences which have most
contributed to its formation. When the philosophy is universally
accepted the idea that a science can be _a priori_, that is both
absolute and immutable, will have disappeared. Precisely because it
is the most perfect type of a positive science, mathematics will no
longer claim these characteristics, and its ancient connection with
metaphysics will be finally severed.
FOOTNOTES:
[102] Cours, I, 101.
[103] Cours, I, 121-4.
[104] Cours, I, 112
[105] Cours, I, 256.
[106] Cours, I, 195-7.
[107] Cours, I, 286-7.
[108] Elements de philosophie, I, p. 132-3.
[109] Cours, I, 298. sq.
[110] Cours, i, 314-16.
[111] Cours, i, 383-4.
[112] Cours, i. 322-3.
[113] Cours, i. 422. sq.
[114] Cours, i, 455-463.
[115] Revue générale des sciences pures et appliquées, 30 septembre
1897.
CHAPTER II
ASTRONOMY
The object of astronomy is the discovery of the laws of the geometrical
and mechanical phenomena presented by the celestial bodies; and, by the
knowledge of these laws to obtain the precise and rational prevision of
the state of our system at any given period whatever. It is in a word,
“the application of mathematics to celestial phenomena.”[116]
Mr. H. Spencer has taken occasion of this definition to criticise
the place assigned by Comte to astronomy in his classification of
the sciences. He makes him contradict himself. He says: you term
fundamental sciences the abstract sciences which do not study beings in
nature, but the laws which govern phenomena in those beings; by what
right is astronomy placed among these sciences, between mathematics and
physics? Is not the object of astronomy the study of certain beings
in nature? In what does the application of mathematics to celestial
phenomena differ from their application to other cases? It appears
evident that here Comte introduces into the series of abstract sciences
a science which is really concrete, or at least, according to Mr.
Spencer’s expression, abstract-concrete.
Comte had foreseen the objection. The answer which he makes throws
a strong light upon the sense in which he understands the words
“abstract” and “general” as applied to the sciences. He partly accepts
the objection. The true astronomical notions, he says, only differ
from purely mathematical notions by their special restriction to
the celestial case; and this, at first sight, must appear contrary
to the essentially abstract nature of the speculations which belong
to the first philosophy. But on the other hand, these speculations
bear upon the phenomena given in experience, and the order of the
abstract sciences should reproduce the real order of dependence
of the phenomena. Thus the first of these sciences, mathematics,
determines the essential laws of the most general phenomena, which
are common to all material beings (form, position, movement). Now,
are not the most general phenomena after these, those “of which the
the continuous ascendency inevitably dominates the course of all the
other phenomena?”[117] In other words, before passing to the study of
physical, chemical, biological phenomena, etc., it is indispensable
to know the general laws of the _milieu_ in which these phenomena
are manifested. Outside of this _milieu_, they would be impossible,
or at any rate, it so conditions them that, were it otherwise, these
phenomena would also be different from what they are.
The character of generality which, with that of abstraction, is made
use of to institute the hierarchy of phenomena is thus reduced to
the idea of dependence. It is the consideration of this dependence
which assigns to astronomy its place between mathematics and physics
in the encyclopædic ladder of the sciences. Considered singly in
themselves, the phenomena studied by astronomy are purely geometrical
and mechanical. They would not, therefore, constitute the object of a
science distinct from mathematics. But positive philosophy considers
everything from the point of view of humanity. Now, for humanity, this
“special case” is of unequalled importance. All the other phenomena
given to us by experience (except the mathematical phenomena) depend,
in a more or less direct manner, upon astronomical phenomena. The
knowledge of astronomical laws is therefore the necessary condition
for the knowledge of all the others. Thus, the infringement of the
principle of the hierarchy of fundamental sciences is only apparent. An
analogous case is found in chemistry. The analysis of air and water is
incorporated in abstract chemistry, because air and water constitutes
the general _milieu_, “in which all ulterior phenomena occur.”[118]
The place given to astronomy is therefore justified. This science,
moreover, remains abstract. For it to be a concrete science, all
aspects of the existence of celestial bodies would have to be studied
and considered in their relations, to each other in it. But, on the
contrary, astronomy only studies the geometrical and mechanical
phenomena in the celestial bodies, all physical and chemical
considerations, etc., being eliminated. Comte concludes that in passing
on to the celestial case mathematics does not lose its abstract nature.
It only becomes more developed in the case of a special example, whose
extreme importance demands such a specialisation.
The abstract character of astronomy belongs to it almost _a priori_.
The facts upon which it rests are only revealed to us by one of our
senses, the most intellectual of them indeed, but by which we are only
informed of the mathematical properties of bodies. Our eyes alone
touch the stars. There is no astronomy for a blind race. Dark stars,
if such there be, are for ever hidden from us. All that is given to
us, therefore, is the shape, the position and the motion of visible
celestial bodies. We can never by any means know how to study their
chemical composition, nor their mineral structure, nor _a fortiori_
the nature of the organic bodies which may live upon them. Comte might
have formulated in less categorical terms affirmations which were
soon to be contradicted by spectral analysis and by photography. But
he was confirmed in the entirely abstract and mathematical conception
which he had of astronomy by his persuasion that no discoveries of so
far-reaching a nature were possible.
Thus, astronomy appeared to be an excellent type of a positive
science, because it is at once natural and abstract, and in it these
two characteristics are equally apparent, which was not the case in
mathematics. In this science the share of observation is so limited,
so transient, that it becomes inappreciable. In astronomy, on the
contrary, determination of certain facts evidently plays a part in the
science. But, at the same time, nowhere do we see more clearly that
science does not consist in the mere apprehension of facts. Here they
are so simple, and moreover so uninteresting, that their connexion
and the knowledge of their laws alone deserves the name of science.
In general, what is an astronomical fact? None other than this: such
a star has been seen at such a precise instant, and under such an
angle duly measured. The more or less profound elaboration of these
observations is indispensable to science, even in its most imperfect
state. Astronomy, says Comte, did not really come into being when
the priests of Egypt or Chaldea made a series of more or less exact
empirical observations in the heavens; but only when the first Greek
philosophers began to reduce the general phenomenon of diurnal motion
to a few geometrical laws.[119]
Of all the natural sciences, after mathematics, astronomy is also
the most perfectly free from all theological and metaphysical
considerations. From every point of view it is positive. Astronomers no
longer have recourse to a Providence, which as the intelligent cause
of the order of the celestial world, would in its turn, witness to
the existence of this cause. They do not inquire any more into the
intimate nature of forces (gravitation, attraction, etc.). Astronomy
is content to determine the invariable relations of phenomena with
the greatest possible precision. It is here that philosophical minds
can study the essential characteristics of a positive science. In
it they will also see how disinterested it must be in order to
become useful. “Without the highest speculations of geometers upon
celestial mechanics, which have so greatly increased the precision of
astronomical tables, it would be impossible to determine the longitude
of a ship with the degree of accuracy which is now attainable.”[120]
Finally no science has exercised a greater influence upon the evolution
of the human mind than this one. The great epochs in astronomy are
also those in cosmological philosophy. The desperate resistance
which was offered by theological dogmatism to Galileo’s discovery
responded to a just apprehension of the consequences involved in this
discovery. To admit that the earth was not the centre of the world
was to take a first and a decisive step in the way which leads away
from the anthropocentric prejudice. It was like pledging oneself to
substitute sooner or later the relative point of view to the absolute
one in philosophy. It was introducing the positive spirit, to-day in
speculative physics, to-morrow in speculative ethics.
II.
Although astronomy is an “eminently mathematical” science, the method
of working by observation is used in it. The astronomer observes before
calculating, and he observes again after having calculated. The art of
observation for which there is no use in mathematics appears here then,
and, with it, the inductive method.
Indeed there is no “absolute separation” between observing and
reasoning.[121] The mind does not first observe facts in a receptive
or “passive” manner, in order to work out combinations of these facts
afterwards. In reality every observation is a combination, and this
is particularly true in astronomical observation. The facts which
we observe are really constructed. We can only see simultaneous or
successive directions, according to which the mind must construct the
form or the movement which the eye could not take in. The necessary
and constant association “between prevision and inspection” is more
intimate and more evident here than in any other science.
In the same way, hypothesis (which is inseparable from observation)
can be studied in astronomy in its most simple form. Here it is
presented in its clearest aspect, and, if one may say so, in the one
which most reveals its essential nature. Now, hypothesis in astronomy
“serves to fill up the necessary gaps in observation.” It provisionally
supplements the knowledge--not indeed of causes, for positive science
seeks nothing of this kind--but of facts and laws which we ignore.
For instance, the simple geometrical sketch of a diurnal motion would
remain impossible without an abstract hypothesis which being compared
with the concrete spectacle presented by the movement itself enables us
to connect together the various celestial positions. Modern astronomy,
which has destroyed primitive assumptions regarded as real laws of
the world, has maintained their permanent value for conveniently
representing phenomena provisionally. And, as we are not deceived as
to the reality of such assumptions we can use without scruple any one
which seems to us most advantageous.[122]
The use of hypothesis, as it is employed in astronomy, must be carried
into the other sciences. This mode of procedure everywhere remains
like to itself, although we do not always conceive it so clearly.
“Its normal domain coincides with that of observation.” An hypothesis
completes by anticipation what we know of facts and of their laws.
Consequently, it is subject to be modified, corrected, or contradicted
by a wider or deeper knowledge of facts. Hypotheses then are only valid
during the time when they are advantageous, that is to say, as long as
they serve to unite and co-ordinate our observations. As has been said,
they labour to render themselves useless. But they are indispensable,
and science, without them, could neither advance nor even begin. Far
from giving too small a share to hypothesis, like Bacon, Comte would
rather incur the reproof of having given it too large a one. He made
too much use of it himself at the end of his life. But the theory
which he gave of it in the _Cours de philosophie positive_ and of
which certain features appeal again in Claude Bernard’s _Introduction
a l’étude de la médecine experiméntale_, was a careful study of its
nature and function.
III.
Astronomy, or at least that part of astronomy which bears the name of
celestial mechanics, of all the physical sciences is the one which has
been carried to the highest degree of perfection. Nowhere else have
the phenomena been better reduced to a supreme law which allows us to
foresee them with sufficient precision. But this result could only have
been obtained by substituting the notion of a solar world to that of
a universe.[123] This world is the only one which we can comprehend
as a system. If the object of astronomy were the general laws of the
universe, this science would be extraordinarily imperfect, not to say
impossible. For what do we know about cosmic laws?[124] We do not even
know whether Newton’s law applies to any or all systems of stars.
We must then distinguish between astronomy as the science of our world
and sidereal astronomy. The latter is not absolutely forbidden us, but
we know very little on this subject, and we shall probably never know
much more. Do the innumerable suns scattered in space form a general
system, or do independent systems exist? Is space limitless? Is the
number of celestial bodies an infinite one? philosophers ask. In truth
the consideration of our world is positive. The consideration of the
universe is not.
History helps us to understand the transition which led from one to the
other. Ancient philosophy made the earth the centre of the universe.
Notwithstanding the diversity of their particular characteristics and
of their motions, it was natural then for all the celestial bodies to
be conceived as the parts of a single system. A more or less clearly
expressed postulate supported this astronomical conception: the purpose
of the universe was the existence of man. There was no occasion to
distinguish our world from the whole world. But could this conception
stand when the earth was reduced to the condition of a planet revolving
round a sun so like a multitude of other suns. Suddenly the stars were
carried to distances infinitely more considerable than the greatest
planetary intervals. Undoubtedly the human mind could continue to
regard the very small groups of which the earth forms a part as a
system. But the system (if it exists) which embraces the whole of the
celestial bodies ceased henceforth to be within our reach. Since then
“the notion of the world has become clear and habitual, and that of the
universe has become uncertain and almost unintelligible.”[125]
It matters little, moreover, for, according to one of Comte’s favourite
maxims, what we have no means of knowing, neither have we any need
to know; and every thing which it is our interest to learn we can
also attain. Nor should we see in this any providential harmony. That
which it is our interest to know must always in some way influence
the conditions of our existence. By the mere fact that this action
makes itself felt, it is inevitable that sooner or later, directly
or indirectly, we should come to know of it. This reflection can be
well applied to astronomy. The study of the laws of the solar system,
of which we form a part, is of supreme interest for us: and we have
reached very great precision on this point. On the contrary, the exact
notion of the universe is inaccessible to us; but it is unimportant
to us leaving out of the question our “insatiable curiosity.” The
independence of our world is certain. The phenomena which take place
within the solar system do not appear to be affected by the more
general phenomena which relate to the mutual action of suns. Our
tables of celestial events, drawn up long beforehand and taking into
consideration no other world than our own, so far accord strictly with
direct observations. Supposing the law of gravitation to extend to the
entire universe, the perturbation in our world caused by a mass equal
to a million times its own, and which would be situated at the distance
of the nearest sun to our own, would be several thousand million times
less than that which brings about our tides, that is to say practically
nil.
Here, says Comte, is the only exception to the encyclopædic law
according to which the more general phenomena control the more
particular ones without being influenced by them.[126] From this
he simply concludes that the phenomena of our system are the most
general to which positive research can extend, and that the study of
the universe must henceforth be excluded from natural philosophy.
The encyclopædic law then remains true for the whole of positive
philosophy.
The delimitation of the object of astronomy is one of the points where
we can best follow the successive modifications of Comte’s thought. In
the second volume of the _Cours de philosophie positive_ he gave to
astronomy the place which is generally conceded to it by scientific
men. He even claims, as a condition for its utility, the most perfect
disinterestedness of scientific research in the whole extent of its
province. The example which he gives of it (the determination of
longitude at sea), is borrowed from Condorcet. Undoubtedly, Comte
already insists upon the distinction between the ideas of world
and universe, the former only being positive. Nevertheless, he
still admits that we should not give up all hope of obtaining some
sidereal knowledge,[127] and that it would be very precious for us
to know the relative motions of multiple stars, etc. But already in
the sixth volume of the _Cours_ he condemns entirely the “so-called
sidereal astronomy, which to-day constitutes the only grave scientific
aberration peculiar to celestial studies.”[128] Ten years later, in the
first volume of the _Politique positive_, he “regenerates” astronomy
from the synthetic point of view. He is no longer content to limit it
to the knowledge of the solar system. He confines the particular study
of our world within narrow limits. Astronomy, like the other sciences,
from objective must become subjective. Instead of the vague (that is to
say indefinite) study of the heavens its end must be the knowledge of
the earth, and the consideration of the other celestial bodies only in
their relation to the human planet. At this price alone can the unity
of this science be secured.[129]
Thus Comte came back to Aristotle’s closed world with the earth as its
centre. He points it out himself in showing in what way he differs
from the ancient conception. “This unity,” he says, “existed for the
ancients, but was of an absolute character which at that time was
legitimate.” When the motion of our planet became known, the ancient
constitution of celestial science might merely have been modified “by
preserving in it, as subjective, the centre which was at first supposed
to be objective.” That would have sufficed to change astronomy from
an absolute science to a relative one. Undoubtedly the ancients were
deceived in believing the earth to be the centre of the world; but, in
order to correct their error, it sufficed to say, the centre of _our_
world. The subjective synthesis “indeed concentrates the celestial
studies round the earth.” The other stars only deserve our attention
in so far as the knowledge of our planet requires it. Comte ends by
saying in the fourth volume of the _Politique positive_ that, strictly
speaking, the study of the sun and moon would suffice. We may add to
them the ancient planets, but not the “little telescopic planets.”[130]
This progressive narrowing of the astronomical domain does not
indicate a radical change in Comte’s philosophical thought. It only
results from the growing subordination of the scientific interest to
other superior interests. To know for the sake of knowing, appears to
Comte to be a wrong use of the human intellect. The Newtons and the
Laplaces in the past have fulfilled a necessary function, and humanity
owes them eternal gratitude. They struck a decisive blow against
theological and metaphysical philosophy; and secured the victory for
the positive spirit. In their time scientific speculation which tended
to the discovery of the laws of phenomena, and especially of celestial
phenomena, was at once the most sublime and the most useful occupation
which those men of genius could set themselves. But now that their
efforts have culminated in the foundation of positive philosophy, and
this philosophy itself in the “final religion,” there is no longer
any reason to continue researches with which henceforth humanity can
dispense. We must even “cut down many idle acquisitions.”[131] In a
word, from the religious point of view, Comte, in order to remedy the
anarchy of science, suppresses its liberty.
These extreme, but logically deduced consequences, are part of the
whole of Comte’s religious conceptions, that is to say of a distant
ideal. They must not blind us to the profundity of his philosophical
considerations on astronomy. His reflections upon the relation between
the ideas of the world and of the universe correspond, from the
positive point of view, to the first antinomy of the transcendental
Dialectics in the _Critique de la raison pure_. Can we ever be more
fully conscious of the relativity of our knowledge, that when we see
that what we know of celestial phenomena is admirably precise so long
as the solar system is concerned, but is reduced to almost nothing if
we look beyond it?
Our world will perish, and its disappearance like its existence, will
perhaps be an imperceptible incident. By the continued resistance
of the general _milieu_, says Comte, in the end our world must be
re-united to the solar mass from which it came, until, in the immensity
of future ages, a fresh dilatation of this mass shall organise a new
world in the same manner, destined to repeat more or less completely
the former cycle. Moreover, all these immense alternatives of
destruction and of renewal have to be accomplished without influencing
in any way the more general phenomena due to solar interaction; so
that the great revolutions in our world would only be secondary and,
so to speak, local events, in relation to transformations of a really
universal character.[132]
This outlook into the “immensity” of space and of duration suffices
to show that Comte was not a prisoner in the little solar fatherland
in which he seems to seclude himself. It may be that for moral and
religious reasons he will not allow himself to go beyond it. But,
like Pascal, he well knows that he inhabits “a little out of the way
district of nature.”
CHAPTER III.
THE SCIENCES OF THE INORGANIC WORLD
If we do not separate chemistry from physics, their common object is
the knowledge of the laws of the inorganic world. In this way they are
clearly distinguished on one hand from astronomy which we may consider
as an “emanation from mathematical science,” and on the other hand
from biology. The distinction between physics and chemistry presents a
greater difficulty. Nevertheless this distinction must be maintained,
since the physical phenomena are more “general,” and the chemical
phenomena more “special,” that is to say, the latter depend upon the
former, without this dependence being for the most part reciprocal.
Even if some day we succeeded in establishing that chemical phenomena
are in reality physical, the distinction would none the less subsist,
in this sense, that in a fact termed chemical, there is always
something more than in a fact which is simply physical, namely, the
characteristic alteration which the molecular composition of bodies
undergoes, and which consequently affects the totality of their
properties.[133]
To speak only of physics in the first place, this science presents
different characteristics from those of astronomy. The speculative
perfection of a science is measured by two correlative although
distinct considerations, by the more or less complete co-ordination
of the laws, and by the more or less accurate prevision of facts.
Now, under one aspect or the other, even supposing that physics
should make very important progress, it will always remain very much
behind astronomy. Indeed, the celestial science presents an almost
perfect unity; physics, on the contrary, is composed of several
branches which are almost isolated from one another, and each one
taken by itself cannot even reduce all its laws to a more general
law. And, as to the second point, while a very small number of direct
observations allows of rational and exact prevision of the whole of the
celestial phenomena, physics only renders possible predictions which
are generally founded upon experience at once immediate and within
easy reach. Undoubtedly some parts of physics allow of the use of
mathematical analysis (we shall see presently under what conditions).
Nevertheless, the part played by experience is infinitely greater in
physics than in astronomy. So it is in the former science that we first
meet with the inductive method, which is afterwards used and developed
in the other positive sciences. Although deduction continues to fulfil
an important part, it already ceases to predominate here, because, says
Comte, in it the institution of true principles begins to become more
troublesome than the development of accurate consequences.[134]
The inductive method implies these essential processes; 1∘ observation
properly so called, that is to say the direct examination of the
phenomenon such as it appears naturally: 2∘ experimenting, which is
usually defined as the examination of the phenomenon more or less
modified by artificial circumstances instituted by us in order to study
it better; 3∘ comparison, that is to say the gradual consideration of
a succession of analogous cases, in which the phenomenon becomes more
and more simple. Of these three processes astronomy only makes use of
the first. Physics cannot use the third which is reserved for biology;
but it avails itself of the first and institutes the second. This is a
fresh confirmation of the law established by Comte: to the complexity
and increasing difficulty of the sciences, corresponds an increasing
development of the processes of the positive method applicable to them.
Research by way of experiment, which is impossible in Astronomy,
appears in Physics. It is therefore here where it originates that we
must study it. It is also here that it is most successful, and gives
the greatest number of results. Indeed, to experiment successfully we
must be able to compare two cases “which present no other difference
direct or indirect, than that which relates to the course of the
phenomenon under analysis.”[135] By experimenting, Comte here clearly
designates what John Stuart Mill will call the method of difference,
that is to say the most powerful of his methods for the investigation
of phenomena.
Now, experimenting, so understood, is extremely difficult when very
complicated phenomena are concerned. In physiology, for instance, the
experiments must be combined in such a way as to maintain the subjects
in the living state, and even, as far as possible, in the normal state.
But any modification of one part of the organism immediately affects
the other parts. The living being reacts instantly, and adapts itself
as best it can to the new conditions in which it has been placed by the
experimentalist. We can therefore hardly ever establish in physiology
what is so easily obtained in physics: two cases exactly similar in all
respects, except in the one which we want to analyse. In chemistry, it
is true, experimenting would seem to be even easier than in physics,
since in it, as a rule, we merely consider facts resulting from
circumstances which are produced by man’s intervention. But this is
to mistake the nature of the experimental method. The essence of this
process does not consist in man’s institution of the circumstances
surrounding the phenomena; it lies in the “freest possible choice of
the case best suited to show the law of the phenomenon,” whether this
case be, moreover, natural or artificial. Now, this choice is nearly
always easier in physics than in chemistry. For the chemical phenomena
more complex in themselves, in general can only be brought about by the
co-operation of a great number of different influences; for this reason
in chemistry, it is more difficult to modify the circumstances under
which phenomena are produced, and still more difficult to isolate as
completely as in physics the various conditions by which phenomena are
determined.
To the use of the experimental method, physics can often join that of
mathematical analysis. But in the employment of the latter it must be
extremely cautious, and we must only have recourse to this application
of mathematics after having “carefully considered the reality of
the starting point,” which alone can guarantee the solidity of the
deductions. In a word, the spirit proper to physical investigation,
must constantly direct the use of this powerful instrument. Now, this
condition has not always been fulfilled. Too often the preponderance of
mathematical analysis has been the cause of the neglect of experimental
studies. Not only has mathematical analysis in this way retarded the
progress of physics but it has even tended to vitiate the conception
of that science, and to bring it back to a state of obscurity and
uncertainty which, says Comte, notwithstanding the apparent severity
of the forms differs little, at bottom, from its old metaphysical
state.[136]
For this reason, the application of analysis to physics must not be
left to geometers who are chiefly concerned with the instrument. It
must belong to the physicists who before all things consider the use
to be made of it. Mathematicians have often encumbered physics with a
quantity of analytical labour founded upon very doubtful hypothesis;
they must give way to physicists trained in experimental studies, and,
nevertheless, with sufficient knowledge of mathematics to make use of
the analysis whenever it is possible. Within these limits mathematical
analysis will render the greatest service to the science of physics.
Would optics, acoustics, the theories of heat and of electricity have
reached the point where we see them to-day without the powerful help
of analysis? Yet even here, physical researches are almost always so
complex that, in order to assume a mathematical form, they demand the
setting aside of a more or less essential portion of the conditions of
the problem. Indeed we are here in presence of the general problem of
the translation of the concrete into the abstract. This problem, which
is admirably solved in mathematics, and sufficiently in astronomy,
is only imperfectly solved in physics. The art of closely combining
experience and analysis, says Comte, is still almost unknown. It
constitutes the final progress of the method proper to the deeper
study of physics.[137] We may add, and this is in Comte’s mind, that
conversely the progress made by this art would be useful to analysis
itself.
II.
Astronomy has reached a perfect state of “positivity.” All trace of
the metaphysical spirit has disappeared from it. Can we say as much of
physics? It would not seem so, when we see the hypotheses which play so
great a part in this science, and of which a few are keenly contested
by Comte.
How can we distinguish the valuable hypotheses from the useless ones,
those which are useful to physics from those which are merely an
encumbrance and should be rejected? This is not a question which can
be solved by referring to abstract rules. In order to answer it,
we must study the use of hypotheses where it is perfect, and decide
according to this example. To my mind, says Comte, the deeper study of
the art of hypotheses in astronomy can alone establish the rules which
are suitable to direct the use of this precious artifice in physics,
and more so still in the remainder of natural philosophy.[138] Now of
what use is it to astronomers? To anticipate the results of deduction
or of induction, “by making a provisional supposition concerning
some of the very notions which constitute the final object of the
research.” It is a process of which the methods of approximation used
by geometers originally suggested the general idea. They “supposed”
that the circumference was the limit of the perimeters of inscribed and
circumscribed polygons the number of whose sides went on increasing.
In the same way, hypotheses provisionally fill up the “lacunæ” of our
knowledge.
An hypothesis should always be open to a positive verification, “whose
degree of precision is in harmony with that of the corresponding
phenomena.” For it only expresses beforehand what experience and
reasoning might have made known immediately, if the circumstances of
the problem had been more favourable. If, therefore, an hypothesis
claimed to attain that which in its nature is inaccessible to
observation and to reasoning, it would immediately become illegitimate
and harmful. In a word, it must bear exclusively upon laws, and never
upon causes or the modes of production of phenomena.
In the physics of his own time Comte finds the two kinds of hypotheses,
but he also finds more bad hypotheses than good ones. He especially
protests against the ethers and the fluids to which the phenomena
of heat, light, electricity and magnetism were attributed. These
hypotheses, according to him, are destined to disappear from science.
It is true that the physicists deny that they attribute an objective
reality to their ethers and their fluids. They claim to need them
absolutely in order to facilitate the conception and the combination
of phenomena. However, in spite of themselves, they are drawn into
speaking of their ethers as if they really existed. Moreover, do they
not see that astronomy gets on very well without similar hypotheses?
In order to conceive the phenomena it is enough to observe and analyse
them attentively. And, as to combining them, that depends upon the
knowledge which has been obtained of their positive relations.
The corpuscular theory is, on the contrary, an example of a good
hypothesis in physics, where it plays a part analogous to that of the
inertia of bodies in mechanics.[139] The innermost structure of bodies
is unknown to us. But we have a right to introduce all the hypotheses
which can help us in our research, and in particular the hypothesis of
atoms, so long as we do not understand it as something representing a
reality.
The ethers and the fluids tend to “explain” the physical phenomena by
the nature of the agent which produces them. It is here that these
hypotheses bear the mark of the metaphysical spirit. To understand
the appearance and especially the persistence of these hypotheses, it
is not enough to consider them in themselves. We must get back to the
history of physics, and compare it with that of the other fundamental
sciences. Was it possible for physics to pass suddenly from the period
in which phenomena are referred to causes and essences, to the positive
period where they are conceived as simply subject to laws? A period of
transition was necessary. The scholastic entities, before disappearing,
became semi-materialised. They were transformed into fluids. What is
heat conceived as existing apart from a hot body, light independent
of a luminous body, electricity separated from an electric body? They
are the old entities in a new garment, more easily grasped, in spite of
their “equivocal corporeity.” They gradually lead to the more and more
exclusive consideration of phenomena and of laws, until, in their turn,
they disappear.
Astronomy went through the same phases before Physics. In it we have
also seen hypotheses which cannot be verified come to facilitate
the transition from the theological to the positive state. Such was
the conception of Descartes who explained the celestial motions by
the system of vortices. Those famous vortices introduced the idea
of a mechanism where Kepler himself had only dared to conceive the
incomprehensible action of souls and genii. Then Newton came, who
preserved the idea of mechanism, while giving up the vortices. In vain
did the Cartesians fight against his entirely positive conception.
Their arguments in favour of fluids and ethers were as plausible
as those of the physicists of our own time. But we have ceased to
listen to them. Having become entirely positive, astronomy no longer
seeks anything but the laws at work in the phenomena observed. Every
accessory hypothesis aiming at anything else has no further interest
for us.
The most advanced portions of physics have already reached this point.
Take, for instance, the study of gravitation. There was not perhaps
a single scientific man of any importance in the XVII. century, even
long after Galileo, who did not construct or adopt a system concerning
the fall of bodies. At that time any science on this subject seemed
impossible without a hypothesis of this kind. Who troubles himself with
it to-day? We may be allowed to think that the other parts of physics
will follow the same line, and that in turn they will conform to this
rule of the positive method: “Every hypothesis must bear exclusively
upon the laws of phenomena, and never upon their modes of production.”
III.
In the series of the fundamental sciences Chemistry appears to fill a
somewhat secondary and subordinate place. In it the positive method
is not enriched by any process of capital importance, but it confines
itself to developing the processes already made use of in physics.
In spite of appearances, even experimenting is less easy and less
fertile in chemistry than in physics. The only new process which we see
appearing is the art of nomenclature. Whenever we wish to study this
art “at its source” we shall have to refer to chemistry.[140]
The phenomena which it studies are the most complicated of the
inorganic world. If then physics is extremely imperfect, it is not
surprising that chemistry should be much more so. In the greater number
of its researches “the chemistry of the present day hardly deserves the
name of science.”[141] But this inferiority of chemistry is not only
due to the nature of its object. There are other causes which it would
be easier to remedy. The progress of chemistry is retarded: 1, by the
wrong direction given to much of its work up to the present time; 2, by
the defective education of the majority of the scientific men who give
themselves to its study.
Before all things, chemists lack a clear and rational idea of their
science, of its relation to the sciences which stand nearest to it and
the way in which its problems should be stated. Being intermediate
between physics and biology, chemistry has suffered from the vicinity
of both. As the more advanced sciences always have a marked tendency
to encroach upon those above them, chemistry must in the first place
defend itself against the ascendency of physics, as physics itself
must fight against that of mathematics. The chemist must undoubtedly
have studied physics, in order to make use of the results obtained
by this science, and to turn them, if he can, into a method for
his own use. The relation of these two sciences is very close, and
a knowledge of the laws of calorific and electric phenomena, for
instance, is of the highest importance for chemical research. But, for
all this, the chemist has his own point of view. He studies, (which the
physicist does not do), the laws of the phenomena of composition and
decomposition which are the result of the molecular and specific action
of diverse natural or artificial substances upon each other. He must
therefore make use of physics, but not subordinate himself to it.
On the other hand physiological research is not within the province
of chemistry. What has been called “biological chemistry” belongs,
according to Comte, to biology alone. For the physiologist to have gone
through the school of chemistry is natural and even indispensable.
But his point of view is quite different from that of the chemist.
As a matter of fact, chemists have shown themselves unqualified for
physiological studies. None of their numerous attempts have succeeded
in establishing a single point of general doctrine, in biology. They
merely furnished materials. Moreover these cannot be used just as they
are by the physiologist, who is obliged to take up the researches again
“under the preponderating influence of biological considerations.”
Comte admires the self-confidence of the chemists who approach
physiological questions without having measured or even suspected the
special difficulties. It is, however, clear that the most carefully
made chemical analyses must be fruitless here so long as they are not
directed in the first place by a precise physiological notion of the
whole of the phenomenon, and then modified by the knowledge of the
limits of the normal variations to which the phenomena may be liable.
Now, for proceeding in this manner, the physiologists alone are
competent.[142]
Analogous considerations lead Comte to reject even organic chemistry.
Although the chemical phenomena present characteristics which in the
inorganic world come nearest to the solidarity which subsists between
the elements of living forms, nevertheless chemical phenomena remains
irreducible to living phenomena. That which is chemical is not yet
organic; and that which is organic is no longer purely chemical. We
must do away with this heterogenous and fictitious grouping which is
called organic chemistry, to unite the different parts, according
to their respective nature, some to chemistry proper, the others to
biology.[143]
How can we define the object of this science, so imperfectly determined
at the present time? Comte knows that he is about to depart from the
methods generally in use among chemists, but he is not afraid of this.
For, he says, in order to understand the real nature of a science,
we must always suppose it to be perfect.[144] As chemistry, is in
an extreme state of imperfection, the “scientific type” which the
philosopher conceives respecting it will appear to be very far removed
from what exists at present. It matters little so long as this type is
perfectly “rational.”
What is essential to science is the possibility of foreseeing
phenomena. Given the characteristic properties of the simple or complex
substances placed in chemical relations with each other under well
defined circumstances, the object of chemistry will therefore be to
determine exactly in what their action will consist, and what will be
the properties of the new substances produced.[145] According to this
definition, the fundamental data of chemistry should be ultimately,
reducible to the knowledge of the essential properties of the simple
elements alone, which would lead to that of the various immediate
chemical substances, and consequently to the most complex and distant
combinations. Obviously, the study of simple bodies can only be made
by means of experiments, which alone reveal their properties. But,
once this basis is laid down, “all the other chemical phenomena,
notwithstanding their immense variety, should be capable of rational
solutions, according to a small number of invariable laws, established
by the science of chemistry for the various classes of combinations.”
Thus, Comte sees clearly that the complexity of the chemical phenomena
prevents us from expressing their relations in a form which allows of
the use of mathematical analysis. But none the less, in this science as
in the preceding ones, he persists in making the experimental method a
mere starting-point. The experimental method furnishes the data which
it alone can supply. But these data are afterwards elaborated without
its intervention. The scientific ideal in chemistry, as in physics and
in astronomy, is _to substitute as much as possible rational prevision
to experimental verification_. Science always seeks to _deduce_ the
greatest number of consequences from the smallest number of data, and
the smallest number of data in this case are the properties of simple
bodies. Deduction will establish _a priori_ what the properties of a
given combination of two simple bodies, or of two complex bodies will
be.
In the name of this scientific ideal, Comte reproaches the chemists
with the superabundance of their analytical work. In default of a
rational conception of chemistry they do not make their work bear
upon the necessary points. What is the use of studying such and such
a body, placed in such and such conditions, in an arbitrary way and
according to the fancy of investigation? The progress of chemistry
should consist far less in the acquisition of new materials than in the
systematisation of those which we already possess. Chemistry is to-day
as rich in details as it is imperfectly constituted as a science.[146]
Its present state in no way gives an idea of what its normal state will
be.
Not content with showing to chemists the “scientific type” towards
which their science should tend, Comte suggests a contrivance in method
which will bring them nearer to it. It is in no way like the hypothesis
of affinities, for this appears to him to be even more “ontological”
than the hypothesis of imaginary fluids or ethers. As always happens
when we are concerned with metaphysical conceptions, the explanations
which we draw from affinities consist in the reproduction in abstract
terms of the very statement of the phenomenon.[147] To this hypothesis,
which is not a scientific one since it bears up the mode of production
of facts, Comte substitutes what he calls the “dualist hypothesis.” We
ignore, he says, and it is not for us to seek the real manner in which
the elements of which bodies are composed come to be grouped together.
But, consequently, it is lawful for us, in the very circumscribed
sphere of our positive research, to conceive the immediate composition
of any substance whatever as merely _binary_, each of the two bodies so
separated being able, according as the case may be, to lend itself to
a similar analysis, equally binary, and so on, as the occasion arises.
We do not affirm that dualism is a real law of nature. It will be a
fundamental contrivance in chemistry, like the hypothesis of inertia in
mechanics, and that of atoms in physics. It will serve to “simplify our
elementary conceptions” in chemistry, and in having recourse to it we
do not exceed “the special kind of liberty” of which our intellect may
avail itself, in the institution of science.[148]
The use of this hypothesis would allow us to endow chemistry with a
“fine” character of unity and rationality which it lacks to-day. It is
true that Comte himself confessed that this hypothesis, proposed by
him in 1838, had yet “produced nothing” in 1851. But he explains this
sterility to himself by the metaphysical spirit, from which chemists
are not sufficiently freed.
IV.
We can now take in at a single glance the relations of the sciences
of the inorganic world (including astronomy), with the totality of
positive philosophy.[149]
In several ways these sciences have contributed to the progress of the
positive spirit. By their constitution, they allowed and prepared the
formation of the more complex sciences of Biology and of Sociology.
Moreover, their development struck a mortal blow at theological and
metaphysical philosophy. Through them minds became familiarised with
the idea of natural law. This idea was not so clearly brought to light
by mathematics on account of their almost purely abstract character,
and of the imperceptible part played in them by observation. It
appears, on the contrary, as the mainspring of astronomy, of physics,
and of chemistry. The whole effort of these sciences tends to discover
invariable relations between phenomena given in experience.
Theological philosophy is the “explanation” of nature which the
human mind first makes for itself. In order that it may give up this
“explanation” some contrary evidence must oblige it to do so. It may
see for instance, that phenomena can be predicted with a perfect
exactness which is always confirmed by experience, or that man, under
certain conditions, can modify them with certainty. Astronomy gives us
an example of the former case. It studies phenomena which, it is true,
are removed from our sphere of action. But, in return, it predicts them
with a certainty of which the effect has been practically infallible
in the long run. It is astronomy which has done most to discredit the
religious and philosophical doctrine of final causes.[150] Not only has
it proved that the universe is not disposed with reference to man, but
it has shown the imperfections of our solar system. It has helped more
than any other science to check the mental habit of seeking the mode of
production of phenomena.
Physics is far from allowing of a rational prevision which is
comparable to that practised by astronomy. But, as a compensation, it
shows how the knowledge of laws gives the power to cause phenomena
to vary with certainty. This second way leads us no less surely than
the first to the positive conception of nature. For example, Franklin
destroyed the religious theory of thunder, even in the least cultivated
intellects. The discovery of the means of directing lightning therefore
had the same effect, in another way, as the exact prevision of the
return of comets.[151]
On the other hand the sciences of the inorganic world furnish the
general positive method with some of its most powerful processes.
Astronomy introduces observation and hypothesis into this method,
Physics adds experimenting to it, and Chemistry the art of
nomenclatures. The inductive method, which virtually consists in simple
scientific observation, becomes, however, enriched and is developed,
according as the phenomena in question become more complicated.
But, in return, positive philosophy exercises a considerable influence
over these sciences. It claims nothing less than to direct and
“regenerate” them. Viewing them from above and as a whole, philosophy
can bring a remedy to the difficulties which arise from their
specialism. It sets an exact limit to each of the sciences. It delivers
physics from the “algebraical yoke,” and protects the independence of
chemists against the encroachments of the physicists. It places the
entirety of the positive method at the service of each particular
science. For instance, it directs the use of hypothesis in physics by
the theory drawn from the use which is made of it in astronomy; for
classifications, it extends to chemistry the use of the comparative
method which properly belongs to biology. When, later, the integral and
final constitution of the philosophy of our age shall have organised
the relations between all the sciences, it will be almost impossible,
save from the historical point of view, to understand how the study of
nature was ever conceived and directed otherwise.[152]
Positive philosophy organises labour within each science, and puts
an end to “anarchy.” It distinguishes between “idle” researches, and
those which should be pursued. It avoids waste of efforts and prevents
digressions. We have seen within what limits Comte wishes to enclose
astronomy in the name of philosophy. He does not perceive the means
by which he can unite the various branches of physics; but he claims
to replace the fragmentary and scattered chemistry of his time by a
single systematic science, which will forsake the researches of detail
which are without interest for humanity. “Almost the whole of those
innumerable compounds will not finally be worthy of any scientific
attention. Some well-chosen series may even be able to satisfy the
logical requirements of chemistry for the discovery of the abstract
laws which belong to each order of composition.”[153]
Finally positive philosophy causes the disappearance of the last
remains of the theological and metaphysical spirit from the sciences of
inorganic nature. This philosophy has already shown that mathematics
is not a more absolute science than the others, and that it originates
in experience. In physics and in chemistry it banishes the hypotheses
which, more or less avowedly, tend to make us conceive the essence or
the mode of production of phenomena. It is thus that it demands a
science of physics freed from ethers and fluids, and a wholly rational
chemistry which shall give up affinities.