constituted, the Positive hierarchy becomes the condensation of all real sciences, and the basis of all practical conceptions, as it brings the classification of the arts into coincidence with that of the sciences.

The conclusion here reached is the last step in our explanation of the construction of the doctrinal system, which from the synthetical point of view is now complete. Before, however, I enter on its analytical constitution, it is important to throw out into relief the threefold preamble just accomplished by affixing to it a name adapted to remind us of it as a whole. For this we may use the expression First Philosophy, limited by me above to the system of the fifteen universal laws, so giving definiteness to the vague design of Bacon, after making his aspiration a reality. Since this system of laws is but the intermediate and principal portion of the basic introduction to the definitive coordination of the Positive doctrine, the denomination which I originally reserved for it, being practically at liberty, may be applied to the whole introduction. All that is requisite is to treat it as inseparable from the institution of abstraction on which it rests as its basis, and from the hierarchical construction for which it gives the basis. Thus viewed, the First Philosophy forms a distinct and definite whole, a whole which gives systematic form to the subjective synthesis idealised in the worship, and which must be our guide in our objective analysis, to enable us to develope the Positive doctrine on a scale answering to its destination. I shall bring out the importance of this First Philosophy in the following chapter, by making it the object of a special study at the outset of our encyclopædic education, where it is our only direct safeguard against degeneration into scholastic puerilities.

There is and can be but one synthetical arrangement of the Positive dogma, for such arrangement treats the several sciences as branches of moral science, without giving beforehand any specific division, but leaving the way open for all suitable subdivisions. The contrary is true of the analytical arrangement; it admits of several distinct forms, according to the degree of connection we introduce between the different terms of the encyclopedic hierarchy. From the objective point of view, it is not possible to fix the number of the sciences, since the generalisation of thought is as appropriate for theory, as the specialisation of action is requisite for practice. In reality the name attached

The First

Philosophy

in its full

sense.

Analytical degina ad

form of the

mits of

several ar

rangements.

Seven analytical arrangements.

Two Bi

nary.

(a) Dogma toy, So

tic. CosmoSocio

logy.

cal.

ral, loso

to each science merely indicates the group of investigations generally acknowledged to have a certain unity, and this may vary at different times and for different minds. From the subjective point of view, the division of the sciences is equally fluctuating, as when so considered it marks the several resting places of the intelligence in its encyclopædic course, and that course may always be continuous whatever the number of its stages.

Be this as it may, the seven sciences which we established as the result of the preparatory evolution of the race, will not need, as a rule, subdivision, when the human mind has attained greater power of synthesis, allowing always for educational requirements. At the same time the number is one that will always lend itself to the establishment of a satisfactory continuity. But their hierarchical combination, with the object cf bringing objective analysis into closer relations with subjective synthesis, this admits of many different forms. Of all the forms possible in the abstract, I select for present treatment those only which have a real utility both for theory and practice. The selection gives the seven analytical arrange. ments of the Positive sciences, which I proceed to explain, one after the other, in the order in which they are derived from the synthetical arrangement above examined.

One and the same subdivision of the synthetical arrangement gives two binary arrangements, the one more objective and dogmatical, the other more subjective and historical. The Histori- first sanctions the most marked distinction admissible throughNatu-) Phi- out the whole range of real investigations, the distinction, that Moral phy. is, between the domain of the inorganic world and the system of the organic, in other words between the study of the earth and the study of man, Cosmology and Sociology. In the second we break up the one great whole by separating the external or physical order from the human or moral order; hence the division of the general term philosophy into natural and moral. Thus the two binary arrangements of the doctrinal system Positivism differ only as to Biology, Biology standing in the one case as the introduction to Sociology, in the other as the complement of Cosmology. This last conception best represents the natural course of scientific education, the other is the most appropriate for our ultimate studies, as manifesting the imprac ticability of an objective synthesis. If we look to practical

of

results, the two modes have distinct yet equivalent merits.

find that the historical arrangement fixes attention especially on the highest kind of progress, by marking off into a separate class the most modifiable phenomena, those in which invariability was but of late recognition. The dogmatical arrangement on the other hand expresses the systematisation of the activity of the Great Being, which consists in bringing all vital power whatever to bear on the modification of the world of pure matter.

nary.

a

rial order.

2. Vital order. 3. Human

order.

1. Physical

This last dualism would seem as valuable as the other, yet Two Terit is the other, as more easily divisible, to which we have 1. Materecourse for our ternary arrangements, from which we likewise draw the succeeding ones. Subdivide the external order or the human order, and the result is two ternary arrangements, each endowed with important properties. The first best gratifies the craving for continuity, as viewing the order of the world in reference to the normal series-material, vital, and human. The second is more favourable to the dignity of our studies and practical exertions; in it the Positive hierarchy is formed by the subordination of physical to intellectual and both to moral laws. This last mode represents the theory of the brain and the economy of Sociocracy, whereas the other is the systematic expression of the abstract evolution and the concrete series of existences.

b

laws.

2. Intel

lectual

laws.

3. Moral laws.

ternary.

logy.

a

3. Sociology.

As the two are of equal importance, it will be often advisable Two Quato combine them, and form a quaternary arrangement by a subdivision of the human order or of the physical laws. This 1. Cosmomode was adopted in the second volume, and makes Positive 2. Biology philosophy consist in the normal hierarchy of Cosmology, 4. Morals. Biology, Sociology, and Morals. It enables us to state clearly the main series of the introductory sciences, whilst not concealing the science which is their ulterior object.

A second quaternary arrangement may be formed by the combination of each term of the encyclopædic scale with its successor, so that we rise to Morals by a progression formed of three couples, inferior, middle, and superior. This mode was introduced in my discourse upon the Positive spirit, and represents the closest degree of connection which exists between the several branches of science, since each of the preliminary sciences is more nearly connected with the one that precedes it than with the one that follows it, as is shown by the order of their genesis.

b

The three

couples with

Morals as

their crown.

Prefixed to
Populaire.

Astronomie

One Qui

nary.

1. Mathematics.

2. Physics.

4. Sociology.

5. Morals.

Only one quinary arrangement is admissible, drawn from the first quaternary arrangement by breaking up its first term, on the basis of the distinction between Mathematics and 3. Biology. Physics as a whole. Although this mode, which is at once historical and dogmatical, is less convenient for our ultimate investigations than for systematic education, it has this advantage, that it begins the encyclopædic series with that branch of study which is directly accessible. At this point, however, our objective analysis immediately tends to full completeness; to return, that is, by virtue of the twofold subdivision of physics to the primary arrangement of the scale, the only one admitting of satisfactory continuity.

Rest of the chapter less general, elaborating the hierarchy of the

ces.

Such, amid the possible analytical arrangements, are the seven by which we bridge over the space between the complete developement of the encyclopædic series, and the systematic unity which it is the object of that series to promote or to prepare. Apply them and compare them, and we shall feel more fully the value of the subjective synthesis, which alone combines in itself all the several excellences of the various stages of the objective analysis. The comparison will at the same time evidence the main advantages of the Positive scale, which, in a more or less developed form, suffices for all our intellectual wants.

To complete the systematisation of the doctrine, the remainder of the chapter must be devoted to less general considerations, to such an elaboration of the basic hierarchy of the seven scien- sciences as may make it an adequate expression of the order of the world. Each of the seven sciences which it establishes, will always form a distinct branch of human study, an object for the speculative and practical reason of man, first during the period of education, and subsequently even during the whole course of the normal existence. The maintenance of the distinction between the sciences is the condition on which the objective analysis secures for the subjective synthesis its requisite clearness and coherence. But as these distinct sciences always tend to divert attention from the general unity, it is important to reduce them within the narrowest possible limits, according to the rule laid down in the first volume of this work. All I have to do here is to explain the agreement which necessarily exists between this law of restriction and all the grounds on which we properly and persistently eliminate all idle speculations.

tial step in

order must

studied.

Our aims in studying the order of the world are a noble Each essensubmission to, and a wise modification of, that order; we must the universal therefore examine, singly and by itself, each of its independent be separately phases, the phases which, following one another in regular Invariasuccession, result in a relative, to the exclusion of any absolute, an inductive conception of the whole. Nor is such a separation indispensable principle. merely to satisfy our unintermitting need of speculation and of action, it is the sole condition of our attaining an adequate conviction of the great primary principle of invariability. For that principle will never admit of deductive demonstration, inasmuch as by its nature it is itself the common basis of all Positive deductions. It will always rest on convictions of an essentially inductive character, convictions therefore to be formed separately for each distinct class of irreducible phenomena. Allow its full power to philosophic analogy, and yet the whole course of our scientific initiation shows that human reason persists in not recognising the universal applicability of the Positive principle, so long as it has not in detail been applied to each and all of the natural categories. Scientific prejudices notwithstanding, it is possible, and that without inconsistency, to consider phenomena as generally and in large majority subject to immutable laws, whilst one exceptional class is left alone under the dominion of arbitrary wills. This is a state of mind which is not removed by virtue of the real connection which exists between the different laws, for such connection is traceable only when the several laws have been separately recognised; its removal can only be the result of a direct and special extension of the Positive principle to each distinct province of the domain of science.

How invamade com

riability is

pletely

general.

It is concrete knowledge alone that admits of a really deductive demonstration of the principle of invariability, nay, without deduction we were here powerless to conceive it as applicable, for we shall never know the greater part of the laws proper to complex events. But as these depend of necessity upon the simple phenomena, we are warranted in looking on them as being, equally with those simple phenomena, subject to the Positive principle, although the difficulty of the inductions and deductions is so great, that we cannot in regard to them carry it out in detail. From this point of view the word chance no longer stands for the empire of caprice; it comes to Chance and Le simply the general designation for the laws which we do not