Auguste Comte and Positivism
 See the Chapter on Efficient Causes in Reid's "Essays on the Active Powers," which is
avowedly grounded on Newton's ideas.
 Mr Herbert Spencer, who also distinguishes between abstract and concrete sciences, employs
the terms in a different sense from that explained above. He calls a science abstract when its
truths are merely ideal; when, like the truths of geometry, they are not exactly true of real things -
or, like the so-called law of inertia (the persistence in direction and velocity of a motion once
impressed) are "involved" in experience but never actually seen in it, being always more or less
completely frustrated. Chemistry and biology he includes, on the contrary, among concrete
sciences, because chemical combinations and decompositions, and the physiological action of
tissues, do actually take place (as our senses testify) in the manner in which the scientific
propositions state them to take place. We will not discuss the logical or philological propriety of
either use of the terms abstract and concrete, in which twofold point of view very few of the
numerous acceptations of these words are entirely defensible: but of the two distinctions M.
Comte's answers to by far the deepest and most vital difference. Mr Spencer's is open to the
radical objection, that it classifies truths not according to their subject-matter or their mutual
relations, but according to an unimportant difference in the manner in which we come to know
them. Of what consequence is it that the law of inertia (considered as an exact truth) is not
generalized from our direct perceptions, but inferred by combining with the movements which we
see, those which we should see if it were not for the disturbing causes? In either case we are
equally certain that it is an exact truth: for every dynamical law is perfectly fulfilled even when it
seems to be counteracted. There must, we should think, be many truths in physiology (for
example) which are only known by a similar indirect process; and Mr Spencer would hardly
detach these from the body of the science, and call them abstract and the remainder concrete.
 Systeme de Politique Positive, ii. 36.
 The strongest case which Mr Spencer produces of a scientifically ascertained law, which,
though belonging to a later science, was necessary to the scientific formation of one occupying an
earlier place in M. Comte's series, is the law of the accelerating force of gravity; which M. Comte
places in Physics, but without which the Newtonian theory of the celestial motions could not have
been discovered, nor could even now be proved. This fact, as is judiciously remarked by M.
Littre, is not valid against the plan of M. Comte's classification, but discloses a slight error in the
detail. M. Comte should not have placed the laws of terrestrial gravity under Physics. They are
part of the general theory of gravitation, and belong to astronomy. Mr Spencer has hit one of the
weak points in M. Comte's scientific scale; weak however only because left unguarded.
Astronomy, the second of M. Comte's abstract sciences, answers to his own definition of a
concrete science. M. Comte however was only wrong in overlooking a distinction. There is an
abstract science of astronomy, namely, the theory of gravitation, which would equally agree with
and explain the facts of a totally different solar system from the one of which our earth forms a
part. The actual facts of our own system, the dimensions, distances, velocities, temperatures,
physical constitution, &c., of the sun, earth, and planets, are properly the subject of a concrete
science, similar to natural history; but the concrete is more inseparably united to the abstract
science than in any other case, since the few celestial facts really accessible to us are nearly all