3. This last example may appear to most readers doubtful. I have purposely pursued the enumeration till I came to a doubtful example, because it is, and I conceive always will be, impossible to extend this general view to all the Sciences. On the contrary, this doctrine applies at present to only a very few of the sciences, even in the eyes of those who hold the existence of ideal truths. The doctrine extends at present to a few only of the sciences, even if it extend to one or two besides those which have been mentioned—Geometry, Mechanics, Chemistry, Mineralogy: and though it may hereafter appear that Ideal Truths are possible and attainable for a few other sciences, yet the laws disclosed by sciences which cannot be reduced to ideal elements will, I conceive, always very far outnumber those which can be so reduced. The great body of our scientific knowledge will always be knowledge obtained by mere observation, not knowledge obtained by the use of theories alone.
4. The survey of the history and philosophy of the Sciences which we have attempted in previous works enables us to offer a sort of estimate of the relative portions of science which have and which have not thus been idealized. For the Aphorisms[317] which we have collected from that survey, contain Axioms which may be regarded as the Ideal portions of the various sciences; and the inspection of that series of aphorisms will show us to how such a portion of science, anything of this axiomatic or ideal character can he applied. These Axioms are the Axioms of Geometry (Aphorism XXVI); of Arithmetic (XXXVI); of Causation (XLVII); of a medium for the sensation of secondary qualities (LVIII), and their measure (LXIX); of Polarity (LXXII); of Chemical Affinity (LXXVI); of Substance (LXXVII); of Atoms (LXXIX).
Have we any axioms in the sciences which succeed these in our survey, as Botany, Zoology, Biology, Palæontology?
There is the Axiom of Symmetry (LXXX); of Kind, (already in some measure spoken of, (LXXXIII)); of Final Cause (CV); of First Cause (CXVI).
5. (Small extent of necessary truth.)—It is easily seen how small a portion of each of these latter sciences is included in these axioms: while, with regard to the sciences first mentioned, the Axioms include, in a manner, the whole of the science. The science is only the consequence of the Axioms. The whole science of Mechanics is only the development of the Axioms concerning action and reaction, and concerning cause and its measures, which I have mentioned as a part of our Ideal knowledge.
In fact, beginning from Geometry and Arithmetic, and going through the sciences of Mechanics, of Secondary Qualities, and of Chemistry, onwards to the sciences which deal with Organized Beings, we find that our ideal truths occupy a smaller and smaller share of the sciences in succession, and that the vast variety of facts and phenomena which nature offers to us, is less and less subject to any rules or principles which we can perceive to be necessary.
But still, that there are principles,—necessary principles, which prevail universally even in these higher parts of the natural sciences,—appears on a careful consideration of the axioms which I have mentioned:—that in symmetrical natural bodies the similar parts are similarly affected;—that every event must have a cause;—that there must be a First Cause, and the like.
6. It being established, then, that in the progress of science, facts are idealized—that à posteriori truths become à priori truths;—that the world of things is identified with the world of thoughts to a certain extent;—to an extent which grows larger as we see into the world of things more clearly; the question recurs which I have already asked: How can this be?
How can it be that the world without us is thus in some respects identical with the world within us?—that is our question.
7. (How did things come to be as they are?)—It would seem that we may make a step in the solution of this question, if we can answer this other: How did the world without us and the world within us come to be what they are?