Granted; but

these several appearances are produced. you must also grant that without these despised identical propositions Science could not stir a step in explanation.

71. There are truths of various orders, but not of various degrees of certainty. The Law of Multiple Proportions in Chemistry is the abstract expression of observed facts, and as such, is an unshakable truth, even though conceivably some wider Law may include it. The Atomic Theory which interprets the phenomena is a true theory, although based on the hypothesis of Atoms, which cannot be proved, and may some day be dismissed to give place to a better. The Undulatory Theory is true, though the hypothesis of an Ether is possibly doomed to disappear. I mean that the theories are true because they are formulas of facts; that gases consist of separate particles nearly alike, and that in radiants there is periodic motion, are propositions logically equivalent to the experiments; the hypotheses, which are introduced as auxiliaries, may be replaced by better auxiliaries, but there can be no displacement of the experimental facts.

72. The Evolution hypothesis, to which Mr. Darwin has given the name of Natural Selection, is offered in aid of interpreting the observed facts of community of structure and function. The Creation hypothesis, by which naturalists of the opposing school interpret the same facts, is gradually being displaced, as it is now more and more recognized to belong to the class which I have named Illusory Hypotheses.* The observed facts are, that all plants and animals have certain characters in common,

* In answer to the common objection that no new species has been observed to arise within the historical period, Professor Jevons, in a work just published, remarks that we might as well deny the geological changes because no new mountain has risen within the memory of man. "When we know that rain-water falling on limestone will carry away a minute portion of the rock in solution, we do not hesitate to multiply that quantity by millions of millions, and assert that in course of time a mountain may be dissolved away." - Principles of Science, 1874, II. 48.

and certain differences, these resemblances and differences forming the conceptions Organism, Plant, Animal, Genera, Species, etc. Further, it is observed that some groups are widely separated from others. What is called the fixity of species expresses this observation. So long as the question is purely zoölogical, and relates to the facts observed and observable, there is no dispute. But when Zoögeny replaces Zoology, and the question of origin is mooted, the two hypotheses of Creation and Natural Selection struggle for supremacy. The advocate of Creation, throwing the predominant weight of evidence on the observation of Difference and the fixity of types, assumes that these types were constructed once for all, each in its observed position, each without reference to the other, as palaces, public houses, villas, and cottages are erected by men. The other school, admitting all that is really observed in respect to fixity of type, but denying what is inferred in respect to the impossibility of each type arising by infinite infinitesimal increments of variation, assumes that the observed facts of variation point to the evolution of all forms from pre-existing forms, and ultimately, of all from one.

Both these hypotheses of origin must always remain hypotheses. Knowledge of what things are under observed conditions may be absolute; it can never lead to more than hypothetical statements of what things were under other conditions; and since it is manifestly impossible. that we should ever know what were the exact conditions under which organic life emerged, we can do no more than guess at origins. The guesses will have more or less probability in proportion to the ascertained facts on which they rest. When, for example, it is proved that individual organisms vary, the proof is inductively furnished that species vary, since species are but groups of individuals. This, however, does not disturb the truth that the specific type cannot vary; for the type is an abstraction, and the

very terms in which it is expressed exclude variation. The type is what it is; the individual is also what it is. The type is ideal; the individual is real.

73. I have repeatedly insisted on the memorable fact that Science is no transcript of Reality, but an ideal construction framed out of the analysis of the complex phenomena given synthetically in Feeling, and expressed in abstractions. In all analysis there is abstraction, which rejects much more than is expressed; this rejected remainder may in turn be analyzed, but at each step there is an unexplored remainder. As, in the speculation of Laplace, there are dark stars scattered through space, but hidden from observation because they are dark; so in every phenomenon there are numberless factors at work which are hidden from observation, and only speculatively postulated. Sometimes these speculative inferences, which always have some basis in observation or analogy, suggest the means of objective verification. Thus, Newton inferred that bodies at the earth's surface gravitated towards each other; it was an inference from analogy, but was then beyond experimental proof.* It has since been experimentally verified, and thus exhibited not only as an ideal truth, but one having real application.

74. It is requisite to bear in mind that no general statement can be real, no ideal truth be a transcript of the actual order in its real complexity. "Until we know thoroughly the nature of matter, and the forces which produce its motions, it will be utterly impossible to submit to mathematical reasoning the exact conditions of any physical question," † and even then it will only be mathematical relations which will be formulated. The approximate solutions which are reached "are obtained by a species of abstraction, or rather limitation of the * NEWTON, Principia, III. Prop. vii. Corol. i. + THOMSON AND TAIT, Natural Philosophy, I. 337.

data," and thus "the infinite series of forces really acting may be left out of consideration; so that the mathematical investigation deals with a finite (and generally small) number of forces, instead of a practically infinite number."

If, then, Science is, in its nature, an ideal construction, and its truths are only truths of symbols which approximate to realities, there is an internal necessity of movement in scientific thought, which transforms existing theories according to ever-widening experience. We can never reach the finality of Existence, for we are always having fresh experiences, and fresh theories to express them. We also need hypotheses to supplement the deficiencies of observation; and that hypothesis is the best which introduces most congruity among our ascertained truths. Yet throughout this shifting of the limits there is a constant principle of Certitude, and the truth of yesterday is not proved false because it is included in the wider truth of to-day; the two truths express two limits of Experience.

75. In conclusion, we may say that various theories are ideal representations of the External Order, and are severally true, in so far as the import of their terms includes no more than has been verified by the reduction of Inference to Intuition or Sensation; severally false, in so far as their terms include what is inconsistent with such verified import; and severally doubtful, in so far as the terms include what has not been thus verified. To express it in a more abstract phrase: Truth is the equivalence of the terms of a proposition; and the equivalence is tested by the reduction of the terms to an identical proposition.†

* Loc. cit.

+ In the Appendix will be found an attempt to apply this result to an examination of the axioms of Geometry, usually accepted as embodying truths of the highest order of exactness. If we find the test applicable there, we may the more readily admit its applicability in other sciences. See Appendix, A.

CHAPTER V.

THE LOGICAL PRINCIPLES.

76. THE Principle of Equivalence, which has been expounded in the preceding pages, is free from the ambiguities which have caused many philosophers to reject the three scholastic principles, Identity, Contradiction, and the Excluded Middle. It is, moreover, the positive statement of the negative formula advanced by Mr. Herbert Spencer, as the Universal Postulate, or the inconceivableness of the contrary of a proposition. This formula has been much criticised and much misunderstood. In the republication of his Principles of Psychology, Mr. Spencer has given a re-statement of his views, freeing them from some ambiguities of expression. Thus, in place of the much-criticised phrase, "Beliefs which invariably exist," he proposes, "Cognitions of which the predicates invariably exist along with their subjects." His position may be thus stated: whenever a subject and predicate can be united in the same intuition, the proposition is thinkable: it may be true, or not true; at any rate, it admits of being presented to the mind. Whenever a subject and predicate not only can be thus united, but must be, the one term being incapable of appearing to thought without the other, the proposition is necessary; and its negative being unthinkable, the proposition itself must be true.

77. I do not quite go along with Mr. Spencer when he argues for the necessity of some unproved truth, as a fun