quate to account for the existence of the universe and of all that is in it.

II. The Absolute Being must be a person. Energizing Reason and it alone, adequately accounts for all that is. The vindication of this proposition requires the presentation of the reasons why we believe that the personal God exists, and does not come within the design of this book. It is therefore relegated to Natural Theology.

CHAPTER XIII.

THE THREE GRADES OF SCIENTIFIC KNOWLEDGE.

57. Definition of Science.

SCIENTIFIC knowledge is distinguished from unscientific. Every one recognizes the distinction; but the attempts to define it have not been satisfactory. This is due in part to the fact that the word science is variously defined and used with a variety of meanings. It is idle to debate whether a particular branch of knowledge is science or not, so long as the disputants are not agreed as to the meaning of the word. It is due also to a certain relativity essential in the idea of science.

Scientific knowledge is not distinguished from unscientific knowledge by being true or real knowledge. The unscientific knowledge that stones fall when unsupported and that grass grows is as true and real knowledge as is the scientific knowledge of the same facts.

Knowledge is distinguished as scientific by the aim and method of the intellectual process by which it is attained. Its aim in respect to any reality investigated is to attain knowledge definite, well substantiated, exactly enunciated, complete, and systemized; its method is to regard all the true laws of thought, to investigate all sources of knowledge, and to use all the instruments and means which ingenuity has contrived to give greater exactness and wider scope to knowledge. The knowledge acquired by such a process is called scientific knowledge. The collected results of such investigations respecting any particular class of realities, enunciated in propositions, proved, and systemized constitute a particular science, as the science of Astronomy or Chemistry.

Hence a science will realize in a greater or less degree the ends aimed at by scientific thought. It will present knowledge having as close an approximation to definiteness as man with his present information and means of investigation can attain; substantiated by convincing evidence; enunciated in exact terms-in some sciences, as in chemistry and botany, in a nomenclature peculiar to itself; complete, as far as men can yet make it; and presenting the object treated in its relation to other things and to the universal system.

It is not essential to science that it be at any given time complete or free from error. It is called science in reference to the aims and methods of the intellectual process of which it is the result, not in reference to its own absolute correctness and completeness. The Chaldeans and Egyptians had a science of astronomy as really as we. The Ptolemaic System of astronomy was science as really as is the Copernican. Otherwise no science exists so long as it is possible to attain any new knowledge on the subject or to correct any errors.

It is not essential to constitute knowledge scientific, that it be the knowledge of a law of nature. Comte held that knowledge is science only when it enables us to foresee and foretell events; that is, that science is distinctively and essentially the knowledge of the laws of nature. But if so history, geography, philology, anatomy, descriptive geology, and all descriptive sciences, so-called, are not sciences. This is admitted and they are therefore excluded from the hierarchy of sciences by Comte, the most consistent of thinkers in boldly accepting the legitimate consequences of his own principles. Also all knowledge of particular facts would be excluded from science, as the knowledge of the diameter of the earth or of Mars, the time of their rotation on their axis and of their revolution around the sun; also all colligation of facts, as that by which we know that Cuba is an island and that the orbit of Mars is a particular geometrical figure.

58. The Three Grades of Science Defined.

There are three grades of scientific knowledge, by which the mind must ascend in attaining knowledge of all that may be known respecting any object whatever. They may be named respectively, Empirical, Rationalistic or Noetic, and Theological Science; or Empiricism, Rationalism, and Theology.

I. The first grade of scientific knowledge is Empirical Science. This is the knowledge of particular realities either by observation or by inference, of their unity in coexisting relations, of their co-ordination in the invariable sequences of causal connection, and thus of their unity in a system.

The first step in empirical science is gaining knowledge of individual realities; as an astronomer observes a transit of Venus, a chemist learns by experiment the properties of a quantity of oxygen, an entomologist observes an insect. The second step is learning how the object is in unity with other things in coexistent relations. Of this, classification by resemblance is an example. The third step is co-ordination in uniform sequences. Here we obtain those general facts which are called laws of nature, such as the law of gravitation, or of the conservation and correlation of force. Lastly, empirical science, by the

knowledge of the unity of particular realities in their static or coexisting relations, and of their co-ordination in uniform sequences in their dynamic relations, attains to the knowledge of their unity in a system; for example, the unity of the sun and planets in the solar system.

Empirical Science answers the question, what is the fact?

There are two divisions of empirical science: Physical Science, or the science of nature, founded on sense-perception; and Psychology, or the science of mind, founded on self-consciousness and the observation and history of men.

II. The second grade of scientific knowledge is Noetic or Rationalistic Science. This is founded on the four norms or standards of reason. It is the scientific knowledge of the truths, laws, ideals, and ends of Reason; of all the truths necessarily involved in them or inferable from them; and of all empirically known reality in its relation thereto. Empirical science starts with the particular realities presented in senseperception or self-consciousness; even the realities not immediately perceived but only inferred, are realities which are in their nature perceptible, as the attracting of iron by a magnet which I have not actually seen. Rationalistic science starts with the universal principles known in rational intuition; but it has already been shown that the first principles of reason in themselves have no content and give no knowledge; and they are known in consciousness only by some occasion in experience. Hence this second branch of science must find its content in the realities empirically known; it is the scientific knowledge of empirically known reality in its relation to the truths, laws, ideals, and ends of Reason. Empirical science is the knowledge of particular facts; rationalistic science is the knowledge of the universal and necessary in its relation to the particular and contingent, and of the particular and contingent in its relation to the universal and the necessary. Empirical science recognizes reality as it is known in senseperception and self-consciousness; rationalistic science recognizes it as it is known by the intuitive Reason. The fact that man is constituted capable both of perceptive intuition and rational, is the basis of the distinction of empirical science and noetic. The distinction necessarily results from the constitution of man.

There is no name which, as actually used, denotes precisely this second grade of science. It is often called Metaphysics. But this word is used to denote the science of mind, as the opposite of Physics or the science of nature. The science of mind is empirical as well as noetic; while the science of nature is noetic or rationalistic as well as empirical. On the other hand metaphysics, as used, never includes mathematics, which is indisputably a noetic science as I have here de

fined it. The word Metaphysics, as used, includes a part of empirical science and excludes a part of noetic science; and if employed as the name of the latter would inevitably mislead. In the lack of an ade

quate name in actual use, I have chosen the words, rationalistic or noetic, as indicating the distinctive relation of this branch of science to the principles and ideas of reason.

There are three divisions of noetic science, Mathematics, Logic and Philosophy.

1. Mathematics is the science deduced from certain definitions and axioms of reason pertaining exclusively to the forms of space and number. Pure mathematics has scarcely any content of empirically known reality other than the geometrical figures and arithmetical and algebraical symbols necessary to aid the mind in thinking. Space and number themselves are but forms of things. Mathematics is applied to measure whatever has measurable quantity.

J. S. Mill has made the desperate attempt to explain mathematics as an empirical science. In his Autobiography he says that "the chief strength of this false philosophy" (which recognizes the validity of first principles or rational intuitions) "in morals, politics, and religion lies in the appeal which it is accustomed to make to the evidence of mathematics and the cognate branches of physical science. To expel it from these is to drive it from its stronghold," (pp. 225, 226.) And to accomplish this, he tells us, he wrote the discussion of mathematical evidence in his Logic. Mr. Mill here admits that mathematics properly ranks with metaphysics, and is one division of this second grade of scientific knowledge. Prof. W. K. Clifford, in his Lectures. and Essays, goes farther than Mr. Mill, and denies both the exactness and the certainty of the axioms of mathematics and its demonstrated conclusions. The animus of both writers seems to be to get rid of the argument from mathematics in support of the validity of rational intuitions and of metaphysical science. No arguments, however, are likely to convince men that they have learned the principles and demonstrated the conclusions of mathematics by observation and experiment. Till they are thus convinced they must acknowledge the validity of knowledge through the intuitions of reason and of the noetic or rationalistic sciences founded upon them.

2. Logic is the science of the laws of thought, deduced from certain axioms of Reason pertaining to reflective thought. This science pertains to the forms and laws of thought rather than to its matter or

content.

3. The third division of rationalistic science is Philosophy. This is

Logic. Book II., Chaps. v. and vi.