hypothesis-"Hypotheses non fingo." The fact is that as his theory of gravitation rested upon the greatest and most successful of hypotheses, so his views of the material nature of light and the causes of its peculiar phenomena involved a false hypothesis, which has long since been completely disproved.

The word theory has constantly been used in the last few lessons, and deserves some examination. It comes from the Greek dewpía, meaning contemplation, reflection or speculation; but this gives us little clue to its modern use. In reality the word is highly ambiguous, being sometimes used as equivalent to hypothesis, at other times as equivalent to general law or truth. When people form theories concerning comets, the sun, the cause of earthquakes, &c., they imagine a great many things which may or may not exist; such theories are really complicated hypotheses, and should be so called. In this sense there are two theories of electricity, one of which supposes the existence of a single fluid which accumulates in some places and has then a tendency to discharge itself towards places where there is a deficiency, just as water always tends to find its level; the other supposes the existence of two fluids which are commonly united, but when separated tend to rush back into union again. These so-called theories are really hypotheses, because we have no independent evidence of the existence of any fluid, and it is now almost certain that there is no such thing. The atomic theory, again, is really a hypothesis suggested by Dalton to explain the remarkable laws which he detected in the proportions of chemical elements which combine together. It is a valid hypothesis in so far as it does really explain the fixedness of the quantities which combine; but it is purely hypothetical as regards the shapes, properties or absolute magnitudes of the atoms, because we have no facts which it can har

monise in these respects, and no apparent means of gaining them.

In another and more proper sense theory is opposed to practice, just as the general is opposed to the particular. The theory of gravitation means all the more general laws of motion and attraction on which Newton founded his system of the Universe. We may know what those laws are without being able to determine the place of a planet or make any practical use of them; the particular results must be calculated out by skilful astronomers before navigators, travellers or others can make practical use of them in the determination of the latitude or longitude. When we speak of the mathematical theory of sound, the lunar theory, the theory of the tides, the word is employed without any special reference to hypothesis, and is merely equivalent to general knowledge or science, implying the possession of a complete series of general and accurate laws, but in no way distinguishing them from accurate knowledge in general. When a word is really used in an equivocal manner like theory, it is not desirable to attempt to give it an accurate definition which would be imaginary and artificial.

The word fact is used very often in this as in most books, and demands a few remarks. It is derived from factum, the past participle of facere, to do, and would thus mean something which is done, an act, or deed; but the meaning is evidently greatly extended by analogy. We usually oppose to each other fact and theory, but just as theory seems to have two ambiguous meanings, so I believe that fact is ambiguous. Sometimes it means what is certain and known by the evidence of the senses, as opposed to what is known only probably by hypothesis and inference; at other times it is contrasted to a general law, and is equivalent to a particular instance or case. A law of great generality may often be as certain and true,

especially in mathematics, as the particular facts coming under it, so that the contrast must in this case be that between the general and particular. We often use the word too in common life, as merely equivalent to truth; thus we might say, “It is a fact that the primary laws of thought are the foundation of reasoning." In short, as theory means ambiguously what is hypothetical, general, abstract or uncertain, so fact is equally ambiguous, and means confusedly what is intuitively known, particular, concrete or certain.

Mill's System of Logic, Book III. Chapters 12, 13 and 14, Of Explanation, and Hypothesis.

LESSON XXXII.

CLASSIFICATION, AND ABSTRACTION.

IN an earlier Lesson, upon the subject of the Predicables, we considered the doctrine of classification as it was treated by logicians many centuries ago. The progress of science, however, during the last two centuries has caused great attention to be given to the true principles on which we can arrange a great multitude of diverse objects in order, and we have to consider what are the characteristics of a natural and perfect system of classification.

It may be said, indeed, that the subject we are treating is coextensive with the science of logic. All thought, all reasoning, so far as it deals with general names or general notions, may be said to consist in classification. Every common or general name is the name of a class, and every name of a class is a common name. "Metal" is the name

of one class of substances so often used in our syllogistic examples; "Element" of another class, of which the former class is part. Reasoning has been plausibly represented to consist in affirming of the parts of a class whatever may be affirmed of the whole. Every law of nature which we arrive at enables us to classify together a number of facts, and it would hardly be too much to define logic as the theory of classification.

Here we deal, however, with that more conscious and distinct arrangement of objects or notions, which is especially employed in the natural sciences, such as Botany, Zoology, Mineralogy and Palæontology.

The derivation of the word class is somewhat curious. In ancient Rome it was the practice to summon the whole people together at certain periods, and this ceremony was known as a clãsis, from the Greek λáois, or Kλños, derived from kaλéw, to call together. Servius Tullius is said to have divided the people into six orders, according to the amount of tribute they could pay, and these orders were not unnaturally called the classes of the people. Hence the name came by degrees to be applied to any organized body of people, such as an army; thence it was transferred to a fleet of vessels as marshalled in a fixed order, and was finally extended by analogy to any collection of objects carefully arranged. When, however, we now speak of the lower or higher classes of the people it is curious that we are restoring the word very nearly to its original meaning.

Classification may perhaps be best defined as the arrangement of things, or our notions of them, according to their resemblances or identities. Every class should so be constituted as to contain objects exactly resembling each other in certain definite qualities, which are stated in the definition of the class. The more numerous and extensive the resemblances which are thus indicated by

any system of classes, the more perfect and useful must that system be considered.

Mr Mill thus describes his view of the meaning— "Classification is a contrivance for the best possible ordering of the ideas of objects in our minds; for causing the ideas to accompany or succeed one another in such a way as shall give us the greatest command over our knowledge already acquired, and lead most directly to the acquisition of more. The general problem of classification, in reference to these purposes, may be stated as follows: To provide that things shall be thought of in such groups, and those groups in such an order, as will best conduce to the remembrance, and to the ascertainment of their laws."

A collection of objects may generally be classified in an indefinite number of ways. Any quality which is possessed by some and not by others may be taken as the first difference, and the groups thus distinguished may be subdivided in succession by any other qualities taken at will. Thus a library of books might be arranged, (1) according to their size, (2) according to the language in which they are written, (3) according to the alphabetic order of their authors' names, (4) according to their subjects; and in various other ways. In large libraries and in catalogues such modes of arrangement are adopted and variously combined. Each different arrangement presents some peculiar convenience, and that mode must be selected which best meets the especial purpose of the library or catalogue. The population of a kingdom, again, may be classified in an almost endless number of ways with regard to different purposes or sciences. The population of the United Kingdom may be divided according to their place of birth, as English, Welsh, Scotch, Irish, colonial-born, and aliens. The ethnographer would divide them into Anglo-Saxons, Cymri, Gaels, Picts,