Logic, Inductive and Deductive

by William Minto

"The truth is—as most readers of Plato know, only it is a truth difficult to retain and apply—that what we gain by discussing a definition is often but slightly represented in the superior fitness of the formula that we ultimately adopt; it consists chiefly in the greater clearness and fulness in which the characteristics of the matter to which the formula refers have been brought before the mind in the process of seeking for it. While we are apparently aiming at definitions of terms, our attention should be really fixed on distinctions and relations of fact. These latter are what we are concerned to know, contemplate, and as far as possible arrange and systematise; and in subjects where we cannot present them to the mind in ordinary fulness by the exercise of the organs of sense, there is no way of surveying them so convenient as that of reflecting on our use of common terms.... In comparing different definitions our aim should be far less to decide which we ought to adopt, than to apprehend and duly consider the grounds on which each has commended itself to reflective minds. We shall generally find that each writer has noted some relation, some resemblance or difference, which others have overlooked; and we shall gain in completeness, and often in precision, of view by following him in his observations, whether or not we follow him in his conclusions."[²]

Mr. Sidgwick's own discussions of Wealth, Value, and Money are models. A clue is often found to the meaning in examining startlingly discrepant statements connected with the same leading word. Thus we find some authorities declaring that "style" cannot be taught or learnt, while others declare that it can. But on trying to ascertain what they mean by "style," we find that those who say it cannot be taught mean either a certain marked individual character or manner of writing—as in Buffon's saying, Le style c'est l'homme même—or a certain felicity and dignity of expression, while those who say style can be taught mean lucid method in the structure of sentences or in the arrangement of a discourse. Again in discussions on the rank of poets, we find different conceptions of what constitutes greatness in poetry lying at the root of the inclusion of this or the other poet among great poets. We find one poet excluded from the first rank of greatness because his poetry was not serious; another because his poetry was not widely popular; another because he wrote comparatively little; another because he wrote only songs or odes and never attempted drama or epic. These various opinions point to different conceptions of what constitutes greatness in poets, different connotations of "great poet". Comparing different opinions concerning "education" we may be led to ask whether it means more than instruction in the details of certain subjects, whether it does not also import the formation of a disposition to learn or an interest in learning or instruction in a certain method of learning.

Historically, dialectic turning on the use of words preceded the attempt to formulate principles of Definition, and attempts at precise definition led to Division and Classification, that is to systematic arrangement of the objects to be defined. Attempt to define any such word as "education," and you gradually become sensible of the needs in respect of method that forced themselves upon mankind in the history of thought. You soon become aware that you cannot define it by itself alone; that you are beset by a swarm of more or less synonymous words, instruction, discipline, culture, training, and so on; that these various words represent distinctions and relations among things more or less allied; and that, if each must be fixed to a definite meaning, this must be done with reference to one another and to the whole department of things that they cover.

The first memorable attempts at scientific arrangement were Aristotle's treatises on Ethics and Politics, which had been the subjects of active dialectic for at least a century before. That these the most difficult of all departments to subject to scientific treatment should have been the first chosen was due simply to their preponderating interest: "The proper study of mankind is man". The systems of what are known as the Natural Sciences are of modern origin: the first, that of Botany, dates from Cesalpinus in the sixteenth century. But the principles on which Aristotle proceeded in dividing and defining, principles which have gradually themselves been more precisely formulated, are principles applicable to all systematic arrangements for purposes of orderly study. I give them in the precise formulæ which they have gradually assumed in the tradition of Logic. The principles of Division are often given in Formal Logic, and the principles of Classification in Inductive Logic, but there is no valid reason for the separation. The classification of objects in the Natural Sciences, of animals, plants, and stones, with a view to the thorough study of them in form, structure, and function, is more complex than classifications for more limited purposes, and the tendency is to restrict the word classification to these elaborate systems. But really they are only a series of divisions and subdivisions, and the same principles apply to each of the subordinate divisions as well as to the division of the whole department of study.

II.—Principles of Division or Classification and Definition.

Confusion in the boundaries of names arises from confused ideas regarding the resemblances and differences of things. As a protective against this confusion, things must be clearly distinguished in their points of likeness and difference, and this leads to their arrangement in systems, that is, to division and classification. A name is not secure against variation until it has a distinct place in such a system as a symbol for clearly distinguished attributes. Nor must we forget, further, that systems have their day, that the best system attainable is only temporary, and may have to be recast to correspond with changes of things and of man's way of looking at them.

The leading principles of Division may be stated as follows:—

I. Every division is made on the ground of differences in some attribute common to all the members of the whole to be divided.

This is merely a way of stating what a logical division is. It is a division of a generic whole or genus, an indefinite number of objects thought of together as possessing some common character or attribute. All have this attribute, which is technically called the fundamentum divisionis, or generic attribute. But the whole is divisible into smaller groups (species), each of which possesses the common character with a difference (differentia). Thus, mankind may be divided into White men, Black men, Yellow men, on ground of the differences in the colour of their skins: all have skins of some colour: this is the fundamentum divisionis: but each subdivision or species has a different colour: this is the differentia. Rectilineal figures are divided into triangles, quadrangles, pentagons, etc., on the ground of differences in the number of angles.