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But why is it that a man cannot get rid of an idea? Why does it force itself upon him as a belief? Association, custom, explains how it got there, but not why it persists in staying.

To explain this we must call in our first fallacious principle, the Impatience of Doubt or Delay, the imperative inward need for a belief of some sort.

And this leads to another remark, that though for convenience of exposition, we separate these various influences, they are not separated in practice. They may and often do act all together, the Inner Sophist concentrating his forces.

Finally, it may be asked whether, seeing that illusions are the offspring of such highly respectable qualities as excess of energy, excess of feeling, excess of docility, it is a good thing for man to be disillusioned. The rose-colour that lies over the world for youth is projected from the abundant energy and feeling within: disillusion comes with failing energies, when hope is "unwilling to be fed". Is it good then to be disillusioned? The foregoing exposition would be egregiously wrong if the majority of mankind did not resent the intrusion of Reason and its organising lieutenant Logic. But really there is no danger that this intrusion succeeds to the extent of paralysing action and destroying feeling, and uprooting custom. The utmost that Logic can do is to modify the excess of these good qualities by setting forth the conditions of rational belief. The student who masters those conditions will soon see the practical wisdom of applying his knowledge only in cases where the grounds of rational belief are within his reach. To apply it to the consequences of every action would be to yield to that bias of incontinent activity which is, perhaps, our most fruitful source of error.

There are certain principles known as the Laws of Thought or the Maxims of Consistency. They are variously expressed, variously demonstrated, and variously interpreted, but in one form or another they are often said to be the foundation of all Logic. It is even said that all the doctrines of Deductive or Syllogistic Logic may be educed from them. Let us take the most abstract expression of them, and see how they originated. Three laws are commonly given, named respectively the Law of Identity, the Law of Contradiction and the Law of Excluded Middle.

But why did Aristotle consider it necessary to lay down a principle so obvious? Simply because among the subtle dialecticians who preceded him the principle had been challenged. The Platonic dialogue Euthydemus shows the farcical lengths to which such quibbling was carried. The two brothers vanquish all opponents, but it is by claiming that the answer No does not preclude the answer Yes. "Is not the honourable honourable, and the base base?" asks Socrates. "That is as I please," replies Dionysodorus. Socrates concludes that there is no arguing with such men: they repudiate the first principles of dialectic.

There were, however, more respectable practitioners who canvassed on more plausible grounds any form into which ultimate doctrines about contraries and contradictions, truth and falsehood, could be put, and therefore Aristotle considered it necessary to put forth and defend at elaborate length a statement of a first principle of demonstration. "Contradictions cannot both be true of the same subject at the same time and in the same sense." This is the original form of the Law of Contradiction.

Aristotle acknowledges that this first principle cannot itself be demonstrated, that is, deduced from any other. If it is denied, you can only reduce the denier to an absurdity. And in showing how to proceed in so doing, he says you must begin by coming to an agreement about the words used, that they signify the same for one and the other disputant. No dialectic is possible without this understanding. This first principle of Dialectic is the original of the Law of Identity. While any question as to the truth or falsehood of a question is pending, from the beginning to the end of any logical process, the words must continue to be accepted in the same sense. Words must have an identical reference to things.

Incidentally in discussing the Axiom of Contradiction , Aristotle lays down what is now known as the Law of Excluded Middle. Of two contradictories one or other must be true: we must either affirm or deny any one thing of any other: no mean or middle is possible.

In their origin, then, these so-called Laws of Thought were simply the first principles of Dialectic and Demonstration. Consecutive argument, coherent ratiocination, is impossible unless they are taken for granted.

If we divorce or abstract them from their original application, and consider them merely as laws of thinking or of being, any abstract expression, or illustration, or designation of them may easily be pushed into antagonism with other plain truths or first principles equally rudimentary. Without entering into the perplexing and voluminous discussion to which these laws have been subjected by logicians within the last hundred years, a little casuistry is necessary to enable the student to understand within what limits they hold good.

That throughout any logical process a word must signify the same object, is one proposition: that the object signified by a general name is identical with the sum of the individuals to each of whom it is applicable, or with the sum of the characters that they bear in common, is another proposition. Logic assumes both: Aristotle assumed both: but it is the first that is historically the original of all expressions of the Law of Identity in modern text-books.

To turn next to the Laws of Contradiction and Excluded Middle. These also may be subjected to Casuistry, making clearer what they assert by showing what they do not deny.

They do not deny that things change, and that successive states of the same thing may pass into one another by imperceptible degrees. A thing may be neither here nor there: it may be on the passage from here to there: and, while it is in motion, we may say, with equal truth, that it is neither here nor there, or that it is both here and there. Youth passes gradually into age, day into night: a given man or a given moment may be on the borderland between the two.

A difference, however, must be recognised between logical negation and the negations of common thought and common speech. The latter are definite to a degree with which the mere Logic of Consistency does not concern itself. To realise this is to understand more clearly the limitations of Formal Logic.

In common speech, to deny a quality of anything is by implication to attribute to it some other quality of the same kind. Let any man tell me that "the streets of such and such a town are not paved with wood," I at once conclude that they are paved with some other material. It is the legitimate effect of his negative proposition to convey this impression to my mind. If, proceeding on this, I go on to ask: "Then they are paved with granite or asphalt, or this or that?" and he turns round and says: "I did not say they were paved at all," I should be justified in accusing him of a quibble. In ordinary speech, to deny one kind of pavement is to assert pavement of some kind. Similarly, to deny that So-and-so is not in the Twenty-first Regiment, is to imply that he is in another regiment, that he is in the army in some regiment. To retort upon this inference: "He is not in the army at all," is a quibble: as much so as it would be to retort: "There is no such person in existence".

Whether the scope of Logic ought to be extended is another question. It seems to me that the scope of Logic may legitimately be extended so as to take account both of the positive implication of negatives and the negative implication of positives. I therefore deal with this subject in a separate chapter following on the ordinary doctrines of Immediate Inference, where I try to explain the simple Law of Thought involved. When I say that the extension is legitimate, I mean that it may be made without departing from the traditional view of Logic as a practical science, conversant with the nature of thought and its expression only in so far as it can provide practical guidance against erroneous interpretations and inferences. The extension that I propose is in effect an attempt to bring within the fold of Practical Logic some of the results of the dialectic of Hegel and his followers, such as Mr. Bradley and Mr. Bosanquet, Professor Caird and Professor Wallace.

The logical processes formulated by Aristotle are merely stages in the movement of thought towards attaining definite conceptions of reality. To treat their conclusions as positions in which thought may dwell and rest, is an error, against which Logic itself as a practical science may fairly be called upon to guard. It may even be conceded that the Aristotelian processes are artificial stages, courses that thought does not take naturally, but into which it has to be forced for a purpose. To concede this is not to concede that the Aristotelian logic is useless, as long as we have reason on our side in holding that thought is benefited and strengthened against certain errors by passing through those artificial stages.

THE LOGIC OF CONSISTENCY. SYLLOGISM AND DEFINITION.

THE ELEMENTS OF PROPOSITIONS.

GENERAL NAMES AND ALLIED DISTINCTIONS.

To discipline us against the errors we are liable to in receiving knowledge through the medium of words--such is one of the objects of Logic, the main object of what may be called the Logic of Consistency.

Strictly speaking, we may receive knowledge about things through signs or single words, as a nod, a wink, a cry, a call, a command. But an assertory sentence, proposition, or predication, is the unit with which Logic concerns itself--a sentence in which a subject is named and something is said or predicated about it. Let a man once understand the errors incident to this regular mode of communication, and he may safely be left to protect himself against the errors incident to more rudimentary modes.

A proposition, whether long or short, is a unit, but it is an analysable unit. And the key to syllogistic analysis is the General Name. Every proposition, every sentence in which we convey knowledge to another, contains a general name or its equivalent. That is to say, every proposition may be resolved into a form in which the predicate is a general name. A knowledge of the function of this element of speech is the basis of all logical discipline. Therefore, though we must always remember that the proposition is the real unit of speech, and the general name only an analytic element, we take the general name and its allied distinctions in thought and reality first.

How propositions are analysed for syllogistic purposes will be shown by-and-by, but we must first explain various technical terms that logicians have devised to define the features of this cardinal element. The technical terms CLASS, CONCEPT, NOTION, ATTRIBUTE, EXTENSION or DENOTATION, INTENSION or CONNOTATION, GENUS, SPECIES, DIFFERENTIA, SINGULAR NAME, COLLECTIVE NAME, ABSTRACT NAME, all centre round it.

From the examples it will be seen that a general name logically is not necessarily a single word. Any word or combination of words that serves a certain function is technically a general name. The different ways of making in common speech the equivalent of a general name logically are for the grammarian to consider.

In the definition of a general name attention is called to two distinct considerations, the individual objects to each of which the name is applicable, and the points of resemblance among them, in virtue of which they have a common name. For those distinctions there are technical terms.

CLASS is the technical term for the objects, different yet agreeing, to each of which a general name may be applied.

The points of resemblance are called the common ATTRIBUTES of the class.

Technical terms are wanted also to express the relation of the individuals and the attributes to the general name. The individuals jointly are spoken of as the DENOTATION, or EXTENSION or SCOPE of the name; the common attributes as its CONNOTATION, INTENSION, COMPREHENSION, or GROUND. The whole denotation, etc., is the class; the whole connotation, etc., is the concept. The limits of a "class" in Logic are fixed by the common attributes. Any individual object that possesses these is a member. The statement of them is the DEFINITION.

To predicate a general name of any object, as, "This is a cat," "This is a very sad affair," is to refer that object to a class, which is equivalent to saying that it has certain features of resemblance with other objects, that it reminds us of them by its likeness to them. Thus to say that the predicate of every proposition is a general name, expressed or implied, is the same as to say that every predication may be taken as a reference to a class.

Ordinarily our notion or concept of the common features signified by general names is vague and hazy. The business of Logic is to make them clear. It is to this end that the individual objects of the class are summoned before the mind. In ordinary thinking there is no definite array or muster of objects: when we think of "dog" or "cat," "accident," "book," "beggar," "ratepayer," we do not stop to call before the mind a host of representatives of the class, nor do we take precise account of their common attributes. The concept of "house" is what all houses have in common. To make this explicit would be no easy matter, and yet we are constantly referring objects to the class "house". We shall see presently that if we wish to make the connotation or concept clear we must run over the denotation or class, that is to say, the objects to which the general name is applied in common usage. Try, for example, to conceive clearly what is meant by house, tree, dog, walking-stick. You think of individual objects, so-called, and of what they have in common.

DEGREES OF GENERALITY. One class is said to be of higher generality than another when it includes that other and more. Thus animal includes man, dog, horse, etc.; man includes Aryan, Semite, etc.; Aryan includes Hindoo, Teuton, Celt, etc.

The technical names for higher and lower classes are GENUS and SPECIES. These terms are not fixed as in Natural History to certain grades, but are purely relative one to another, and movable up and down a scale of generality. A class may be a species relatively to one class, which is above it, and a genus relatively to one below it. Thus Aryan is a species of the genus man, Teuton a species of the genus Aryan.

Vertebrates . | Mammals, Birds, Reptiles, etc. . | Rodents, Ruminants, Carnivors, etc. . | Rats, Squirrels, Beavers, etc. . | Brown rats, Mice, etc. .

If we subdivide a large class into smaller classes, and, again, subdivide these subdivisions, we come at last to single objects.

The attribute or attributes whereby a species is distinguished from other species of the same genus, is called its DIFFERENTIA or DIFFERENTIAE. The various species of houses are differentiated by their several uses, dwelling-house, town-house, ware-house, public-house. Poetry is a species of Fine Art, its differentia being the use of metrical language as its instrument.

Other attributes of classes as divided and defined, have received technical names.

An attribute common to all the individuals of a class, found in that class only, and following from the essential or defining attributes, though not included among them, is called a PROPRIUM.

An attribute that belongs to some, but not to all, or that belongs to all, but is not a necessary consequence of the essential attributes, is called an ACCIDENT.

The clearest examples of Propria are found in mathematical figures. Thus, the defining property of an equilateral triangle is the equality of the sides: the equality of the angles is a proprium. That the three angles of a triangle are together equal to two right angles is a proprium, true of all triangles, and deducible from the essential properties of a triangle.

That horses run wild in Thibet: that gold is found in California: that clergymen wear white ties, are examples of Accidents. Learning is an accident in man, though educability is a proprium.

What is known technically as an INSEPARABLE ACCIDENT, such as the black colour of the crow or the Ethiopian, is not easy to distinguish from the Proprium. It is distinguished only by the third character, deducibility from the essence.

Accidents that are both common and peculiar are often useful for distinguishing members of a class. Distinctive dresses or badges, such as the gown of a student, the hood of a D.D., are accidents, but mark the class of the individual wearer. So with the colours of flowers.

Given such a fixed scheme, very nice questions may be raised as to whether a particular attribute is a defining attribute, or a proprium, or an accident, or an inseparable accident. Such questions afford great scope for the exercise of the analytic intellect.

We shall deal more particularly with degrees of generality when we come to Definition. This much has been necessary to explain an unimportant but much discussed point in Logic, what is known as the inverse variation of Connotation and Denotation.

It is obviously wrong to say that they vary in inverse proportion. Double or treble the number of attributes, and you do not necessarily reduce the denotation by one-half or one-third.

It is just possible to increase the connotation without decreasing the denotation, to thicken or deepen the concept without diminishing the class. This is possible only when two properties are exactly co-extensive, as equilaterality and equiangularity in triangles.

SINGULAR and PROPER NAMES. A Proper or Singular name is a name used to designate an individual. Its function, as distinguished from that of the general name, is to be used purely for the purpose of distinctive reference.

In the expressions "a Napoleon," "a Hotspur," "a Harry," the names are not singular names logically, but general names logically, used to signify the possession of certain attributes.

A man may be nicknamed on a ground, but if the name sticks and is often used, the original meaning is forgotten. If it suggests the individual in any one of his qualities, any point in which he resembles other individuals, it is no longer a Proper or Singular name logically, that is, in logical function. That function is fulfilled when it has called to mind the individual intended.

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