Yet another expression of a Law of Identity which is really distinct from and an addition to Aristotle's original. _Socrates was an Athenian, a philosopher, an ugly man, an acute dialectician, etc._ Let it be granted that the word Socrates bears the same signification throughout all these and any number more of predicates, we may still ask: "But what is it that Socrates signifies?" The title Law of Identity is sometimes given[9] to a theory on this point. _Socrates is Socrates._ "An individual is the identity running through the totality of its attributes." Is this not, it may be asked, to confuse thought and being, to resolve Socrates into a string of words? No: real existence is one of the admissible predicates of Socrates: one of the attributes under which we conceive him. But whether we accept or reject this "Law of Identity," it is an addition to Aristotle's dialectical "law of identity"; it is a theory of the metaphysical nature of the identity signified by a Singular name. And the same may be said of yet another theory of Identity, that, "An individual is identical with the totality of its predicates," or (another way of putting the same theory), "An individual is a conflux of generalities".

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.

Logic does not deny the existence of indeterminate margins: it merely lays down that for purposes of clear communication and coherent reasoning the line must be drawn somewhere between _b_, and not-_b_.

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".

Now Logic does not take account of this implication, and nothing has contributed more to bring upon it the reproach of quibbling. In Logic, to deny a quality is simply to declare a repugnance between it and the subject; negation is mere sublation, taking away, and implies nothing more. Not-_b_ is entirely indefinite: it may cover anything except _b_.

Is Logic then really useless, or even misleading, inasmuch as it ignores the definite implication of negatives in ordinary thought and speech? In ignoring this implication, does Logic oppose this implication as erroneous? Does Logic shelter the quibbler who trades upon it? By no means: to jump to this conclusion were a misunderstanding. The fact only is that nothing beyond the logical Law of Contradiction needs to be assumed for any of the processes of Formal Logic. Aristotle required to assume nothing more for his syllogistic formulae, and Logic has not yet included in its scope any process that requires any further assumption. "If not-_b_ represent everything except _b_, everything outside _b_, then that A is _b_, and that A is not-_b_, cannot both be true, and one or other of them must be true."

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.[10]

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.

[Footnote 1: The first statement of the Law of Identity in the form _Ens est ens_ is ascribed by Hamilton (_Lectures_, iii.

91) to Antonius Andreas, a fourteenth century commentator on the _Metaphysics_. But Andreas is merely expounding what Aristotle sets forth in iii. 4, 1006 _a, b_. _Ens est ens_ does not mean in Andreas what A is A means in Hamilton.]

[Footnote 2: Greek: to gar auto hama huparchein te kai me huparchein adynaton to auto kai kata to auto, . . . ahute de pason esti bebaiotate ton archon. iii. 3, 1005_b_, 19-23.]

[Footnote 3: Hamilton credits Andreas with maintaining, "against Aristotle," that "the principle of Identity, and not the principle of Contradiction, is the one absolutely first".

Which comes first, is a scholastic question on which ingenuity may be exercised. But in fact Aristotle put the principle of Identity first in the above plain sense, and Andreas only expounded more formally what Aristotle had said.]

[Footnote 4: [Greek: Metaxu antiphaseos endechetai einai outhen, all' ananke e phanai e apophanai en kath henos hotioun.]

_Metaph._ iii. 7, 1011_b_, 23-4.]

[Footnote 5: Prof. Caird's _Hegel_, p. 138.]

[Footnote 6: See Venn, _Empirical Logic_, 1-8.]

[Footnote 7: _E.g._, Hamilton, lect. v.; Veitch's _Institutes of Logic_, chaps, xii., xiii.]

[Footnote 8: The confusion probably arises in this way. First, these "laws" are formulated as laws of thought that Logic assumes. Second, a notion arises that these laws are the only postulates of Logic: that all logical doctrines can be "evolved" from them. Third, when it is felt that more than the identical reference of words or the identity of a thing with itself must be assumed in Logic, the Law of Identity is extended to cover this further assumption.]

[Footnote 9: _E.g._, Bosanquet's _Logic_, ii. 207.]

[Footnote 10: Bradley, _Principles of Logic_; Bosanquet, _Logic or The Morphology of Knowledge_; Caird, _Hegel_ (in Blackwood's Philosophical Classics); Wallace, _The Logic of Hegel_.]

BOOK I.

THE LOGIC OF CONSISTENCY. SYLLOGISM AND DEFINITION.

PART I.

THE ELEMENTS OF PROPOSITIONS.

CHAPTER I.

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.

A general name is a name applicable to a number of different things on the ground of some likeness among them, as _man_, _ratepayer_, _man of courage_, _man who fought at Waterloo_.

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.

A class may be constituted on one attribute or on several.

_Ratepayer_, _woman ratepayer_, _unmarried woman ratepayer_; _soldier_, _British soldier_, _British soldier on foreign service_.

But every individual to which the general name can be applied must possess the common attribute or attributes.

These common attributes are also called the NOTION of the class, inasmuch as it is these that the mind notes or should note when the general name is applied. CONCEPT is a synonym perhaps in more common use than notion; the rationale of this term (derived from _con_ and _capere_, to take or grasp together) being that it is by means of the points of resemblance that the individuals are grasped or held together by the mind. These common points are the one in the many, the same amidst the different, the identity signified by the common name.

The name of an attribute as thought of by itself without reference to any individual or class possessing it, is called an ABSTRACT name. By contradistinction, the name of an individual or a class is CONCRETE.

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.[1] 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.

A class may be constituted on one property or on many. There are several points common to all houses, enclosing walls, a roof, a means of exit and entrance. For the full concept of the natural kinds, _men_, _dogs_, _mice_, etc., we should have to go to the natural historian.