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self that is seeking for truth-satisfaction; we should then be concerned with the profoundest questions with Freedom, Personality, Perfection, Immortality, God-questions which spring from the unrest and dissatisfaction of our deepest self. But if by Knowledge we understand, not Self-Knowledge, but Knowledge about Things, Knowledge of that which we apprehend through the senses, we may well be content with a less intimate specification of the meaning of Truth. We reach this more restricted conception of Truth through marking out the realm of fact which we take to be relevant to the limited requirements of a pre-philosophical treatment-in a word, by defining what we here mean by Reality.

Under 'Reality' we shall include two main aspects of Fact : 1. The world as common sense understands it (or some conventionally restricted fragment of it).

2. Nature, understood as the subject-matter of Science.

In bringing the worlds of Science and Common Sense thus closely together, we are making an assumption which it is important to notice. We are assuming that the attitude of common sense to the more or less fragmentary world within which its interest is restricted is, on its own humbler level, similar to the attitude of Science towards Nature. It may, however, be objected with good reason that in thus characterizing the common-sense attitude towards reality as pre-scientific, we are doing injustice to the ordinary consciousness, which, over and above its interest in a world external to it, has interests of a personal and social kind. The objection in itself is perfectly legitimate. The ordinary consciousness is religious as well as practical, and has inward as well as outward looking views as to the nature of truth. If sense-experience rests its beliefs on an 'I have seen,' the intuitionism of the moral and religious consciousness rests its beliefs on an 'I have felt.' In the one case truth is taken to be the truth about an object, the truth about a fact; in the other, it is taken as the truth for a subject, the truth for a person.

The implications of the more inward conception of the meaning of truth are of fundamental importance, and, at a more advanced stage of logical inquiry, their discussion becomes imperative. But for our present purpose-i.e., for the purposes of a pre-philosophical Logic-we propose to ignore this personal, inward interpretation of the truth-problem, and the deeper view of Reality which would correspond to it. At the same time we must remember that the definition we have provisionally laid down does not do full justice to the truth as it is presented to common sense. It imposes a restriction which reduces common sense to an infra-scientific standpoint. Only when common sense is thus restricted can Science be regarded as its completion and rectification. Only when we have eliminated as irrelevant the relation of truth to personal experience can we fairly describe Science as organized Common

Sense.

The deliberate exclusion of the personal element from the definition of truth may appear to some to be unjustifiable even when the definition is given solely from the scientific and infra-scientific points of view. The objection may be raised that, since the reference to reality which is implied in all truth-seeking, whether scientific or infra-scientific, can be characterized and defined only through relation to logical purpose, we cannot study Reality at any stage without introducing the personal element. It is quite true that the truth-definition which we have adopted explicitly includes a refer. ence to purpose. But this mere reference to purpose in no way commits us to a personalistic view of truth or of reality. On the contrary, it may so define the reference to reality as to render such a view irrelevant and impossible. How this reality-reference has been defined, in the interest of a pre-philosophical treatment, we have already seen. The limitation ensures that Truth shall be truth about fact, and not the truth of personal realization. To reach the philosophical conception of truth, we must study Fact in the light of a philosophical truth-interest, and adopt a correspondingly philosophical conception of reality.

It is true that reference to purpose implies reference to a deeper reality than that reality of nature the conception of which it serves to define, and that in this important sense the scientific point of view implies and presupposes the philosophic; but the implication remains latent, and the scientific and pre-scientific conceptions of truth and reality correspondingly impersonal and objective.

There are, we may say, three main stages in the life of Logic. In its first, formal, or common-sense stage, Logic presents itself as a propædeutic, or preliminary discipline, and the truth-ideal which it then presents to thought is truth as involving the relation of thought not to the reality of the Natural Order, but to a reality of a more or less restricted and conventional kind. The point of view, in a word, is essentially formal in the sense of conventional. There is no reference to a permanent order like that of Nature as conceived by Science, but only to such conventionally restricted aspects of it as answer to the requirements of some particular purpose.

In the second, real, or scientific stage, the casual, disconnected grasp on Reality which these conventional restrictions involve is definitely abandoned. Thought ceases to play with Reality in the interests of discussion, or of other requirements of practical intercourse. Armed with the idea of natural law, it now disposes itself to face the full force of that great realm of fact which has no limit but that of the applicability of the idea itself.

And yet this second stage is not final. It presupposes a relation of externality between fact and idea, and is broken through when this externality is done away with, and Truth shows itself as the intimate oneness of idea with fact. The complete setting forth of this unity is the function of a philosophical Logic. Briefly, it amounts to the idealizing of fact and the realizing of ideas within a conception of experienced fact larger than is possible to Science or appropriate to its restricted point of view. In this third stage, Thought, as Hegel would say, finds itself at home with itself, freed from all fettering abstraction, and at the very heart of the reality it is its mission to understand. What remains is then just the systematic articulation of the structure of this experienced fact, at once most real and most ideal-the Logic of spiritual experience.

This Personalistic Logic, as already stated, lies beyond the scope of the present treatise; the following course covers only the first two stages. The earlier stages, however, are essential to the proper grasp of the third and last. For the lessons of each earlier stage are taken up into the succeeding one in a form determined by the richer, concreter conditions of the latter. Thus, what is gained at the one level is not lost at the next, but transcended and redeemed. The 'Reason' of Philosophy must have assimilated the 'Understanding' of Science, the passion for distinctness and precision, which is characteristic of the scientific attitude, and its loyalty to relevant fact. Loyalty to ideals can bestead Philosophy but little if it does not, in its own appropriate way, include reverence for fact as an integral requisite of all true spiritual experience.

In the foregoing attempt to define the point of view adopted in the following treatise, the meaning of the word 'formal' deserves particular consideration. For it is more customary to identify the term 'Formal Logic' with a Logic of Validity than with a treatment in which is implied a merely 'formal' reference to reality. In particular, the word 'formal' is associated with the so-called Forms or Formal Laws of Thought as the principles upon which consistent thinking ultimately depends. Thus, in using this ambiguous term, it is essential that we should not confuse the two meanings. We propose, therefore, in the interests of clearness, to adopt the following device. When 'Formal' is being used in its fundamental sense of 'abstractly valid,' we shall employ a capital F; when it is being used in the sense of 'conventional,' we shall write the word with a small 'f.' Should the word open the sentence, and the capital letter be indispensable, we shall leave it to the context to decide in which of its two senses the word is being used.* The distinction between a formal and a real logical treatment is a distinction within a unity. Both methods equally imply a funda

* Perhaps the strongest reason for retaining two such closely similar words to designate meanings apparently so different is that the meanings are not so unrelated as they appear to be. A 'Formal' treatment of Logic might be considered as a 'limiting case' of a 'formal' treatment of the subject the case, namely, where the conventional restriction put upon the meaning of Reality is such as to reduce it to an essentially hypothetical status (vide p. 145).

mental respect for consistency, and they both involve a reference to reality, though the reference is occasional in the one case and systematic in the other. We do not, then, propose to keep the two methods separate. We propose, on the contrary, to discuss the real in close connexion with the formal aspect, and thereby to secure a unity of treatment which would be forfeited by the attempt to deal with the two aspects successively and in isolation from each other. When we are interested in emphasizing what is common to these two types of logical treatment, we propose to use the word 'material' to cover both. Thus, a material logical treatment may be either formal or real.

In contrast with a material treatment of Logic, we have what is customarily known as a purely Formal treatment. We shall find that at a certain stage in the development of our subject it becomes essential to abstract entirely from the reference of thought to reality as we have defined it (vide p. 4),* and to concentrate our whole attention on the logical conditions of valid thinking. When our logical interest is thus rigidly restricted, and reduced to an interest in validity, the treatment ceases to be material, and becomes Formal.

The chapters on the Laws of Thought and their application to the problems of Opposition, Eduction, and Syllogism are the chapters essential to a strictly Formal treatment. The ideal of (material) truth, which alone gives meaning to the distinction between 'formal' and 'real,' here gives place to the ideal of validity. The reference to reality implied in all reasoning whatsoever is tacitly ignored as 'accidental,' and the primary logical requisite, the requisite of validity, monopolizes the attention. Whatever reference to truth or falsity there is in Formal Logic is wholly hypothetical. If the statements 'All donkeys are daffodils' and 'All dragons are donkeys' are both accepted, accepted as though they were true (whether, as a matter of fact, they are true is here a completely irrelevant question), then Formal Logic insists that the statement 'All dragons are daffodils' must also be accepted, accepted as though it were true.

The Validity-Ideal, which is regulative of a Formal logical treatment, implies the twofold requisite of Self-consistency and of Interconsistency. A statement or an argument is self-consistent when it so hangs together that thought may pass through it, as it were, from beginning to end without falling into contradiction with itself by the way. The statement, 'Square tables are round' violates this fundamental requirement. So does the following argument :

'All men are rational animals.
Nebuchadnezzar was a man.

Therefore, Nebuchadnezzar was not a rational animal.'

* Vide note, p. 9.

We cannot maintain, without illegitimate variation in our use of words, that all men are rational, and that one is not so.

The Interconsistency of our statements is as important as their Self-Consistency. The diligent reader may discover on different pages of a connected treatise statements which no charity can construe as interconsistent. The statements may be separated by more than a hundred pages, but the requisite of Interconsistency will still compel a logical readjustment of the passages such as will make them maintainable together by one and the same thinker in one and the same discourse. The coherency of our thinking is essentially dependent upon a faithful observance of the requisite of interconsistency.

Logical Consistency should be carefully distinguished from Material Compatibility. Whether the assertion that my friend takes no regular exercise is compatible with the statement that he continues to enjoy robust health, and is in that sense 'consistent' with it, is a question that concerns material truth. A treatment which ignores all considerations of truth and falsity* cannot possibly say anything relevant upon the matter.

Logical Consistency should be distinguished from logical Validity. The meaning of the former is at once wider and more negative than that of the latter. Consistency implies mere freedom from selfcontradiction; Validity, a connexion so close that the severing of it would involve a contradiction. If we say 'Some people are reasonable,' it is quite consistent to add 'Some people are not reasonable'; but, as we shall see (vide p. 174), we could not validly infer that some people are not reasonable from the statement that some people are. An argument is said to be valid when the conclusion drawn from the premisses is such that we must accept it, once the premisses have been accepted. A conclusion drawn in this way from its premisses is said to be drawn from them with logical necessity, and is known as a valid conclusion. So, again, the proposition 'If all men are mortals, some mortals are men' is a valid proposition, since the acceptance of the 'if' clause necessitates our accepting its consequent. The statement 'If all men are mortals, all mortals are men,' is invalid if taken as asserting a logical connexion, though it is not inconsistent.

We should also note the distinctively negative character of Logical Consistency. Logical Consistency does not amount to systematic coherency. The coherency of a scientific system means much more than mere freedom from self-contradiction.

We conclude this Introductory Chapter with the following brief résumé of its main points :

Logic is the Science of Right Thinking.

To think rightly we must think both consistently and truly.

* Vide note, p. 9.

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