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To think consistently is to avoid all self-contradiction. If we
think as logical necessity requires, our thought is said to
be valid.

Consistent = not involving contradiction = not inconsistent.
Valid = involving logical necessity.

Inconsistent = involving self-contradiction.

Invalid = not involving logical necessity.

To think truly is to think under the control exercised by that aspect of Reality which is relevant to the purpose of our thinking.

Under Reality, as relevant to the truth-interest of a pre-philosophical discipline, we include the world of Common Sense -the world in relation to our various practical interestsand Nature as understood by Science.

In either case, this reality is conceived as having a nature sufficiently stable to control our tentative thought about it. When the reality we have in view is limited by some practical interest, the logical ideal is satisfied in proportion as our ideas adjust themselves to the control exercised by this conventionally limited reality. Ideas so adjusted may be said to be formally or conventionally true, true in relation to our restricted practical purpose.

When the reality is Nature as conceived by Science, the controlling of our ideas through reality is said to give us real or scientific truth.

Finally, when our sole interest is in the validity of our thinking, the question whether the reference of our thought to reality is formal or real ceases to be relevant; for we are here no longer concerned that our thought shall be true, but only that it shall be valid.

The treatment of right thinking which is thus exclusively regu-
lated by the Ideal of Validity is known as Formal Logic.
Whatever reference there is to truth or falsity in Formal
Logic is wholly hypothetical.

The Formal treatment of right thinking should be carefully dis-
tinguished from a formal reference to reality, a Formal
treatment being a treatment in accordance with the Formal
Laws of Thought, the laws of logical Validity.

By 'Formal' we mean dominated by the Ideal of Validity. By 'formal' we mean 'conventional.'

NOTE. There is a certain misconception with regard to our use of the term 'Formal,' which our very definition of a Formal treatment may have served to foster. We have stated that a logical treatment can be called Formal only in so far as we abstract from all reference to truth or reality; and if the definitions which, in the interest of a pre-philosophical treatment, we have given of these same terms are not borne carefully in mind, the reader may be left with a very poor opinion as to the status of Formal Logic. Formal Logic will seem to be concerned essentially with some abstract department of Non-Being.

If we turn, however, to the definitions of truth and reality, as given on pp. 1, 4, or in the résumé, p. 9, we shall readily see that no such disparagement of a Formal treatment is intended or implied. In abstracting from all reference to reality as we have defined it, we do not abstract from all reference to all reality. It is only when the pre-philosophical definition of reality which we have adopted is mistaken for the ultimate meaning of reality that a Formal treatment of Thought appears unreal, and, in its detailed application, tends to degenerate into mere mechanical drudgery, on the one hand, or, on the other, into irresponsible explorations within a purely artificial world.

The abstraction from all reference to material reality and truth still leaves us with the reference of thought to itself; and when this self-reference of thought, together with the problem of Validity which it involves, is studied under the redeeming conditions of philosophical insight, Formal Thinking gains a vital, a spiritually vital significance. Assuming a philosophical definition of Truthas we understand the term 'philosophical '-the interest in Validity is itself an interest in Truth.

II.

LOGIC IN ITS RELATION TO LANGUAGE.

(i.) Words, their function and right use (ch. i.).

(ii.) Definition and the Predicables (ch. ii.).

(iii.) The Testing of Definitions (ch. iii.).

(iv.) Definition and Division: Logical Division (ch. iv.).

(v.) Classification (ch. v.).

(vi.) Scientific Terminology and Nomenclature (ch. vi.).

(vii.) Connotation and Denotation (ch. vii.).

(viii.) Concrete and Abstract Terms (ch. viii.).

CHAPTER I.

II. (i.) WORDS, THEIR FUNCTION AND RIGHT USE.

The Function of Words.

PROPOSING as we do to start in the humblest and most methodical way in our investigation of the nature and conditions of Truth, we look first to the tool or instrument we shall be dependent on all through-namely, Language.

Logic, like every other science, depends on language, written or spoken, as its only suitable instrument. In Grammar, which considers words in themselves and in relation to each other, Language is the subject-matter treated of as well as the instrument ; but it is not so in Logic. Logic is concerned with language only as an instrument of thought, and its aim is so to handle the instrument as to make it a help and not a hindrance to correct thinking. Since thought can be handled only in verbal form, the regulative function of Logic, directed primarily upon thought itself, is inevitably pressed upon language as well. Language must reveal thought and not falsify it.

Rhetoric, too, is concerned with language and the right use of words. But whereas Logic aims at the right use of words with a view to correct thinking, Rhetoric aims at the right use of words with a view to persuasion. The purpose of Rhetoric is to prove practically effective, and its appeal is therefore made to the whole man, to his emotions and humours as well as to his reason. As a science, at any rate, Logic is concerned with theoretical soundness rather than with practical efficiency. As an art it may be said to aim at practical efficiency, but its appeal is still made exclusively to the reason.

Over this instrument, Speech, Logic proposes to exercise appropriate supervision. But supervision, to be logical, must be in accordance with the nature of what is supervised. Before we consider the right use of words, we must learn something of their natural function in relation to thought.

The main function of words is to fix meanings or ideas both in our own minds and in those of our fellows. If I wish to see an object clearly, I bring it into the focus of vision. This I do instinctively through the help of a number of delicate eye move

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