# Logic - deductive and inductive - Carveth Read- PDF ebook

## Logic - deductive and inductive

Excerpt from the introduction:

1. Logic is the science that explains what conditions must be fulfilled in order that a proposition may be proved if it admits proof. Not, indeed, every such proposition; for as to those that declare the equality or inequality of numbers or other magnitudes, to explain the conditions of their proof belongs to Mathematics: they are said to be quantitative.

But as to all other propositions, called qualitative, like most of those that we meet with in conversation, in literature, in politics, and even in the sciences that are not treated mathematically (say, Botany and Psychology); propositions that merely tell us That something happens (as that salt dissolves in water), or that something has a certain property (as that the east wind is baneful), or that something is related to a class of things (as that Englishmen are good sailors): as to these, it belongs to Logic to show how we may judge whether they are true, or false, or doubtful.

When propositions are expressed with the universality and definiteness that belongs to scientific statements, they are called laws; and laws, so far as they are not laws of quantity, are tested by the principles of Logic, if they at all admit of proof. But it is plain that the process of proving cannot go on forever; something must be taken for granted; and this is usually * considered to be the case with those highest laws that are called axioms or first principles, of which we can only say that we know of no exceptions to them, that we cannot help believing them, and that they are indispensable to science and to consistent thought Logic, then, maybe briefly defined as the science of proof with respect to qualitative laws and propositions, except those that are axiomatic.

2. Proof may be of different degrees or stages of completeness. Absolute proof would require that a proposition should be shown to agree with all experience and with the systematic explanation of experience, to be a necessary part of an all-embracing and self-consistent philosophy or theory of the universe; but as no one hitherto has been able to frame such a philosophy, we must at present put up with something less than absolute proof. Logic, assuming certain principles to be true of experience, or at least to be conditions of consistent discourse, distinguishes the kinds of propositions that can be shown to agree with these principles, and explains by what means the agreement can best be exhibited. These principles will be found in chaps, vi., ix., xiii., xiv.

To bring a proposition or an argument under them, or to show that it agrees with them, is logical proof. The extent to which proof is requisite, again, depends upon circumstances; whether our aim is a general truth for its own sake, or merely to compare a proposition with our own convictions, or to satisfy the doubts of a friend. If A and B are conversing, and A asserts that some white races have straight black hair, and B doubts this but is willing to grant that some races with straight black hair are white, A may perhaps prove his point to the satisfaction of B by showing that these two propositions are intrinsically the same, as only differing in the order of the words. This is called proof by Immediate Inference, or by the equivalence of meaning. Again, if B is ready to admit that the Basques and Finns are white races, and also that they have straight black hair, then when A puts these two propositions together thus The Basques and Finns have straight black hair;

The Basques and Finns are white races; Therefore, some white races have straight black hair the truth of the last proposition is not likely to be disputed any longer. And this is called proof by Mediate Inference: that is to say, a connection between some white races and straight black hair is supposed not to be directly perceivable, but to be discovered by finding that both are connected in a certain way with, Basques and Finns. If, however, B does not grant that the Basques or the Finns are a white race, or that they have straight black hair, and A tries to prove these propositions, his difficulties greatly increase and may become insuperable. He must collect ethnological evidence, and convince B of its sufficiency j and if his friend be of a sceptical turn of mind, or desire a reputation for ingenuity ^. rather than for good sense, the conclusion that some white races have straight black hair may be indefinitely postponed. In fact, to fellow out, this illustration would be altogether unsuitable to an introductory chapter \ we had better turn to a simpler case.

### Some contents of the book

CHAPTER I

INTRODUCTORY
i. Definition of Logic . . x
2. General character of proof 2
3. Division of the subject 4
J 4. Uses of Logic 5
5. Relation of Logic to other sciences ..... 7
to Mathematics (p. 7); to concrete Sciences (p. 9); to
Metaphysics (p. 9); to regulative sciences (p. 10)
6. Schools of Logicians .10
Relation to Psychology (p. n)

CHAPTER II
GENERAL ANALYSIS OF PROPOSITIONS
i. Propositions and Sentences 15
2. Subject, Predicate and Copula 16
3. Compound Propositions ....... 16
4. Import of Propositions . . . . . . . . 18
5. Form and Matter 21
6. Formal and Material Logic 22
7. Symbols used in Logic 23

CHAPTER III
OF TERMS AND THEIR DENOTATION
PAGE
i. Some Account of Language necessary 26
2. Logic, Grammar and Rhetoric 27
3. Words are Categoremetric or Syncategoremetric . . 28
4. Terms Concrete or Abstract 29
5. Concrete Terms, Singular, General or Collective, . 32

CHAPTER IV
THE CONNOTATION OF TERMS
i. Connotation of General Names 36
2. Question of Proper Names 37
other Singular Names (p. 39)
3. Question of Abstract Terms 39
4. Univocal and Equivocal Terms 40
Connotation determined by the suppositio (p. 42)
5. Absolute and Relative Terms ...... 42
6. Relation of Denotation to Connotation .... 45
8. Positive and Negative Terms 48
Infinite ; Primitives; Contraries (p. 49)

CHAPTER V
CLASSIFICATION OF PROPOSITIONS
i. As to Quantity . . , 51
Quantity of the Predicate (p. 54)
2. As to Quality 54
Infinite Propositions (p. 55)
3. A. I. E. O. . 56

4. As to Relation 57
Change of Relation (p. 58)
5. As to Modality. , .... . . . . 62
6. Verbal and Real Propositions 63

CHAPTER VI
CONDITIONS OF IMMEDIATE INFERENCE
i. Meaning of Inference 66
2. Immediate and Mediate Inference 67
3. The Laws of Thought 69
4. Identity 70
5. Contradiction and Excluded Middle . . . . , 71
6. The Scope of Formal Inference 73