TABLE OF CONTENTS.

CHAPTER I.

The Physical Foundations of Inference, or the World as the Logician

regards it an exposition of the principal assumptions demanded

for the establishment of a Material or Objective System of Logic.

(pp. 1-44)

I (1) The distinct duality consisting of the phenomena on the one hand,

and the observer on the other. (1-4)

II.

III.

IV.

V.

VI.

(2) A long antecedent process of synthesis, or the grouping of the mere

elements of externality into definite objects. (4-8)

Objective uniformity of the phenomenal world. (9—11)

The world must be postulated as being essentially the same to all

observers: (11, 12)

(1) This involves no insuperable difficulty as regards the present time;

(13)

(2) As regards the remote past and future it involves the difficulty that the

conceptions, and therefore in a sense the objects, must correspond to

our own realization of them rather than to how they were, or will be,

realized by contemporary observers. (14-18)

Necessity that the logician shall leave the external world entirely
undisturbed, if his inferential processes are to be theoretically valid.
(18-21)

The fundamental duality postulated in Logic is occasionally disregarded

by over-objectifying the science, on the one hand; and by under-

estimating this external character of it on the other hand. (21—27)

We postulate the general distinction between truth and falsehood (28—

32); but are not necessarily bound to one rather than another of the

three following tests ;-

(1) The test of mere conceivability, sometimes adopted by the conceptualist

logicians: (32-34)

(2) The test of accordance with general experience, universally adopted in

Science and in common life: (35)

(3) The test of adherence to authority or precedent, as adopted in Heraldry,
Fiction, &c. (36, 37)

VII. As regards Language, we must assume;

(1) Identity of signification amongst those who inter-communicate; (37-

41)

(2) License to substitute equivalent terms. (41—44)

CHAPTER II.

The Foundations of Logic considered more in detail, and especially in

respect of what is demanded for Inference; (I.) Sequences of Pheno-

mena, or Laws of Causation. (pp. 45-72)

(47–51)

Causation as understood by the Aristotelians.

Exposition of successive stages in the modern treatment;-

I. The primitive or popular view of Causation. (52—55)

II.

III.

The popular view as rendered more precise by the logicians;

(1) In respect of completer enumeration of antecedents: (55, 56)

(2) In respect of closeness of sequence. (56-58)

Consequence of the above rendering: Plurality of Causes (61-64)

Further refinements of the sequence-account of Causation.

(1) Attempt at absolute inclusion of all the antecedents. (64, 65)

(2) Insistence on immediateness of sequence. (66)

This view admits of two interpretations:-

(1) That of the recurrence of cycles in the world's history. (67)

(2) That of affording an indication of initial tendencies only. (68)

Both of these interpretations render the Causal relation hypothetical,

and inapplicable to concrete events. (69–72)

CHAPTER III.

Continuation of the previous subject in respect of (II.) Co-existences; and

comparison of these with Sequences through the same three stages of

advancing precision and completeness. (pp. 73—92)

In the primitive or popular stage no distinction as regards validity of inference

is commonly recognized between the two kinds of Uniformity. (74, 75)

In the improved, or popular scientific stage some difference arises, owing to

the absence of the differentiating element of Time; but the formula admits

of re-statement in modified shape. (75-78)

In the final stage, of ultra-refinement, the formula again becomes impervious

to attack; but proves to be hypothetical and inapplicable. (78—81)

Consideration of the principal existent classes of Co-existence;—

(1) Properties of Natural Substances: (81, 82)

(2) Properties of Natural kinds: (82, 83)

(3) Groups of Conventional actions: (84, 85)

(4) Geometrical properties. (86)

Are there any Universal Laws of Co-existence? (87)

Do the two factors of the Co-existence mutually determine each other? (88) *

Further illustration of the significance of Co-existence. (89-92)

CHAPTER IV.

The Uniformity of Nature; or that wide conception of Regularity in the

external world, which is the objective counterpart of Inferribility.

(pp. 93-110)

I.

II.

Besides the subdivisions of the last two Chapters; (viz.

III.

IV.

V.

VI.

Uniformities of Sequence, divisible into;

(1) Laws of Nature, commonly so-called: (94)

(2) Empirical laws : (94)

Uniformities of Co-existence, similarly divisible into those which are

(1) strictly interpreted; (95)

(2) popularly regarded. (95))

We must also assume the Repetition of Similar Cases, in order to render

the above available for use. (96-100)

Uniformities of a Rhythmic character. (101, 102)

The Conservation of Energy. This extends the area of ordinary Causation
by embracing;

(1) Continuous changes as opposed to discrete events.

(103)

(2) By supplying connecting links between different sciences. (103)

(3) By leading to quantitative results. (104)

Statistical Uniformities of the kind characteristic of Probability. (105,

106)

Uniformities of mere Persistence. (106-110)

CHAPTER V.

The Subjective Foundations of Induction, or the principal postulates

demanded on the Mental side. (pp. 111-136)

I.

II.

For the purpose of Inductive Inference it is necessary that we should postu-

late:-

III.

Ordinary powers of Observation:-Difficulty in deciding where to draw

the line between Observation and Inference. (111–116)

The Faculty of Memory: which is necessary even for the formation of

Terms and of Judgments. (116-118)

The Belief in Uniformity; as distinct from, but correspondent to, the
objective Uniformity itself:

(1) This distinction is significant, since either element might conceivably

exist without the other. (119,120)

(2) It is variously described as involving the step from the past to the

future, from the known to the unknown, from the observed to the

unobserved. (121124)

Discussion of the so-called Ground of Induction; or the difficulty attending
the origin of the belief in Uniformity.

Detailed examination of a physical example, and discussion of the

problem as it might be raised (1) in Deduction (2) in Induction. (125

-128)

Answers of Whately, the Scotch school,-Mill,-Hume. (128-132)

The Difficulty psychological rather than logical. (132-136)

CHAPTER VI.

Language: a discussion of the principal questions involved in its reference,

functions, medium, and varieties. (pp. 137-159)

I.

II.

III.

IV.

The reference of Language: whether to our conceptions or to the

phenomena themselves? (137-141)

The functions of Language:

(1) The communication of ideas from one person to another. (142)

(2) The recording of them for ourselves and others. (142)

(3) The acquisition of ideas, by aiding the processes of synthesis and

analysis. (143—146)

The visual or image-language of the uneducated. (147, 148)

The medium by which Language is conveyed, as viewed in relation to;—

(1) The sense to which it appeals. (149-151)

(2) The organ or other appliance by which it is produced. (152, 153)

The main requisites which thence determine the choice of the medium.

(153-156)

The various distinct kinds of language in use: The spoken, and heard:-

The written, and read:-The fingered, and seen or felt. (156—159)

I.

II.

CHAPTER VII.

Terms; as interpreted and subdivided in Logic. (pp. 160-195)

Individual Terms; where the plurality of the constituent elements is
subordinate to their unity;-

(1) Proper, or logically unmeaning' terms. (161-163)

(2) Demonstrative terms. (163, 164)

(3) General terms conventionally restricted. (165)

(4) Combination of general terms. (166, 167)

(5) General terms with time or place limitations. (167)

Collective Terms; where the unity and plurality are nearly equally

conspicuous. (169-173)

III. General Terms; where the plurality of the constituent elements becomes
predominant. These are practically equivalent to Connotative terms.

IV.

V.

(1) Connotation and Denotation inversely variable: (174)

(2) Denotation real; Connotation notional: (175, 176)

(3) Connotation theoretically the leading element of the two: (176, 177)

(4) The range or extent of the Denotation: (178-180)

(5) Range of the Connotation: conflicting and extreme views on this

point: suggestion and implication of terms. (181-187)

Concrete and Abstract Terms: this distinction relative, and grammatical

more than logical. (187-190)

Positive and Negative Terms:

Contradiction, material and formal: contrariety: disparateness. (191

-196)

CHAPTER VIII.

Propositions: their general nature and composition. (pp. 196-217)

The Subject and Predicate arrangement: its convenience ;-

(1) Economy of this arrangement: (198, 199)

(2) Its aid in the progress of thought. (199, 200)

Gradations of suitability for the Subject and Predicate form of speech ;-

(1) Physical substances and their present attributes: (200)

(2) Complex, remote, and contingent attributes: (201-203)

(3) Mixed modes', and conventional groups of events: (204)

(4) Nature of existential propositions: (205-207)

(5) The subject and predicate in hypothetical propositions. (207)

General nature of the distinction between Subject and Predicate: which

is the prior element? which is the more important? Occasional absence

of this distinction. (208-212)

The Proposition regarded as the answer to a possible question. (213)

Affirmative and Negative propositions: (214)

1.

This distinction as developed in Symbolic Logic. (216)

2. The distinction real, though often difficult of application. (216, 217)

CHAPTER IX.

Propositions continued: the various ways in which they may be arranged

and subdivided for logical purposes. (pp. 218-238)

I.

II.

III.

IV.

:-

The traditional logical, or A. E. I. O scheme :-

(1) In this arrangement the subject is viewed as denoting a class, and the

predicate an attribute. (219-221)

(2) Detailed statement of the six resultant forms of assertion and denial:
(222-225)

Reduction of these six to the customary four: significance and use of

particular propositions. (226, 227)

The Class-inclusion and exclusion scheme, and its resultant five forms of

proposition. (228)

The Existential scheme; in which the logical distinction between subject

and predicate is obliterated. (229)

(1) Predication of existence on the part of an object: (232)

(2) Impersonal propositions. (233-235)

Certain other propositions employed in common life and in science:

(1) Vague quantitative or numerical assertions. (236)

(2) Definite assertions of a proportional kind. (237)