III. Continuation of the Subject.-Visionary Theories of some

Logicians, occasioned by their inattention to the Essential

Distinction between Mathematics and other Sciences

IV. Continuation of the Subject.-Peculiar and supereminent

Advantages possessed by Mathematicians, in consequence of

their definite Phraseology

SECTION III.-Of Mathematical Demonstration

I. Of the Circumstance on which Demonstrative Evidence es-

sentially depends

II. Continuation of the Subject.-How far it is true that all

Mathematical Evidence is resolvable into Identical Proposi-

SECTION IV.

III. Continuation of the Subject.-Evidence of the Mechanical

Philosophy, not to be confounded with that which is properly

called Demonstrative or Mathematical.-Opposite Errour of

some late Writers

II. Continuation of the Subject. Of that Permanence or Sta-

bility in the Order of Nature, which is presupposed in our

Reasonings concerning Contingent Truths

102

Of our Reasonings concerning Probable or Contingent Truths 116

I. Narrow Field of Demonstrative Evidence.-Of Demonstra-

tive Evidence, when combined with that of SENSE, as in

Practical Geometry; and with those of Sense and of INDUC-

TION, as in the Mechanical Philosophy.-Remarks on a Fun-

damental Law of Belief, involved in all our Reasonings con-

cerning Contingent Truths

IV. Continuation of the Subject.-Evidence of Testimon tacit-

ly recognised as a Ground of Belief, in our most certain con-

clusions concerning contingent Truths.-Difference between

the Logical and the Popular Meanings of the word Proba-

bility

CHAPTER III.-Of the Aristotelian Logic

SECTION I. Of the Demonstrations of the Syllogistic Rules given by Aris-
totle and his Commentators

80

84

86

86

94

III. Continuation of the Subject.-General Remarks on the

Difference between the Evidence of Experience, and that of

Analogy

131

116

120

137

139

139

SECTION II.-General Reflections on the Aim of the Aristotelian Logic, and

on the intellectual Habits which the study of it has a tendency to form.—

That the improvement of the power of reasoning ought to be regarded as

only a secondary Object in the culture of the Understanding

153

SECTION III.—In what respects the study of the Aristotleian Logic may be

useful to disputants.-A general acquaintance with it justly regarded as

an essential accomplishment to those who are liberally educated.-Doubts

suggested by some late writers, concerning Aristotle's claims to the inven-

tion of the Syllogistic Theory

SECTION I.-Mistakes of the Ancients concerning the proper object of Philo-

phy.-Ideas of Bacon on the same subject.-Inductive Reasoning.-Ana-

lysis and Synthesis.-Essential difference between Legitimate and hypo-

thetical Theories

CHAPTER IV.-Of the Method of Inquiry pointed out in the Experimental or

Inductive Logic .

174

SECTION II.-Continuation of the Subject.-The Induction of Aristotle

compared with that of Bacon

SECTION III. Of the Import of the Words Analysis and Synthesis, in the

Language of Modern Philosophy

II. Critical Remarks on the vague Use, among Modern Writers,

of the Terms Analysis and Synthesis

SECTION IV.-The Consideration of the Inductive Logic resumed

I. Additional Remarks on the distinction between Experience

and Analogy. Of the grounds afforded by the latter for

Scientific Inference and Conjecture

I. Preliminary Observations on the Analysis and Synthesis of

the Greek Geometricians

200

II. Use and Abuse of Hypotheses in Philosophical Inquiries.—

Difference between Gratuitous Hypotheses, and those which

are supported by presumptions suggested by Analogy.-In-

direct Evidence which a Hypothesis may derive from its

agreement with the Phenomena.-Cautions against extend-

ing some of these conclusions to the Philosophy of the Hu-

man Mind

III. Supplemental Observations on the words INDUCTION and

ANALOGY, as used in Mathematics.

SECTION V. Of certain misapplications of the words Experience and Induc-

tion in the phraseology of Modern Science.-Illustrations from Medicine

and from Political Economy

SECTION VI. Of the Speculation concerning Final Causes

163

I. Opinion of Lord Bacon on the subject.-Final Causes reject-

ed by Des Cartes, and by the majority of French Philoso-

phers. Recognised as legitimate Objects of research by

Newton. Tacitly acknowledged by all as a useful logical

174

191

200

206

215

215

226

240

245

254

Guide, even in Sciences which have no immediate relation

to Theology

II. Danger of confounding Final with Physical Causes in the

Philosophy of the Human Mind

254

265

271

277

310