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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-
tions
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
SECTION IV.
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
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
III. Continuation of the Subject.-General Remarks on the
Difference between the Evidence of Experience, and that of
Analogy
IV. Continuation of the Subject.-Evidence of Testimony 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
116
120
131
137
CHAPTER III.-Of the Aristotelian Logic
139
SECTION I. Of the Demonstrations of the Syllogistic Rules given by Aris-
totle and his Commentators
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
CHAPTER IV.-Of the Method of Inquiry pointed out in the Experimental or
Inductive Logic
163
174
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
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
191
200
I. Preliminary Observations on the Analysis and Synthesis of
the Greek Geometricians
II. Critical Remarks on the vague Use, among Modern Writers,
of the Terms Analysis and Synthesis
206
215
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
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
226
III. Supplemental Observations on the words INDUCTION and
ANALOGY, as used in Mathematics
240
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
245
SECTION VI. Of the Speculation concerning Final Causes
254
I. Opinion of Loid 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
Guide, even in Sciences which have no immediate relation
to Theology
II. Danger of confounding Final with Physical Causes in the