Logic: deductive and inductive

Preface

The present work aims at embracing a full course of Logic, both Formal and Inductive.

In an introductory chapter, are set forth such doctrines of psychology as have a bearing on Logic, the nature of knowledge in general, and the classification of the sciences ; the intention being to avoid doctrinal digressions in the course of the work. Although preparatory to the understanding of what follows, this chapter may be passed over lightly on a first perusal of the work.

The part on Deduction contains the usual doctrines of the Syllogism, with the additions of Hamilton, and a full abstract of the novel and elaborate schemes of De Morgan and Boole.

The Inductive portion comprises the methods of inductive research, and all those collateral topics brought forward by Mr. Mill, as part of the problem of Induction ; various modifications being made in the manner of statement, the order of topics, and the proportion of the handling. The greatest innovation is the rendering of Cause by the new doctrine called the Conservation, Persistence, or Correlation of Force.

Mr. Mill's view of the relation of Deduction and Induction is fully adopted, as being the solution of the otherwise inextricable puzzle of the syllogism, and the means of giving unity and comprehensiveness to Logic.

Jv PREFACE.

rate division is appropriated to the Logic of the , with the view of still further exemplifying the ;il methods, and of throwing light upon various points in the sciences themselves. The review comprises all the Tetical or fundamental sciences — Mathematics, Physics, iiistry, Biology, and Psychology ; the sciences of Classiion, or Natural History; and two leading Practical —Politics and Medicine.

The department of Definition is, for the first time, ■;ht under a methodical scheme, and rendered of co-ordinate value with Deduction and Induction, as a branch g ical method. The modes of defining, as a generalizing gfgfc are given under two canons, a positive and a live; and attention is called to the chief obstacles — uncertainty in the denotation of words, and the gradual transition of qualities into their opppsites.

In discussing Fallacies, I have canvassed the grounds

for the usual practice of detaching the violations of logical

rules from the exposition of the rules themselves ; and

endeavoured to show that the only portions of the

subject proper to reserve for separate handling, are the

Fallacious tendencies of the Mind, and Fallacies of Con-

n. As these are subjects of great moment, and admit

: .de illustration, both are considered with some minute-

ne of the controversies in the subject are overlooked ; but it has been deemed advisable to separate them from the main body of the work. In an Appendix, are emad the various Classifications of the Sciences, the Pro- B of Logic, the Classification of Nameable Things, the ll Postulate, the meanings of Analysis and Synbl Theories of Induction, the Art of Discovery, and the maxims of Historical Evidence.

To adapt the work to an elementary course of Logic,

PREFACE. V

the parts to be omitted are the Additions to the Syllogism, the Logic of the Sciences, and the chapters in the Appendix. The junior student, or the candidate for a pass examination, without attempting to master or commit these reserved portions, might yet find their perusal of service in understanding the rest.

There is a general conviction that the utility of the purely Formal Logic is but small ; and that the rules of Induction should be exemplified even in the most limited course of logical discipline. I would suggest that an increased attention should be bestowed on Definition and Classification, with reference both to scientific study and to matters not ordinarily called scientific.

As I may be open to the charge of presumption in appearing as a rival to Mr. Mill, I will venture the remark, that an attempt to carry out still more thoroughly the enlarged scheme of logical method, seems the one thing hitherto wanting to the success of his great work.

Aberdeen, March, l&7d

Introduction

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BOOK L

NAMES, NOTIONS, AND PROPOSITIONS.

CM XT.

I. Names or Terms ...... 42

II. Classes, Notions, or Concepts . . . . 61

IIL Propositions . ... 73

BOOK IL

DEDUCTION.

I. The Syllogism . . . . . 1 33

II. Recent Additions to the Syllogism . . . .178

IIL Functions and Value of the Syllogism . ... 207

IT. Trains of Reasoning and Deductive Sciences . . .214

V. Demonstration — Axioms — Necessary Truth . . 219

BOOK IIL

INDUCTION.

I. Meaning and Scope of Induction . . . 231

IL The Ground of Induction — Uniformity of Nature — Laws of Nature ....... 238

IIL Induction of Coexistence . . . . 241

IV. Law of Causation . . . . . . 245

V. Elimination of Cause and Effect — Observation and Experiment 271 VL The Experimental Methods . . . . .279

VII. Examples of the Methods ..... 297

VIII. Frustration of the Methods . . . . .306

IX Chance, and its Elimination . . . .314

X. Induction aided by Deduction ..... 325

XL Secondary Laws — Empirical and Derivative . . 332

XIL Explanation of Nature ...... 346

XIIL Hypotheses . . . . .358

XIV. Approximate Generalizations and Probable Evidence . . 365

XV. Analogv 370

2CVL Credibility and Incredibility . . . . .378

\ 111

CONTENTS.

BOOK IV.

DEFINITION.

pitr.

i mods of Definition II. (i. noiai Names III Classification

PAGB

384 401 414

BOOK V

LOGIC OF THE SCIENCES.

I. Logic of Mathematics ....

. 429

II. Logic of Physics .....

III. Lo^ie of Chemistry ....

. 472

IV. Lo^ic of Biology .....

V Logic of Psychology . . . . .

. 505

\ I. S .mes of Classification ....

522 ,

VII. Logic of Practice

. 545

VIII. Logic of Politics .....

IX. Logic of Medicine . . ..

. 575

BOOK VI

FALLACIES.

I. Mill's Classification of Fallacies

II. The Position of Fallacies

III. Fallacious Tendencies of the Mind

IV. Fallacies of Confusion .

V. Logical Fallacies

Appendix

A. — Classifications of the Sciences

B. — The Province of Logic

< — Enumeration of Things .

I' —The Universal Postulate

E — Aristotelian and Scholastic Fallacies

F— Analysis and Synthesis

irowth of the Logic of Induction D. — Art of Discovery I. — Historical Evidence K— Explanation of Some Logical Terms