CONTENTS

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[Preface][v]
[CHAPTER I]
INTRODUCTORY
[§1.]Definition of Logic[1]
[§2.]General character of proof[2]
[§3.]Division of the subject[5]
[§4.]Uses of Logic[6]
[§5.]Relation of Logic to other sciences[8]
to Mathematics (p. [8]); to concrete Sciences (p. [10]);to Metaphysics (p. [10]); to regulative sciences (p. [11])
[§6.]Schools of Logicians[11]
Relation to Psychology (p. [13])
[CHAPTER II]
GENERAL ANALYSIS OF PROPOSITIONS
[§1.]Propositions and Sentences[16]
[§2.]Subject, Predicate and Copula[17]
[§3.]Compound Propositions[17]
[§4.]Import of Propositions[19]
[§5.]Form and Matter[22]
[§6.]Formal and Material Logic[23]
[§7.]Symbols used in Logic[24]
[CHAPTER III]
OF TERMS AND THEIR DENOTATION
[§1.]Some Account of Language necessary[27]
[§2.]Logic, Grammar and Rhetoric[28]
[§3.]Words are Categorematic or Syncategorematic[29]
[§4.]Terms Concrete or Abstract[30]
[§5.]Concrete Terms, Singular, General or Collective[33]
[CHAPTER IV]
THE CONNOTATION OF TERMS
[§1.]Connotation of General Names[37]
[§2.]Question of Proper Names[38]
other Singular Names (p. [40])
[§3.]Question of Abstract Terms[40]
[§4.]Univocal and Equivocal Terms[41]
Connotation determined by the suppositio (p. [43])
[§5.]Absolute and Relative Terms[43]
[§6.]Relation of Denotation to Connotation[46]
[§7.]Contradictory Terms[47]
[§8.]Positive and Negative Terms[50]
Infinites; Privitives; Contraries (pp. [50]-[51])
[CHAPTER V]
CLASSIFICATION OF PROPOSITIONS
[§1.]As to Quantity[53]
Quantity of the Predicate (p. [56])
[§2.]As to Quality[57]
Infinite Propositions (p. [57])
[§3.]A. I. E. O.[58]
[§4.]As to Relation[59]
Change of Relation (p. [60]); Interpretation of 'either, or' (p. [63]);Function of the hypothetical form (p. [64])
[§5.]As to Modality[66]
[§6.]Verbal and Real Propositions[67]
[CHAPTER VI]
CONDITIONS OF IMMEDIATE INFERENCE
[§1.]Meaning of Inference[69]
[§2.]Immediate and Mediate Inference[70]
[§3.]The Laws of Thought[72]
[§4.]Identity[73]
[§5.]Contradiction and Excluded Middle[74]
[§6.]The Scope of Formal Inference[76]
[CHAPTER VII]
IMMEDIATE INFERENCES
[§1.]Plan of the Chapter[79]
[§2.]Subalternation[79]
[§3.]Connotative Subalternation[80]
[§4.]Conversion[82]
Reciprocality (p. [84])
[§5.]Obversion[85]
[§6.]Contrary Opposition[87]
[§7.]Contradictory Opposition[87]
[§8.]Sub-contrary Opposition[88]
[§9.]The Square of Opposition[89]
[§10.]Secondary modes of Immediate Inference[90]
[§11.]Immediate Inferences from Conditionals[93]
[CHAPTER VIII]
ORDER OF TERMS, EULER'S DIAGRAMS, LOGICAL EQUATIONS,EXISTENTIAL IMPORT OF PROPOSITIONS
[§1.]Order of Terms in a proposition[95]
[§2.]Euler's Diagrams[97]
[§3.]Propositions considered as Equations[101]
[§4.]Existential Import of Propositions[104]
[CHAPTER IX]
FORMAL CONDITIONS OF MEDIATE INFERENCE
[§1.]Nature of Mediate Inference and Syllogism[107]
[§2.]General Canons of the Syllogism[108]
Definitions of Categorical Syllogism; Middle Term;Minor Term; Major Term; Minor and Major Premise (p. [109]);Illicit Process (p. [110]); Distribution of the Middle (p. [110]); Negative Premises (p. [112]); Particular Premises (p. [113])
[§3.]Dictum de omni et nullo[115]
[§4.]Syllogism in relation to the Laws of Thought[116]
[§5.]Other Kinds of Mediate Inference[118]
[CHAPTER X]
CATEGORICAL SYLLOGISMS
[§1.]Illustrations of the Syllogism[121]
[§2.]Of Figures[122]
[§3.]Of Moods[123]
[§4.]How valid Moods are determined[124]
[§5.]Special Canons of the Four Figures[126]
[§6.]Ostensive Reduction and the Mnemonic Verses[127]
[§7.]Another version of the Mnemonic Verses[132]
[§8.]Indirect Reduction[132]
[§9.]Uses of the several Figures[134]
[§10.]Scientific Value of Reduction[135]
[§11.]Euler's Diagrams for the Syllogism[136]
[CHAPTER XI]
ABBREVIATED AND COMPOUND ARGUMENTS
[§1.]Popular Arguments Informal[138]
[§2.]The Enthymeme[139]
[§3.]Monosyllogism, Polysyllogism, Prosyllogism, Episyllogism[141]
[§4.]The Epicheirema[142]
[§5.]The Sorites[142]
[§6.]The Antinomy[145]
[CHAPTER XII]
CONDITIONAL SYLLOGISMS
[§1.]The Hypothetical Syllogism[147]
[§2.]The Disjunctive Syllogism[152]
[§3.]The Dilemma[154]
[CHAPTER XIII]
TRANSITION TO INDUCTION
[§1.]Formal Consistency and Material Truth[159]
[§2.]Real General Propositions assert more than has beendirectly observed[160]
[§3.]Hence, formally, a Syllogism's Premises seem to beg theConclusion[162]
[§4.]Materially, a Syllogism turns upon the resemblance of theMinor to the Middle Term and thus extends theMajor Premise to new cases[163]
[§5.]Restatement of the Dictum for material reasoning[165]
[§6.]Uses of the Syllogism[167]
[§7.]Analysis of the Uniformity of Nature, considered as theformal ground of all reasoning[169]
[§8.]Grounds of our belief in Uniformity[173]
[CHAPTER XIV]
CAUSATION
[§1.]The most important aspect of Uniformity in relation toInduction is Causation[174]
[§2.]Definition of "Cause" explained: five marks of Causation[175]
[§3.]How strictly the conception of Cause can be applieddepends upon the subject under investigation[183]
[§4.]Scientific conception of Effect. Plurality of Causes[185]
[§5.]Some condition, but not the whole cause, may long precedethe Effect; and some co-effect, but not the whole effect, may long survive the Cause[187]
[§6.]Mechanical Causes and the homogeneous Intermixture of Effects;Chemical Causes and the heteropathic Intermixture of Effects[188]
[§7.]Tendency, Resultant, Counteraction, Elimination, Resolution,Analysis, Reciprocity[189]
[CHAPTER XV]
INDUCTIVE METHOD
[§1.]Outline of Inductive investigation[192]
[§2.]Induction defined[196]
[§3.]"Perfect Induction"[196]
[§4.]Imperfect Induction methodical or immethodical[197]
[§5.]Observation and Experiment, the material ground ofInduction, compared[198]
[§6.]The principle of Causation is the formal ground of Induction[201]
[§7.]The Inductive Canons are derived from the principle ofCausation, the more readily to detect it in facts observed[202]
[CHAPTER XVI]
THE CANONS OF DIRECT INDUCTION
[§1.]The Canon of Agreement[206]
Negative Instances (p. [208]);Plurality of Causes (p. [208])
Agreement may show connection without direct Causation (p. [209])
[§2.]The Canon of Agreement in Presence and in Absence[212]
It tends to disprove a Plurality of Causes (p. [213])
[§3.]The Canon of Difference[216]
May be applied to observations (p. [221])
[§4.]The Canon of Variations[222]
How related to Agreement and Difference (p. [222]);The Graphic Method (p. [227]); Critical points (p. [230]); Progressive effects (p. [231]);Gradations (p. [231])
[§5.]The Canon of Residues[232]
[CHAPTER XVII]
COMBINATION OF INDUCTION WITH DEDUCTION
[§1.]Deductive character of Formal Induction[236]
[§2.]Further complication of Deduction with Induction[238]
[§3.]The Direct Deductive (or Physical) Method[240]
[§4.]Opportunities of Error in the Physical Method[243]
[§5.]The Inverse Deductive (or Historical) Method[246]
[§6.]Precautions in using the Historical Method[251]
[§7.]The Comparative Method[255]
[§8.]Historical Evidence[261]
[CHAPTER XVIII]
HYPOTHESES
[§1.]Hypothesis defined and distinguished from Theory[266]
[§2.]An Hypothesis must be verifiable[268]
[§3.]Proof of Hypotheses[270]
(1) Must an hypothetical agent be directly observable? (p. [270]);Vera causa (p. [271])
(2) An Hypothesis must be adequate to its pretensions (p. [272]);Exceptio probat regulam (p. [274])
(3) Every competing Hypothesis must be excluded (p. [275]);Crucial instance (p. [277])
(4) Hypotheses must agree with the laws of Nature (p. [279])
[§4.]Hypotheses necessary in scientific investigation[280]
[§5.]The Method of Abstractions[283]
Method of Limits (p. [284]);In what sense all knowledge is hypothetical (p. [286])
[CHAPTER XIX]
LAWS CLASSIFIED; EXPLANATION; CO-EXISTENCE; ANALOGY
[§1.]Axioms; Primary Laws; Secondary Laws, Derivative or Empirical;Facts[288]
[§2.]Secondary Laws either Invariable or Approximate Generalisations[292]
[§3.]Secondary Laws trustworthy only in 'Adjacent Cases'[293]
[§4.]Secondary Laws of Succession or of Co-existence[295]
Natural Kinds (p. [296]); Co-existence of concrete things to be deduced fromCausation (p. [297])
[§5.]Explanation consists in tracing resemblance, especiallyof Causation[299]
[§6.]Three modes of Explanation[302]
Analysis (p. [302]); Concatenation (p. [302]); Subsumption (p. [303])
[§7.]Limits of Explanation[305]
[§8.]Analogy[307]
[CHAPTER XX]
PROBABILITY
[§1.]Meaning of Chance and Probability[310]
[§2.]Probability as a fraction or proportion[312]
[§3.]Probability depends upon experience and statistics[313]
[§4.]It is a kind of Induction, and pre-supposes Causation[315]
[§5.]Of Averages and the Law of Error[318]
[§6.]Interpretation of probabilities[324]
Personal Equation (p. [325]); meaning of 'Expectation' (p. [325])
[§7.]Rules of the combination of Probabilities[325]
Detection of a hidden Cause (p. [326]); oral tradition (p. [327]);circumstantial and analogical evidence (p. [328])
[CHAPTER XXI]
DIVISION AND CLASSIFICATION
[§1.]Classification, scientific, special and popular[330]
[§2.]Uses of classification[332]
[§3.]Classification, Deductive and Inductive[334]
[§4.]Division, or Deductive Classification: its Rules[335]
[§5.]Rules for testing a Division[337]
[§6.]Inductive Classification[339]
[§7.]Difficulty of Natural Classification[341]
[§8.]Darwin's influence on the theory of Classification[342]
[§9.]Classification of Inorganic Bodies also dependent on Causation[346]
[CHAPTER XXII]
NOMENCLATURE, DEFINITION, PREDICABLES
[§1.]Precise thinking needs precise language[348]
[§2.]Nomenclature and Terminology[349]
[§3.]Definition[352]
[§4.]Rules for testing a Definition[352]
[§5.]Every Definition is relative to a Classification[353]
[§6.]Difficulties of Definition[356]
Proposals to substitute the Type (p. [356])
[§7.]The Limits of Definition[357]
[§8.]The five Predicables[358]
Porphyry's Tree (p. [361])
[§9.]Realism and Nominalism[364]
[§10.]The Predicaments[366]
[CHAPTER XXIII]
DEFINITION OF COMMON TERMS
[§1.]The rigour of scientific method must be qualified[369]
[§2.]Still, Language comprises the Nomenclature of an imperfectClassification, to which every Definition is relative;[370]
[§3.]and an imperfect Terminology[374]
[§4.]Maxims and precautions of Definition[375]
[§5.]Words of common language in scientific use[378]
[§6.]How Definitions affect the cogency of arguments[380]
[CHAPTER XXIV]
FALLACIES
[§1.]Fallacy defined and divided[385]
[§2.]Formal Fallacies of Deduction[385]
[§3.]Formal Fallacies of Induction[388]
[§4.]Material Fallacies classified[394]
[§5.]Fallacies of Observation[394]
[§6.]Begging the Question[396]
[§7.]Surreptitious Conclusion[398]
[§8.]Ambiguity[400]
[§9.]Fallacies, a natural rank growth of the Human mind, noteasy to classify, or exterminate[403]
[Questions][405]

LOGIC

CHAPTER I

INTRODUCTORY

§ 1. Logic is the science that explains what conditions must be fulfilled in order that a proposition may be proved, if it admits of 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 sciences so far as they 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 ice is cold): 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 belong 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 for ever; something must be taken for granted; and this is usually considered to be the case (1) with particular facts that can only be perceived and observed, and (2) 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, may be briefly defined as the science of proof with respect to qualitative laws and propositions, except those that are axiomatic.