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 been directly observed 160 §3. Hence, formally, a Syllogism's Premises seem to beg the Conclusion 162 §4. Materially, a Syllogism turns upon the resemblance of the Minor to the Middle Term and thus extends the Major Premise to new cases 163 §5. Restatement of the Dictum for material reasoning 165 §6. Uses of the Syllogism