§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