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70 OPPOSITION OF PROPOSITIONS. includes the truth of the particular. But if we only know the truth of the particulars i.e., only know that " at least some S is or that P," P " " at least some S is not we do not know whether the respective universals are true or not. The six relations which we have explained are shown in a diagram called the square of opposition, which would be more accurately called the " square of relation." sub-contraries O Fig. 6. The results of this section may be summed up in the following table : EXERCISE III. Give the contradictory of each proposition contained in Exercise II., questions i to n inclusive, and 14. [Before the contradictory of a proposition can be given, it must of course be expressed in strict logical form.]
IMMEDIATE INFERENCE. 77 The essentials of the doctrine of opposition which we have explained were clearly stated by Aristotle. He says that formally (Kara Tr\v Xet*>, An. Prior., ii. 15) there are four kinds of opposition : (a) when one asserts of the whole what the other denies of the part (A and O) ; (d) when one denies of the whole what the other asserts of the part (E and I). In both these cases the propositions are said to be opposed as contradictories (avrifyaTiicws avruKelcrOai). Contradictory propositions admit of no third alternative, and there is no middle way between them. The two other forms of opposition mentioned by Aristotle are : (c) when one proposition the other denies of the whole (A and E) : affirms of the whole what in this case they are said to be contraries (eWzmo)? avriicelaOai), and both may be false. (d) When one affirms of a part what the other denies of a part (I and O). In this case Aristotle says quite truly that the " " is opposition merely verbal. Part III. Immediate Inference. 8. Immediate Inference is the name given to the process by which, from a single given proposition, we derive another whose truth is implied in the former. 1 Hence opposition is a variety of Immediate Infer ence ; E and O, and the truth of I : from for from the truth of A we may infer the falsity of falsity of A and I, and the truth of O : the truth of E, the from the truth 1 The process is rather a transformation of the proposition than an addition to our knowledge ; hut it is more than a merely verbal change (see ch. V. i).
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AN INTRODUCTORY TEXT-BOOK OF LOGIC
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OQf I AN INTRODUCTORY TEXT-BOOK OF
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VI PREFACE. A text-book constructed
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PREFACE. logical mistakes. Some of
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X CONTENTS. 10. Three fundamental L
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Xll CONTENTS. CHAPTER VII. CONDITIO
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CORRECTIONS AND NOTES. PAGE LINE 21
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2 THE GENERAL AIM OF LOGIC. truths
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4 THE GENERAL AIM OF LOGIC. agreeme
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; dently THE GENERAL AIM OF LOGIC.
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10 THE GENERAL AIM OF LOGIC. "
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12 THE GENERAL AIM OF LOGIC. ledge,
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14 THE NAME, THE TERM, THE CONCEPT,
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1 8 THE NAME, THE TERM, THE CONCEPT
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126 MEDIATE INFERENCE hence there i
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128 MEDIATE INFERENCE does not forb
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I3O MEDIATE INFERENCE II, IO, OI, a
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132 MEDIATE INFERENCE one premise a
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134 MEDIATE INFERENCE are universal
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136 MEDIATE INFERENCE (4) The mood
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138 MEDIATE INFERENCE and ask, not
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140 MEDIATE INFERENCE Crusoe s foot
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142 MEDIATE INFERENCE examples of t
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144 MEDIATE INFERENCE We must add t
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146 MEDIATE INFERENCE But in the fo
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148 MEDIATE INFERENCE Fig. iii. 1.
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150 MEDIATE INFERENCE The first s i
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152 MEDIATE INFERENCE The new syllo
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154 MEDIATE INFERENCE at ; a subjec
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156 MEDIATE INFERENCE expression, w
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158 MEDIATE INFERENCE principle, or
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160 MEDIATE INFERENCE a Buddhist, o
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162 MEDIATE INFERENCE (2) (a] Every
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164 MEDIATE INFERENCE. NOTE. When w
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1 66 THE PREDICABLES. entirely agre
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I7O Porphyry explains the THE PREDI
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I?2 DEFINITION. anything, and carri
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1/4 become a " DEFINITION. &qu
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176 DEFINITION. An obviously circul
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ISO DEFINITION. matics, our definit
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l82 DEFINITION. that of "Induc
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1 84 DEFINITION. A scientific syste
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188 DEFINITION. goes back to Plato.
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IQO THE CATEGORIES OR PREDICAMENTS.
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192 THE CATEGORIES OR PREDICAMENTS.
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196 CHAPTER VII. CONDITIONAL ARGUME
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198 CONDITIONAL ARGUMENTS AND 2. Co
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222 CONDITIONAL ARGUMENTS AND NOTE
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224 CHAPTER VIII. THE GENERAL NATUR
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226 THE GENERAL NATURE OF INDUCTION
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264 CHAPTER IX. THE THEORY OF INDUC
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306 THE THEORY OF INDUCTION examine
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308 THE THEORY OE INDUCTION bodies
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310 THE THEORY OF INDUCTION made wi
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312 (c) " THE THEORY OF INDUCT
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314 FALLACIES. (irepl <jo$i(
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3l6 Pyrrhus : FALLACIES. " Aio
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322 FALLACIES. not an argument at a
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324 FALLACIES. conclusion are separ
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326 FALLACIES. what is called a Log
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328 FALLACIES. (c) Mai-observation
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330 THE PROBLEMS WHICH WE HAVE RAIS
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350 THE PROBLEMS wnicii WE HAVE RAI
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NOTE. THE following mechanical devi
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358 Bosanquet, on Connotation of Pr
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360 222. (See also Immediate In fer
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3 62 of Disjunctive Syllogism, 205-
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PERIODS OF EUROPEAN LITERATURE: A C
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List of Books Published by ALMOND.
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32 Books Published by William Black
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