CHAP. XV.: On immediate negative propositions - Aristotle, Posterior Analytics 
Aristotle’s Posterior Analytics, trans. E.S. Bouchier, B.A. (Oxford: Blackwell, 1901).
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- Introductory Note.
- Book I.
- Chap. I.: Whether a Demonstrative Science Exists
- Chap. II.: What Knowing Is, What Demonstration Is, and of What It Consists
- Chap. III.: A Refutation of the Error Into Which Some Have Fallen Concerning Science and Demonstration
- Chap. IV.: The Meaning of ‘distributive,’ ‘essential,’ ‘universal’
- Chap. V.: From What Causes Mistakes Arise With Regard to the Discovery of the Universal. How They May Be Avoided
- Chap. VI.: Demonstration Is Founded On Necessary and Essential Principles
- Chap. VII.: The Premises and the Conclusion of a Demonstration Must Belong to the Same Genus
- Chap. VIII.: Demonstration Is Concerned Only With What Is Eternal
- Chap. IX.: Demonstration Is Founded Not On General, But On Special and Indemonstrable Principles; Nor Is It Easy to Know Whether One Really Possesses Knowledge Drawn From These Principles
- Chap. X.: The Definition and Division of Principles
- Chap. XI.: On Certain Principles Which Are Common to All Sciences
- Chap. XII.: On Questions, And, In Passing, On the Way In Which Sciences Are Extended
- Chap. XIII.: The Difference Between the Demonstration and Science of a Thing’s Nature and Those of Its Cause
- Chap. XIV.: The Figure Proper to Demonstrate Syllogism
- Chap. XV.: On Immediate Negative Propositions
- Chap. XVI.: On Ignorance Resulting From a Defective Arrangement of Terms In Mediate Propositions
- Chap. XVII.: On Ignorance Resulting From a Defective Arrangement of Terms In Immediate Propositions
- Chap. XVIII.: On Ignorance As Resulting From Defective Sense Perception
- Chap. XIX.: Whether the Principles of Demonstration Are Finite Or Infinite
- Chap. XX.: Middle Terms Are Not Infinite
- Chap. XXI.: In Negations Some Final and Ultimate Point Is Reached Where the Series Must Cease
- Chap. XXII.: In Affirmations Some Final and Ultimate Point Is Reached Where the Series Must Cease
- Chap. XXIII.: Certain Corollaries
- Chap. XXIV.: Whether Universal Or Particular Demonstration Is Superior
- Chap. XXV.: That Affirmative Is Superior to Negative Demonstration
- Chap. XXVI.: Direct Demonstration Is Superior to Reduction Per Impossible
- Chap. XXVII.: What Science Is More Certain and Prior, and What Less Certain and Inferior
- Chap. XXVIII.: What Constitutes One Or Many Sciences
- Chap. XXIX.: Concerning Many Demonstrations of the Same Thing
- Chap. XXX.: On Fortuitous Occurrences
- Chap. XXXI.: Sense Perception Cannot Give Demonstrative Science
- Chap. XXXII.: On the Difference of Principles Corresponding to the Difference of Syllogisms
- Chap. XXXIII.: The Distinction Between Science and Opinion
- Chap. XXXIV.: On Sagacity
- Book II.
- Chap. I.: On the Number and Arrangements of Questions
- Chap. II.: Every Question Is Concerned With the Discovery of a Middle Term
- Chap. III.: The Distinction Between Definition and Demonstration
- Chap. IV.: The Essence of a Thing Cannot Be Attained By Syllogism
- Chap. V.: Knowledge of the Essence Cannot Be Attained By Division
- Chap. VI.: The Essence Cannot Be Proved By the Definition of the Thing Itself Or By That of Its Opposite
- Chap. VII.: Whether the Essence Can In Any Way Be Proved
- Chap. VIII.: How the Essence Can Be Proved
- Chap. IX.: What Essences Can and What Cannot Be Proved
- Chap. X.: The Nature and Forms of Definition
- Chap. XI.: The Kinds of Causes Used In Demonstration
- Chap. XII.: On the Causes of Events Which Exist, Are In Process, Have Happened, Or Will Happen
- Chap. XIII.: On the Search For a Definition
- Chap. XIV.: On the Discovery of Questions For Demonstration
- Chap. XV.: How Far the Same Middle Term Is Employed For Demonstrating Different Questions
- Chap. XVI.: On Inferring the Cause From the Effect
- Chap. XVII.: Whether There Can Be Several Causes of the Same Thing
- Chap. XVIII.: Which Is the Prior Cause, That Which Is Nearer the Particular, Or the More Universal?
- Chap. XIX.: On the Attainment of Primary Principles
- Appendix. Prior Analytics. Book II.
- Chap. XXIII.: On Induction
- XXIV.: On Example
On immediate negative propositions
Yet demonstration is possible in the other figures, and if of a negative character is as valid in the second figure as in the first.
Just as the quality A may inhere in B without the intervention of a middle term, so it may not inhere without such intervention. By these expressions I mean that there is no middle term connecting A and B. In that case inherence and non-inherence will no longer depend on the presence of a third term. When then either A or B, or both, are true of the whole of a third term, it is impossible that A should not be true of B immediately. We may suppose all C to be A. Then if all C is not B (for it is possible that all of a subject should be A, but none of it B) the conclusion will follow that B is not A. For if all A is C, and no B is C, then no B is A.
The same proof will be adopted if both terms are distributively predicable of a third. That B need not be predicable of a subject of which A is distributively predicable, and conversely that A need not be predicable of a third term of which B is distributively predicable may be seen clearly from a consideration of those series of terms wherein no term of the one series can be interchanged with one in the other series. Thus if none of the terms in the series A, C, D are predicable of any in the series B, E, F; if further A is distributively predicable of G, a term belonging to the same series, then it is clear that no G will be B, for otherwise these distinct series would have interchangeable terms. So too if B is distributively predicable of some other subject. If, however, neither A nor B is distributively predicable of any third term, and if A is not predicable of B, A must be not predicable of B immediately. This is so because if any middle term were present, one of the two terms named would have to be distributively predicable of a third term, since the syllogism must be either in the first or the second figure. Now if it be in the first, B will be distributively predicable of a third term, for in this case the premise must be affirmative; if it be in the second A or B may be distributively predicable of a third term, for when either premise is of a negative character a conclusion may be attained, though this is impossible when both premises are negative.
It is plain therefore that one term may be proved to be deniable of another immediately, and we have now shewn when and how this may happen.