The Online Library of Liberty

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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

CHAP. XX.

Middle terms are not infinite

That the intervening terms of a predication cannot be infinite if predications terminate both in an upward and a downward direction is obvious. [I mean by ‘upward’ that which is more in the direction of universal, by ‘downward’ that which is nearer to the particular]. For if, when A is predicated of F, the intervening terms (here designated as B) could be infinite, it is clear that if one proceeded from A in the direction of the particular one could continue to predicate one term of another to infinity, [the terms intervening between A and F are here regarded as infinite]; and similarly, if one proceeded from F in the direction of the more general, one would traverse an infinite number of terms before arriving at A. If, however, there can be no such infinite progress or regress, the terms intervening between A and F cannot be infinite.

It is of no avail to maintain that some of the intervening terms, say A, B, C, follow one another so closely as to admit of no further intervening term, while others of the series are not so closely connected. For whichever of the B’s I care to select must have a certain relation to A or to F, and the intervening terms must be finite or infinite. To enquire from what starting point one begins the process to infinity, and whether this process is mediate or immediate is not to the purpose, for everything which follows any given point must be looked on as limitless.