The Propositional Logic of Avicenna

The main purpose of this work is to provide an English translation of and commentary on a recently published Arabic text dealing with con­ ditional propositions and syllogisms. The text is that of A vicenna (Abu represents his views on the subject as they were held throughout his life.

Translation—Al-Qiy?s Book V.- One On Conditional Propositions and Their Types.- The kinds of syllogisms which lead to predicative conclusions and those leading to conditional conclusions.- A general definition of conditional propositions.- The two kinds of conditional propositions.- Complete and incomplete connection.- Complete and incomplete conflict.- Different views on conditional propositions.- The two kinds of following: (a) implication; (b) chance connection The restricted conditional.- The different senses of the particles used in connective propositions.- The antecedent and the consequent of the connective proposition are not statement-making sentences.- The restricted and the unrestricted connective proposition.- An implication is true when both its parts are false.- And when the antecedent is false and the consequent is true.- It is false when the antecedent is true and the consequent is false.- Two On Separative-Conditional Propositions.- The different ways of expressing conflict.- A separative proposition expresses (1) real conflict and the particle it takes is ‘It is exclusively’.- (2) The case where both its parts may be false.- (3) The case where both its parts may be true.- Other usages of ‘either’.- The antecedent and the consequent of the separative proposition are interchangeable, but not so in the connective.- An analysis of (1), (2) and (3) are compared with each other.- A comparison between (1) on the one hand and (2) and (3) on the other.- There is no separative proposition in which the meanings of the antecedent and the consequent are not related.- Other forms of conditional propositions.- Three Onthe Kinds of Combinations in Pure Conditional.- Propositions and in the Conditional Compounded of Predicative and Conditional Propositions The different forms the antecedent and the consequent of a conditional proposition take.- The separative can have more than two parts; but the connective has only two.- The subject and/or the predicate of the parts of a conditional can be identical.- The reduction of conditionals to predicative propositions.- ‘If’ and ‘Either’ etc. can be put after or before the subject of the antecedent; and in the first case the proposition would be indeterminable.- The view that the connective is an affirmative statement and the separative a negative one. His view on what affirmation and negation in conditional propositions are.- The truth conditions of the connective and the separative.- Four On Explaining the Meaning of the Universal, the Particular, the Indefinite and the Singular [Connective-] Conditional Proposition.- A certain view on how to determine the quantity of a connective proposition. His view on this issue.- When is a conditional considered universal or indefinite?.- When is the conditional regarded as singular?.- A criticism of the view that a universal connective is equal to a universal predicative.- The universal affirmative connective proposition.- Can a connective expressing chance connection be universally affirmed?.- Is ‘Always: when every donkey talks, then every man brays’ true in either one of the senses of following?.- An objection and an answer related to the above issue.- A proposition expressing chance connection is true when the consequent is true.- The antecedent of a connective proposition is not a statement-making sentence.- A return to the discussion of universal affirmative connective propositions.- Would they be affected if impossible conditions are added to their antecedents? Particular Connective Propositions: The first kind of particular connective propositions.- The second kind of particular connective propositions.- Is it possible for the particular connective to have universal parts?.- Five On the Universal Negative in [Connective-] Conditional Propositions.- The universal negative connective proposition.- The two kinds of negation in connective propositions.- (1) The universal negation of chance connection (2) The universal negation of implication.- Can a connective with a false antecedent and consequent be universally negated? The Four Forms of Separative Propositions: The universal affirmative separative proposition.- The universal negative separative proposition.- Can the separative have universal parts?.- The particular affirmative separative proposition.- Modal conditional propositions.- Book VI.- One On the Syllogisms Compounded of Connective-Conditional Propositions Arranged in Three Figures.- The three figures of the syllogisms compounded of connective premisses.- Thefirst figure.- Its moods.- An objection against the first figure and an answer to it.- The second figure.- Its moods.- The third figure.- Its moods.- Two On the Syllogisms Compounded of Connective and Separative Propositions.- When the minor is connective and the major a real separative; and the middle part is the consequent of the minor and the antecedent of the major.- I A/I.- AI/-It is productive when either one of the premisses is particular.- No production when the separative is negative.- No production from two negative or two particular premisses.- When the minor is connective and the major is unreal separative; and the middle part is the consequent of the first and the antecedent of the second.- Sterile moods.- The connective is particular.- The separative is particular.- No production when the separative is negative.- No production when the premisses are particular.- The same figure but the middle is negative.- When the premisses are affirmative and one of them is universal it will be sterile.- and when one of them is particular it will be sterile.- When the separative is negative it is sterile.- When the parts of the separative are negative.- When the separative is real and the middle part is the antecedent of both premisses.- When either one of the premisses is particular.- When the separative is particular.- When the separative is unreal and the middle part in the same position and it is affirmative.- The separative is particular.- The connective is particular.- No production when the separative is negative.- Now the middle part is negative.- One of the premisses is particular.- When the connective is negative and one of the premisses is particular.- No production when the separative is negative.- The separative with both parts negative.- When the connective is the major premiss and the middle part is the antecedent of both.- The separative is particular.- The connective is particular.- The connective is particular negative.- When the separative is unreal and the middle is in the same position.- The separative is particular.- No production when the connective is particular.- No production when the separative is negative.- The separative is particular.- No production when the connective is particular.- When the middle is negative and it is the consequent of the first and the antecedent of the second The separative is particular.- No production when the connective is particular No production when the separative is negative.- The separative is particular negative.- No production when the connective is particular negative.- When the separative is real and the middle is the consequent of both premisses.- The separative is particular.- The connective is particular.- No production when the separative is negative.- The separative is particular negative.- The connective is particular negative.- When the separative is unreal and the middle is the consequent of both premisses and it is affirmative.- The separative is particular.- The connective is particular.- Three On the Syllogisms Compounded of Separative Propositions.- Syllogisms from two separative premisses and the conditions for their produc- tion.- II/-.- There are no figures in this kind of syllogism.- The mood where both premisses are affirmative one of which has a negative part.- There is no production if the premiss with the negative part is negative.- There is no production if one of the premisses is particular; or when the negative premiss has affirmative parts.- No production if one premiss is a real separative.- When both premisses are unreal separative and the middle part is affirmative, the conclusion is not affirmative.- When the premisses are particular, the conclusion would be a connective proposition.- When the premisses are unreal and the middle is negative.- When the premisses are affirmative.- When one premiss is particular.- When one premiss is negative there will be no production.- No production when both premisses are particular or when one of them has two negative parts. If between them they have three negative parts they produce when the middle is negative.- Other combinations.- Four Onthe Syllogisms Compounded of Predicative and Conditional Propositions.- Syllogisms from a conditional and a predicative premiss;.- (i) the predicative is the major premiss and the middle term occurs in the consequent of the conditional and the predicative.- The first figure and the conditions for its production.- When the connective is universal affirmative.- When the connective is particular affirmative.- When the connective is universal negative.- When the connective is particular negative.- The second figure.- When the connective is universal affirmative.- When the connective is particular affirmative.- When the connective is universal negative.- The third figure.- . When the connective is universal affirmative.- When the connective is particular affirmative.- When the connective is universal negative.- When the connective is particular negative.- (ii) When the connective is the major premiss.- The first figure.- When the connective is universal affirmative.- When the connective is particular affirmative.- When it is universal negative.- When it is particular negative.- The second figure.- When the connective is univ?rsal affirmative.- When the connective is particular affirmative.- When it is universal negative.- When it is particular negative.- The third figure.- When the premisses are universal affirmative.- When the connective is universal negative.- When the connective is particular negative.- Five On the Three Figures of the Syllogisms Compounded of a Predicative and a Conditional Proposition Where the Predicative Shares [Either Its Subject or Its Predicate] with [the Subject or the Predicate] of the Antecedent (of the Conditional Proposition).- (iii) When the middle term occurs in the antecedent of the conditional and the predicative.- The first figure.- When the connective is universal affirmative.- When the connective is universal negative.- When the connective is particular affirmative.- When the connective is particular negative.- When the connective is universal affirmative.- When the connective is universal negative.- The second figure.- When the connective is universal affirmative.- When the connective is universal negative.- When the connective is universal affirmative.- When the connective is universal negative.- The connective is universal affirmative.- The connective is universal affirmative.- The connective is universal affirmative.- When the connective is universal affirmative.- The connective is universal negative.- When the connective is universal affirmative.- When the connective is universal negative.- The third figure.- When the connective is universal affirmative.- When the connective is universal negative.- The connective is particular affirmative.- When the connective is universal affirmative.- When the connective is universal negative.- (iv) When the predicative is the major premiss.- The first figure.- The connective is universal affirmative.- The second figure.- When the connective is universal affirmative.- The third figure.- When the connective is universal affirmative.- Six On the Three Figures of the Divided Syllogism.- The difference between the divided syllogism and induction.- A separative and several predicative premisses which share their predicates. The first figure.- The second figure.- The third figure.- A separative premiss and several predicatives not sharing their predicates.- The first figure.- The second figure.- The third figure.- One separative and one predicative premiss.- The first figure.- The second and the third figures.- Two separative premisses.- The first figure.- The second figure.- The connective is the minor and the separative is the major premiss.- The first figure.- The second figure.- Book VII.- One On Equipollence and Opposition Between Connective-Conditional Propositions.- Universal connective propositions.- Particular connective propositions.- Two On the Opposition Between Separative-Conditional Propositions and Separative- and Connective-Conditional Propositions and the State of Their Equipollence.- Inferences from separatives to connectives and vice versa.- Inferences involving separative propositions.- Back to the subject of immediate inference from separative to connective propositions and vice versa.- Three On the Conversion of the Connective Proposition.- Book VIII.- One On the Definition of the Exceptive Syllogism.- The difference between exceptive and conjunctive syllogisms.- When the connective expresses complete implication; (i) we assert the antecedent deducing the consequent.- When the connective is incomplete implication; (i) we assert the antecedent deducing the consequent.- The connective is complete implication; (ii) we assert the consequent deducing the antecedent.- The connection is complete implication; (ii) we deny the consequent deducing the denial of the antecedent.- The connective is incomplete implication. No production when the antecedent is denied.- Or when the consequent is asserted.- The connective is complete implication; (iii) we deny the antecedent deducing the denial of the consequent.- (iv) we deny the consequent deducing the denial of the antecedent.- Two On the Enumeration of the Exceptive Syllogisms [which have a Separative-Conditional Premiss].- (ii) or denying any part deducing the other.- When the real separative has more than two parts, then (i) if we assert one part we (a) deny everyone of the others or (b) deny the separative consisting of the others.- (ii) If we deny one of the parts, we produce a separative consisting of the others.- Both parts of the separative may be true. If one of the parts is denied the other must be asserted.- Both parts of the separative may be false.- When one of the parts is asserted, the other must be denied.- Book IX.- One On Explaining that Exceptive Syllogisms Cannot Be Completed Except by Conjunctive Syllogisms.- Commentary.- Book V.- Book VI.- Book VII.- Book VIII.- Book IX.