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.

Inhalt

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 p…