Document Type : Original Article
Highlights
Extended Abstract
In Modern Logic, the universal categorical propositions are translated to conditionals, and the particular categorical propositions to conjunctions. For example, “Every man is an animal” is equivalent to “Everything if it is a man, it is an animal”; likewise, “Some men are farmers” is equivalent to “Some things are both men and farmers.” Many opponents of modern logic think that this analysis is inconsistent with the spirit of Traditional Logic, and that logicians of past centuries did not believe in the identity or equivalence of categorical and conditional propositions. Incidentally, this claim is supported by the history of Arabic traditional logic, thus in Avicennian logic, categorical and conditional propositions, as well as categorical and conditional syllogisms, are discussed completely separately, and this is a very good confirmation that these two classes of propositions are not the same. However, the fact is that on various occasions, Muslim logicians emphasized the identity or equivalence of categorical and conditional propositions.
It is well known that Aristotle’s logic is the logic of categoricals and the logic of the Stoics is that of conditionals; and this distinction is due to the different metaphysics on which Aristotelian and Stoic logics are based. If these famous statements are correct, it can probably be said that these logicians considered categorical and conditional propositions to be of two very different types. Examining the truth or falsity of this claim requires very extensive studies in classical Greek works (both Peripatetic and Stoic), which are beyond the scope of this author’s research. Therefore, I have limited my study to the works of Muslim logicians and especially to the works of Avicenna. Since I have not found any explicit information about the relationship between categorical and conditional propositions in Al-Fārābī’s works, I will only discuss Avicenna’s views and ideas in this article, and since the views of logicians after Avicenna are very diverse, I examined their views in another study (Fallahi, 2025). (See also Fakhouri 1980, Fallahi 2009, 2011, 2016, Gelenbevi 1310AH and 1347AH, Nabavi 1998, Samarqandī 2020 and 2024, Yazdi 1948).
Comparing the views of traditional logicians with modern logic, in the author’s opinion, greatly contributes to the clarity of the subject; however, in order not to mix historical discussions with comparative discussions, I have included the proposed formulations of Avicenna’s propositions only in footnotes.
In this article, I have examined two very important logical works of Avicenna (1964, 1970 and 2017), Al-Shifā and Al-Mukhtaṣar Al-Awsaṭ fī al-Manṭiq. Other logical works of Avicenna, such as the section on the logic of Salvation and al-Ishārāt, were too condensed to give any important point related to the subject of the article.
The following are the results obtained in the article.
1. Avicenna explicitly denies the “identity” between categorical and conditional propositions, except in one case, which is a categorical whose subject is impossible.
2. Nevertheless, Avicenna emphasizes the “equivalence” between categorical and conditional propositions, especially when the antecedent and consequent of a conditional share the same subject such as: “Every human being is an animal” and “Whenever something is a human being, it is an animal”.
3. From this perspective, it can be said that Avicenna’s statement is very close to the statement of modern logicians, although it is not the same, because modern logicians consider these two propositions to be “identical”, but Avicenna only considers them to be “equivalent”.
4. Of course, from Avicenna’s point of view, the aforementioned “equivalence” is limited to conditionals and does not include disjunctives. He correctly distinguishes between the categorical with disjunctive predicates (such as “All numbers are either even or odd”) and the pure disjunctives (such as “Either all numbers are even or all numbers are odd”).
5. The distinction mentioned in the last item between conditionals and disjunctions is not correct because if the categorical is singular and the antecedent and consequent of the conditional are also singular, then equivalence will hold, and it does not matter whether the proposition is conditional or disjunctive (for example, consider the equivalence between “This number is either even or odd” and “Either this number is even or this number is odd”). If the categorical proposition and the antecedent and consequent of the conditional one are quantified, then equivalence will no longer hold, and here too, it does not matter whether the proposition is conditional or disjunctive (for example, consider the non-equivalence between “If all men are two meters tall then all men are equal-sized with each other” and “Each man if he is two meters tall he is equal-sized with each other man”).
6. Avicenna also holds that equivalence exists between categoricals and conditionals whose antecedent and consequent are existential:
Every human being is an animal ⊣⊢ Whenever a human being exists, an animal exists.
7. Here, however, there exist some counter-examples which prove that this equivalence is not true:
Whenever a perfect cause exists, the effect exists ⊣⊬ Every perfect cause is an effect.
Whenever white exists, whiteness exists ⊣⊬ Every white is whiteness
In both the examples, the categorical propositions entail the conditionals, but not vice versa.
8. Zia Movahed found it inconsistent that Avicenna had criticized the “identity” of categoricals and conditionals and at the same time had accepted the “equivalence” of categoricals and conditions in other cases. I show that by distinguishing between “identity” and “equivalence”, this inconsistency can be easily removed from Avicenna’s thinking.
References
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