Document Type : Research Paper

Author

• Asadollah Fallahi

Associate Profesor in Iranian Institute of Philosophy

Abstract

In his second period of logical research, which includes several books and treatises, Athir al-Din al-Abhari is the only Avicennan logician who vindicated as invalid one of the two most important Avicennan novelties: iqtirani conditional syllogism. His exposition and reasons for this invalidity in these books and treatises are various and rooted in numerous kinds of conditionals and their truth-conditions and their developments in the books and treatises. His most important reason to deny conditional syllogism is notice to the manifold assumptions used to prove the syllogisms. In this paper, we deal with the main reason, studying the mentioned differences and developments. Citing successor logicians’ points of views on Abhari’s claim and assessment of all of them is out of the purposes of this paper and in need to other researches.

Highlights

Athır Al-Din Al-Abhari on Condıtıonal Syllogısm

Asadollah Fallahi

Associate Profesor in Iranian Institute of Philosophy, E-mail: falahiy@yahoo.com

 

Abstract

In his second period of logical research, which includes several books and treatises, Athir al-Din al-Abhari is the only Avicennan logician who vindicated as invalid one of the two most important Avicennan novelties: iqtirani conditional syllogism. His exposition and reasons for this invalidity in these books and treatises are various and rooted in numerous kinds of conditionals and their truth-conditions and their developments in the books and treatises. His most important reason to deny conditional syllogism is notice to the manifold assumptions used to prove the syllogisms. In this paper, we deal with the main reason, studying the mentioned differences and developments. Citing successor logicians’ points of views on Abhari’s claim and assessment of all of them is out of the purposes of this paper and in need to other researches.

Keywords: Abhari, conditional syllogism, cogent conditional, assumption.

 

 

 

 

 

 

 

 

Introductıon                                   

Athir al-Din al-Abhari has denied one of the two most important logical novelties of Avicenna, i.e. conditional syllogism. Avicenna has proposed a paradox or doubt on this kind of syllogism by offering the following simple counterexample:

If two is odd then it is a number.

If two is a number it is even.

Therefore, if two is odd it is even.

There are some solutions proposed by Arabic logicians as to this paradox, two of which has been offered before Abhari:

1. Avicenna himself dissolved the paradox by saying that the minor is indeed false [1, 296-97].

2.  However, Afdal al-Din al-Khunaji presented the second solution, i.e. the falsity of the major [2, 319].

Contrary to both, Abhari came to accept the invalidity of conditional syllogism [3, 254-256]. He generalized the claim for all of the four figures of the Avicennan conditional syllogism, denying their validity.

Abharı's Vıew on Avıcenna's Falsıfyıng the Mınor of the Counterexample

In another place, Abhari rejects Avicenna's claim as to the falsity of the conditional 'if five is even then it will be a number,' which resembles the minor in Avicenna's counterexample. Avicenna had claimed that if five is even it may be not the case that all events are numbers. Abhari protested that:

1. either the concept of 'being a number' is in the concept of 'even', in which case, the mentioned categorical proposition 'all events are numbers' is true analytically in modern jargon and cannot be false in any case, so, if five is even it follows that it is a number by definition of 'even';

2. or the concept of 'being a number' is a necessary consequence of the concept 'even', in which case it must be true too that if five is even it will be a number. [4, 493].

Abharı's Reasons to Deny Valıdıty of Condıtıoal Syllogısm

Abhari's reasons for invalidity are different in his various logical books. But the overall point which clearly can be derived from his reasons is that in the Barbara mood, for example, the antecedent of the minor can be inconsistent with the major in its totality. So, if that antecedent is supposed true then, even though the consequent is true, the major will be false and so the two latter cannot provide us with the consequent of the major by Modus Ponens. This reason recalls the possible-world or situation semantics, in which, supposing the antecedent of the minor means transporting to an alternative world or situation in which the major would be false. In this world or situation, the antecedent of the major must be true but the major false. So there is no reason to prove its consequent in the world or situation. Thus, we can find a world or situation in which the antecedent of the conclusion is true and it's consequent false; hence the falsity of the conclusion.

However, Abhari accepted disjunctive conclusions from conditional syllogisms. For example, he announced the validity of the following mood:

p → q,

q → r, 

 ~ p  r. [5, 213-14].

This can be justified that in Abhari's view, contrary to conditional, disjunction is an extensional or truth-functional combination and does not need a possible world or situation semantics.

1. The futurt of ashari’s innovations

Abhari's views on the invalidity of conditional syllogism have not attracted the subsequent Muslim logicians, even though Shams al-Din al-Samarqandi partially accepted invalidity of some moods of the four figures of the Avicennan conditional syllogism [6, 293-95]. Samarqandi accepted as valid only the following moods: the two affirmative ones in the first figure, the two with affirmative minors in the second figure, and the two with affirmative majors in the third. He expressively announced all moods of the fourth figure as invalid [7].

Although Abhari and Samarqandi's views have not been popularized in the later development of Arabic logic, their importance can be seen by noticing that some later developments of mathematical logic as well deny conditional syllogism (especially the transitivity of the conditional, i.e. the mentioned Barbara mood (p → q, q → r,  p → r), doubted by Avicenna). See for example [8, 82].

References

-        Abhari, Athir al-Din, (1974) Tanzil al-Afkar fi Tahrir al-Afkar, edited by Abdollah Nurani, Maniq va Mabaheth Alfaz (Collected Texts and Papers on Logic and Language), eds. Mehdi Mohaghegh and Tushi Hiko Izutso, Tehran University Publication, Tehran.

-        Abhari, Athir al-Din, (2016) Muntaha al-Afkar, edited by Mahdi Azimi and Hashem Qurbani, Hekmat Publication, Tehran.

-        Abhari, Athir al-Din, (2017) Khulast al-Afkar, edited by Mahdi Azimi, Iranian Institute of Philosophy, Tehran.

-        Avicenna, (1964) Al-Shifa, Al-Qias, edited by Saeed Zaid, Dar al-Kutub, Cairo.

-        Fallahi, Asadollah, (2015) 'Manteq e rabt nazde shams al-din Samarqandi' (Samarqandi on relevance logic), Manteq Pazouhi, 5, 2, 71-103.

-        Khunaji, Afdal al-Din, (2010), Kashf al-Asrar an Ghawamid al-Afkar, edited by Khalid El-Rouayheb.

-        Priest, Graham, (2008) Introduction to non-classical logics, from if to is, second edition, Cambridge University Press, Cambridge.

-        Samarqandi, Shams al-Din, (2014) Kistas al-Afkar fi Tahqiq al-Asrar, edited by Necmettin Pehlivan, Istanbul, Turkiye Yazma Eserler Kurumu Baskandigi, Istanbul.

Keywords

• Abhari
• conditional syllogism
• cogent conditional
• assumption