The exceptive syllogism

Proof · al-qiyās al-istithnāʾī · pp. 84–85

القِياسُ الاسْتِثْنائِيُّ

مسودہ · نظرِ ثانی کا منتظر

Persian text after the print of Kanpur 1279/1862–63 · translation by The Mantiqi, draft

About this text

al-Kubrā الكُبْرَى

al-Sayyid al-Sharīf al-Jurjānī (d. 816/1413)

Text: Persian, transcribed by The Mantiqi from the lithograph, without its marginal glosses: Majmūʿa-yi manṭiq, Maṭbaʿ-i Alṭāfī, Kanpur 1279/1862–63, pp. 1–42 View the scan
Lessons follow: al-Manṭiq al-manhajī li-l-mubtadiʾīn: al-Ṣughrā wa-l-Awsaṭ wa-l-Kubrā, Arabic version and arrangement by Muḥammad Anwar al-Badakhshānī (Jāmiʿat al-ʿUlūm al-Islāmiyya, ʿAllāma Banūrī Town), Islam Insight, Karachi 1420/1999, pp. 42–86. The lessons are The Mantiqi's own explanations in the order of this edition; its text is under copyright and is not reproduced.
Translation: The Mantiqi's own, into English and into vocalised Arabic; a draft. The Arabic is translated from the Persian, not taken from a printed Arabic version.
Review: Draft, awaiting review by Ustadh Muhammad Yusuf.

The text

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Persian original, Majmūʿa-yi manṭiq, Kanpur 1279/1862–63

قیاس استثنائی بر دو قسم است: یکی اتصالی و دوم انفصالی. اتصالی آنست که مرکب باشد از متصلهٔ لزومیه با وضع مقدم، و آن را نتیجه وضع تالی باشد، چنانکه گوئی که اگر این جسم انسان باشد حیوان باشد لیکن انسان است پس حیوان باشد؛ یا مرکب از متصلهٔ لزومیه با رفع تالی، و آن را نتیجه رفع مقدم است، چنانکه گوئی در مثال مذکور لیکن حیوان نیست پس انسان نباشد. و اما انفصالی آنست که مرکب باشد از منفصلهٔ حقیقیه و وضع احد الجزئین، این را نتیجه رفع جزو دیگر باشد، و با رفع احد الجزئین آن را نتیجه وضع جزو دیگر باشد، پس او را چهار نتیجه باشد، چنانکه گوئی این عدد زوج است یا فرد لیکن زوج است پس فرد نیست، لیکن فرد است پس زوج نیست، لیکن زوج نیست پس فرد باشد، لیکن فرد نیست پس زوج باشد؛ یا مرکب باشد از منفصلهٔ مانعة الجمع با وضع احد الجزئین، و او را نتیجه رفع جزو دیگر باشد، پس او را دو نتیجه باشد، چنانکه گوئی این جسم یا شجر است یا حجر لیکن شجر است پس حجر نیست، لیکن حجر است پس شجر نیست؛ یا مرکب باشد از منفصلهٔ مانعة الخلو با رفع احد الجزئین، و او را نتیجه وضع جزو دیگر باشد، پس نتیجهٔ او دو است، چنانکه گوئی این جسم یا لا حجر است یا لا شجر لکن حجر است پس لا شجر باشد، لکن شجر است پس لا حجر باشد. تمام شد رسالهٔ کبری در علم منطق.

The exceptive syllogism is of two kinds, connective and disjunctive. The connective is made of a necessary connective with the affirmation of the antecedent, and its conclusion is the affirmation of the consequent, as when you say “if this body is a man, it is an animal; but it is a man, so it is an animal”; or of a necessary connective with the denial of the consequent, and its conclusion is the denial of the antecedent, as when you say in the same example “but it is not an animal, so it is not a man”. The disjunctive is made of a real disjunctive with the affirmation of one of its two parts, whose conclusion is the denial of the other part, or with the denial of one of its two parts, whose conclusion is the affirmation of the other part; so it has four conclusions, as when you say “this number is either even or odd; but it is even, so it is not odd; but it is odd, so it is not even; but it is not even, so it is odd; but it is not odd, so it is even”. Or it is made of a disjunctive that excludes being together with the affirmation of one of its parts, whose conclusion is the denial of the other; so it has two conclusions, as when you say “this body is either a tree or a stone; but it is a tree, so it is not a stone; but it is a stone, so it is not a tree”. Or it is made of a disjunctive that excludes being absent with the denial of one of its parts, whose conclusion is the affirmation of the other; so it too has two conclusions, as when you say “this body is either not a stone or not a tree; but it is a stone, so it is not a tree; but it is a tree, so it is not a stone”. Here ends the Kubrā on the science of logic.

Arabic translation

الْقِيَاسُ الِاسْتِثْنَائِيُّ قِسْمَانِ: اتِّصَالِيٌّ وَانْفِصَالِيٌّ. فَالِاتِّصَالِيُّ مَا تَرَكَّبَ مِنْ مُتَّصِلَةٍ لُزُومِيَّةٍ مَعَ وَضْعِ الْمُقَدَّمِ، وَنَتِيجَتُهُ وَضْعُ التَّالِي، كَقَوْلِكَ: إِنْ كَانَ هٰذَا الْجِسْمُ إِنْسَانًا فَهُوَ حَيَوَانٌ، لٰكِنَّهُ إِنْسَانٌ فَهُوَ حَيَوَانٌ، أَوْ مِنْ مُتَّصِلَةٍ لُزُومِيَّةٍ مَعَ رَفْعِ التَّالِي، وَنَتِيجَتُهُ رَفْعُ الْمُقَدَّمِ، كَقَوْلِكَ فِي الْمِثَالِ الْمَذْكُورِ: لٰكِنَّهُ لَيْسَ بِحَيَوَانٍ فَلَيْسَ بِإِنْسَانٍ. وَالِانْفِصَالِيُّ مَا تَرَكَّبَ مِنْ مُنْفَصِلَةٍ حَقِيقِيَّةٍ مَعَ وَضْعِ أَحَدِ الْجُزْأَيْنِ، وَنَتِيجَتُهُ رَفْعُ الْجُزْءِ الْآخَرِ، أَوْ مَعَ رَفْعِ أَحَدِهِمَا، وَنَتِيجَتُهُ وَضْعُ الْآخَرِ، فَلَهُ أَرْبَعُ نَتَائِجَ، كَقَوْلِكَ: هٰذَا الْعَدَدُ إِمَّا زَوْجٌ أَوْ فَرْدٌ، لٰكِنَّهُ زَوْجٌ فَلَيْسَ بِفَرْدٍ، لٰكِنَّهُ فَرْدٌ فَلَيْسَ بِزَوْجٍ، لٰكِنَّهُ لَيْسَ بِزَوْجٍ فَهُوَ فَرْدٌ، لٰكِنَّهُ لَيْسَ بِفَرْدٍ فَهُوَ زَوْجٌ. أَوْ تَرَكَّبَ مِنْ مُنْفَصِلَةٍ مَانِعَةِ الْجَمْعِ مَعَ وَضْعِ أَحَدِ جُزْأَيْهَا، وَنَتِيجَتُهُ رَفْعُ الْآخَرِ، فَلَهُ نَتِيجَتَانِ، كَقَوْلِكَ: هٰذَا الْجِسْمُ إِمَّا شَجَرٌ أَوْ حَجَرٌ، لٰكِنَّهُ شَجَرٌ فَلَيْسَ بِحَجَرٍ، لٰكِنَّهُ حَجَرٌ فَلَيْسَ بِشَجَرٍ. أَوْ تَرَكَّبَ مِنْ مُنْفَصِلَةٍ مَانِعَةِ الْخُلُوِّ مَعَ رَفْعِ أَحَدِ جُزْأَيْهَا، وَنَتِيجَتُهُ وَضْعُ الْآخَرِ، فَلَهُ أَيْضًا نَتِيجَتَانِ، كَقَوْلِكَ: هٰذَا الْجِسْمُ إِمَّا لَا حَجَرٌ أَوْ لَا شَجَرٌ، لٰكِنَّهُ حَجَرٌ فَهُوَ لَا شَجَرٌ، لٰكِنَّهُ شَجَرٌ فَهُوَ لَا حَجَرٌ. تَمَّتِ الرِّسَالَةُ الْكُبْرَى فِي عِلْمِ الْمَنْطِقِ.

Google Translate ↗pp. 41–42

The lesson

The is or . The connective one is made of a necessary connective with the of the , which produces the affirmation of the : “if this body is a man, it is an animal; but it is a man; so it is an animal” — affirming the antecedent means stating it with “but” (lākin). Or with the denial of the consequent, which produces the denial of the antecedent: “but it is not an animal; so it is not a man”.

The one, made of a real disjunctive, works both ways: affirm one part and the other is denied, deny one and the other is affirmed, giving four : “this number is either even or odd; but it is even, so it is not odd; or it is odd, so not even; or it is not even, so it is odd; or it is not odd, so it is even”.

Made of a that excludes being together, it works only by affirming one part, which denies the other, giving two : “this body is either a tree or a stone; but it is a tree, so it is not a stone; or it is a stone, so it is not a tree”. Made of one that excludes being absent, it works only by denying one part, which affirms the other, again two conclusions: “this body is either not a stone or not a tree; but it is a stone, so it is not a tree; or it is a tree, so it is not a stone”. With this the Kubrā, and al-Jurjānī's two primers, come to an end.

Terms

الاسْتِثْنائِيُّ الاتِّصالِيُّ al-istithnāʾī al-ittiṣālī: connective exceptive syllogism
الاسْتِثْنائِيُّ الانْفِصالِيُّ al-istithnāʾī al-infiṣālī: disjunctive exceptive syllogism
وَضْعُ المُقَدَّمِ waḍʿ al-muqaddam: affirming the antecedent
رَفْعُ التّالِي rafʿ al-tālī: denying the consequent
لٰكِنْ lākin: “but”: the word of exception

Examples

إِنْ كانَ هٰذا الجِسْمُ إِنْسانًا فَهُوَ حَيَوانٌ لٰكِنَّهُ لَيْسَ بِحَيَوانٍ فَلا يَكُونُ إِنْسانًا
denying the consequent
هٰذا العَدَدُ إِمّا زَوْجٌ وَإِمّا فَرْدٌ لٰكِنَّهُ زَوْجٌ فَلَيْسَ بِفَرْدٍ
a real disjunctive: affirming one part

اپنا امتحان لیں

3 questions on this lesson. With 6 out of 10 or more (two stars) the next lesson opens.

سوال 1
“If this is a man, it is an animal; but it is not an animal; so…”
سوال 2
How many conclusions does a real disjunctive give in an exceptive syllogism?
سوال 3
With a disjunctive that excludes being together, which exception produces a conclusion?

This was the last lesson of al-Kubrā.

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