The middle term and the first figure

Proof · al-ḥadd al-awsaṭ wa-l-shakl al-awwal · pp. 80–81

الحَدُّ الأَوْسَطُ وَالشَّكْلُ الأَوَّلُ

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

فصل. قیاس اقترانی یا حملی باشد یعنی مرکب از حملیات صرف یا غیر حملی باشد، و قسم اول اظهر است پس بر وی اقتصار کنیم، و آن بر چهار نوع است، زیرا که نسبت میان موضوع و محمول چون مجهول باشد احتیاج افتد بمتوسطی که او را با هر دو طرف نسبت باشد تا بواسطهٔ وی نسبت میان موضوع مطلوب و محمول آن معلوم شود، و آن را حد اوسط خوانند، چنانکه موضوع مطلوب را اصغر خوانند و محمول وی را اکبر. و حد اوسط اگر محمول شود اصغر را و موضوع شود اکبر را آن را شکل اول خوانند، و اگر عکس این باشد آن را شکل رابع خوانند، و اگر محمول شود هر دو را آن را شکل ثانی خوانند، و اگر موضوع باشد هر دو را آن را شکل ثالث خوانند. فصل. شکل اول را شرط انتاج آنست که صغری وی یعنی قضیه که مشتمل بر اصغر است موجبه باشد تا افراد اصغر در اوسط مندرج شود، و کبری وی یعنی قضیه که مشتمل بر اکبر است کلیه باشد تا حکم از اوسط متعدی باصغر شود بیقین. پس صغری شکل اول همیشه موجبه باشد و کبری او کلیه، و ضروب منتجه در وی چهار است: اول موجبتین کلیتین و نتیجه موجبهٔ کلیه باشد؛ دوم موجبهٔ جزئیه صغری با موجبهٔ کلیه کبری باشد؛ سوم موجبهٔ کلیه صغری با سالبهٔ کلیه کبری، نتیجه سالبهٔ کلیه باشد؛ چهارم موجبهٔ جزئیه صغری با سالبهٔ کلیه کبری، نتیجه سالبهٔ جزئیه باشد. پس شکل اول منتج محصورات اربعه است.

Section. A conjunctive syllogism is either categorical, that is, made of categoricals alone, or not categorical; the first kind is the clearer, so we confine ourselves to it. It is of four kinds, because when the relation between subject and predicate is unknown, there is need of a middle that has a relation to both sides, so that through it the relation between the subject of what is sought and its predicate becomes known. This is called the middle term, just as the subject of what is sought is called the minor term and its predicate the major term. If the middle term is the predicate of the minor and the subject of the major, it is called the first figure; if the reverse, the fourth figure; if it is the predicate of both, the second figure; and if it is the subject of both, the third figure. Section. The condition for the first figure to produce a conclusion is that its minor premise, the proposition that contains the minor term, be affirmative, so that the individuals of the minor fall under the middle; and that its major premise, the proposition that contains the major term, be universal, so that the judgement passes from the middle to the minor with certainty. So the minor premise of the first figure is always affirmative and its major universal, and its productive moods are four: first, two universal affirmatives, concluding a universal affirmative; second, a particular affirmative minor with a universal affirmative major, concluding a particular affirmative; third, a universal affirmative minor with a universal negative major, concluding a universal negative; fourth, a particular affirmative minor with a universal negative major, concluding a particular negative. So the first figure produces all four quantified propositions.

Arabic translation

فَصْلٌ. الْقِيَاسُ الِاقْتِرَانِيُّ إِمَّا حَمْلِيٌّ، أَيْ مُرَكَّبٌ مِنَ الْحَمْلِيَّاتِ الصِّرْفَةِ، وَإِمَّا غَيْرُ حَمْلِيٍّ، وَالْقِسْمُ الْأَوَّلُ أَظْهَرُ فَنَقْتَصِرُ عَلَيْهِ. وَهُوَ أَرْبَعَةُ أَنْوَاعٍ؛ لِأَنَّ النِّسْبَةَ بَيْنَ الْمَوْضُوعِ وَالْمَحْمُولِ إِذَا كَانَتْ مَجْهُولَةً احْتِيجَ إِلَى مُتَوَسِّطٍ لَهُ نِسْبَةٌ إِلَى كِلَا الطَّرَفَيْنِ، لِيُعْلَمَ بِوَاسِطَتِهِ النِّسْبَةُ بَيْنَ مَوْضُوعِ الْمَطْلُوبِ وَمَحْمُولِهِ، وَيُسَمَّى الْحَدَّ الْأَوْسَطَ، كَمَا يُسَمَّى مَوْضُوعُ الْمَطْلُوبِ أَصْغَرَ وَمَحْمُولُهُ أَكْبَرَ. فَالْحَدُّ الْأَوْسَطُ إِنْ كَانَ مَحْمُولًا لِلْأَصْغَرِ مَوْضُوعًا لِلْأَكْبَرِ سُمِّيَ الشَّكْلَ الْأَوَّلَ، وَإِنْ كَانَ بِالْعَكْسِ سُمِّيَ الشَّكْلَ الرَّابِعَ، وَإِنْ كَانَ مَحْمُولًا لَهُمَا سُمِّيَ الشَّكْلَ الثَّانِيَ، وَإِنْ كَانَ مَوْضُوعًا لَهُمَا سُمِّيَ الشَّكْلَ الثَّالِثَ. فَصْلٌ. شَرْطُ إِنْتَاجِ الشَّكْلِ الْأَوَّلِ أَنْ تَكُونَ صُغْرَاهُ، أَعْنِي الْقَضِيَّةَ الْمُشْتَمِلَةَ عَلَى الْأَصْغَرِ، مُوجَبَةً، لِتَنْدَرِجَ أَفْرَادُ الْأَصْغَرِ تَحْتَ الْأَوْسَطِ، وَأَنْ تَكُونَ كُبْرَاهُ، أَعْنِي الْقَضِيَّةَ الْمُشْتَمِلَةَ عَلَى الْأَكْبَرِ، كُلِّيَّةً، لِيَتَعَدَّى الْحُكْمُ مِنَ الْأَوْسَطِ إِلَى الْأَصْغَرِ يَقِينًا. فَصُغْرَى الشَّكْلِ الْأَوَّلِ مُوجَبَةٌ أَبَدًا وَكُبْرَاهُ كُلِّيَّةٌ، وَضُرُوبُهُ الْمُنْتِجَةُ أَرْبَعَةٌ: الْأَوَّلُ مِنْ مُوجَبَتَيْنِ كُلِّيَّتَيْنِ، وَالنَّتِيجَةُ مُوجَبَةٌ كُلِّيَّةٌ، وَالثَّانِي مِنْ مُوجَبَةٍ جُزْئِيَّةٍ صُغْرَى وَمُوجَبَةٍ كُلِّيَّةٍ كُبْرَى، وَالنَّتِيجَةُ مُوجَبَةٌ جُزْئِيَّةٌ، وَالثَّالِثُ مِنْ مُوجَبَةٍ كُلِّيَّةٍ صُغْرَى وَسَالِبَةٍ كُلِّيَّةٍ كُبْرَى، وَالنَّتِيجَةُ سَالِبَةٌ كُلِّيَّةٌ، وَالرَّابِعُ مِنْ مُوجَبَةٍ جُزْئِيَّةٍ صُغْرَى وَسَالِبَةٍ كُلِّيَّةٍ كُبْرَى، وَالنَّتِيجَةُ سَالِبَةٌ جُزْئِيَّةٌ. فَالشَّكْلُ الْأَوَّلُ يُنْتِجُ الْمَحْصُورَاتِ الْأَرْبَعَ.

Google Translate ↗pp. 36–38

The lesson

The Kubrā keeps to syllogisms made of , the clearest kind. The reason a has is this: when the relation between the and the of what is sought is unknown, we need something between them, tied to each, through which we learn how they stand to one another. That is the ; the subject of what is sought is the , its predicate the . With the middle term predicate in the and subject in the major, the figure is the first; the reverse, the fourth; predicate in both, the second; subject in both, the third.

The first produces a on two conditions: the is , so that the individuals of the fall under the middle; and the is , so that the judgement passes from the to the minor with certainty. If the major were , the might hold only of some middle terms other than those the minor term falls under.

So its are four. Both : the is universal affirmative. , universal affirmative: particular affirmative. Minor universal affirmative, major : universal negative. Minor particular affirmative, major universal negative: . The first thus yields all four .

Terms

الحَدُّ الأَوْسَطُ al-ḥadd al-awsaṭ: middle term: ties the subject and predicate of what is sought
المَطْلُوبُ al-maṭlūb: what is sought: the conclusion
إِيجابُ الصُّغْرَى ījāb al-ṣughrā: the minor premise affirmative
كُلِّيَّةُ الكُبْرَى kulliyyat al-kubrā: the major premise universal
الضُّرُوبُ المُنْتِجَةُ al-ḍurūb al-muntija: productive moods

Examples

كُلُّ إِنْسانٍ حَيَوانٌ وَكُلُّ حَيَوانٍ جِسْمٌ فَكُلُّ إِنْسانٍ جِسْمٌ
first figure, first mood
بَعْضُ الحَيَوانِ إِنْسانٌ وَلا شَيْءَ مِنَ الإِنْسانِ بِحَجَرٍ فَبَعْضُ الحَيَوانِ لَيْسَ بِحَجَرٍ
first figure, fourth mood

اپنا امتحان لیں

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

سوال 1
What are the two conditions of the first figure?
سوال 2
Minor particular affirmative, major universal negative, in the first figure. The conclusion is…
سوال 3
Why must there be a middle term?

اگلا سبق: The second and third figures

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