Contradiction; the kinds of conditional

Assents · al-tanāquḍ wa-aqsām al-sharṭiyya · pp. 75–76

التَّناقُضُ وَأَقْسامُ الشَّرْطِيَّةِ

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. نقیض قضیه قضیهٔ دیگر باشد که با وی در سلب و ایجاب و در کلیت و جزئیت و جهت مخالف باشد بحیثیتی که صدق هر یک لذاته مستلزم کذب دیگری باشد و کذب هر یک لذاته مستلزم صدق دیگری باشد، پس نقیض موجبهٔ کلیه سالبهٔ جزئیه باشد و نقیض سالبهٔ کلیه موجبهٔ جزئیه. فصل. قضیهٔ شرطیهٔ متصله لزومیه باشد اگر اتصال یا سلب اتصال ضروری باشد چنانکه گذشت، و اتفاقیه باشد اگر اتصال یا سلب وی ضروری نباشد چنانکه اگر انسان ناطق است حمار ناهق است. و قضیهٔ منفصله یا حقیقیه باشد اگر انفصال در وجود و عدم باشد، چون این عدد یا زوج باشد یا فرد، یعنی هر دو مجتمع نشوند و مرتفع نشوند؛ و یا مانعة الجمع باشد اگر انفصال در وجود باشد، چنانکه گوئی این چیز یا شجر باشد یا حجر، یعنی هر دو مجتمع نشوند لیکن ارتفاع شاید؛ و یا مانعة الخلو باشد اگر انفصال در عدم باشد، چنانکه گوئی زید یا در دریاست یا غرق نشود، یعنی هر دو مرتفع نشوند لیکن اجتماع شاید. فصل. تناقض و عکس در شرطیات بر قیاس حملیات معلوم شود.

Section. The contradictory of a proposition is another proposition that differs from it in negation and affirmation, in universality and particularity, and in modality, in such a way that the truth of each in itself entails the falsehood of the other, and the falsehood of each in itself entails the truth of the other. So the contradictory of the universal affirmative is the particular negative, and the contradictory of the universal negative is the particular affirmative. Section. A connective conditional is necessary (luzūmiyya) if the connection, or its denial, is necessary, as has been seen; and coincidental (ittifāqiyya) if the connection, or its denial, is not necessary, as in “if man is rational, the donkey brays”. A disjunctive is real if the separation holds in being and not being, like “this number is either even or odd”, that is, the two are neither found together nor both absent; or it excludes being together if the separation holds in being only, as when you say “this thing is either a tree or a stone”, that is, the two are not found together, but both may be absent; or it excludes being absent if the separation holds in not being only, as when you say “Zayd is either in the sea or does not drown”, that is, the two are not both absent, but they may be found together. Section. Contradiction and conversion among conditionals are known by analogy with categoricals.

Arabic translation

فَصْلٌ. نَقِيضُ الْقَضِيَّةِ قَضِيَّةٌ أُخْرَى تُخَالِفُهَا فِي السَّلْبِ وَالْإِيجَابِ وَفِي الْكُلِّيَّةِ وَالْجُزْئِيَّةِ وَفِي الْجِهَةِ، بِحَيْثُ يَسْتَلْزِمُ صِدْقُ كُلٍّ مِنْهُمَا لِذَاتِهِ كَذِبَ الْأُخْرَى، وَكَذِبُ كُلٍّ مِنْهُمَا لِذَاتِهِ صِدْقَ الْأُخْرَى. فَنَقِيضُ الْمُوجَبَةِ الْكُلِّيَّةِ السَّالِبَةُ الْجُزْئِيَّةُ، وَنَقِيضُ السَّالِبَةِ الْكُلِّيَّةِ الْمُوجَبَةُ الْجُزْئِيَّةُ. فَصْلٌ. الشَّرْطِيَّةُ الْمُتَّصِلَةُ لُزُومِيَّةٌ إِنْ كَانَ الِاتِّصَالُ أَوْ سَلْبُهُ ضَرُورِيًّا كَمَا مَرَّ، وَاتِّفَاقِيَّةٌ إِنْ لَمْ يَكُنْ الِاتِّصَالُ أَوْ سَلْبُهُ ضَرُورِيًّا، كَقَوْلِنَا: إِنْ كَانَ الْإِنْسَانُ نَاطِقًا فَالْحِمَارُ نَاهِقٌ. وَالْمُنْفَصِلَةُ إِمَّا حَقِيقِيَّةٌ إِنْ كَانَ الِانْفِصَالُ فِي الْوُجُودِ وَالْعَدَمِ، كَقَوْلِنَا: هٰذَا الْعَدَدُ إِمَّا زَوْجٌ أَوْ فَرْدٌ، أَيْ لَا يَجْتَمِعَانِ وَلَا يَرْتَفِعَانِ، وَإِمَّا مَانِعَةُ الْجَمْعِ إِنْ كَانَ الِانْفِصَالُ فِي الْوُجُودِ فَقَطْ، كَقَوْلِكَ: هٰذَا الشَّيْءُ إِمَّا شَجَرٌ أَوْ حَجَرٌ، أَيْ لَا يَجْتَمِعَانِ وَلٰكِنْ قَدْ يَرْتَفِعَانِ، وَإِمَّا مَانِعَةُ الْخُلُوِّ إِنْ كَانَ الِانْفِصَالُ فِي الْعَدَمِ فَقَطْ، كَقَوْلِكَ: زَيْدٌ إِمَّا أَنْ يَكُونَ فِي الْبَحْرِ وَإِمَّا أَلَّا يَغْرَقَ، أَيْ لَا يَرْتَفِعَانِ وَلٰكِنْ قَدْ يَجْتَمِعَانِ. فَصْلٌ. وَيُعْلَمُ التَّنَاقُضُ وَالْعَكْسُ فِي الشَّرْطِيَّاتِ عَلَى قِيَاسِ الْحَمْلِيَّاتِ.

Google Translate ↗pp. 32–33

The lesson

is the difference of two in and , in universality and particularity, and in modality, such that the truth of one entails the falsehood of the other by that difference itself and not for another reason. The contradictory of the is the , “every man is an animal” and “some man is not an animal”, and the reverse; the contradictory of the is the , “no man is a stone” and “some man is a stone”.

A is necessary (luzūmiyya) when the connection, affirmed or denied, is necessary: “if the sun is up, it is day”. It is coincidental (ittifāqiyya) when it is not: “if man is rational, the donkey brays” — the two are both true, but neither brings the other.

A is real (ḥaqīqiyya) when the separation holds in being and not being: “this number is either even or odd” — the two can neither be together nor both be absent. It excludes being together (māniʿat al-jamʿ) when the separation is in being only: “this thing is either a tree or a stone” — it cannot be both, but it can be something else, a man. It excludes being absent (māniʿat al-khuluww) when the separation is in absence only: “this thing is either not a stone or not a tree” — both parts cannot be false, for then it would be a stone and a tree at once, but both can be true, as with a horse. and of conditionals follow those of .

Terms

التَّناقُضُ al-tanāquḍ: contradiction
اللُّزُومِيَّةُ al-luzūmiyya: necessary connective
الاتِّفاقِيَّةُ al-ittifāqiyya: coincidental connective
الحَقِيقِيَّةُ al-ḥaqīqiyya: real disjunctive
مانِعَةُ الجَمْعِ māniʿat al-jamʿ: excludes being together
مانِعَةُ الخُلُوِّ māniʿat al-khuluww: excludes being absent

Examples

إِنْ كانَ الإِنْسانُ ناطِقًا فَالحِمارُ ناهِقٌ
a coincidental connective
هٰذا الشَّيْءُ إِمّا شَجَرٌ وَإِمّا حَجَرٌ
excludes being together
هٰذا الشَّيْءُ إِمّا لا حَجَرٌ وَإِمّا لا شَجَرٌ
excludes being absent

اپنا امتحان لیں

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

سوال 1
What is the contradictory of “no man is a stone”?
سوال 2
“If man is rational, the donkey brays” is…
سوال 3
“This thing is either a tree or a stone” — what can it be?

اگلا سبق: Proof and its three kinds; the definition of the syllogism

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