The exceptive syllogism

The syllogism · al-qiyās al-istithnāʾī · pp. 102–104

القِياسُ الاسْتِثْنائِيُّ

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Our own lessons with quotations from the print of Cairo 1324/1906 · translation by The Mantiqi, draft

About this text

Ḥāshiyat al-Bājūrī ʿalā al-Sullam حاشِيَةُ الباجُورِيِّ عَلَى السُّلَّمِ

Ibrāhīm al-Bājūrī (d. 1276/1860)

Text: Arabic: passages quoted in the lessons, transcribed by The Mantiqi from this print (the whole text is not reproduced): Ḥāshiyat al-Bājūrī ʿalā matn al-Sullam, with al-Anbābī's taqrīr in the margin, al-Maṭbaʿa al-Azhariyya al-Miṣriyya (2nd printing), Cairo 1324/1906, pp. 26–112 (passages) View the scan
Lessons follow: The lessons are The Mantiqi's own explanations of the Sullam, verse by verse, following Ibrāhīm al-Bājūrī; his words are quoted where they matter most.
Translation: The Mantiqi's own; a draft.
Review: Draft, awaiting review by Ustadh Muhammad Yusuf.

In Ibrāhīm al-Bājūrī's words

Need another language? “Google Translate” opens a passage in Google's machine translation — handy for a first idea, but not checked by us. Or copy the text into a translator of your choice.

Quoted from the Arabic of Ḥāshiyat al-Bājūrī ʿalā matn al-Sullam, with al-Anbābī's taqrīr in the margin, Cairo 1324/1906

وَاعْلَمْ أَنَّ الاسْتِثْنائِيَّ مُؤَلَّفٌ مِنْ مُقَدِّمَتَيْنِ: إِحْداهُما شَرْطِيَّةٌ وَتُسَمَّى كُبْرَى، وَالأُخْرَى اسْتِثْنائِيَّةٌ وَتُسَمَّى صُغْرَى، وَلِذٰلِكَ يُسَمَّى بِاسْمَيْنِ … فَالأَوَّلُ هُوَ الاسْتِثْنائِيُّ لِاشْتِمالِهِ عَلَى الاسْتِثْنائِيَّةِ، وَالثّانِي هُوَ الشَّرْطِيُّ لِاشْتِمالِهِ عَلَى الشَّرْطِيَّةِ.

Know that the exceptive syllogism is composed of two premises: one conditional, called the major, and the other exceptive, called the minor. That is why it has two names … The first, “exceptive”, because it contains the exceptive premise; the second, “conditional”, because it contains the conditional.

Google Translate ↗p. 102

فَإِذا قُلْتَ مَثَلًا: إِمّا أَنْ يَكُونَ هٰذا الجِسْمُ أَبْيَضَ وَإِمّا أَنْ يَكُونَ أَسْوَدَ، لٰكِنَّهُ أَبْيَضُ، أَنْتَجَ أَنَّهُ لَيْسَ بِأَسْوَدَ … وَقَوْلُهُ دُونَ عَكْسٍ، أَيْ لِأَنَّهُ لا يَمْتَنِعُ ارْتِفاعُهُما، فَلا يُنْتِجُ رَفْعُ أَحَدِهِما وَضْعَ الآخَرِ، فَلَوْ قُلْتَ فِي المِثالِ المَذْكُورِ: لٰكِنَّهُ لَيْسَ بِأَبْيَضَ، لَمْ يُنْتِجْ أَنَّهُ أَسْوَدُ.

If you say, for instance, “This body is either white or black; but it is white”, it follows that it is not black … His words “not the reverse”: because both may be absent, denying one does not yield affirming the other; if in that example you said “but it is not white”, it would not follow that it is black.

Google Translate ↗p. 104

The lesson

The Sullam treats the : a with a second premise that affirms or denies one of its sides, introduced by “but” (lākin). Al-Bājūrī explains its two names. It has two premises, a conditional one, called the , and an exceptive one, called the ; it is called exceptive after the second and conditional after the first.

With a (“if it is a human, it is an animal”), affirming the yields the and denying the consequent yields the denial of the antecedent. With a real disjunction (“the number is even or odd”), affirming either side yields the denial of the other and denying either yields the other.

With a disjunction that only bars joining, al-Bājūrī's example: “this body is either white or black; but it is white” yields “it is not black”. But not the reverse: since a body may be neither, “but it is not white” does not yield “it is black”.

Terms

الاسْتِثْنائِيُّ al-istithnāʾī: exceptive syllogism: a conditional with a premise affirming or denying one side
مانِعَةُ الجَمْعِ māniʿat al-jamʿ: a disjunction that bars joining: both cannot be true
مانِعَةُ الخُلُوِّ māniʿat al-khuluww: a disjunction that bars lacking both: both cannot be false

Examples

إِمّا أَنْ يَكُونَ هٰذا الجِسْمُ أَبْيَضَ وَإِمّا أَنْ يَكُونَ أَسْوَدَ
“this body is either white or black”: affirming one denies the other, not the reverse

Проверьте себя

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

Вопрос 1
Why does the exceptive syllogism have two names, according to al-Bājūrī?
Вопрос 2
“This body is either white or black; but it is not white.” What follows?
Вопрос 3
Which premise of the exceptive syllogism is called the major?

Следующий урок: Compound syllogism, induction and analogy

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