The exceptive syllogism

The syllogism · al-qiyās al-istithnāʾī · pp. 28–29

الْقِيَاسُ الِاسْتِثْنَائِيُّ

Draft · awaiting review

Arabic text after the print of Jakarta 1434/2013 · translation by The Mantiqi, draft

About this text

al-Sullam al-munawraq السُّلَّمُ الْمُنَوْرَقُ

ʿAbd al-Raḥmān al-Akhḍarī (d. 983/1575)

Text: Arabic, transcribed by The Mantiqi from this print: Mutūn al-manṭiq wa-l-ḥikma: Īsāghūjī wa-l-Sullam al-munawraq, Dār al-Kutub al-Islāmiyya, Jakarta 1434/2013, pp. 20–32 View the scan
Lessons follow: The lessons are The Mantiqi's own explanations, chapter by chapter of the text itself.
Translation: The Mantiqi's own; a draft.
Review: Draft, awaiting review by Ustadh Muhammad Yusuf.

The text

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Arabic original, Mutūn al-manṭiq wa-l-ḥikma: Īsāghūjī wa-l-Sullam al-munawraq, Jakarta 1434/2013

وَمِنْهُ مَا يُدْعَى بِالِاسْتِثْنَائِييُعْرَفُ بِالشَّرْطِيِّ بِلَا امْتِرَاءِ

وَهْوَ الَّذِي دَلَّ عَلَى النَّتِيجَةِأَوْ ضِدِّهَا بِالْفِعْلِ لَا بِالْقُوَّةِ

Another kind is called the exceptive, known as the conditional syllogism without doubt: it is the one that shows the conclusion or its contrary in actuality, not potentially.

Google Translate ↗p. 28

فَإِنْ يَكُ الشَّرْطِيُّ ذَا اتِّصَالِأَنْتَجَ وَضْعُ ذَاكَ وَضْعَ التَّالِي

وَرَفْعُ تَالٍ رَفْعَ أَوَّلٍ وَلَايَلْزَمُ فِي عَكْسِهِمَا لِمَا انْجَلَى

If the conditional is connective, affirming the antecedent produces the affirmation of the consequent, and denying the consequent the denial of the antecedent; it does not follow in the reverse of these, as has become clear.

Google Translate ↗p. 29

وَإِنْ يَكُنْ مُنْفَصِلًا فَوَضْعُ ذَايُنْتِجُ رَفْعَ ذَاكَ وَالْعَكْسُ كَذَا

وَذَاكَ فِي الْأَخَصِّ ثُمَّ إِنْ يَكُنْمَانِعَ جَمْعٍ فَبِوَضْعِ ذَا زُكِنْ

رَفْعٌ لِذَاكَ دُونَ عَكْسٍ وَإِذَامَانِعَ رَفْعٍ كَانَ فَهْوَ عَكْسُ ذَا

If it is disjunctive, affirming this produces denying that, and the reverse likewise — that is in the narrowest, the real one. Then, if it excludes being together, by affirming this the denial of that is known, without the reverse; and when it excludes absence, it is the reverse of this.

Google Translate ↗p. 29

The lesson

The or shows the or its contrary in actuality, in so many words. With a : affirming the gives the , “if it is a man it is an animal; but it is a man, so it is an animal”; denying the consequent denies the antecedent, “but it is not an animal, so it is not a man”. The reverse does not follow: affirming the consequent or denying the antecedent proves nothing.

With a real , affirming one part denies the other and denying one affirms the other. With one that excludes being together, affirming one denies the other, but not the reverse. With one that excludes being absent, it is the reverse: denying one affirms the other.

Terms

الِاسْتِثْنَائِيُّ al-istithnāʾī: exceptive: the conclusion is in it in actuality
وَضْعُ الْمُقَدَّمِ waḍʿ al-muqaddam: affirming the antecedent
رَفْعُ التَّالِي rafʿ al-tālī: denying the consequent
مَانِعُ الْجَمْعِ / مَانِعُ الرَّفْعِ māniʿ al-jamʿ / māniʿ al-rafʿ: excluding being together / being absent

Examples

إِنْ كَانَ هٰذَا إِنْسَانًا فَهُوَ حَيَوَانٌ لٰكِنَّهُ لَيْسَ بِحَيَوَانٍ فَلَيْسَ بِإِنْسَانٍ
denying the consequent denies the antecedent

Test yourself

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

Question 1
“If it is a man, it is an animal; but it is an animal.” What follows?
Question 2
With a disjunctive that excludes being together, which works?
Question 3
The exceptive syllogism shows the conclusion…

Next lesson: Compound syllogism, induction and analogy

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