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Conjunctive syllogism

al-qiyās al-iqtirānī

القِيَاسُ الاقْتِرَانِيّ

A conjunctive syllogism (iqtirānī) is one in which neither the conclusion nor its contradictory is stated in the premises.

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In a picture

Every human is an animal (minor premise); every animal is mortal (major premise); so every human is mortal (conclusion).

Explanation

“Every human is an animal; every animal is a body; so every human is a body.” The conclusion is assembled from the premises, not quoted in them.

Also written as: iqtirani, categorical syllogism.

In the text

وَهُوَ إِمَّا اقْتِرَانِيٌّ كَقَوْلِنَا: كُلُّ جِسْمٍ مُؤَلَّفٌ، وَكُلُّ مُؤَلَّفٍ حَادِثٌ، فَكُلُّ جِسْمٍ حَادِثٌ؛ وَإِمَّا اسْتِثْنَائِيٌّ كَقَوْلِنَا: إِنْ كَانَتِ الشَّمْسُ طَالِعَةً فَالنَّهَارُ مَوْجُودٌ، لَكِنِ النَّهَارُ لَيْسَ بِمَوْجُودٍ، فَالشَّمْسُ لَيْسَتْ بِطَالِعَةٍ.It is either conjunctive, as in “Every body is composite, and everything composite came to be, so every body came to be”; or exceptive, as in “If the sun has risen, it is day; but it is not day, so the sun has not risen.”وَالْقِيَاسُ الِاقْتِرَانِيُّ يَتَرَكَّبُ إِمَّا مِنَ الْحَمْلِيَّتَيْنِ كَمَا مَرَّ؛ وَإِمَّا مِنَ الْمُتَّصِلَتَيْنِ كَقَوْلِنَا: إِنْ كَانَتِ الشَّمْسُ طَالِعَةً فَالنَّهَارُ مَوْجُودٌ، وَإِنْ كَانَ النَّهَارُ مَوْجُودًا فَالأَرْضُ مُضِيئَةٌ، يُنْتِجُ: إِنْ كَانَتِ الشَّمْسُ طَالِعَةً فَالأَرْضُ مُضِيئَةٌ؛The conjunctive syllogism is composed either of two categoricals, as above; or of two connectives, as in “If the sun has risen, it is day; and if it is day, the earth is lit”, which produces “If the sun has risen, the earth is lit”;وَإِمَّا مِنَ الْمُنْفَصِلَتَيْنِ كَقَوْلِنَا: كُلُّ عَدَدٍ إِمَّا زَوْجٌ أَوْ فَرْدٌ، وَكُلُّ زَوْجٍ فَهُوَ إِمَّا زَوْجُ الزَّوْجِ أَوْ زَوْجُ الْفَرْدِ، يُنْتِجُ: كُلُّ عَدَدٍ إِمَّا فَرْدٌ أَوْ زَوْجُ الزَّوْجِ أَوْ زَوْجُ الْفَرْدِ.or of two disjunctives, as in “Every number is either even or odd, and every even number is either evenly even or oddly even”, which produces “Every number is either odd, evenly even or oddly even”;أَوْ مِنْ حَمْلِيَّةٍ وَمُتَّصِلَةٍ، كَقَوْلِنَا: كُلَّمَا كَانَ هَذَا إِنْسَانًا فَهُوَ حَيَوَانٌ، وَكُلُّ حَيَوَانٍ جِسْمٌ، يُنْتِجُ: كُلَّمَا كَانَ هَذَا إِنْسَانًا فَهُوَ جِسْمٌ؛or of a categorical and a connective, as in “Whenever this is a human, it is an animal; and every animal is a body”, which produces “Whenever this is a human, it is a body”;وَإِمَّا مِنْ حَمْلِيَّةٍ وَمُنْفَصِلَةٍ، كَقَوْلِنَا: كُلُّ عَدَدٍ إِمَّا زَوْجٌ أَوْ فَرْدٌ، وَكُلُّ زَوْجٍ فَهُوَ مُنْقَسِمٌ بِمُتَسَاوِيَيْنِ، يُنْتِجُ: كُلُّ عَدَدٍ إِمَّا فَرْدٌ أَوْ مُنْقَسِمٌ بِمُتَسَاوِيَيْنِ؛or of a categorical and a disjunctive, as in “Every number is either even or odd, and every even number divides into two equal parts”, which produces “Every number is either odd or divides into two equal parts”;أَوْ مِنْ مُتَّصِلَةٍ وَمُنْفَصِلَةٍ، كَقَوْلِنَا: كُلَّمَا كَانَ هَذَا إِنْسَانًا فَهُوَ حَيَوَانٌ، وَكُلُّ حَيَوَانٍ فَهُوَ إِمَّا أَبْيَضُ أَوْ أَسْوَدُ، يُنْتِجُ: كُلَّمَا كَانَ هَذَا إِنْسَانًا فَهُوَ إِمَّا أَبْيَضُ أَوْ أَسْوَدُ.or of a connective and a disjunctive, as in “Whenever this is a human, it is an animal; and every animal is either white or black”, which produces “Whenever this is a human, it is either white or black.”

Related terms

Practise

12 questions on this term, in the practice set for syllogism.

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