The second, third and fourth figures

فصل

ويُشْتَرَطُ في إنْتاجِ الشَّكْلِ الثّانِي بحَسَبِ الكَيْفِ ـ أي الإيجابِ والسَّلْبِ ـ اخْتِلافُ المُقَدِّمَتَيْنِ؛ فإنْ كانَتِ الصُّغْرى مُوجَبَةً كانَتِ الكُبْرى سالِبَةً، وبالعَكْسِ؛ وبحَسَبِ الكَمِّ ـ أي الكُلِّيَّةِ والجُزْئِيَّةِ ـ كُلِّيَّةُ الكُبْرى، وإلّا يَلْزَمِ الاخْتِلافُ المُوجِبُ لعَدَمِ الإنْتاجِ، أي صِدْقُ القِياسِ مَعَ إيجابِ النَّتِيجَةِ تارَةً ومَعَ سَلْبِها أُخْرى. ونَتِيجَةُ هذا الشَّكْلِ لا يَكُونُ إلّا سالِبَةً، وضُرُوبُهُ النّاتِجَةُ أيْضًا أرْبَعَةٌ: أحَدُها مِن كُلِّيَّتَيْنِ والصُّغْرى مُوجَبَةٌ، يُنْتِجُ سالِبَةً كُلِّيَّةً، كقَوْلِنا: «كُلُّ ج ب، ولا شَيْءَ مِن ا ب»، «فلا شَيْءَ مِن ج ا». والدَّلِيلُ على هذا الإنْتاجِ عَكْسُ الكُبْرى؛ فإنّكَ إذا عَكَسْتَ الكُبْرى صارَ «لا شَيْءَ مِن ب ا»، وبانْضِمامِها إلى الصُّغْرى انْتَظَمَ الشَّكْلُ الأوَّلُ، ويُنْتِجُ النَّتِيجَةَ المَطْلُوبَةَ. الضَّرْبُ الثّانِي مِن مُوجَبَةٍ كُلِّيَّةٍ كُبْرى وسالِبَةٍ كُلِّيَّةٍ صُغْرى، كقَوْلِنا: «لا شَيْءَ مِن ج ب، وكُلُّ ا ب» يُنْتِجُ: «لا شَيْءَ مِن ج ا». والدَّلِيلُ على الإنْتاجِ عَكْسُ الصُّغْرى وجَعْلُها كُبْرى ثُمَّ عَكْسُ النَّتِيجَةِ. الضَّرْبُ الثّالِثُ مِن مُوجَبَةٍ جُزْئِيَّةٍ صُغْرى وسالِبَةٍ كُلِّيَّةٍ كُبْرى، يُنْتِجُ سالِبَةً جُزْئِيَّةً، كقَوْلِكَ: «بَعْضُ ج ب، ولا شَيْءَ مِن ا ب»، «فلَيْسَ بَعْضُ ج ا». الضَّرْبُ الرّابِعُ مِن سالِبَةٍ جُزْئِيَّةٍ صُغْرى ومُوجَبَةٍ كُلِّيَّةٍ كُبْرى، يُنْتِجُ سالِبَةً جُزْئِيَّةً؛ تَقُولُ: «بَعْضُ ج لَيْسَ ب، وكُلُّ ا ب»، «فبَعْضُ ج لَيْسَ ا».

For the second figure to produce, it is required, with respect to quality (that is, affirmation and negation), that the two premises differ: if the minor premise is affirmative, the major premise is negative, and the reverse. With respect to quantity (that is, universality and particularity), it is required that the major premise be universal. Otherwise there follows the discrepancy (ikhtilāf) that entails sterility, that is, the syllogism being true at one time with the conclusion affirmative and at another with it negative. The conclusion of this figure is only ever negative. Its productive moods are also four. The first is made of two universals, the minor premise being affirmative; it produces a universal negative, as when we say: “Every J is B, and no A is B”, “so no J is A”. The proof of this productivity is the conversion of the major premise: if you convert the major premise, it becomes “No B is A”; joined to the minor premise, it makes up the first figure, and this produces the conclusion sought. The second mood is made of a universal affirmative major premise and a universal negative minor premise, as when we say: “No J is B, and every A is B”, which produces “No J is A”. The proof of its productivity is converting the minor premise and making it the major premise, then converting the conclusion. The third mood is made of a particular affirmative minor premise and a universal negative major premise; it produces a particular negative, as when you say: “Some J is B, and no A is B”, “so not some J is A”. The fourth mood is made of a particular negative minor premise and a universal affirmative major premise; it produces a particular negative. You say: “Some J is not B, and every A is B”, “so some J is not A”.

al-Mirqāt · p. 40

فصل

شَرْطُ إنْتاجِ الشَّكْلِ الثّالِثِ كَوْنُ الصُّغْرى مُوجَبَةً، وكَوْنُ أحَدِ المُقَدِّمَتَيْنِ كُلِّيَّةً؛ فضُرُوبُهُ النّاتِجَةُ سِتَّةٌ: أحَدُها «كُلُّ ب ج، وكُلُّ ب ا، فبَعْضُ ج ا»، وثانِيها «كُلُّ ب ج، ولا شَيْءَ مِن ب ا، فبَعْضُ ج لَيْسَ ا»، وثالِثُها «بَعْضُ ب ج، وكُلُّ ب ا، فبَعْضُ ج ا»، ورابِعُها «بَعْضُ ب ج، ولا شَيْءَ مِن ب ا، فبَعْضُ ج لَيْسَ ا»، وخامِسُها «كُلُّ ب ج، وبَعْضُ ب ا، فبَعْضُ ج ا»، وسادِسُها «كُلُّ ب ج، وبَعْضُ ب لَيْسَ ا، فبَعْضُ ج لَيْسَ ا».

The condition for the third figure to produce is that the minor premise be affirmative and that one of the two premises be universal. So its productive moods are six. The first: “Every B is J, and every B is A, so some J is A.” The second: “Every B is J, and no B is A, so some J is not A.” The third: “Some B is J, and every B is A, so some J is A.” The fourth: “Some B is J, and no B is A, so some J is not A.” The fifth: “Every B is J, and some B is A, so some J is A.” The sixth: “Every B is J, and some B is not A, so some J is not A.”

al-Mirqāt · p. 41

فصل

وشَرائِطُ إنْتاجِ الشَّكْلِ الرّابِعِ مَعَ كَثْرَتِها وقِلَّةِ جَدْواها مَذْكُورَةٌ في المَبْسُوطاتِ، فلا عَلَيْنا لو تَرَكْنا ذِكْرَها، وكذا شَرائِطُ سائِرِ الأشْكالِ بحَسَبِ الجِهَةِ لا يَتَحَمَّلُ أمْثالُ رِسالَتِي هذه لِبَيانِها.

The conditions for the fourth figure to produce, many as they are and of little use, are set out in the extensive works, so there is no blame on us if we leave them unmentioned. Likewise the conditions of the other figures with respect to modality (jiha): a treatise such as this one of mine cannot bear setting them out.

al-Mirqāt · p. 41

فائدة

ولَعَلَّكَ عَلِمْتَ مِمّا ألْقَيْنا عَلَيْكَ أنّ النَّتِيجَةَ في القِياسِ تَتْبَعُ أدْوَنَ المُقَدِّمَتَيْنِ في الكَيْفِ والكَمِّ، والأدْوَنُ في الكَيْفِ هو السَّلْبُ، وفي الكَمِّ هو الجُزْئِيَّةُ؛ فالقِياسُ مِن مُوجَبَةٍ وسالِبَةٍ يُنْتِجُ سالِبَةً، والمُرَكَّبُ مِن كُلِّيَّةٍ وجُزْئِيَّةٍ إنّما يُنْتِجُ جُزْئِيَّةً. وأمّا المُرَكَّبُ مِنَ الكُلِّيَّتَيْنِ فرُبَّما يُنْتِجُ كُلِّيَّةً، وقد يُنْتِجُ جُزْئِيَّةً.

Perhaps you have learned from what we have put before you that the conclusion of a syllogism follows the weaker (adwan) of the two premises in quality and in quantity. The weaker in quality is negation, and in quantity particularity. So a syllogism made of an affirmative and a negative produces a negative, and one composed of a universal and a particular produces only a particular. As for one composed of two universals, it may produce a universal, and it may produce a particular.

al-Mirqāt · p. 41