The syllogism and the first figure

فصل

وإذْ قد فَرَغْنا عن مَباحِثِ القَضايا والعُكُوسِ الّتي كانَتْ مِن مَبادِئِ الحُجَّةِ، فحَرِيٌّ بنا أنْ نَتَكَلَّمَ في مَباحِثِ الحُجَّةِ؛ فنَقُولُ: الحُجَّةُ على ثَلاثَةِ أقْسامٍ: أحَدُها القِياسُ، وثانِيها الاسْتِقْراءُ، وثالِثُها التَّمْثِيلُ؛ فلْنُبَيِّنْ هذه الثَّلاثَةَ في ثَلاثَةِ فُصُولٍ.

Now that we have finished the discussions of propositions and of the conversions, which were among the principles of argument, it is fitting for us to speak about the discussions of argument. So we say: argument is of three kinds: the first is the syllogism, the second induction, and the third analogy. Let us, then, explain these three in three sections.

al-Mirqāt · p. 37

فصل في القياس

وهو قَوْلٌ مُؤَلَّفٌ مِن قَضايا يَلْزَمُ عَنْها قَوْلٌ آخَرُ بَعْدَ تَسْلِيمِ تِلْكَ القَضايا؛ فإنْ كانَ النَّتِيجَةُ أو نَقِيضُها مَذْكُورًا فيه يُسَمّى اسْتِثْنائِيًّا، كقَوْلِنا: «إنْ كانَ زَيْدٌ إنْسانًا كانَ حَيَوانًا، لكِنَّهُ إنْسانٌ» يُنْتِجُ: «فهو حَيَوانٌ»، و«إنْ كانَ زَيْدٌ حِمارًا كانَ ناهِقًا، لكِنَّهُ لَيْسَ بناهِقٍ» يُنْتِجُ: «أنّه لَيْسَ بحِمارٍ». وإنْ لم تَكُنِ النَّتِيجَةُ ونَقِيضُها مَذْكُورًا يُسَمّى اقْتِرانِيًّا، كقَوْلِكَ: «زَيْدٌ إنْسانٌ، وكُلُّ إنْسانٍ حَيَوانٌ» يُنْتِجُ: «زَيْدٌ حَيَوانٌ».

It is a statement composed of propositions from which another statement follows once those propositions are granted. If the conclusion or its contradictory is stated in it, it is called exceptive (istithnāʾī), as when we say “If Zayd is a human, he is an animal; but he is a human”, which produces “so he is an animal”; and “If Zayd is a donkey, he brays; but he does not bray”, which produces “that he is not a donkey”. If neither the conclusion nor its contradictory is stated, it is called conjunctive (iqtirānī), as when you say “Zayd is a human, and every human is an animal”, which produces “Zayd is an animal”.

al-Mirqāt · p. 37

فصل في القياس الاقتراني

وهو قِسْمانِ: حَمْلِيٌّ وشَرْطِيٌّ. ومَوْضُوعُ النَّتِيجَةِ في القِياسِ يُسَمّى أصْغَرَ لكَوْنِهِ أقَلَّ أفْرادًا في الأغْلَبِ، ومَحْمُولُهُ يُسَمّى أكْبَرَ لكَوْنِهِ أكْثَرَ أفْرادًا غالِبًا. والقَضِيَّةُ الّتي جُعِلَتْ جُزْءَ قِياسٍ تُسَمّى مُقَدِّمَةً، والمُقَدِّمَةُ الّتي فيها الأصْغَرُ تُسَمّى صُغْرى، والّتي فيها الأكْبَرُ كُبْرى، والجُزْءُ الّذي تَكَرَّرَ بَيْنَهُما يُسَمّى حَدًّا أوْسَطَ، واقْتِرانُ الصُّغْرى بالكُبْرى يُسَمّى قَرِينَةً وضَرْبًا، والهَيْئَةُ الحاصِلَةُ مِن كَيْفِيَّةِ وَضْعِ الأوْسَطِ عِنْدَ الأصْغَرِ والأكْبَرِ تُسَمّى شَكْلًا. والأشْكالُ أرْبَعَةٌ، وَجْهُ الضَّبْطِ أنْ يُقالَ: الحَدُّ الأوْسَطُ إمّا مَحْمُولُ الصُّغْرى ومَوْضُوعُ الكُبْرى، كما في قَوْلِنا: «العالَمُ مُتَغَيِّرٌ، وكُلُّ مُتَغَيِّرٍ حادِثٌ» يُنْتِجُ: «العالَمُ حادِثٌ»، فهو الشَّكْلُ الأوَّلُ؛ وإنْ كانَ مَحْمُولًا فيهما فهو الشَّكْلُ الثّانِي، كما تَقُولُ: «كُلُّ إنْسانٍ حَيَوانٌ، ولا شَيْءَ مِنَ الحَجَرِ بحَيَوانٍ»، فالنَّتِيجَةُ: «لا شَيْءَ مِنَ الإنْسانِ بحَجَرٍ»؛ وإنْ كانَ مَوْضُوعًا فيهما فهو الشَّكْلُ الثّالِثُ، نحوُ: «كُلُّ إنْسانٍ حَيَوانٌ، وبَعْضُ الإنْسانِ كاتِبٌ» يُنْتِجُ: «بَعْضُ الحَيَوانِ كاتِبٌ»؛ وإنْ كانَ مَوْضُوعًا في الصُّغْرى ومَحْمُولًا في الكُبْرى فهو الشَّكْلُ الرّابِعُ، نحوُ قَوْلِنا: «كُلُّ إنْسانٍ حَيَوانٌ، وبَعْضُ الكاتِبِ إنْسانٌ» يُنْتِجُ: «بَعْضُ الحَيَوانِ كاتِبٌ».

It is of two kinds: categorical and conditional. The subject of the conclusion in a syllogism is called the minor term, because it mostly has fewer individuals; and its predicate is called the major term, because it usually has more individuals. A proposition made part of a syllogism is called a premise; the premise containing the minor term is called the minor premise, and the one containing the major term the major premise. The part repeated between them is called the middle term. The joining of the minor premise with the major is called a combination (qarīna) and a mood (ḍarb); and the form that results from the way the middle term is placed with respect to the minor and major terms is called a figure (shakl). The figures are four. The way to establish this is to say: the middle term is either the predicate of the minor premise and the subject of the major, as when we say “The world is changing, and everything changing came to be”, which produces “The world came to be”: this is the first figure. If it is the predicate in both, it is the second figure, as you say: “Every human is an animal, and no stone is an animal”, so the conclusion is “No human is a stone”. If it is the subject in both, it is the third figure, as in “Every human is an animal, and some human is a writer”, which produces “Some animal is a writer”. If it is the subject in the minor premise and the predicate in the major, it is the fourth figure, as when we say “Every human is an animal, and some writer is human”, which produces “Some animal is a writer”.

al-Mirqāt · p. 37

فصل

وأشْرَفُ الأشْكالِ مِنَ الأرْبَعَةِ الشَّكْلُ الأوَّلُ، ولذلك كانَ إنْتاجُهُ بَيِّنًا بَدِيهِيًّا يَسْبِقُ الذِّهْنُ فيه إلى النَّتِيجَةِ سَبْقًا طَبْعِيًّا مِن دُونِ حاجَةٍ إلى فِكْرٍ وتَأَمُّلٍ. ولَهُ شَرائِطُ وضُرُوبٌ؛ أمّا الشَّرائِطُ فاثْنانِ: أحَدُهُما إيجابُ الصُّغْرى، وثانِيهِما كُلِّيَّةُ الكُبْرى؛ فإنْ يُفْقَدا مَعًا أو يُفْقَدْ أحَدُهُما لا يَلْزَمِ النَّتِيجَةُ، كما يَظْهَرُ عِنْدَ التَّأَمُّلِ. وأمّا الضُّرُوبُ فأرْبَعَةٌ؛ لأنّ الاحْتِمالاتِ في كُلِّ شَكْلٍ سِتَّةَ عَشَرَ؛ لأنّ الصُّغْرى أرْبَعَةٌ والكُبْرى أيْضًا أرْبَعَةٌ، أعْنِي المُوجَبَةَ الكُلِّيَّةَ والمُوجَبَةَ الجُزْئِيَّةَ والسّالِبَةَ الكُلِّيَّةَ والجُزْئِيَّةَ، والأرْبَعَةُ في الأرْبَعَةِ سِتَّةَ عَشَرَ. وأسْقَطَ شَرائِطُ الشَّكْلِ الأوَّلِ اثْنَيْ عَشَرَ، وهو الصُّغْرى السّالِبَةُ الكُلِّيَّةُ مَعَ الكُبْرَياتِ الأرْبَعِ، والصُّغْرى السّالِبَةُ الجُزْئِيَّةُ مَعَ تِلْكَ الأرْبَعِ، وهذه ثَمانِيَةٌ، والكُبْرى المُوجَبَةُ الجُزْئِيَّةُ والسّالِبَةُ الجُزْئِيَّةُ مَعَ الصُّغْرى المُوجَبَةِ الجُزْئِيَّةِ والكُلِّيَّةِ، وهذه أرْبَعَةٌ؛ فبَقِيَ أرْبَعَةُ ضُرُوبٍ مُنْتِجَةٍ. الضَّرْبُ الأوَّلُ مُرَكَّبٌ مِن مُوجَبَةٍ كُلِّيَّةٍ صُغْرى ومُوجَبَةٍ كُلِّيَّةٍ كُبْرى، يُنْتِجُ مُوجَبَةً كُلِّيَّةً، نحوُ: «كُلُّ ج ب، وكُلُّ ب د» يُنْتِجُ: «ج د». والضَّرْبُ الثّانِي مُؤَلَّفٌ مِن مُوجَبَةٍ كُلِّيَّةٍ صُغْرى وسالِبَةٍ كُلِّيَّةٍ كُبْرى، يُنْتِجُ سالِبَةً كُلِّيَّةً، نحوُ: «كُلُّ إنْسانٍ حَيَوانٌ، ولا شَيْءَ مِنَ الحَيَوانِ بحَجَرٍ» يُنْتِجُ: «لا شَيْءَ مِنَ الإنْسانِ بحَجَرٍ». والضَّرْبُ الثّالِثُ مُلْتَئِمٌ مِن مُوجَبَةٍ جُزْئِيَّةٍ صُغْرى ومُوجَبَةٍ كُلِّيَّةٍ كُبْرى، والنَّتِيجَةُ مُوجَبَةٌ جُزْئِيَّةٌ، نحوُ: «بَعْضُ الحَيَوانِ فَرَسٌ، وكُلُّ فَرَسٍ صَهّالٌ» يُنْتِجُ: «بَعْضُ الحَيَوانِ صَهّالٌ». والضَّرْبُ الرّابِعُ مُزْدَوِجٌ مِن مُوجَبَةٍ جُزْئِيَّةٍ صُغْرى وسالِبَةٍ كُلِّيَّةٍ كُبْرى، يُنْتِجُ سالِبَةً جُزْئِيَّةً، كقَوْلِنا: «بَعْضُ الحَيَوانِ ناطِقٌ، ولا شَيْءَ مِنَ النّاطِقِ بناهِقٍ»، فالنَّتِيجَةُ: «بَعْضُ الحَيَوانِ لَيْسَ بناهِقٍ».

The noblest of the four figures is the first. For that reason its production [of a conclusion] is evident and self-evident: in it the mind runs ahead to the conclusion naturally, with no need for thought and reflection. It has conditions and moods. The conditions are two: the first is that the minor premise be affirmative, the second that the major premise be universal. If both are missing, or one of them, the conclusion does not follow, as becomes clear on reflection. The moods are four. For the possibilities in each figure are sixteen, since the minor premise is of four kinds and the major premise also of four, I mean the universal affirmative, the particular affirmative, the universal negative and the particular [negative]; and four times four is sixteen. The conditions of the first figure drop twelve: the universal negative minor premise with the four major premises, and the particular negative minor premise with those four, which makes eight; and the particular affirmative and particular negative major premise with the particular and universal affirmative minor premise, which makes four. So four productive moods remain. The first mood is composed of a universal affirmative minor premise and a universal affirmative major premise, and produces a universal affirmative, as in “Every J is B, and every B is D”, which produces “[Every] J is D”. The second mood is made up of a universal affirmative minor premise and a universal negative major premise, and produces a universal negative, as in “Every human is an animal, and no animal is a stone”, which produces “No human is a stone”. The third mood is formed of a particular affirmative minor premise and a universal affirmative major premise, and the conclusion is a particular affirmative, as in “Some animal is a horse, and every horse neighs”, which produces “Some animal neighs”. The fourth mood is paired from a particular affirmative minor premise and a universal negative major premise, and produces a particular negative, as when we say “Some animal is rational, and nothing rational brays”, so the conclusion is “Some animal does not bray”.

al-Mirqāt · p. 38

تنبيه

إنْتاجُ المُوجَبَةِ الكُلِّيَّةِ مِن خَواصِّ الشَّكْلِ الأوَّلِ، كما أنّ الإنْتاجَ لِلنَّتائِجِ الأرْبَعَةِ أيْضًا مِن خَصائِصِهِ، والصُّغْرى المُمْكِنَةُ غَيْرُ مُنْتِجَةٍ في هذا الشَّكْلِ فَقَطْ. ووَضَحَ بما ذَكَرْنا أنّه لا بُدَّ في هذا الشَّكْلِ كَيْفًا إيجابُ الصُّغْرى، وكَمًّا كُلِّيَّةُ الكُبْرى، وجِهَةً فِعْلِيَّةُ الصُّغْرى.

Producing a universal affirmative is one of the properties of the first figure, just as producing all four kinds of conclusion is also one of its distinctive features; and a possible minor premise is unproductive in this figure only. What we have said makes clear that in this figure the minor premise must be affirmative, as to quality; the major premise must be universal, as to quantity; and the minor premise must be actual (fiʿliyya), as to mode.

al-Mirqāt · p. 40