Particular and universal, and the relations between universals

فَصْلٌ

المَفْهُومُ، أَيْ ما حَصَلَ فِي الذِّهْنِ، قِسْمانِ: أَحَدُهُما جُزْئِيٌّ، وَالثّانِي كُلِّيٌّ. أَمّا الجُزْئِيُّ فَهُوَ ما يَمْنَعُ نَفْسُ تَصَوُّرِهِ عَنْ صِدْقِهِ عَلَى كَثِيرِينَ، كَـ«زَيْدٍ» وَ«عَمْرٍو» وَ«هٰذا الفَرَسِ» وَ«هٰذا الجِدارِ»؛ وَأَمّا الكُلِّيُّ فَهُوَ ما لا يَمْنَعُ نَفْسُ تَصَوُّرِهِ عَنْ وُقُوعِ الشَّرِكَةِ فِيهِ وَعَنْ صِدْقِهِ عَلَى كَثِيرِينَ، كَالإِنْسانِ وَالفَرَسِ. وَقَدْ يُفَسَّرُ الكُلِّيُّ وَالجُزْئِيُّ بِتَفْسِيرَيْنِ آخَرَيْنِ: أَمّا الكُلِّيُّ فَهُوَ ما جَوَّزَ العَقْلُ تَكَثُّرَهُ مِنْ حَيْثُ تَصَوُّرُهُ، وَأَمّا الجُزْئِيُّ فَهُوَ ما لا يَكُونُ كَذٰلِكَ.

A concept (mafhūm), that is, what is attained in the mind, is of two kinds: one is particular, the other universal. A particular (juzʾī) is that whose very conception prevents it from being true of many, like “Zayd”, “ʿAmr”, “this horse” and “this wall”. A universal (kullī) is that whose very conception does not prevent its being shared, or its being true of many, like “human” and “horse”. The universal and the particular are sometimes explained in two other ways: the universal is that which reason allows to be many insofar as it is conceived, and the particular is that which is not so.

al-Mirqāt · p. 14

فَصْلٌ

الكُلِّيُّ أَقْسامٌ: أَحَدُها ما يَمْتَنِعُ وُجُودُ أَفْرادِهِ فِي الخارِجِ، كَاللّاشَيْءِ وَاللّامُمْكِنِ وَاللّامَوْجُودِ؛ وَثانِيها ما يُمْكِنُ أَفْرادُهُ وَلَمْ تُوجَدْ، كَالعَنْقاءِ وَجَبَلٍ مِنَ الياقُوتِ؛ وَثالِثُها ما أَمْكَنَتْ أَفْرادُهُ وَلَمْ يُوجَدْ مِنْ أَفْرادِهِ إِلّا فَرْدٌ واحِدٌ، كَالشَّمْسِ وَالواجِبِ تَعالَى؛ وَرابِعُها ما وُجِدَتْ لَهُ أَفْرادٌ كَثِيرَةٌ، إِمّا مُتَناهِيَةٌ، كَالكَواكِبِ السَّيّارَةِ، فَإِنَّها سَبْعٌ: الشَّمْسُ وَالقَمَرُ وَالمِرِّيخُ وَالزُّهَرَةُ وَزُحَلُ وَعُطارِدُ وَالمُشْتَرِي؛ أَوْ غَيْرُ مُتَناهِيَةٍ، كَأَفْرادِ الإِنْسانِ وَالفَرَسِ وَالغَنَمِ وَالبَقَرِ. وَقَدْ أُورِدَ عَلَى تَعْرِيفِ الكُلِّيِّ وَالجُزْئِيِّ سُؤالٌ تَقْرِيرُهُ: أَنَّ الصُّورَةَ الحاصِلَةَ مِنَ البَيْضَةِ المُعَيَّنَةِ، وَالشَّبَحَ المَرْئِيَّ مِنْ بَعِيدٍ، وَمَحْسُوسَ الطِّفْلِ فِي مَبْدَإِ الوِلادَةِ، كُلُّها جُزْئِيّاتٌ، مَعَ أَنَّهُ يَصْدُقُ عَلَيْها تَعْرِيفُ الكُلِّيِّ؛ لِأَنَّ فِي هٰذِهِ الصُّوَرِ فَرْضَ صِدْقِها عَلَى كَثِيرِينَ غَيْرُ مُمْتَنِعٍ. وَالجَوابُ: أَنَّ المُرادَ بِصِدْقِ المَفْهُومِ فِي تَعْرِيفِ الكُلِّيِّ هُوَ الصِّدْقُ عَلَى وَجْهِ الاِجْتِماعِ، وَهٰذِهِ الصُّوَرُ، أَعْنِي صُورَةَ البَيْضَةِ المُعَيَّنَةِ وَغَيْرَها، إِنَّما يَصْدُقُ عَلَى كَثِيرِينَ بَدَلًا لا مَعًا؛ فَإِنَّ الوَحْدَةَ مَأْخُوذَةٌ فِي هٰذِهِ الصُّوَرِ ضَرُورَةَ أَنَّها مَأْخُوذَةٌ مِنْ مادَّةٍ مُعَيَّنَةٍ جُزْئِيَّةٍ، وَلَوْلا فِيها اعْتِبارُ التَّوَحُّدِ لَكانَتْ كُلِّيَّةً مِنْ غَيْرِ لُزُومِ إِشْكالٍ، هٰذا.

The universal has several kinds. The first is that whose individuals cannot exist in the outside world, like “non-thing”, “non-possible” and “non-existent”. The second is that whose individuals are possible but do not exist, like the ʿanqāʾ [a legendary bird] and a mountain of ruby. The third is that whose individuals are possible but of whose individuals only one exists, like the sun and the Necessarily Existent, exalted is He. The fourth is that which has many existing individuals, either finite, like the planets, which are seven: the Sun, the Moon, Mars, Venus, Saturn, Mercury and Jupiter; or infinite, like the individuals of human, horse, sheep and cattle. An objection has been raised against the definitions of the universal and the particular, which runs as follows. The form that comes from a particular egg, the shape seen from afar, and what an infant perceives by the senses at the beginning of its birth are all particulars; and yet the definition of the universal is true of them, since in these forms it is not impossible to suppose that they are true of many. The answer is that what is meant by a concept's being true [of many] in the definition of the universal is its being true of them jointly. These forms, I mean the form of the particular egg and the others, are true of many only alternately, not together. For oneness is taken into account in these forms, because they are necessarily taken from a determinate, particular matter; were oneness not considered in them, they would be universal and no difficulty would follow. Mark this.

al-Mirqāt · p. 15

فَصْلٌ فِي النِّسْبَةِ بَيْنَ الكُلِّيَّيْنِ

اِعْلَمْ أَنَّ النِّسْبَةَ بَيْنَ الكُلِّيَّيْنِ تُتَصَوَّرُ عَلَى أَنْحاءٍ أَرْبَعَةٍ؛ لِأَنَّكَ إِذا أَخَذْتَ كُلِّيَّيْنِ فَإِمّا أَنْ يَصْدُقَ كُلٌّ مِنْهُما عَلَى كُلِّ ما يَصْدُقُ عَلَيْهِ الآخَرُ، فَهُما مُتَساوِيانِ، كَالإِنْسانِ وَالنّاطِقِ؛ لِأَنَّ كُلَّ إِنْسانٍ ناطِقٌ وَكُلَّ ناطِقٍ إِنْسانٌ؛ أَوْ يَصْدُقُ واحِدُهُما عَلَى كُلِّ ما يَصْدُقُ عَلَيْهِ الآخَرُ وَلا يَصْدُقُ الآخَرُ عَلَى جَمِيعِ أَفْرادِ أَحَدِهِما، فَبَيْنَهُما عُمُومٌ وَخُصُوصٌ مُطْلَقًا، كَالحَيَوانِ وَالإِنْسانِ، فَيَصْدُقُ الحَيَوانُ عَلَى كُلِّ ما يَصْدُقُ عَلَيْهِ الإِنْسانُ، وَلا يَصْدُقُ الإِنْسانُ عَلَى كُلِّ ما يَصْدُقُ عَلَيْهِ الحَيَوانُ، بَلْ عَلَى بَعْضِهِ؛ أَوْ لا يَصْدُقُ شَيْءٌ مِنْهُما عَلَى شَيْءٍ مِمّا يَصْدُقُ عَلَيْهِ الآخَرُ، فَهُما مُتَبايِنانِ، كَالإِنْسانِ وَالفَرَسِ؛ أَوْ يَصْدُقُ بَعْضُ كُلِّ واحِدٍ مِنْهُما عَلَى بَعْضِ ما يَصْدُقُ عَلَيْهِ الآخَرُ، فَبَيْنَهُما عُمُومٌ وَخُصُوصٌ مِنْ وَجْهٍ، كَالأَبْيَضِ وَالحَيَوانِ، فَفِي البَطِّ يَصْدُقُ كُلٌّ مِنْهُما، وَفِي الفِيلِ يَصْدُقُ الحَيَوانُ فَقَطْ، وَفِي الثَّلْجِ وَالعاجِ يَصْدُقُ الأَبْيَضُ فَقَطْ. فَهٰذِهِ أَرْبَعُ نِسَبٍ: التَّساوِي، وَالتَّبايُنُ، وَالعُمُومُ وَالخُصُوصُ مُطْلَقًا، وَالعُمُومُ وَالخُصُوصُ مِنْ وَجْهٍ؛ فَاحْفَظْ ذٰلِكَ.

Know that the relation between two universals can be conceived in four ways. For if you take two universals, then either each of them is true of everything the other is true of, and the two are equivalent (mutasāwiyān), like human and rational, since every human is rational and every rational being is human; or one of them is true of everything the other is true of, while the other is not true of all the individuals of the first, and then between them there is generality and specificity absolutely, like animal and human: animal is true of everything human is true of, but human is not true of everything animal is true of, only of some of it; or neither of them is true of anything the other is true of, and the two are mutually exclusive (mutabāyinān), like human and horse; or some of each of them is true of some of what the other is true of, and then between them there is generality and specificity in some respect, like white and animal: in the duck both are true, in the elephant only animal is true, and in snow and ivory only white is true. So these are four relations: equivalence, mutual exclusion, generality and specificity absolutely, and generality and specificity in some respect. Remember this well.

al-Mirqāt · p. 15

فَصْلٌ

قَدْ يُقالُ الجُزْئِيُّ لِمَعْنًى آخَرَ، وَهُوَ ما كانَ أَخَصَّ تَحْتَ الأَعَمِّ؛ فَالإِنْسانُ عَلَى هٰذا التَّعْرِيفِ جُزْئِيٌّ؛ لِدُخُولِهِ تَحْتَ الحَيَوانِ، وَكَذا الحَيَوانُ؛ لِدُخُولِهِ تَحْتَ الجِسْمِ النّامِي، وَكَذا الجِسْمُ النّامِي؛ لِدُخُولِهِ تَحْتَ الجِسْمِ المُطْلَقِ، وَكَذا الجِسْمُ المُطْلَقُ؛ لِدُخُولِهِ تَحْتَ الجَوْهَرِ. وَالنِّسْبَةُ بَيْنَ الجُزْئِيِّ الحَقِيقِيِّ وَبَيْنَ هٰذا الجُزْئِيِّ المُسَمَّى بِالجُزْئِيِّ الإِضافِيِّ عُمُومٌ وَخُصُوصٌ مُطْلَقًا؛ لِاجْتِماعِهِما فِي زَيْدٍ مَثَلًا، وَصِدْقِ الإِضافِيِّ بِدُونِ الحَقِيقِيِّ فِي الإِنْسانِ، فَإِنَّهُ جُزْئِيٌّ إِضافِيٌّ وَلَيْسَ بِجُزْئِيٍّ حَقِيقِيٍّ؛ لِأَنَّ صِدْقَهُ عَلَى كَثِيرِينَ غَيْرُ مُمْتَنِعٍ.

“Particular” is sometimes used in another sense: what is more specific, falling under something more general. On this definition human is a particular, because it falls under animal; and so is animal, because it falls under growing body; and so is growing body, because it falls under body as such; and so is body as such, because it falls under substance. The relation between the real particular and this particular, which is called the relative particular, is generality and specificity absolutely: the two meet in Zayd, for example, and the relative is true without the real in human, for human is a relative particular and not a real particular, since its being true of many is not impossible.

al-Mirqāt · p. 16