Contradiction

فصل

وإذْ قد فَرَغْنا عن بَيانِ القَضايا وذِكْرِ أقْسامِها الأوَّلِيَّةِ والثّانَوِيَّةِ، فحانَ لَنا أنْ نَذْكُرَ شَيْئًا مِن أحْكامِها؛ فنَقُولُ: مِن أحْكامِها التَّناقُضُ والعُكُوسُ، فلْنَعْقِدْ لِبَيانِها فُصُولًا، ونَذْكُرْ فيها أُصُولًا.

Now that we have finished explaining propositions and mentioning their primary and secondary divisions, it is time for us to mention some of their rules. So we say: among their rules are contradiction and the conversions. Let us, then, devote sections to explaining them and set out some basic principles in them.

al-Mirqāt · p. 32

فصل

التَّناقُضُ هو اخْتِلافُ القَضِيَّتَيْنِ بالإيجابِ والسَّلْبِ بحَيْثُ يَقْتَضِي لِذاتِهِ صِدْقَ إحْداهُما كَذِبَ الأُخْرى أو بالعَكْسِ، كقَوْلِنا: «زَيْدٌ قائِمٌ» و«زَيْدٌ لَيْسَ بقائِمٍ». وشَرْطُ تَحَقُّقِ التَّناقُضِ بَيْنَ القَضِيَّتَيْنِ المَخْصُوصَتَيْنِ وَحَداتٌ ثَمانِيَةٌ، فلا يَتَحَقَّقُ بِدُونِها: وَحْدَةُ المَوْضُوعِ ووَحْدَةُ المَحْمُولِ، ووَحْدَةُ المَكانِ، ووَحْدَةُ الزَّمانِ، ووَحْدَةُ القُوَّةِ والفِعْلِ، ووَحْدَةُ الشَّرْطِ، ووَحْدَةُ الجُزْءِ والكُلِّ، ووَحْدَةُ الإضافَةِ. وقَدِ اجْتَمَعَتْ في هٰذَيْنِ البَيْتَيْنِ، بيت: «در تناقض هشت وحدة شرط دان * وحدة موضوع ومحمول ومكان وحدة شرط واضافت جزو وكل * قوة وفعل است در آخر زمان» فإذا اخْتَلَفَتا فيها لم تَتَناقَضا، نحوُ: «زَيْدٌ قائِمٌ» و«عَمْرٌو لَيْسَ بقائِمٍ»، و«زَيْدٌ قاعِدٌ» و«زَيْدٌ لَيْسَ بقائِمٍ»، و«زَيْدٌ مَوْجُودٌ» أي في الدّارِ و«زَيْدٌ لَيْسَ بمَوْجُودٍ» أي في السُّوقِ، و«زَيْدٌ نائِمٌ» أي في اللَّيْلِ و«زَيْدٌ لَيْسَ بنائِمٍ» أي في النَّهارِ، و«زَيْدٌ مُتَحَرِّكُ الأصابِعِ» أي بشَرْطِ كَوْنِهِ كاتِبًا و«زَيْدٌ لَيْسَ بمُتَحَرِّكِ الأصابِعِ» أي بشَرْطِ كَوْنِهِ غَيْرَ كاتِبٍ، و«الخَمْرُ في الدَّنِّ مُسْكِرٌ» أي بالقُوَّةِ و«الخَمْرُ لَيْسَ بمُسْكِرٍ في الدَّنِّ» أي بالفِعْلِ، و«الزِّنْجِيُّ أسْوَدُ» أي كُلُّهُ و«الزِّنْجِيُّ لَيْسَ بأسْوَدَ» أي جُزْؤُهُ أعْنِي أسْنانَهُ، و«زَيْدٌ أبٌ» أي لِبَكْرٍ و«زَيْدٌ لَيْسَ بأبٍ» أي لِخالِدٍ. وبَعْضُهُمُ اكْتَفَوْا بوَحْدَتَيْنِ، أي وَحْدَةِ المَوْضُوعِ والمَحْمُولِ، لانْدِراجِ البَواقِي فيهما، وبَعْضُهُمْ قَنِعُوا بوَحْدَةِ النِّسْبَةِ فَقَطْ؛ لأنّ وَحْدَتَها مُسْتَلْزِمَةٌ بجَمِيعِ الوَحَداتِ.

Contradiction is the difference of two propositions in affirmation and negation such that it requires, by itself, that the truth of one [goes with] the falsity of the other, or the reverse; as when we say “Zayd is standing” and “Zayd is not standing”. The condition for contradiction to hold between two singular propositions is eight unities; without them it does not hold: unity of subject, unity of predicate, unity of place, unity of time, unity of potentiality and actuality, unity of condition, unity of part and whole, and unity of relation (iḍāfa). They have been gathered in these two lines of verse: “در تناقض هشت وحدة شرط دان * وحدة موضوع ومحمول ومكان وحدة شرط واضافت جزو وكل * قوة وفعل است در آخر زمان” [Know that eight unities are a condition for contradiction: unity of subject, predicate and place; unity of condition and relation, part and whole; potentiality and actuality, and at the end, time.] So if the two differ in any of these, they do not contradict each other, as in “Zayd is standing” and “ʿAmr is not standing”; “Zayd is sitting” and “Zayd is not standing”; “Zayd is present”, that is, in the house, and “Zayd is not present”, that is, in the market; “Zayd is asleep”, that is, at night, and “Zayd is not asleep”, that is, by day; “Zayd's fingers are moving”, that is, on condition that he is writing, and “Zayd's fingers are not moving”, that is, on condition that he is not writing; “Wine in the jar intoxicates”, that is, potentially, and “Wine in the jar does not intoxicate”, that is, actually; “The Zanjī is black”, that is, all of him, and “The Zanjī is not black”, that is, part of him, I mean his teeth; “Zayd is a father”, that is, of Bakr, and “Zayd is not a father”, that is, of Khālid. Some contented themselves with two unities, the unity of subject and of predicate, since the rest are included in them; and some were satisfied with the unity of the relation (nisba) alone, since its unity entails all the unities.

al-Mirqāt · p. 32

فصل

لا بُدَّ في التَّناقُضِ في المَحْصُورَتَيْنِ مِن كَوْنِ القَضِيَّتَيْنِ مُخْتَلِفَتَيْنِ في الكَمِّ، أعْنِي الكُلِّيَّةَ والجُزْئِيَّةَ؛ فإذا كانَ أحَدُهما كُلِّيَّةً تَكُونُ الأُخْرى جُزْئِيَّةً؛ لأنّ الكُلِّيَّتَيْنِ قد تَكْذِبانِ، كما تَقُولُ: «كُلُّ حَيَوانٍ إنْسانٌ» و«لا شَيْءَ مِنَ الحَيَوانِ بإنْسانٍ»، والجُزْئِيَّتَيْنِ قد تَصْدُقانِ، كقَوْلِكَ: «بَعْضُ الحَيَوانِ إنْسانٌ» و«بَعْضُ الحَيَوانِ لَيْسَ بإنْسانٍ»، ويَكُونُ ذلك في كُلِّ مادَّةٍ يَكُونُ المَوْضُوعُ أعَمَّ فيها. ولا بُدَّ في تَناقُضِ القَضايا المُوَجَّهَةِ مِنَ الاخْتِلافِ في الجِهَةِ؛ فنَقِيضُ الضَّرُورِيَّةِ المُطْلَقَةِ المُمْكِنَةُ العامَّةُ، ونَقِيضُ الدّائِمَةِ المُطْلَقَةِ المُطْلَقَةُ العامَّةُ، ونَقِيضُ المَشْرُوطَةِ العامَّةِ الحِينِيَّةُ المُمْكِنَةُ، ونَقِيضُ العُرْفِيَّةِ العامَّةِ الحِينِيَّةُ المُطْلَقَةُ؛ وهذا في البَسائِطِ المُوَجَّهَةِ. ونَقائِضُ المُرَكَّباتِ مِنْها مَفْهُومٌ مُرَدَّدٌ بَيْنَ نَقِيضَيْ بَسائِطِها، والتَّفْصِيلُ يُطْلَبُ مِن مُطَوَّلاتِ الفَنِّ.

For contradiction between two quantified propositions, the two must differ in quantity, I mean universality and particularity: if one is universal, the other is particular. For two universals can both be false, as you say “Every animal is human” and “No animal is human”; and two particulars can both be true, as when you say “Some animal is human” and “Some animal is not human”. This happens in every case (mādda) in which the subject is more general. For contradiction between modal propositions, they must differ in mode (jiha). So the contradictory of the absolute necessary is the general possible; the contradictory of the absolute perpetual is the general absolute; the contradictory of the general conditional is the possible while-proposition (ḥīniyya mumkina); and the contradictory of the general conventional is the absolute while-proposition (ḥīniyya muṭlaqa). This is for the simple modals. The contradictories of the composite ones are a concept that alternates between the contradictories of their simple [components]. The details are to be sought in the longer works of the discipline.

al-Mirqāt · p. 33

فصل

ويُشْتَرَطُ في أخْذِ نَقائِضِ الشَّرْطِيّاتِ الاتِّفاقُ في الجِنْسِ والنَّوْعِ، والمُخالَفَةُ في الكَيْفِ؛ فنَقِيضُ المُتَّصِلَةِ اللُّزُومِيَّةِ المُوجَبَةِ سالِبَةٌ مُتَّصِلَةٌ لُزُومِيَّةٌ، ونَقِيضُ المُنْفَصِلَةِ العِنادِيَّةِ المُوجَبَةِ سالِبَةٌ مُنْفَصِلَةٌ عِنادِيَّةٌ، وهٰكَذا؛ فإذا قُلْتَ: «دائِمًا كُلَّما كانَ ا ب فـج د» كانَ نَقِيضُهُ «لَيْسَ كُلَّما كانَ ا ب فـج د»، وإذا قُلْتَ: «دائِمًا إمّا أنْ يَكُونَ هذا العَدَدُ زَوْجًا أو فَرْدًا» فنَقِيضُهُ «لَيْسَ دائِمًا إمّا أنْ يَكُونَ هذا العَدَدُ زَوْجًا أو فَرْدًا».

In taking the contradictories of conditionals, the condition is that they agree in genus [connective or disjunctive] and in species [implicative, oppositional and so on] and differ in quality. So the contradictory of an affirmative implicative connective is a negative implicative connective, the contradictory of an affirmative oppositional disjunctive is a negative oppositional disjunctive, and so on. If you say “Always: whenever A is B, J is D”, its contradictory is “Not whenever A is B is J D”; and if you say “Always, this number is either even or odd”, its contradictory is “Not always is this number either even or odd”.

al-Mirqāt · p. 34