Ulumalaعلوم الآلة

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    Quantified proposition

    al-maḥṣūra

    المَحْصُورَة

    A quantified proposition (maḥṣūra) states, by a quantifier (sūr), whether the judgement covers all or some of the subject.

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    In a picture

    SPEvery S is PكُلُّSPNo S is Pلَا شَيْءَSPSome S is PبَعْضُSPNot every S is Pلَيْسَ بَعْضُ
    The four quantified propositions, drawn as circles. The shaded part is what the proposition says exists.

    Explanation

    The four forms: universal affirmative (“every”), universal negative (“no”), particular affirmative (“some”) and particular negative (“not every”).

    A proposition about one individual is singular (shakhṣiyya); one without a quantifier is indefinite (muhmala), and is treated as particular.

    Also written as: mahsura, quantified proposition, sur.

    In the text

    وَكُلُّ وَاحِدَةٍ مِنْهُمَا إِمَّا مَخْصُوصَةٌ كَمَا ذَكَرْنَا، وَإِمَّا كُلِّيَّةٌ مُسَوَّرَةٌ كَقَوْلِنَا: كُلُّ إِنْسَانٍ كَاتِبٌ، وَلَا شَيْءَ مِنَ الإِنْسَانِ بِكَاتِبٍ، وَإِمَّا جُزْئِيَّةٌ مُسَوَّرَةٌ كَقَوْلِنَا: بَعْضُ الإِنْسَانِ كَاتِبٌ، وَبَعْضُ الإِنْسَانِ لَيْسَ بِكَاتِبٍ، وَإِمَّا أَنْ لَا يَكُونَ كَذَلِكَ وَتُسَمَّى: مُهْمَلَةً كَقَوْلِنَا: الإِنْسَانُ كَاتِبٌ، وَالإِنْسَانُ لَيْسَ بِكَاتِبٍ.Each of the two is either singular, as in the examples given; or universal with a quantifier, as in “Every human is a writer” and “No human is a writer”; or particular with a quantifier, as in “Some human is a writer” and “Some human is not a writer”; or neither, and then it is called indefinite, as in “Man is a writer” and “Man is not a writer.”وَالْمَحْصُورَتَانِ لَا يَتَحَقَّقُ التَّنَاقُضُ بَيْنَهُمَا إِلَّا بَعْدَ اخْتِلَافِهِمَا فِي الْكَمِّيَّةِ، لِأَنَّ الْكُلِّيَّتَيْنِ قَدْ تَكْذِبَانِ كَقَوْلِنَا: كُلُّ إِنْسَانٍ كَاتِبٌ، وَلَا شَيْءَ مِنَ الإِنْسَانِ بِكَاتِبٍ، وَالْجُزْئِيَّتَيْنِ قَدْ تَصْدُقَانِ كَقَوْلِنَا: بَعْضُ الإِنْسَانِ كَاتِبٌ، وَبَعْضُ الإِنْسَانِ لَيْسَ بِكَاتِبٍ.Between two quantified propositions there is contradiction only when they also differ in quantity, because two universals can both be false, as in “Every human is a writer” and “No human is a writer”, and two particulars can both be true, as in “Some human is a writer” and “Some human is not a writer.”

    Examples

    • كُلُّ إِنْسَانٍ حَيَوَانٌEvery human is an animal (universal affirmative)

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