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إِيسَاغُوجِي
Athīr al-Dīn al-Abharī (d. 663/1265) · Arabic after Mutūn al-manṭiq wa-l-ḥikma: Īsāghūjī wa-l-Sullam al-munawraq, ʿAlawī Abū Bakr Muḥammad al-Saqqāf (ḍabṭ wa-taʿlīq), Jakarta: Dār al-Kutub al-Islāmiyya, 1434/2013
نَحْمَدُ اللهَ تَعَالَى عَلَى تَوْفِيقِهِ، وَنَسْأَلُهُ طَرِيقَةً هَادِيَةً، وَنُصَلِّي عَلَى سَيِّدِنَا مُحَمَّدٍ وَعِتْرَتِهِ أَجْمَعِينَ.
We praise God, exalted is He, for the success He grants, ask Him for a path that guides, and send blessings on our master Muḥammad and all his family.
p. 5
أَمَّا بَعْدُ؛ فَهَذِهِ رِسَالَةٌ فِي الْمَنْطِقِ، أَوْرَدْنَا فِيهَا مَا يَجِبُ اسْتِحْضَارُهُ لِمَنْ يَبْتَدِئُ فِي شَيْءٍ مِنَ الْعُلُومِ، مُسْتَعِينًا بِاللهِ تَعَالَى، إِنَّهُ مُفِيضُ الْخَيْرِ وَالْجُودِ.
To proceed: this is a treatise on logic. In it we have set out what anyone beginning any of the sciences needs to have at hand, seeking the help of God, exalted is He; He is the one who pours out goodness and generosity.
p. 5
إِيسَاغُوجِي: اللَّفْظُ الدَّالُّ يَدُلُّ عَلَى مَا وُضِعَ لَهُ بِالْمُطَابَقَةِ، وَعَلَى جُزْئِهِ بِالتَّضَمُّنِ إِنْ كَانَ لَهُ جُزْءٌ، وَعَلَى مَا يُلَازِمُهُ فِي الذِّهْنِ بِالِالْتِزَامِ،
Īsāghūjī (Introduction): a signifying utterance signifies what it was coined for by correspondence, a part of that if it has a part by inclusion, and what accompanies it in the mind by implication,
p. 5–6
كَالإِنْسَانِ، فَإِنَّهُ يَدُلُّ عَلَى الْحَيَوَانِ النَّاطِقِ بِالْمُطَابَقَةِ، وَعَلَى أَحَدِهِمَا بِالتَّضَمُّنِ، وَعَلَى قَابِلِ الْعِلْمِ وَصَنْعَةِ الْكِتَابَةِ بِالِالْتِزَامِ؛
as with “human”: it signifies “rational animal” by correspondence, one of the two by inclusion, and “capable of knowledge and of the craft of writing” by implication.
p. 6
وَالدَّلَالَةُ فِعْلِيَّةٌ وَعَقْلِيَّةٌ وَطَبِيعِيَّةٌ وَوَضْعِيَّةٌ.
Signification is by action, by reason, by nature, or by convention.
p. 6
ثُمَّ اللَّفْظُ إِمَّا مُفْرَدٌ: وَهُوَ الَّذِي لَا يُرَادُ بِالْجُزْءِ مِنْهُ دَلَالَةٌ عَلَى جُزْءِ مَعْنَاهُ كَالإِنْسَانِ، وَإِمَّا مُؤَلَّفٌ: وَهُوَ الَّذِي لَا يَكُونُ كَذَلِكَ كَرَامِي الْحِجَارَةِ.
Next, an utterance is either simple, one whose part is not meant to signify a part of its meaning, like “human”; or composite, one that is not so, like “thrower of stones”.
p. 6
وَالْمُفْرَدُ إِمَّا كُلِّيٌّ: وَهُوَ الَّذِي لَا يَمْنَعُ نَفْسُ تَصَوُّرِ مَفْهُومِهِ وُقُوعَ الشَّرِكَةِ فِيهِ كَالإِنْسَانِ، وَإِمَّا جُزْئِيٌّ: وَهُوَ الَّذِي يَمْنَعُ نَفْسُ تَصَوُّرِ مَفْهُومِهِ ذَلِكَ كَزَيْدٍ عَلَمًا.
A simple utterance is either universal, one whose meaning, merely by being conceived, does not exclude being shared by many, like “human”; or particular, one whose meaning, merely by being conceived, excludes that, like “Zayd” as a proper name.
p. 6
وَالْكُلِّيُّ إِمَّا ذَاتِيٌّ: وَهُوَ الَّذِي يَدْخُلُ فِي حَقِيقَةِ جُزْئِيَّاتِهِ كَالْحَيَوَانِ بِالنِّسْبَةِ إِلَى الإِنْسَانِ وَالْفَرَسِ، وَإِمَّا عَرَضِيٌّ: وَهُوَ الَّذِي يُخَالِفُهُ كَالضَّاحِكِ بِالنِّسْبَةِ إِلَى الإِنْسَانِ.
A universal is either essential, one that enters into the reality of its particulars, like “animal” relative to human and horse; or accidental, one that is otherwise, like “laughing” relative to human.
p. 6
وَالذَّاتِيُّ إِمَّا مَقُولٌ فِي جَوَابِ: مَا هُوَ، بِحَسَبِ الشَّرِكَةِ الْمَحْضَةِ، كَالْحَيَوَانِ بِالنِّسْبَةِ إِلَى الإِنْسَانِ وَالْفَرَسِ، وَهُوَ الْجِنْسُ، وَيُرْسَمُ بِأَنَّهُ كُلِّيٌّ مَقُولٌ عَلَى كَثِيرِينَ مُخْتَلِفِينَ بِالْحَقَائِقِ فِي جَوَابِ: مَا هُوَ؛
The essential is either said in answer to “what is it?” by what is purely shared, like “animal” relative to human and horse: this is the genus, described as a universal said of many that differ in their realities, in answer to “what is it?”;
p. 7
وَإِمَّا مَقُولٌ فِي جَوَابِ: مَا هُوَ، بِحَسَبِ الشَّرِكَةِ وَالْخُصُوصِيَّةِ مَعًا، كَالإِنْسَانِ بِالنِّسْبَةِ إِلَى زَيْدٍ وَعَمْرٍو وَهُوَ النَّوْعُ، وَيُرْسَمُ بِأَنَّهُ كُلِّيٌّ مَقُولٌ عَلَى كَثِيرِينَ مُخْتَلِفِينَ بِالْعَدَدِ دُونَ الْحَقِيقَةِ فِي جَوَابِ: مَا هُوَ؛
or it is said in answer to “what is it?” by what is shared and specific together, like “human” relative to Zayd and ʿAmr: this is the species, described as a universal said of many that differ in number, not in reality, in answer to “what is it?”;
p. 7
وَإِمَّا غَيْرُ مَقُولٍ فِي جَوَابِ: مَا هُوَ، بَلْ مَقُولٌ فِي جَوَابِ: أَيُّ شَيْءٍ هُوَ فِي ذَاتِهِ، وَهُوَ الَّذِي يُمَيِّزُ الشَّيْءَ عَمَّا يُشَارِكُهُ فِي الْجِنْسِ، كَالنَّاطِقِ بِالنِّسْبَةِ إِلَى الإِنْسَانِ، وَهُوَ الْفَصْلُ، وَيُرْسَمُ بِأَنَّهُ كُلِّيٌّ يُقَالُ عَلَى الشَّيْءِ فِي جَوَابِ: أَيُّ شَيْءٍ هُوَ فِي ذَاتِهِ.
or it is not said in answer to “what is it?” but in answer to “which thing is it in its essence?”, and it separates a thing from what shares its genus, like “rational” relative to human: this is the differentia, described as a universal said of a thing in answer to “which thing is it in its essence?”.
p. 7
وَأَمَّا الْعَرَضِيُّ فَإِمَّا أَنْ يَمْتَنِعَ انْفِكَاكُهُ عَنِ الْمَاهِيَّةِ وَهُوَ الْعَرَضُ اللَّازِمُ، أَوْ لَا يَمْتَنِعَ وَهُوَ الْعَرَضُ الْمُفَارِقُ،
As for the accidental, either it cannot be separated from the quiddity, which is the inseparable accident, or it can, which is the separable accident.
p. 7–8
وَكُلُّ وَاحِدٍ مِنْهُمَا إِمَّا أَنْ يَخْتَصَّ بِحَقِيقَةٍ وَاحِدَةٍ وَهُوَ الْخَاصَّةُ كَالضَّاحِكِ بِالْقُوَّةِ وَالْفِعْلِ لِلإِنْسَانِ، وَتُرْسَمُ بِأَنَّهَا كُلِّيَّةٌ تُقَالُ عَلَى مَا تَحْتَ حَقِيقَةٍ وَاحِدَةٍ فَقَطْ قَوْلًا عَرَضِيًّا؛
Each of the two either belongs to one reality only, which is the proprium, like “laughing”, potentially and actually, for human; it is described as a universal said accidentally of what falls under one reality only;
p. 8
وَإِمَّا أَنْ يَعُمَّ حَقَائِقَ فَوْقَ وَاحِدَةٍ وَهُوَ الْعَرَضُ الْعَامُّ كَالْمُتَنَفِّسِ بِالْقُوَّةِ وَالْفِعْلِ بِالنِّسْبَةِ لِلإِنْسَانِ وَغَيْرِهِ مِنَ الْحَيَوَانَاتِ، وَيُرْسَمُ بِأَنَّهُ كُلِّيٌّ يُقَالُ عَلَى مَا تَحْتَ حَقَائِقَ مُخْتَلِفَةٍ قَوْلًا عَرَضِيًّا.
or it covers more than one reality, which is the common accident, like “breathing”, potentially and actually, relative to human and other animals; it is described as a universal said accidentally of what falls under different realities.
p. 8
الْحَدُّ: قَوْلٌ دَالٌّ عَلَى مَاهِيَّةِ الشَّيْءِ، وَهُوَ الَّذِي يَتَرَكَّبُ مِنْ جِنْسِ الشَّيْءِ وَفَصْلِهِ الْقَرِيبَيْنِ، كَالْحَيَوَانِ النَّاطِقِ بِالنِّسْبَةِ إِلَى الإِنْسَانِ، وَهُوَ الْحَدُّ التَّامُّ؛
The essential definition is a statement that signifies the quiddity of a thing. When it is composed of the thing's proximate genus and proximate differentia, like “rational animal” for human, it is the complete essential definition.
p. 8
وَالْحَدُّ النَّاقِصُ: وَهُوَ الَّذِي يَتَرَكَّبُ مِنْ جِنْسِ الشَّيْءِ الْبَعِيدِ وَفَصْلِهِ الْقَرِيبِ، كَالْجِسْمِ النَّاطِقِ بِالنِّسْبَةِ إِلَى الإِنْسَانِ.
The incomplete essential definition is composed of the thing's remote genus and its proximate differentia, like “rational body” for human.
p. 8
وَالرَّسْمُ التَّامُّ: وَهُوَ الَّذِي يَتَرَكَّبُ مِنْ جِنْسِ الشَّيْءِ الْقَرِيبِ وَخَوَاصِّهِ اللَّازِمَةِ لَهُ، كَالْحَيَوَانِ الضَّاحِكِ فِي تَعْرِيفِ الإِنْسَانِ؛
The complete descriptive definition is composed of the thing's proximate genus and the propria that necessarily belong to it, like “laughing animal” in defining human;
p. 9
وَالرَّسْمُ النَّاقِصُ: وَهُوَ الَّذِي يَتَرَكَّبُ مِنْ عَرَضِيَّاتٍ تَخْتَصُّ جُمْلَتُهَا بِحَقِيقَةٍ وَاحِدَةٍ، كَقَوْلِنَا فِي تَعْرِيفِ الإِنْسَانِ: إِنَّهُ مَاشٍ عَلَى قَدَمَيْهِ، عَرِيضُ الأَظْفَارِ، بَادِي الْبَشَرَةِ، مُسْتَقِيمُ الْقَامَةِ، ضَحَّاكٌ بِالطَّبْعِ.
and the incomplete descriptive definition is composed of accidental attributes that, taken together, belong to one reality only, as when we say in defining human: it walks on two feet, has broad nails, bare skin and an upright stature, and laughs by nature.
p. 9
الْقَضِيَّةُ: قَوْلٌ يَصِحُّ أَنْ يُقَالَ لِقَائِلِهِ: إِنَّهُ صَادِقٌ فِيهِ أَوْ كَاذِبٌ.
A proposition is a statement of which it can rightly be said to the one who says it that he speaks truly or falsely.
p. 9
وَهِيَ إِمَّا حَمْلِيَّةٌ كَقَوْلِنَا: زَيْدٌ كَاتِبٌ، وَإِمَّا شَرْطِيَّةٌ مُتَّصِلَةٌ كَقَوْلِنَا: إِنْ كَانَتِ الشَّمْسُ طَالِعَةً فَالنَّهَارُ مَوْجُودٌ، وَإِمَّا شَرْطِيَّةٌ مُنْفَصِلَةٌ كَقَوْلِنَا: الْعَدَدُ إِمَّا أَنْ يَكُونَ زَوْجًا أَوْ فَرْدًا.
It is either categorical, as in “Zayd is a writer”; or conditional and connective, as in “If the sun has risen, it is day”; or conditional and disjunctive, as in “A number is either even or odd.”
p. 9
وَالْجُزْءُ الأَوَّلُ مِنَ الْحَمْلِيَّةِ يُسَمَّى: مَوْضُوعًا، وَالثَّانِي: مَحْمُولًا؛ وَالْجُزْءُ الأَوَّلُ مِنَ الشَّرْطِيَّةِ يُسَمَّى: مُقَدَّمًا، وَالثَّانِي: تَالِيًا.
The first part of a categorical is called the subject and the second the predicate; the first part of a conditional is called the antecedent and the second the consequent.
p. 9
وَالْقَضِيَّةُ إِمَّا مُوجَبَةٌ كَقَوْلِنَا: زَيْدٌ كَاتِبٌ، وَإِمَّا سَالِبَةٌ كَقَوْلِنَا: زَيْدٌ لَيْسَ بِكَاتِبٍ.
A proposition is either affirmative, as in “Zayd is a writer”, or negative, as in “Zayd is not a writer.”
p. 10
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.”
p. 10
وَالْمُتَّصِلَةُ إِمَّا لُزُومِيَّةٌ كَقَوْلِنَا: إِنْ كَانَتِ الشَّمْسُ طَالِعَةً فَالنَّهَارُ مَوْجُودٌ، وَإِمَّا اتِّفَاقِيَّةٌ كَقَوْلِنَا: إِنْ كَانَ الإِنْسَانُ نَاطِقًا فَالْحِمَارُ نَاهِقٌ؛
The connective is either necessary, as in “If the sun has risen, it is day”, or coincidental, as in “If man is rational, the donkey brays.”
p. 10
وَالْمُنْفَصِلَةُ إِمَّا حَقِيقِيَّةٌ كَقَوْلِنَا: الْعَدَدُ إِمَّا زَوْجٌ وَإِمَّا فَرْدٌ.
The disjunctive is either real, as in “A number is either even or odd.”
p. 10
وَهِيَ إِمَّا مَانِعَةُ الْجَمْعِ وَالْخُلُوِّ مَعًا كَمَا ذَكَرْنَا، وَإِمَّا مَانِعَةُ الْجَمْعِ فَقَطْ كَقَوْلِنَا: هَذَا الشَّيْءُ إِمَّا أَنْ يَكُونَ شَجَرًا أَوْ حَجَرًا، وَإِمَّا مَانِعَةُ الْخُلُوِّ فَقَطْ كَقَوْلِنَا: زَيْدٌ إِمَّا أَنْ يَكُونَ فِي الْبَحْرِ، وَإِمَّا أَنْ لَا يَغْرَقَ.
It either excludes both being together and both being absent, as in the example given; or excludes only their being together, as in “This thing is either a tree or a stone”; or excludes only their both being absent, as in “Zayd is either in the sea or not drowning.”
p. 10–11
وَقَدْ تَكُونُ الْمُنْفَصِلَاتُ ذَوَاتِ أَجْزَاءٍ كَقَوْلِنَا: الْعَدَدُ إِمَّا زَائِدٌ أَوْ نَاقِصٌ أَوْ مُسَاوٍ.
Disjunctives may have more than two parts, as in “A number is either abundant, deficient or perfect.”
p. 11
وَالتَّنَاقُضُ هُوَ: اخْتِلَافُ قَضِيَّتَيْنِ بِالإِيجَابِ وَالسَّلْبِ، بِحَيْثُ يَقْتَضِي لِذَاتِهِ أَنْ تَكُونَ إِحْدَاهُمَا صَادِقَةً وَالأُخْرَى كَاذِبَةً، كَقَوْلِنَا: زَيْدٌ كَاتِبٌ، زَيْدٌ لَيْسَ بِكَاتِبٍ.
Contradiction is the difference of two propositions in affirmation and negation such that, of itself, it requires one to be true and the other false, as in “Zayd is a writer” and “Zayd is not a writer.”
p. 11
وَلَا يَتَحَقَّقُ ذَلِكَ إِلَّا بَعْدَ اتِّفَاقِهِمَا فِي الْمَوْضُوعِ، وَالْمَحْمُولِ، وَالزَّمَانِ، وَالْمَكَانِ، وَالإِضَافَةِ، وَالْقُوَّةِ، وَالْفِعْلِ، وَالْجُزْءِ، وَالْكُلِّ، وَالشَّرْطِ.
This holds only when they agree in subject, predicate, time, place, relation, potentiality, actuality, part, whole and condition.
p. 11
وَنَقِيضُ الْمُوجَبَةِ الْكُلِّيَّةِ إِنَّمَا هِيَ السَّالِبَةُ الْجُزْئِيَّةُ، كَقَوْلِنَا: كُلُّ إِنْسَانٍ حَيَوَانٌ، وَبَعْضُ الإِنْسَانِ لَيْسَ بِحَيَوَانٍ. وَنَقِيضُ السَّالِبَةِ الْكُلِّيَّةِ إِنَّمَا هِيَ الْمُوجَبَةُ الْجُزْئِيَّةُ، كَقَوْلِنَا: لَا شَيْءَ مِنَ الإِنْسَانِ بِحَيَوَانٍ، وَبَعْضُ الإِنْسَانِ حَيَوَانٌ.
The contradictory of a universal affirmative is the particular negative, as in “Every human is an animal” and “Some human is not an animal”; and the contradictory of a universal negative is the particular affirmative, as in “No human is an animal” and “Some human is an animal.”
p. 11–12
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.”
p. 12
الْعَكْسُ هُوَ: أَنْ يُصَيَّرَ الْمَوْضُوعُ مَحْمُولًا، وَالْمَحْمُولُ مَوْضُوعًا، مَعَ بَقَاءِ السَّلْبِ وَالإِيجَابِ بِحَالِهِ، وَالتَّصْدِيقِ وَالتَّكْذِيبِ بِحَالِهِ.
Conversion is making the subject the predicate and the predicate the subject, while negation or affirmation stays as it was, and truth or falsity stays as it was.
p. 12
وَالْمُوجَبَةُ الْكُلِّيَّةُ لَا تَنْعَكِسُ كُلِّيَّةً، إِذْ يَصْدُقُ قَوْلُنَا: كُلُّ إِنْسَانٍ حَيَوَانٌ، وَلَا يَصْدُقُ: كُلُّ حَيَوَانٍ إِنْسَانٌ، بَلْ تَنْعَكِسُ جُزْئِيَّةً، لِأَنَّا إِذَا قُلْنَا: كُلُّ إِنْسَانٍ حَيَوَانٌ، يَصْدُقُ: بَعْضُ الْحَيَوَانِ إِنْسَانٌ، فَإِنَّا نَجِدُ الْمَوْضُوعَ شَيْئًا مَوْصُوفًا بِالإِنْسَانِ وَالْحَيَوَانِ، فَيَكُونُ: بَعْضُ الْحَيَوَانِ إِنْسَانًا.
The universal affirmative does not convert as a universal: “Every human is an animal” is true, but “Every animal is human” is not. It converts as a particular: when we say “Every human is an animal”, “Some animal is human” is true, for we find the subject to be something described as both human and animal, so some animal is human.
p. 13
وَالْمُوجَبَةُ الْجُزْئِيَّةُ أَيْضًا تَنْعَكِسُ جُزْئِيَّةً بِهَذِهِ الْحُجَّةِ، وَالسَّالِبَةُ الْكُلِّيَّةُ تَنْعَكِسُ سَالِبَةً كُلِّيَّةً، وَذَلِكَ بَيِّنٌ بِنَفْسِهِ، فَإِنَّهُ إِذَا صَدَقَ: لَا شَيْءَ مِنَ الإِنْسَانِ بِحَجَرٍ، صَدَقَ: لَا شَيْءَ مِنَ الْحَجَرِ بِإِنْسَانٍ.
The particular affirmative likewise converts as a particular, by the same argument. The universal negative converts as a universal negative, and that is evident by itself: if “No human is a stone” is true, then “No stone is human” is true.
p. 13
وَالسَّالِبَةُ الْجُزْئِيَّةُ لَا عَكْسَ لَهَا لُزُومًا، فَإِنَّهُ يَصْدُقُ: بَعْضُ الْحَيَوَانِ لَيْسَ بِإِنْسَانٍ، وَلَا يَصْدُقُ عَكْسُهُ.
The particular negative has no converse that necessarily follows: “Some animal is not human” is true, but its converse is not.
p. 13
الْقِيَاسُ هُوَ: قَوْلٌ مُؤَلَّفٌ مِنْ أَقْوَالٍ، مَتَى سُلِّمَتْ لَزِمَ عَنْهَا لِذَاتِهَا قَوْلٌ آخَرُ.
A syllogism is a statement composed of statements such that, once they are granted, another statement follows from them by themselves.
p. 13–14
وَهُوَ إِمَّا اقْتِرَانِيٌّ كَقَوْلِنَا: كُلُّ جِسْمٍ مُؤَلَّفٌ، وَكُلُّ مُؤَلَّفٍ حَادِثٌ، فَكُلُّ جِسْمٍ حَادِثٌ؛ وَإِمَّا اسْتِثْنَائِيٌّ كَقَوْلِنَا: إِنْ كَانَتِ الشَّمْسُ طَالِعَةً فَالنَّهَارُ مَوْجُودٌ، لَكِنِ النَّهَارُ لَيْسَ بِمَوْجُودٍ، فَالشَّمْسُ لَيْسَتْ بِطَالِعَةٍ.
It is either conjunctive, as in “Every body is composite, and everything composite came to be, so every body came to be”; or exceptive, as in “If the sun has risen, it is day; but it is not day, so the sun has not risen.”
p. 14
وَالْمُكَرَّرُ بَيْنَ مُقَدِّمَتَيِ الْقِيَاسِ يُسَمَّى: حَدًّا أَوْسَطَ، وَمَوْضُوعُ الْمَطْلُوبِ يُسَمَّى: حَدًّا أَصْغَرَ، وَمَحْمُولُهُ يُسَمَّى: حَدًّا أَكْبَرَ؛ وَالْمُقَدِّمَةُ الَّتِي فِيهَا الأَصْغَرُ تُسَمَّى: صُغْرَى، وَالَّتِي فِيهَا الأَكْبَرُ تُسَمَّى: كُبْرَى، وَهَيْئَةُ التَّأْلِيفِ تُسَمَّى: شَكْلًا.
What recurs in both premises of the syllogism is called the middle term; the subject of the conclusion sought is called the minor term, and its predicate the major term. The premise containing the minor term is called the minor premise, the one containing the major term the major premise, and the form of their arrangement is called the figure.
p. 14
وَالأَشْكَالُ أَرْبَعَةٌ، لِأَنَّ الْحَدَّ الأَوْسَطَ إِنْ كَانَ مَحْمُولًا فِي الصُّغْرَى مَوْضُوعًا فِي الْكُبْرَى فَهُوَ: الشَّكْلُ الأَوَّلُ، وَإِنْ كَانَ مَحْمُولًا فِيهِمَا فَهُوَ: الشَّكْلُ الثَّانِي، وَإِنْ كَانَ مَوْضُوعًا فِيهِمَا فَهُوَ: الشَّكْلُ الثَّالِثُ، وَإِنْ كَانَ مَوْضُوعًا فِي الصُّغْرَى مَحْمُولًا فِي الْكُبْرَى فَهُوَ: الشَّكْلُ الرَّابِعُ.
The figures are four, because if the middle term is the predicate in the minor premise and the subject in the major, that is the first figure; if it is the predicate in both, the second; if the subject in both, the third; and if the subject in the minor and the predicate in the major, the fourth.
p. 14–15
وَالثَّانِي يَرْتَدُّ إِلَى الأَوَّلِ بِعَكْسِ الْكُبْرَى، وَالثَّالِثُ يَرْتَدُّ إِلَيْهِ بِعَكْسِ الصُّغْرَى، وَالرَّابِعُ يَرْتَدُّ إِلَيْهِ بِعَكْسِ التَّرْتِيبِ أَوْ بِعَكْسِ الْمُقَدِّمَتَيْنِ جَمِيعًا.
The second figure is brought back to the first by converting the major premise, the third by converting the minor, and the fourth by reversing the order of the premises or by converting both.
p. 15
وَالْكَامِلُ الْبَيِّنُ الإِنْتَاجِ هُوَ الأَوَّلُ، وَالرَّابِعُ مِنْهَا بَعِيدٌ عَنِ الطَّبْعِ جِدًّا، وَالَّذِي لَهُ طَبْعٌ مُسْتَقِيمٌ وَعَقْلٌ سَلِيمٌ لَا يَحْتَاجُ إِلَى رَدِّ الثَّانِي إِلَى الأَوَّلِ؛ وَإِنَّمَا يُنْتِجُ الثَّانِي عِنْدَ اخْتِلَافِ مُقَدِّمَتَيْهِ بِالإِيجَابِ وَالسَّلْبِ.
The perfect figure, whose conclusion is evident, is the first; the fourth is very far from natural thinking. Someone of sound nature and sound mind does not need to bring the second back to the first. The second produces only when its premises differ in affirmation and negation.
p. 15
وَالشَّكْلُ الأَوَّلُ هُوَ الَّذِي جُعِلَ مِعْيَارَ الْعُلُومِ، فَنُورِدُهُ هُنَا لِيُجْعَلَ دُسْتُورًا، وَيُسْتَنْتَجَ مِنْهُ الْمَطَالِبُ كُلُّهَا.
The first figure is the one made the standard of the sciences, so we set it out here as a rule from which every conclusion sought can be drawn.
p. 15
وَضُرُوبُهُ الْمُنْتِجَةُ أَرْبَعَةٌ: الضَّرْبُ الأَوَّلُ: كُلُّ جِسْمٍ مُؤَلَّفٌ، وَكُلُّ مُؤَلَّفٍ حَادِثٌ، فَكُلُّ جِسْمٍ حَادِثٌ. الثَّانِي: كُلُّ جِسْمٍ مُؤَلَّفٌ، وَلَا شَيْءَ مِنَ الْمُؤَلَّفِ بِقَدِيمٍ، فَلَا شَيْءَ مِنَ الْجِسْمِ بِقَدِيمٍ. الثَّالِثُ: بَعْضُ الْجِسْمِ مُؤَلَّفٌ، وَكُلُّ مُؤَلَّفٍ حَادِثٌ، فَبَعْضُ الْجِسْمِ حَادِثٌ. الرَّابِعُ: بَعْضُ الْجِسْمِ مُؤَلَّفٌ، وَلَا شَيْءَ مِنَ الْمُؤَلَّفِ بِقَدِيمٍ، فَبَعْضُ الْجِسْمِ لَيْسَ بِقَدِيمٍ.
Its productive moods are four. First: every body is composite, and everything composite came to be, so every body came to be. Second: every body is composite, and nothing composite is eternal, so no body is eternal. Third: some body is composite, and everything composite came to be, so some body came to be. Fourth: some body is composite, and nothing composite is eternal, so some body is not eternal.
p. 15–16
وَالْقِيَاسُ الِاقْتِرَانِيُّ يَتَرَكَّبُ إِمَّا مِنَ الْحَمْلِيَّتَيْنِ كَمَا مَرَّ؛ وَإِمَّا مِنَ الْمُتَّصِلَتَيْنِ كَقَوْلِنَا: إِنْ كَانَتِ الشَّمْسُ طَالِعَةً فَالنَّهَارُ مَوْجُودٌ، وَإِنْ كَانَ النَّهَارُ مَوْجُودًا فَالأَرْضُ مُضِيئَةٌ، يُنْتِجُ: إِنْ كَانَتِ الشَّمْسُ طَالِعَةً فَالأَرْضُ مُضِيئَةٌ؛
The conjunctive syllogism is composed either of two categoricals, as above; or of two connectives, as in “If the sun has risen, it is day; and if it is day, the earth is lit”, which produces “If the sun has risen, the earth is lit”;
p. 16
وَإِمَّا مِنَ الْمُنْفَصِلَتَيْنِ كَقَوْلِنَا: كُلُّ عَدَدٍ إِمَّا زَوْجٌ أَوْ فَرْدٌ، وَكُلُّ زَوْجٍ فَهُوَ إِمَّا زَوْجُ الزَّوْجِ أَوْ زَوْجُ الْفَرْدِ، يُنْتِجُ: كُلُّ عَدَدٍ إِمَّا فَرْدٌ أَوْ زَوْجُ الزَّوْجِ أَوْ زَوْجُ الْفَرْدِ.
or of two disjunctives, as in “Every number is either even or odd, and every even number is either evenly even or oddly even”, which produces “Every number is either odd, evenly even or oddly even”;
p. 16
أَوْ مِنْ حَمْلِيَّةٍ وَمُتَّصِلَةٍ، كَقَوْلِنَا: كُلَّمَا كَانَ هَذَا إِنْسَانًا فَهُوَ حَيَوَانٌ، وَكُلُّ حَيَوَانٍ جِسْمٌ، يُنْتِجُ: كُلَّمَا كَانَ هَذَا إِنْسَانًا فَهُوَ جِسْمٌ؛
or of a categorical and a connective, as in “Whenever this is a human, it is an animal; and every animal is a body”, which produces “Whenever this is a human, it is a body”;
p. 16
وَإِمَّا مِنْ حَمْلِيَّةٍ وَمُنْفَصِلَةٍ، كَقَوْلِنَا: كُلُّ عَدَدٍ إِمَّا زَوْجٌ أَوْ فَرْدٌ، وَكُلُّ زَوْجٍ فَهُوَ مُنْقَسِمٌ بِمُتَسَاوِيَيْنِ، يُنْتِجُ: كُلُّ عَدَدٍ إِمَّا فَرْدٌ أَوْ مُنْقَسِمٌ بِمُتَسَاوِيَيْنِ؛
or of a categorical and a disjunctive, as in “Every number is either even or odd, and every even number divides into two equal parts”, which produces “Every number is either odd or divides into two equal parts”;
p. 16–17
أَوْ مِنْ مُتَّصِلَةٍ وَمُنْفَصِلَةٍ، كَقَوْلِنَا: كُلَّمَا كَانَ هَذَا إِنْسَانًا فَهُوَ حَيَوَانٌ، وَكُلُّ حَيَوَانٍ فَهُوَ إِمَّا أَبْيَضُ أَوْ أَسْوَدُ، يُنْتِجُ: كُلَّمَا كَانَ هَذَا إِنْسَانًا فَهُوَ إِمَّا أَبْيَضُ أَوْ أَسْوَدُ.
or of a connective and a disjunctive, as in “Whenever this is a human, it is an animal; and every animal is either white or black”, which produces “Whenever this is a human, it is either white or black.”
p. 17
وَأَمَّا الْقِيَاسُ الِاسْتِثْنَائِيُّ فَالشَّرْطِيَّةُ الْمَوْضُوعَةُ فِيهِ إِنْ كَانَتْ مُتَّصِلَةً، فَاسْتِثْنَاءُ عَيْنِ الْمُقَدَّمِ يُنْتِجُ عَيْنَ التَّالِي، كَقَوْلِنَا: إِنْ كَانَ هَذَا إِنْسَانًا فَهُوَ حَيَوَانٌ، لَكِنَّهُ إِنْسَانٌ، فَهُوَ حَيَوَانٌ.
As for the exceptive syllogism: if the conditional in it is connective, affirming the antecedent produces the consequent, as in “If this is a human, it is an animal; but it is a human, so it is an animal.”
p. 17
وَاسْتِثْنَاءُ نَقِيضِ التَّالِي يُنْتِجُ نَقِيضَ الْمُقَدَّمِ، كَقَوْلِنَا: إِنْ كَانَ هَذَا إِنْسَانًا فَهُوَ حَيَوَانٌ، لَكِنَّهُ لَيْسَ بِحَيَوَانٍ، فَلَا يَكُونُ إِنْسَانًا؛
And affirming the contradictory of the consequent produces the contradictory of the antecedent, as in “If this is a human, it is an animal; but it is not an animal, so it is not a human.”
p. 17
وَإِنْ كَانَتْ مُنْفَصِلَةً فَاسْتِثْنَاءُ عَيْنِ أَحَدِ الْجُزْءَيْنِ يُنْتِجُ نَقِيضَ التَّالِي، كَقَوْلِنَا: الْعَدَدُ إِمَّا زَوْجٌ أَوْ فَرْدٌ، لَكِنَّهُ زَوْجٌ، يُنْتِجُ: أَنَّهُ لَيْسَ بِفَرْدٍ، أَوْ لَكِنَّهُ فَرْدٌ، يُنْتِجُ: أَنَّهُ لَيْسَ بِزَوْجٍ، وَاسْتِثْنَاءُ نَقِيضِ أَحَدِهِمَا يُنْتِجُ عَيْنَ الثَّانِي.
If it is disjunctive, affirming one of the two parts produces the contradictory of the other, as in “A number is either even or odd; but it is even”, which produces “It is not odd”; or “but it is odd”, which produces “It is not even.” And affirming the contradictory of one of them produces the other.
p. 17–18
الْبُرْهَانُ هُوَ: قِيَاسٌ مُؤَلَّفٌ مِنْ مُقَدِّمَاتٍ يَقِينِيَّةٍ لِإِنْتَاجِ يَقِينِيَّاتٍ،
Demonstration is a syllogism composed of certain premises in order to produce certain conclusions.
p. 18
وَالْيَقِينِيَّاتُ أَقْسَامٌ: أَحَدُهَا: أَوَّلِيَّاتٌ، كَقَوْلِنَا: الْوَاحِدُ نِصْفُ الِاثْنَيْنِ، وَالْكُلُّ أَعْظَمُ مِنَ الْجُزْءِ؛ وَمُشَاهَدَاتٌ، كَقَوْلِنَا: الشَّمْسُ مُشْرِقَةٌ، وَالنَّارُ مُحْرِقَةٌ؛ وَمُجَرَّبَاتٌ، كَقَوْلِنَا: السَّقَمُونِيَا تُسَهِّلُ الصَّفْرَاءَ؛
Certain premises are of several kinds. First principles, as in “One is half of two” and “The whole is greater than the part”; observations, as in “The sun is shining” and “Fire burns”; experiential premises, as in “Scammony purges bile”;
p. 18
وَحَدْسِيَّاتٌ، كَقَوْلِنَا: نُورُ الْقَمَرِ مُسْتَفَادٌ مِنْ نُورِ الشَّمْسِ؛ وَمُتَوَاتِرَاتٌ، كَقَوْلِنَا: مُحَمَّدٌ صَلَّى اللهُ عَلَيْهِ وَسَلَّمَ ادَّعَى النُّبُوَّةَ، وَظَهَرَتِ الْمُعْجِزَةُ عَلَى يَدِهِ؛ وَقَضَايَا قِيَاسَاتُهَا مَعَهَا، كَقَوْلِنَا: الأَرْبَعَةُ زَوْجٌ بِسَبَبِ وَسَطٍ حَاضِرٍ فِي الذِّهْنِ وَهُوَ: الِانْقِسَامُ بِمُتَسَاوِيَيْنِ.
intuitive premises, as in “The light of the moon comes from the light of the sun”; widely transmitted reports, as in “Muḥammad, God bless him and give him peace, claimed prophethood, and miracles appeared at his hands”; and propositions that carry their proofs with them, as in “Four is even”, because of a middle term present in the mind: being divisible into two equal parts.
p. 18
وَالْجَدَلُ هُوَ: قِيَاسٌ مُؤَلَّفٌ مِنْ مُقَدِّمَاتٍ مَشْهُورَةٍ أَوْ مُسَلَّمَةٍ عِنْدَ النَّاسِ أَوْ عِنْدَ الْخَصْمَيْنِ، كَقَوْلِنَا: الْعَدْلُ حَسَنٌ، وَالظُّلْمُ قَبِيحٌ.
Dialectic is a syllogism composed of premises that are widely accepted, or conceded among people or between two disputants, as in “Justice is good, and injustice is bad.”
p. 19
وَالْخَطَابَةُ هِيَ: قِيَاسٌ مُؤَلَّفٌ مِنْ مُقَدِّمَاتٍ مَقْبُولَةٍ مِنْ شَخْصٍ مُعْتَقَدٍ فِيهِ أَوْ مَظْنُونَةٍ.
Rhetoric is a syllogism composed of premises accepted from a person one trusts, or merely probable.
p. 19
وَالشِّعْرُ: قِيَاسٌ مُؤَلَّفٌ مِنْ مُقَدِّمَاتٍ مَقْبُولَةٍ مُتَخَيَّلَةٍ تَنْبَسِطُ مِنْهَا النَّفْسُ أَوْ تَنْقَبِضُ.
Poetics is a syllogism composed of accepted, imaginative premises at which the soul expands or contracts.
p. 19
وَالْمُغَالَطَةُ: قِيَاسٌ مُؤَلَّفٌ مِنْ مُقَدِّمَاتٍ كَاذِبَةٍ شَبِيهَةٍ بِالْحَقِّ أَوْ بِالْمَشْهُورِ، أَوْ مِنْ مُقَدِّمَاتٍ وَهْمِيَّةٍ كَاذِبَةٍ.
Sophistry is a syllogism composed of false premises that resemble the truth or what is widely accepted, or of false premises of the estimative faculty.
p. 19
وَالْعُمْدَةُ هُوَ الْبُرْهَانُ لَا غَيْرُ. انْتَهَى.
What can be relied on is demonstration, and nothing else. The end.
p. 19