Tahdhīb al-manṭiq Saʿd al-Dīn al-Taftāzānī

فَصْلٌ

دَلالَةُ اللَّفْظِ عَلَى تَمامِ ما وُضِعَ لَهُ مُطابَقَةٌ، وَعَلَى جُزْئِهِ تَضَمُّنٌ، وَعَلَى الخارِجِ التِزامٌ، وَلا بُدَّ مِنَ اللُّزُومِ عَقْلًا أَوْ عُرْفًا، وَتَلْزَمُهُما المُطابَقَةُ وَلَوْ تَقْدِيرًا، وَلا عَكْسَ.

The signification of an utterance on the whole of what it was coined for is correspondence (muṭābaqa), on its part is inclusion (taḍammun), and on what lies outside it is implication (iltizām). For implication there must be a necessary link, by reason or by custom. Correspondence accompanies both of the others, if only by supposition; not the other way round.

· с. 4

فَصْلٌ

وَالمَوْضُوعُ لَهُ إِنْ قُصِدَ بِجُزْءٍ مِنْهُ الدَّلالَةُ عَلَى جُزْءِ المَعْنَى فَمُرَكَّبٌ: إِمّا تامٌّ، خَبَرٌ أَوْ إِنْشاءٌ، وَإِمّا ناقِصٌ، تَقْيِيدِيٌّ أَوْ غَيْرُهُ، وَإِلّا فَمُفْرَدٌ. وَهُوَ إِنِ اسْتَقَلَّ، فَمَعَ الدَّلالَةِ بِهَيْئَتِهِ عَلَى أَحَدِ الأَزْمِنَةِ الثَّلاثَةِ كَلِمَةٌ، وَبِدُونِها اسْمٌ، وَإِلّا فَأَداةٌ. وَأَيْضًا إِنِ اتَّحَدَ مَعْناهُ، فَمَعَ تَشَخُّصِهِ وَضْعًا عَلَمٌ، وَبِدُونِهِ مُتَواطِئٌ إِنِ اسْتَوَتْ أَفْرادُهُ، وَمُشَكِّكٌ إِنْ تَفاوَتَتْ إِمّا بِأَوَّلِيَّةٍ أَوْ أَوْلَوِيَّةٍ؛ وَإِنْ كَثُرَ مَعْناهُ، فَإِنْ وُضِعَ لِكُلٍّ فَمُشْتَرَكٌ، وَإِلّا فَإِنِ اشْتَهَرَ فِي الثّانِي فَمَنْقُولٌ يُنْسَبُ إِلَى النّاقِلِ، وَإِلّا فَحَقِيقَةٌ وَمَجازٌ.

As for the coined utterance: if a part of it is meant to signify a part of the meaning, it is composite (murakkab) — either complete, a report (khabar) or a performative (inshāʾ), or incomplete, restrictive (taqyīdī) or otherwise. If not, it is single (mufrad). The single utterance, if it stands on its own, is a verb (kalima) if by its form it also signifies one of the three times, and a noun (ism) if it does not; otherwise it is a particle (adāt). Again: if its meaning is one, then with its individuation in the coining it is a proper name (ʿalam); without it, it is univocal (mutawāṭiʾ) if its instances are equal, and modulated (mushakkik) if they differ, by priority or by greater fitness. If its meanings are many: if it was coined for each, it is homonymous (mushtarak); if not, then if it became well known in the second meaning it is transferred (manqūl), named after the one who transferred it; otherwise it is literal (ḥaqīqa) and figurative (majāz).

· с. 4–5

فَصْلٌ

المَفْهُومُ إِنِ امْتَنَعَ فَرْضُ صِدْقِهِ عَلَى كَثِيرِينَ فَجُزْئِيٌّ، وَإِلّا فَكُلِّيٌّ، امْتَنَعَتْ أَفْرادُهُ، أَوْ أَمْكَنَتْ وَلَمْ تُوجَدْ، أَوْ وُجِدَ الواحِدُ فَقَطْ مَعَ إِمْكانِ الغَيْرِ أَوِ امْتِناعِهِ، أَوِ الكَثِيرُ مَعَ التَّناهِي أَوْ عَدَمِهِ.

A concept (mafhūm), if supposing it to be true of many is impossible, is particular (juzʾī); otherwise it is universal (kullī) — whether its instances are impossible; or possible but not found; or only one is found, while another is possible, or impossible; or many are found, finite or infinite in number.

· с. 5

وَالكُلِّيّانِ إِنْ تَفارَقا كُلِّيًّا فَمُتَبايِنانِ، وَإِلّا فَإِنْ تَصادَقا كُلِّيًّا مِنَ الجانِبَيْنِ فَمُتَساوِيانِ، وَنَقِيضاهُما كَذٰلِكَ، أَوْ مِنْ جانِبٍ فَأَعَمُّ وَأَخَصُّ مُطْلَقًا، وَنَقِيضاهُما بِالعَكْسِ، وَإِلّا فَمِنْ وَجْهٍ، وَبَيْنَ نَقِيضَيْهِما تَبايُنٌ جُزْئِيٌّ كَالمُتَبايِنَيْنِ. وَقَدْ يُقالُ الجُزْئِيُّ لِلأَخَصِّ، وَهُوَ أَعَمُّ.

Two universals, if they part entirely, are distinct (mutabāyin). If not: if each is true of everything the other is true of, they are equal (mutasāwī), and so are their contradictories; if this holds on one side only, they are more general and more particular absolutely, and their contradictories the other way round; otherwise they are more general and more particular in one respect, and between their contradictories there is a partial distinctness, as between two distinct universals. “Particular” is sometimes said of the more specific, and this is more general.

· с. 5

وَالكُلِّيّاتُ خَمْسٌ: الأَوَّلُ الجِنْسُ، وَهُوَ المَقُولُ عَلَى الكَثْرَةِ المُخْتَلِفَةِ الحَقِيقَةِ فِي جَوابِ ما هُوَ، فَإِنْ كانَ الجَوابُ عَنِ الماهِيَّةِ وَعَنْ بَعْضِ المُشارِكاتِ هُوَ الجَوابَ عَنْها وَعَنِ الكُلِّ فَقَرِيبٌ كَالحَيَوانِ، وَإِلّا فَبَعِيدٌ كَالجِسْمِ النّامِي.

The universals are five. The first is the genus (jins): what is said of a multitude differing in their realities in answer to “What is it?”. If the answer about the quiddity and about some of what shares the genus with it is also the answer about it and about all that shares it, the genus is near (qarīb), like “animal”; otherwise it is remote (baʿīd), like “growing body”.

· с. 5–6

الثّانِي النَّوْعُ، وَهُوَ المَقُولُ عَلَى الكَثْرَةِ المُتَّفِقَةِ الحَقِيقَةِ فِي جَوابِ ما هُوَ، وَقَدْ يُقالُ عَلَى الماهِيَّةِ الكُلِّيَّةِ المَقُولِ عَلَيْها وَعَلَى غَيْرِها الجِنْسُ فِي جَوابِ ما هُوَ، وَيَخْتَصُّ هٰذا النَّوْعُ بِاسْمِ الإِضافِيِّ كَالأَوَّلِ بِالحَقِيقِيِّ، وَبَيْنَهُما عُمُومٌ مِنْ وَجْهٍ، لِتَصادُقِهِما عَلَى الإِنْسانِ، وَتَفارُقِهِما فِي الحَيَوانِ وَالنُّقْطَةِ. ثُمَّ الأَجْناسُ تَتَرَتَّبُ مُتَصاعِدَةً إِلَى العالِي، وَيُسَمَّى جِنْسَ الأَجْناسِ، وَالأَنْواعُ قَدْ تَتَرَتَّبُ مُتَنازِلَةً إِلَى السّافِلِ، وَيُسَمَّى نَوْعَ الأَنْواعِ، وَما بَيْنَهُما مُتَوَسِّطاتٌ.

The second is the species (nawʿ): what is said of a multitude agreeing in their reality in answer to “What is it?”. It is also said of a universal quiddity of which, and of other things, the genus is said in answer to “What is it?”. This species is specially called relative (iḍāfī), as the first is called real (ḥaqīqī). Between the two there is generality in one respect, since both are true of “human”, and they part in “animal” and in “the point”. The genera are ordered ascending to the highest, which is called the genus of genera; the species may be ordered descending to the lowest, which is called the species of species; and what lies between them are intermediates.

· с. 5–6

الثّالِثُ الفَصْلُ، وَهُوَ المَقُولُ عَلَى الشَّيْءِ فِي جَوابِ أَيُّ شَيْءٍ هُوَ فِي ذاتِهِ، فَإِنْ مَيَّزَ عَنِ المُشارِكِ فِي الجِنْسِ القَرِيبِ فَقَرِيبٌ، أَوِ البَعِيدِ فَبَعِيدٌ. وَإِذا نُسِبَ إِلَى ما يُمَيِّزُهُ فَمُقَوِّمٌ، وَإِلَى ما يُمَيَّزُ عَنْهُ فَمُقَسِّمٌ، وَالمُقَوِّمُ لِلعالِي مُقَوِّمٌ لِلسّافِلِ وَلا عَكْسَ، وَالمُقَسِّمُ بِالعَكْسِ.

The third is the differentia (faṣl): what is said of a thing in answer to “What thing is it in its essence?”. If it sets it apart from what shares the near genus with it, it is near; from what shares the remote genus, it is remote. Related to what it sets apart, it is constitutive (muqawwim); related to that from which it sets it apart, it is divisive (muqassim). What constitutes the higher constitutes the lower, not the other way round; and the divisive is the reverse.

· с. 6

الرّابِعُ الخاصَّةُ، وَهُوَ الخارِجُ عَنِ الماهِيَّةِ المَقُولُ عَلَى ما تَحْتَ حَقِيقَةٍ واحِدَةٍ فَقَطْ قَوْلًا عَرَضِيًّا. الخامِسُ العَرَضُ العامُّ، وَهُوَ الخارِجُ المَقُولُ عَلَيْها وَعَلَى غَيْرِها. وَكُلٌّ مِنْهُما إِنِ امْتَنَعَ انْفِكاكُهُ عَنِ الشَّيْءِ فَلازِمٌ، بِالنَّظَرِ إِلَى الماهِيَّةِ أَوْ إِلَى الوُجُودِ؛ ثُمَّ اللّازِمُ إِمّا بَيِّنٌ يَلْزَمُ تَصَوُّرُهُ مِنْ تَصَوُّرِ المَلْزُومِ، أَوْ مِنْ تَصَوُّرِهِما الجَزْمُ بِاللُّزُومِ، أَوْ غَيْرُ بَيِّنٍ، وَهُوَ بِخِلافِهِ. وَإِلّا فَعَرَضٌ مُفارِقٌ، يَدُومُ أَوْ يَزُولُ بِسُرْعَةٍ أَوْ بُطْءٍ.

The fourth is the property (khāṣṣa): what lies outside the quiddity and is said, as an accident, only of what falls under a single reality. The fifth is the common accident (ʿaraḍ ʿāmm): what lies outside and is said of it and of others. Each of them, if it is impossible for it to come apart from the thing, is necessary (lāzim), with regard to the quiddity or to existence. The necessary is either clear (bayyin) — its conception follows from the conception of what it necessarily accompanies, or from conceiving both the certainty of the link follows — or not clear, which is the opposite. Otherwise it is a separable accident, which lasts, or passes quickly or slowly.

· с. 6–7

خاتِمَةٌ

مَفْهُومُ الكُلِّيِّ يُسَمّى كُلِّيًّا مَنْطِقِيًّا، وَمَعْرُوضُهُ طَبِيعِيًّا، وَالمَجْمُوعُ عَقْلِيًّا، وَكَذا الأَنْواعُ الخَمْسَةُ، وَالحَقُّ وُجُودُ الطَّبِيعِيِّ بِمَعْنَى وُجُودِ أَشْخاصِهِ.

The concept of the universal is called the logical universal; what it applies to, the natural universal; and the two together, the mental universal. So too the five kinds. The truth is that the natural universal exists, in the sense that its individuals exist.

· с. 7

فَصْلٌ فِي المُعَرِّفِ وَأَقْسامِهِ

مُعَرِّفُ الشَّيْءِ ما يُقالُ لِإِفادَةِ تَصَوُّرِهِ، فَيُشْتَرَطُ أَنْ يَكُونَ مُساوِيًا أَجْلَى، فَلا يَصِحُّ التَّعْرِيفُ بِالأَعَمِّ وَالأَخَصِّ، وَالمُساوِي مَعْرِفَةً وَالأَخْفَى. وَالتَّعْرِيفُ بِالفَصْلِ القَرِيبِ حَدٌّ، وَبِالخاصَّةِ رَسْمٌ، فَإِنْ كانَ مَعَ الجِنْسِ القَرِيبِ فَتامٌّ، وَإِلّا فَناقِصٌ، وَلَمْ يَعْتَبِرُوا التَّعْرِيفَ بِالعَرَضِ العامِّ، وَقَدْ أُجِيزَ فِي النّاقِصِ أَنْ يَكُونَ أَعَمَّ كَاللَّفْظِيِّ، وَهُوَ ما يُقْصَدُ بِهِ تَفْسِيرُ مَدْلُولِ اللَّفْظِ.

The definer of a thing is what is said in order to give a conception of it. So it must be equal to it and clearer: defining by the more general or the more particular is not sound, nor by what is equal in being known, nor by the more obscure. Definition by the near differentia is a real definition (ḥadd), and by the property a description (rasm); with the near genus they are complete, otherwise incomplete. They did not take account of defining by the common accident. In the incomplete kind it has been allowed to be more general, like the verbal definition, which is meant to explain what an utterance signifies.

· с. 7

المَقْصَدُ الثّانِي فِي التَّصْدِيقاتِ

القَضِيَّةُ قَوْلٌ يَحْتَمِلُ الصِّدْقَ وَالكَذِبَ، فَإِنْ كانَ الحُكْمُ فِيها بِثُبُوتِ شَيْءٍ لِشَيْءٍ أَوْ نَفْيِهِ عَنْهُ فَحَمْلِيَّةٌ، مُوجِبَةٌ وَسالِبَةٌ، وَيُسَمَّى المَحْكُومُ عَلَيْهِ مَوْضُوعًا، وَالمَحْكُومُ بِهِ مَحْمُولًا، وَالدّالُّ عَلَى النِّسْبَةِ رابِطَةً، وَقَدِ اسْتُعِيرَ لَها هُوَ؛ وَإِلّا فَشَرْطِيَّةٌ، وَيُسَمَّى الجُزْءُ الأَوَّلُ مُقَدَّمًا، وَالثّانِي تالِيًا.

A proposition (qaḍiyya) is a statement that admits truth and falsehood. If the judgement in it is that one thing holds of another, or does not, it is categorical (ḥamliyya), affirmative or negative. What is judged about is called the subject (mawḍūʿ), what is judged of it the predicate (maḥmūl), and what signifies the relation the copula (rābiṭa); “huwa” has been borrowed for it. Otherwise it is conditional (sharṭiyya); its first part is called the antecedent (muqaddam) and the second the consequent (tālī).

· с. 7

وَالمَوْضُوعُ فِي الحَمْلِيَّةِ إِنْ كانَ شَخْصِيًّا سُمِّيَتِ القَضِيَّةُ مَخْصُوصَةً، وَإِنْ كانَ نَفْسَ الحَقِيقَةِ فَطَبِيعِيَّةٌ، وَإِلّا فَإِنْ بُيِّنَ كَمِّيَّةُ أَفْرادِهِ كُلًّا أَوْ بَعْضًا فَمَحْصُورَةٌ كُلِّيَّةٌ أَوْ جُزْئِيَّةٌ، وَما بِهِ البَيانُ سُورًا، وَإِلّا فَمُهْمَلَةٌ، وَتُلازِمُ الجُزْئِيَّةَ. وَلا بُدَّ فِي المُوجِبَةِ مِنْ وُجُودِ المَوْضُوعِ، مُحَقَّقًا وَهِيَ الخارِجِيَّةُ، أَوْ مُقَدَّرًا فَالحَقِيقِيَّةُ، أَوْ ذِهْنًا فَالذِّهْنِيَّةُ. وَقَدْ يُجْعَلُ حَرْفُ السَّلْبِ جُزْءًا مِنْ جُزْءٍ فَيُسَمّى مَعْدُولًا.

If the subject of a categorical is an individual, the proposition is called singular (makhṣūṣa); if it is the reality itself, natural (ṭabīʿiyya). Otherwise, if the quantity of its instances is made clear, all or some, it is quantified (maḥṣūra), universal or particular, and what makes it clear is called the quantifier (sūr); if not, it is indefinite (muhmala), and it goes with the particular. In an affirmative the subject must exist: in fact, and that is the external (khārijiyya); or by supposition, the real (ḥaqīqiyya); or in the mind, the mental (dhihniyya). Sometimes the particle of negation is made part of one of the parts; then it is called metathetic (maʿdūl).

· с. 7–8

وَقَدْ يُصَرَّحُ بِكَيْفِيَّةِ النِّسْبَةِ فَمُوَجَّهَةٌ، وَما بِهِ البَيانُ جِهَةٌ. فَإِنْ كانَ الحُكْمُ فِي القَضِيَّةِ بِضَرُورَةِ النِّسْبَةِ ما دامَ ذاتُ المَوْضُوعِ فَضَرُورِيَّةٌ مُطْلَقَةٌ، أَوْ ما دامَ وَصْفُهُ فَمَشْرُوطَةٌ عامَّةٌ، أَوْ فِي وَقْتٍ مُعَيَّنٍ فَوَقْتِيَّةٌ مُطْلَقَةٌ، أَوْ غَيْرِ مُعَيَّنٍ فَمُنْتَشِرَةٌ مُطْلَقَةٌ؛ أَوْ بِدَوامِها ما دامَ الذّاتُ فَدائِمَةٌ مُطْلَقَةٌ، أَوْ ما دامَ الوَصْفُ فَعُرْفِيَّةٌ عامَّةٌ؛ أَوْ بِفِعْلِيَّتِها فَالمُطْلَقَةُ العامَّةُ، أَوْ بِعَدَمِ ضَرُورَةِ خِلافِها فَالمُمْكِنَةُ العامَّةُ؛ فَهٰذِهِ بَسائِطُ.

Sometimes the manner of the relation is stated; then the proposition is modalised (muwajjaha), and what states it is the mode (jiha). If the judgement is that the relation is necessary as long as the subject itself exists, it is the absolute necessary (ḍarūriyya muṭlaqa); as long as its description lasts, the general conditional (mashrūṭa ʿāmma); at a set time, the absolute temporal (waqtiyya muṭlaqa); at an unset time, the absolute spread (muntashira muṭlaqa). If it is that the relation lasts as long as the subject itself exists, the absolute perpetual (dāʾima muṭlaqa); as long as the description lasts, the general conventional (ʿurfiyya ʿāmma). If it is that the relation is actual, the general absolute (muṭlaqa ʿāmma); and if it is that its opposite is not necessary, the general possible (mumkina ʿāmma). These are the simple ones.

· с. 8

وَقَدْ تُقَيَّدُ العامَّتانِ وَالوَقْتِيَّتانِ المُطْلَقَتانِ بِاللّادَوامِ الذّاتِيِّ، فَتُسَمَّى المَشْرُوطَةَ الخاصَّةَ، وَالعُرْفِيَّةَ الخاصَّةَ، وَالوَقْتِيَّةَ، وَالمُنْتَشِرَةَ. وَقَدْ تُقَيَّدُ المُطْلَقَةُ العامَّةُ بِاللّاضَرُورَةِ الذّاتِيَّةِ، فَتُسَمَّى الوُجُودِيَّةَ اللّاضَرُورِيَّةَ، أَوْ بِاللّادَوامِ الذّاتِيِّ، وَتُسَمَّى الوُجُودِيَّةَ اللّادائِمَةَ. وَقَدْ تُقَيَّدُ المُمْكِنَةُ العامَّةُ بِلا ضَرُورَةِ الجانِبِ المُوافِقِ أَيْضًا، وَتُسَمَّى المُمْكِنَةَ الخاصَّةَ. وَهٰذِهِ مُرَكَّباتٌ، لِأَنَّ اللّادَوامَ إِشارَةٌ إِلَى مُطْلَقَةٍ عامَّةٍ، وَاللّاضَرُورَةَ إِشارَةٌ إِلَى مُمْكِنَةٍ عامَّةٍ، مُخالِفَتَيِ الكَيْفِيَّةِ، مُوافِقَتَيِ الكَمِّيَّةِ لِما قُيِّدَ بِهِما.

The two general ones and the two absolute temporals are sometimes restricted by “not perpetually as long as the subject itself exists” (lā dawām dhātī); they are then called the special conditional, the special conventional, the temporal and the spread. The general absolute is sometimes restricted by “not necessarily as long as the subject itself exists” (lā ḍarūra dhātiyya), and is then called the non-necessary existential; or by “not perpetually”, and is then called the non-perpetual existential. The general possible is sometimes restricted by the non-necessity of the matching side as well, and is called the special possible. These are compounds, because “not perpetually” points to a general absolute, and “not necessarily” to a general possible, differing in quality and agreeing in quantity with what they restrict.

· с. 8–9

فَصْلٌ فِي أَقْسامِ الشَّرْطِيَّةِ

الشَّرْطِيَّةُ مُتَّصِلَةٌ إِنْ حُكِمَ فِيها بِثُبُوتِ نِسْبَةٍ عَلَى تَقْدِيرِ أُخْرَى أَوْ نَفْيِها، لُزُومِيَّةٌ إِنْ كانَ ذٰلِكَ لِعَلاقَةٍ، وَإِلّا فَاتِّفاقِيَّةٌ؛ وَمُنْفَصِلَةٌ إِنْ حُكِمَ فِيها بِتَنافِي نِسْبَتَيْنِ أَوْ لا تَنافِيهِما، صِدْقًا وَكَذِبًا وَهِيَ الحَقِيقِيَّةُ، أَوْ صِدْقًا فَقَطْ فَمانِعَةُ الجَمْعِ، أَوْ كَذِبًا فَقَطْ فَمانِعَةُ الخُلُوِّ، وَكُلٌّ مِنْها عِنادِيَّةٌ إِنْ كانَ التَّنافِي لِذاتِ الجُزْأَيْنِ، وَإِلّا فَاتِّفاقِيَّةٌ. ثُمَّ الحُكْمُ فِي الشَّرْطِيَّةِ إِنْ كانَ عَلَى جَمِيعِ التَّقادِيرِ لِلمُقَدَّمِ فَكُلِّيَّةٌ، أَوْ بَعْضِها مُطْلَقًا فَجُزْئِيَّةٌ، أَوْ مُعَيَّنًا فَشَخْصِيَّةٌ، وَإِلّا فَمُهْمَلَةٌ. وَطَرَفا الشَّرْطِيَّةِ فِي الأَصْلِ قَضِيَّتانِ، حَمْلِيَّتانِ أَوْ مُتَّصِلَتانِ أَوْ مُنْفَصِلَتانِ أَوْ مُخْتَلِفَتانِ، إِلّا أَنَّهُما خَرَجَتا بِزِيادَةِ أَداةِ الاتِّصالِ وَالانْفِصالِ عَنِ التَّمامِ.

A conditional is connective (muttaṣila) if it judges that a relation holds, or does not hold, on the supposition of another: implicative (luzūmiyya) if this is because of a link, otherwise coincidental (ittifāqiyya). It is disjunctive (munfaṣila) if it judges that two relations exclude each other, or do not: in truth and in falsehood, and that is the real disjunctive; in truth only, the one that bars joining (māniʿat al-jamʿ); in falsehood only, the one that bars lacking both (māniʿat al-khulūw). Each of these is oppositional (ʿinādiyya) if the exclusion is due to the very parts, otherwise coincidental. The judgement in a conditional is universal if it holds on every supposition of the antecedent; particular if on some of them without specifying; singular if on a specified one; otherwise indefinite. The two sides of a conditional are in origin two propositions — two categoricals, two connectives, two disjunctives or of different kinds — but they have ceased to be complete by the addition of the particle of connection or disjunction.

· с. 9

فَصْلٌ فِي التَّناقُضِ

التَّناقُضُ اخْتِلافُ قَضِيَّتَيْنِ بِحَيْثُ يَلْزَمُ لِذاتِهِ مِنْ صِدْقِ كُلٍّ كَذِبُ الأُخْرَى وَبِالعَكْسِ، وَلا بُدَّ مِنَ الاخْتِلافِ فِي الكَيْفِ وَالكَمِّ وَالجِهَةِ، وَالاتِّحادِ فِيما عَداها. وَالنَّقِيضُ لِلضَّرُورِيَّةِ المُمْكِنَةُ العامَّةُ، وَلِلدّائِمَةِ المُطْلَقَةُ العامَّةُ، وَلِلمَشْرُوطَةِ العامَّةِ الحِينِيَّةُ المُمْكِنَةُ، وَلِلعُرْفِيَّةِ العامَّةِ الحِينِيَّةُ المُطْلَقَةُ، وَلِلمُرَكَّبِ المَفْهُومُ المُرَدَّدُ بَيْنَ نَقِيضَيِ الجُزْأَيْنِ، لٰكِنْ فِي الجُزْئِيَّةِ بِالنِّسْبَةِ إِلَى كُلِّ فَرْدٍ.

Contradiction (tanāquḍ) is a difference between two propositions such that, by itself, the truth of each entails the falsehood of the other, and the other way round. They must differ in quality, quantity and mode, and agree in everything else. The contradictory of the necessary is the general possible; of the perpetual, the general absolute; of the general conditional, the possible while-described (ḥīniyya mumkina); of the general conventional, the absolute while-described (ḥīniyya muṭlaqa); and of a compound, the concept that alternates between the contradictories of its two parts — but in the particular, with respect to each individual.

· с. 9–10

فَصْلٌ

العَكْسُ المُسْتَوِي تَبْدِيلُ طَرَفَيِ القَضِيَّةِ مَعَ بَقاءِ الصِّدْقِ وَالكَيْفِ. وَالمُوجِبَةُ إِنَّما تَنْعَكِسُ جُزْئِيَّةً لِجَوازِ عُمُومِ المَحْمُولِ أَوِ التّالِي، وَالسّالِبَةُ الكُلِّيَّةُ تَنْعَكِسُ كُلِّيَّةً، وَإِلّا لَزِمَ سَلْبُ الشَّيْءِ عَنْ نَفْسِهِ، وَالجُزْئِيَّةُ لا تَنْعَكِسُ أَصْلًا لِجَوازِ عُمُومِ المَوْضُوعِ أَوِ المُقَدَّمِ.

Simple conversion (al-ʿaks al-mustawī) is exchanging the two sides of a proposition while truth and quality remain. The affirmative converts only as a particular, because the predicate or the consequent may be more general. The universal negative converts as a universal, or else a thing would be denied of itself. The particular negative does not convert at all, because the subject or the antecedent may be more general.

· с. 10

وَأَمّا بِحَسَبِ الجِهَةِ، فَمِنَ المُوجِباتِ تَنْعَكِسُ الدّائِمَتانِ وَالعامَّتانِ حِينِيَّةً مُطْلَقَةً، وَالخاصَّتانِ حِينِيَّةً لا دائِمَةً، وَالوَقْتِيَّتانِ وَالوُجُودِيَّتانِ وَالمُطْلَقَةُ العامَّةُ مُطْلَقَةً عامَّةً، وَلا عَكْسَ لِلمُمْكِنَتَيْنِ. وَمِنَ السَّوالِبِ تَنْعَكِسُ الدّائِمَتانِ دائِمَةً، وَالعامَّتانِ عُرْفِيَّةً عامَّةً، وَالخاصَّتانِ عُرْفِيَّةً لا دائِمَةً فِي البَعْضِ، وَالبَيانُ فِي الكُلِّ أَنَّ نَقِيضَ العَكْسِ مَعَ الأَصْلِ يُنْتِجُ المُحالَ، وَلا عَكْسَ لِلبَواقِي بِالنَّقْضِ.

As for the modes: among the affirmatives, the two perpetuals and the two generals convert as an absolute while-described; the two specials as a non-perpetual while-described; the two temporals, the two existentials and the general absolute as a general absolute; and the two possibles do not convert. Among the negatives, the two perpetuals convert as a perpetual; the two generals as a general conventional; the two specials as a conventional non-perpetual in part. The proof throughout is that the contradictory of the converse, together with the original, yields an absurdity; and the rest do not convert, as counter-examples show.

· с. 10

فَصْلٌ

عَكْسُ النَّقِيضِ تَبْدِيلُ نَقِيضَيِ الطَّرَفَيْنِ مَعَ بَقاءِ الصِّدْقِ وَالكَيْفِ، أَوْ جَعْلُ نَقِيضِ الثّانِي أَوَّلًا مَعَ مُخالَفَةِ الكَيْفِ. وَحُكْمُ المُوجِباتِ هٰهُنا حُكْمُ السَّوالِبِ فِي العَكْسِ المُسْتَوِي، وَبِالعَكْسِ، وَالبَيانُ البَيانُ، وَالنَّقْضُ النَّقْضُ، وَبُيِّنَ انْعِكاسُ الخاصَّتَيْنِ مِنَ المُوجِبَةِ الجُزْئِيَّةِ هٰهُنا، وَالسّالِبَةِ الجُزْئِيَّةِ ثَمَّةَ، إِلَى العُرْفِيَّةِ الخاصَّةِ.

Contraposition (ʿaks al-naqīḍ) is exchanging the contradictories of the two sides while truth and quality remain; or putting the contradictory of the second first, with a change of quality. The rule for the affirmatives here is the rule for the negatives in simple conversion, and the other way round; the proof is the same proof and the counter-example the same counter-example. It has been shown that the two specials, from the particular affirmative here and from the particular negative there, convert as a special conventional.

· с. 11

فَصْلٌ فِي القِياسِ

القِياسُ قَوْلٌ مُؤَلَّفٌ مِنْ قَضايا يَلْزَمُ لِذاتِهِ قَوْلٌ آخَرُ، فَإِنْ كانَ مَذْكُورًا فِيهِ بِمادَّتِهِ وَهَيْئَتِهِ فَاسْتِثْنائِيٌّ، وَإِلّا فَاقْتِرانِيٌّ، حَمْلِيٌّ أَوْ شَرْطِيٌّ. وَمَوْضُوعُ المَطْلُوبِ مِنَ الحَمْلِيِّ يُسَمّى أَصْغَرَ، وَمَحْمُولُهُ أَكْبَرَ، وَالمُكَرَّرُ أَوْسَطَ، وَما فِيها الأَصْغَرُ الصُّغْرَى، وَالأَكْبَرُ الكُبْرَى، وَالهَيْئَةُ شَكْلًا.

The syllogism (qiyās) is a statement composed of propositions from which, by itself, another statement follows. If that statement is mentioned in it in its matter and its form, it is repetitive (istithnāʾī); otherwise it is conjunctive (iqtirānī), categorical or conditional. In the categorical, the subject of what is sought is called the minor term, its predicate the major term, and the repeated term the middle term; the premise containing the minor term is the minor premise, the one containing the major the major premise, and the arrangement the figure (shakl).

· с. 11

وَالأَوْسَطُ إِمّا مَحْمُولُ الصُّغْرَى مَوْضُوعُ الكُبْرَى، وَهُوَ الشَّكْلُ الأَوَّلُ، أَوْ مَحْمُولُهُما فَالثّانِي، أَوْ مَوْضُوعُهُما فَالثّالِثُ، أَوْ عَكْسُ الأَوَّلِ فَالرّابِعُ.

The middle term is either the predicate of the minor premise and the subject of the major, which is the first figure; or the predicate of both, the second; or the subject of both, the third; or the reverse of the first, the fourth.

· с. 11–12

وَيُشْتَرَطُ فِي الأَوَّلِ إِيجابُ الصُّغْرَى وَفِعْلِيَّتُها، وَكُلِّيَّةُ الكُبْرَى، لِيُنْتِجَ المُوجِبَتانِ مَعَ المُوجِبَةِ المُوجِبَتَيْنِ، وَمَعَ السّالِبَةِ السّالِبَتَيْنِ بِالضَّرُورَةِ.

In the first figure the minor premise must be affirmative and actual, and the major universal, so that the two affirmatives, with the affirmative, yield the two affirmatives, and with the negative the two negatives — self-evidently.

· с. 11–12

وَفِي الثّانِي اخْتِلافُهُما فِي الكَيْفِ وَكُلِّيَّةُ الكُبْرَى، إِمّا مَعَ دَوامِ الصُّغْرَى، أَوِ انْعِكاسِ سالِبَةِ الكُبْرَى، وَكَوْنُ المُمْكِنَةِ مَعَ ضَرُورِيَّةٍ أَوْ مَعَ كُبْرَى مَشْرُوطَةٍ، لِيُنْتِجَ الكُلِّيَّتانِ سالِبَةً كُلِّيَّةً، وَالمُخْتَلِفَتانِ فِي الكَمِّ أَيْضًا سالِبَةً جُزْئِيَّةً، بِالخُلْفِ أَوْ عَكْسِ الكُبْرَى، أَوِ التَّرْتِيبِ ثُمَّ النَّتِيجَةِ.

In the second, the two must differ in quality and the major must be universal; with the perpetuity of the minor, or the convertibility of the negative major; and the possible must go with a necessary, or with a conditional major. Then the two universals yield a universal negative, and the two that differ in quantity as well a particular negative — shown by reductio (khulf), by converting the major, or by changing the order and then the conclusion.

· с. 12

وَفِي الثّالِثِ إِيجابُ الصُّغْرَى وَفِعْلِيَّتُها مَعَ كُلِّيَّةِ إِحْداهُما، لِيُنْتِجَ المُوجِبَتانِ مَعَ المُوجِبَةِ أَوْ بِالعَكْسِ مُوجِبَةً جُزْئِيَّةً، أَوْ مَعَ السّالِبَةِ الكُلِّيَّةِ أَوِ الكُلِّيَّةُ مَعَ الجُزْئِيَّةِ سالِبَةً جُزْئِيَّةً، بِالخُلْفِ أَوْ عَكْسِ الصُّغْرَى، أَوْ عَكْسِ التَّرْتِيبِ ثُمَّ النَّتِيجَةِ.

In the third, the minor must be affirmative and actual, with one of the two universal. Then the two affirmatives — a universal with a particular or the reverse — yield a particular affirmative; and with the universal negative, or the universal with the particular, a particular negative — shown by reductio, by converting the minor, or by reversing the order and then the conclusion.

· с. 12

وَفِي الرّابِعِ إِيجابُهُما مَعَ كُلِّيَّةِ الصُّغْرَى، أَوِ اخْتِلافُهُما مَعَ كُلِّيَّةِ إِحْداهُما، لِيُنْتِجَ المُوجِبَةُ الكُلِّيَّةُ مَعَ الأَرْبَعِ، وَالجُزْئِيَّةُ مَعَ السّالِبَةِ الكُلِّيَّةِ، وَالسّالِبَتانِ مَعَ المُوجِبَةِ الكُلِّيَّةِ، وَكُلِّيَّتُهُما مَعَ المُوجِبَةِ الجُزْئِيَّةِ، مُوجِبَةً جُزْئِيَّةً إِنْ لَمْ يَكُنْ سَلْبٌ، وَإِلّا فَسالِبَةً، بِالخُلْفِ أَوْ بِعَكْسِ التَّرْتِيبِ ثُمَّ النَّتِيجَةِ، أَوْ بِعَكْسِ المُقَدِّمَتَيْنِ، أَوْ بِالرَّدِّ إِلَى الثّانِي بِعَكْسِ الصُّغْرَى، أَوِ الثّالِثِ بِعَكْسِ الكُبْرَى.

In the fourth, both must be affirmative with the minor universal, or differ with one of them universal. Then the universal affirmative with the four, the particular with the universal negative, the two negatives with the universal affirmative, and their universal with the particular affirmative, yield a particular affirmative if there is no negation, and otherwise a negative — shown by reductio, by reversing the order and then the conclusion, by converting both premises, or by reduction to the second figure by converting the minor, or to the third by converting the major.

· с. 12

فَصْلٌ

الشَّرْطِيُّ مِنَ الاقْتِرانِيِّ إِمّا أَنْ يَتَرَكَّبَ مِنَ المُتَّصِلَتَيْنِ، أَوِ المُنْفَصِلَتَيْنِ، أَوْ مِنْ حَمْلِيَّةٍ وَمُتَّصِلَةٍ، أَوْ حَمْلِيَّةٍ وَمُنْفَصِلَةٍ، أَوْ مُتَّصِلَةٍ وَمُنْفَصِلَةٍ، وَتَنْعَقِدُ فِيهِ الأَشْكالُ الأَرْبَعَةُ، وَفِي تَفْصِيلِها طُولٌ.

The conditional among the conjunctive syllogisms is composed of two connectives, or two disjunctives, or of a categorical and a connective, or a categorical and a disjunctive, or a connective and a disjunctive. The four figures arise in it, and setting them out in detail would be long.

· с. 13

فَصْلٌ

الاسْتِثْنائِيُّ يُنْتِجُ مِنَ المُتَّصِلَةِ وَضْعُ المُقَدَّمِ وَرَفْعُ التّالِي، وَمِنَ الحَقِيقِيَّةِ وَضْعُ كُلٍّ كَمانِعَةِ الجَمْعِ، وَرَفْعُهُ كَمانِعَةِ الخُلُوِّ. وَقَدْ يُخَصُّ بِاسْمِ قِياسِ الخُلْفِ ما يُقْصَدُ بِهِ إِثْباتُ المَطْلُوبِ بِإِبْطالِ نَقِيضِهِ، وَمَرْجِعُهُ إِلَى اسْتِثْنائِيٍّ وَاقْتِرانِيٍّ.

The repetitive syllogism yields, from the connective, the affirming of the antecedent and the denying of the consequent; from the real disjunctive, affirming either, as in the one that bars joining, and denying it, as in the one that bars lacking both. The name “reductio syllogism” (qiyās al-khulf) is sometimes reserved for one meant to prove what is sought by refuting its contradictory; it comes down to a repetitive and a conjunctive syllogism.

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فَصْلٌ

الاسْتِقْراءُ تَصَفُّحُ الجُزْئِيّاتِ لِإِثْباتِ حُكْمٍ كُلِّيٍّ، وَالتَّمْثِيلُ بَيانُ مُشارَكَةِ جُزْئِيٍّ لِآخَرَ فِي عِلَّةِ الحُكْمِ لِيَثْبُتَ فِيهِ، وَالعُمْدَةُ فِي طَرِيقِهِ الدَّوَرانُ وَالتَّرْدِيدُ.

Induction (istiqrāʾ) is going through the particulars to establish a universal judgement. Analogy (tamthīl) is showing that one particular shares with another the cause of the judgement, so that the judgement holds of it; the mainstay of its method is concomitance (dawarān) and sifting (tardīd).

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