Arabic: al-Mirqāt, with al-Shīrkūtī's gloss al-Mirʾāt (gloss not reproduced), checked against the Delhi print of 1286/1869 (Sayyid al-Maṭābiʿ); vowel marks added by The Mantiqi (draft), Kutub Khāna Iʿzāziyya, Deoband after 1336/1917 View the scan
Translation
The Mantiqi's own; a draft.
Review
Draft, awaiting review by Ustadh Muhammad Yusuf.
Draft · translation awaiting review
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Introduction (al-muqaddima)
المُقَدِّمَةُ
Lesson 1 · The opening: knowledge, conception and assent
Praise be to God, who originated the celestial spheres and the earths. Blessings be upon him who was a prophet while Adam was still between water and clay, and upon his family and his companions, all of them.
To proceed: these are a number of chapters on the science of the balance (ʿilm al-mīzān) which anyone of understanding who wishes to take heed must memorise and master. In God is our trust, and He is the one whose help is sought.
Know that the word “” (ʿilm) is used in several senses. The first is the occurrence of a thing's form in the intellect. The second is the form of the thing that has occurred with the intellect. The third is what is present to the one who grasps it. The fourth is the soul's receiving that form. The fifth is the relation that comes about between the knower and the known. Knowledge is divided into two kinds: one is called (taṣawwur), and the other is expressed as (taṣdīq). Conception is a grasp free of judgement (ḥukm). By judgement is meant relating one thing to another affirmatively or negatively; or, if you like, positing [the relation] or removing it. Judgement is also sometimes explained as [grasping] that the relation obtains or does not obtain. [Conception is] as when you conceive Zayd alone, or standing alone, without affirming standing of Zayd or denying it of him. As for assent, according to the philosophers (ḥukamāʾ) it is the judgement accompanied by conceptions; so the three conceptions are a condition for the existence of assent, and for this reason there is no assent without conception. Imām al-Rāzī, however, says that it is the sum of the judgement and the conceptions of the [two] sides. So when you say “Zayd is standing” and accept that Zayd is standing, three pieces of knowledge come to you. The first is the knowledge of Zayd; the second is the grasp of the meaning of “standing”; and the third is the knowledge of the linking meaning, which is expressed in Persian by “hast” [“is”] in and “nīst” [“is not”] in , and in Hindi [Urdu] by “ہے” (hai, “is”) and “نہیں” (nahīṉ, “not”). This meaning is sometimes called the judgement and at other times the relation of judgement (al-nisba al-ḥukmiyya). Once you have mastered what we have taught you, know that the philosopher holds that assent is nothing but the grasp of the linking meaning, while the Imām holds that assent is the sum of the three grasps, I mean the conception of what is judged about, the conception of what is judged of it, and the grasp of the relation of judgement, which is called the judgement.
is of two kinds. One is (badīhī), that is, attained without and effort, like our conception of heat and cold; it is also called ḍarūrī (“necessary”). The other is (naẓarī), that is, it needs thinking and reflection in order to be attained, like our conception of the jinn and the angels: for conceptions such as these we need to take the trouble of thinking and to arrange a reflection. It is also called kasbī (“earned”). too is of two kinds. One is immediate, that is, attained without thinking and effort; the other is acquired, which needs them. Examples of the first are “The whole is greater than the part” and “Two is half of four”; examples of the second are “The world has come into being (ḥādith)” and “The Maker exists”, and the like.
Now that you know, from what we have said, that things in general, whether or , need and thinking, you must know what reflection means. So I say: reflection (naẓar), in their technical usage, is arranging known things so that this arrangement leads to obtaining what is unknown. [It is] as when you arrange the known things you have, namely that the world changes and that everything that changes has come into being, and say: “The world changes, and everything that changes has come into being.” From this reflection and arrangement you obtain of another , which you did not have before, namely “The world has come into being.”
Beware of thinking that every arrangement is correct and leads to sound . How could that be? If things were so, there would be no disagreement and among the people of ; yet there is. One person says “The world has come into being” and argues for it by saying: “The world changes, and everything that changes has come into being; so the world has come into being.” Another claims that the world is eternal (qadīm), not preceded by non-existence, and offers as proof: “The world has no need of anything to bring it about, and everything of this kind is eternal.” I do not think you doubt that one of these two thoughts is sound and true and the other corrupt and mistaken. And since error has occurred in the thinking of rational people, we learn from this that human nature is not enough to tell error from what is correct, or the husk from the kernel. So there arose a need for a rule (qānūn) that protects from error in thinking, in which the ways of acquiring unknown things from known things are set out. This rule is (manṭiq), also called the balance (mīzān). It is called logic (manṭiq) because of its effect on outward speech (nuṭq), I mean speaking: whoever knows it is able to speak in a way that the ignorant cannot. Likewise [because of its effect] on inward speech, I mean grasping: for the logician knows the of things, and knows their genera, their differentiae, their , their concomitants and their , unlike someone who neglects this noble science. It is called the balance (mīzān) because it is a scale for the intellect: by it sound thoughts are weighed, and by it one recognises what is deficient in corrupt thoughts and what is faulty in worthless reflections. For this reason it is called the instrumental science (al-ʿilm al-ālī), since it is an instrument for all the sciences, especially the philosophical sciences.
· p. 5
Lesson 2 · Logic: its founder, definition, subject and aim
Know that the philosopher Aristotle set this science down in writing at the command of Alexander the Greek (al-Iskandar al-Rūmī); this is why he is given the title “the First Teacher”. Al-Fārābī refined this discipline, and he is the Second Teacher. After al-Fārābī's books were lost, the Shaykh Abū ʿAlī ibn Sīnā set it out in detail.
Perhaps you have already learned, from what we recited to you in explaining the need [for ], its and its : it is a science of rules whose observance protects the mind from error in thinking.
The (mawḍūʿ) of any science is that whose accidents (ʿawāriḍ dhātiyya) are investigated in it, like the human body for medicine, and the word and the sentence for grammar. So the subject of is known things, those of and those of ; not absolutely, however, but insofar as they lead to the unknown, whether of conception or of assent.
Know that every science and every craft has an aim (ghāya); otherwise seeking it would be pointless and striving in it idle. The aim of the science of the balance is to be right in thinking and to keep one's judgement from error in .
The , insofar as he is a logician, has no business with investigating . How could he, when this investigation lies far from his purpose and aim? Even so, utterances that signify meanings must be investigated, because conveying to others and receiving it from them depends on this. That is why the discussion of and of utterances comes in books of logic.
(dalāla) in language is guidance; in technical usage it is a thing's being in such a state that knowing it entails knowing something else. Signification is of two kinds, verbal and non-verbal. Verbal signification is that in which the signifier is an ; non-verbal is that in which the signifier is not an utterance. Each of the two is of three kinds, [which gives six]. The first is verbal conventional signification, like the word “Zayd” signifying the one named by it. The second is verbal natural signification, like the word “uḥ” (with a ḍamma on the hamza and the undotted ḥāʾ without a vowel; some say with a fatḥa) signifying pain in the chest: for nature compels one to produce this sound when pain comes on in the chest. The third is verbal rational signification, like the word “dayz”, heard from behind a wall, signifying the existence of someone who uttered it. The fourth is non-verbal conventional signification, like the four signifiers [writing, gestures, finger-knots and markers] signifying what they signify. The fifth is non-verbal natural signification, like a horse's neighing signifying that it wants water and fodder. The sixth is non-verbal rational signification, like smoke signifying fire. These are six kinds of signification. The investigates only verbal conventional signification, because only through it can be conveyed to others and received from them with ease; unlike the others, for conveying and receiving knowledge through them is not free of difficulty.
You should know that verbal conventional , which is what counts in the discourse of the sciences, is of three kinds. The first is by (muṭābaqa): the signifies the whole of what it was coined for, like “human” signifying “animal” and “rational” together. The second is by (taḍammun): the utterance signifies a part of the meaning for which it was coined, like its signifying “animal” only or “rational” only. The third is signification by (iltizām): the utterance signifies neither what it was coined for nor a part of it, but a meaning outside it that is concomitant (lāzim) with what it was coined for. The concomitant is that to which the mind passes from what [the utterance] was coined for, like “human” signifying “capable of and of the craft of writing”, and like the word “blindness” signifying sight.
by and by do not occur without . This is because the part is not without the whole, nor likewise the concomitant without what it accompanies (malzūm); and what follows does not exist without what it follows. Correspondence, however, may occur without the two, since an may be coined for a meaning that has no part and no concomitant. If you say: we do not grant that there is a meaning that has no concomitant, for every meaning certainly has a concomitant, the least of which is that it is “not other than itself”; we reply: by the concomitant is meant the evident concomitant (al-lāzim al-bayyin), to which the mind passes from what it accompanies. Your “not other than itself” is not one of the evident concomitants, for we often conceive meanings without the meaning of “other” even occurring to us, let alone its being “not other than itself”.
A signifying is either or composite. A simple utterance (mufrad) is one whose part is not meant to signify a part of its meaning, like the interrogative hamza signifying its meaning, “Zayd” signifying the one named by it, and “ʿAbd Allāh” signifying its meaning as a proper name. A (murakkab) is one whose part is meant to signify a part of its meaning, like “Zayd is standing” signifying its meaning and “thrower of the arrow” signifying what it conveys. Next, the simple utterance is of three kinds. For if its meaning is independent in being understood, that is, if understanding it does not need anything joined to it, then it is a noun (ism) if that meaning is not tied to one of the three times, and a kalima [the ' verb] if it is tied to one. If its meaning is not independent, it is a tool (adāt) in the usage of the logicians and a particle (ḥarf) in the technical usage of the grammarians. Mark this.
Know that some have thought that the kalima, for the , is what is called the verb (fiʿl) in grammar. This view is not right, because the verb is more general than the kalima. Do you not see that a form like “aḍribu” (“I strike”) or “naḍribu” (“we strike”) and the like is a verb for the grammarians but not a kalima for the logicians? For the kalima is one of the kinds of , while “aḍribu”, for example, is not simple but composite, since a part of the signifies a part of the meaning: the hamza signifies the speaker, and “ḍaraba” the meaning of the act.
The is sometimes divided in another way: its meaning is either one or many. What has one meaning is of three kinds, because that meaning must either be determinate and individuated or not. The first is called a proper name (ʿalam), like “Zayd”, “this” and “he”; it is more fitting to call this kind the real (al-juzʾī al-ḥaqīqī). The second, whose one meaning is not individuated but has many individuals, is of two kinds. In the first, that meaning is true of all its individuals equally, without differing by priority, by greater fittingness, by greater intensity or by greater amount. This kind is called univocal (mutawāṭiʾ), because its individuals agree (tawāṭuʾ) and concur in that general meaning's being true of them, like “human” relative to Zayd, ʿAmr and Bakr. In the second, that general meaning is not true of all its individuals equally: it is true of some individuals with priority, greater intensity or greater fittingness, and of the others with the opposite of these, like “existence” relative to the Necessarily Existent, glorious is His majesty, and relative to the possible, and like “whiteness” relative to snow and ivory. This kind is called graded (mushakkik), because it puts the one who considers it into doubt (shakk) whether it is univocal or homonymous.
An with many meanings has several kinds. The reasoning behind the division is this. If an utterance that has many meanings was coined for each meaning from the start, by several separate acts of coining, it is called homonymous (mushtarak), like “ʿayn”, which was coined once for gold, once for the eye and once for the knee. If it was not coined for each from the start, but was first coined for one meaning and then used for a second meaning because of some affinity between the two, then, if it became well known in the second and its first meaning was abandoned, it is called transferred (manqūl). With respect to who transferred it, the transferred utterance is divided into three kinds. The first is the customary transferred utterance, the transferrer being general usage; the second is the legal transferred utterance, the transferrer being the authorities of the Sacred Law; and the third is the technical transferred utterance, the transferrer being a usage, a specific group. An example of the first is the word “dābba”: it was originally coined for whatever creeps (yadibbu) on the earth, and then common people transferred it to the horse, or to four-legged animals. An example of the second is the word “ṣalāh”: it originally meant supplication, and then the Lawgiver transferred it to the specific set of acts (arkān) [of the prayer]. An example of the third is the word “ism”: in the language it meant elevation (ʿuluww), and then the grammarians transferred it to a word that signifies independently and is not tied to any of the three times. If it did not become well known in the second meaning and the first was not abandoned, but it is used now for the first meaning and now for the second, it is called literal (ḥaqīqa) with respect to the first and figurative (majāz) with respect to the second. An example is “asad” (“lion”) relative to the predatory animal and the brave man: with respect to the first it is literal, and with respect to the second it is figurative.
المُرَكَّبُ قِسْمانِ: أَحَدُهُما المُرَكَّبُ التّامُّ، وَهُوَ ما يَصِحُّ السُّكُوتُ عَلَيْهِ، كَـ«زَيْدٌ قائِمٌ»؛ وَثانِيهِما المُرَكَّبُ النّاقِصُ، وَهُوَ ما لَيْسَ كَذٰلِكَ.
The is of two kinds. One is the complete composite (murakkab tāmm), after which one may rightly fall silent, like “Zayd is standing”; the other is the incomplete composite (murakkab nāqiṣ), which is not so.
The complete composite is of two kinds. One of them is called a report (khabar) and a (qaḍiyya): it is what is meant as an account [of how things are], and it admits of truth and falsity, so that it may be said of the one who says it that he speaks truly or falsely, as in “The sky is above us” and “The world has come into being.” If it is said: our statement “There is no god but God” is a proposition and a report, yet it does not admit of falsity; I reply: the taken by itself admits [of falsity], even if, in view of the specific nature of its two sides, it does not admit of falsity. The second of the two kinds is called non-declarative (inshāʾ), and the non-declarative has several kinds: command, prohibition, wish, hope, question and calling [someone].
The incomplete composite is of several kinds. Among them are the possessive composite (murakkab iḍāfī), like “Zayd's servant” (ghulām Zayd); the descriptive composite (murakkab tawṣīfī), like “the learned man”; and the restrictive composite (murakkab taqyīdī), like “in the house”. Here the discussion of is complete, and now we begin the discussion of meanings.
· p. 14
Lesson 6 · Particular and universal, and the relations between universals
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 (mafhūm), that is, what is attained in the mind, is of two kinds: one is , the other . 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.
The 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 , 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 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 '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.
Know that the relation between two can be 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 : equivalence, mutual exclusion, generality and specificity absolutely, and generality and specificity in some respect. Remember this well.
“” is sometimes used in another sense: what is more specific, falling under something more general. On this 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.
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Lesson 7 · Genus and species, and how they are ordered
The are five. The first [is the ]: a universal said of many that differ in their , in answer to “what is it?”, like animal. It is said of human, horse and sheep when they are asked about with “what is it?”: one says “Human and horse, what are they?”, and the answer is: animal.
The second is the : a said of many that agree in their , in answer to “what is it?”. The species also has another sense, and in that sense it is called the relative species: a of which, and of something else, the is said in answer to “what is it?”. Between the real species and the relative species there is generality and specificity in some respect: both are true of human; the real is true without the relative in the point; and the relative is true without the real in animal.
A is either lowest: one that has no genus beneath it but has a genus above it, with only a beneath it, like animal, for beneath it is human, which is a species, and above it is growing body, which is a genus, so animal is a lowest genus; or intermediate: one that has a genus beneath it and also a genus above it, like growing body, for beneath it is animal and above it is body as such; or highest: one that has no genus above it, and it is also called the genus of genera, like substance, for there is no genus above it, and beneath it are body as such, growing body and animal.
The highest genera are ten, and there is nothing in the world that falls outside these genera. These highest genera are also called the ten categories (al-maqūlāt al-ʿashr). One of them is substance (jawhar), and the remaining nine categories belong to accident (ʿaraḍ). Substance is what exists not in a (mawḍūʿ), that is, a substrate (maḥall), but subsists by itself, like bodies; and accident is what exists in a subject, that is, a substrate. The categories are: quantity (kamm), quality (kayf), relation (iḍāfa), where (ayn), possession (milk), action (fiʿl), passion (infiʿāl), when (matā) and position (waḍʿ). This Persian verse gathers them:
“مردی دراز نیکو دیدم بشهر امروز * با خواسته نشسته از کردِ خویش فیروز” [“Today in the city I saw a tall, handsome man, sitting with his riches, triumphant through his own deeds”]
Know that are sometimes arranged in descending order. A species may have a species beneath it and no species above it: this is the highest species. It may have a species beneath it and a species above it: this is the intermediate species. Or it may have no species beneath it and a species above it: this is the lowest species, which is also called the species of species.
The third is the : a said of a thing in answer to “which thing is it in its ?”, as when it is asked “Human: by which thing is it [distinguished] in its essence?” and the answer is that it is rational. It is of two kinds, and . The proximate is what distinguishes [a thing] from what shares its proximate , and the remote is what distinguishes [it] from what shares its remote genus. The first is like rational for human, and the second like sensing for it. The differentia has a relation to the , in which it is called constitutive (muqawwim), because it enters into the make-up (qiwām) and the of the species; and a relation to the genus, in which it is called divisive (muqassim), because it divides the genus and produces a division of it. Take rational: it is constitutive of human, because human is the rational animal; and it is divisive of animal, because through rational animal comes to have two divisions, one the rational animal and the other the non-rational animal.
Whatever is constitutive of the higher is constitutive of the lower. Take “receptive of dimensions”: it is constitutive of body, and so it is constitutive of growing body, animal and human. Or take growing: just as it is constitutive of growing body, it is also constitutive of animal and of human. Or take sensing and moving by will: just as they are constitutive of animal, so they are constitutive of human. But not everything constitutive of the lower is constitutive of the higher: rational is constitutive of human but not constitutive of animal.
Every that is divisive of the lower is divisive of the higher: just as rational divides animal into rational and non-rational, so it divides body as such into these two. But not everything divisive of the higher is divisive of the lower: sensing, for example, divides growing body into the sensing and the non-sensing growing body, but it does not divide animal into these two, for every animal is sensing, and no non-sensing animal exists.
The fourth is the (khāṣṣa): a universal lying outside the of the individuals, of individuals that fall under one reality only, like laughing for human, and writing for it.
The fifth of the is the : the universal lying outside [the ], said of the individuals of one reality and of others too, like walking, which is of the individuals of human and of horse.
Now that you have learned from what we have said that the are five, the first the , the second the , the third the , the fourth the and the fifth the , know that the first three are called the essentials (dhātiyyāt) and the last two the accidentals (ʿaraḍiyyāt). The name “” is sometimes restricted to the genus and the differentia only, and in this usage the word “essential” is not applied to the species.
The , I mean the and the , divides into (lāzim) and (mufāriq). The inseparable is what cannot be separated from the thing. This is either with regard to the , like evenness for four and oddness for three, for the separation of evenness from four and of oddness from three is impossible; or with regard to existence, like blackness for the Abyssinian, for the separation of blackness from the existence of the Abyssinian is impossible, but not from his quiddity, since his quiddity is human, and it is evident that blackness is not inseparable from human. The separable accident is that whose separation from what it accompanies (malzūm) is not impossible, like actual writing for a human, and actual walking for him.
The is of two kinds. The first is one whose follows from the conception of what it accompanies (malzūm), like sight for blindness. The second is one where conceiving what it accompanies and conceiving the inseparable [accident] itself entail certainty of the inseparability, like evenness for four: whoever conceives four and conceives the concept of evenness is certain, immediately, that four is even and divisible into two equal parts.
The , I mean what can be separated from what it attaches to (maʿrūḍ), is also of two kinds. One is that whose attaching to what it accompanies is permanent, like motion for the celestial sphere. The second is that which passes away from it, either quickly, like the redness of embarrassment and the pallor of fear, or slowly, like grey hair and youth.
The definer (muʿarrif) of a thing is what is of it to convey a of it. It is of four kinds: the complete (ḥadd tāmm), the incomplete essential definition (ḥadd nāqiṣ), the complete (rasm tāmm) and the incomplete descriptive definition (rasm nāqiṣ). If the is by the and the proximate , it is called a complete essential definition, like defining human as rational animal. If it is by the genus and the proximate differentia, or by the latter alone, it is called an incomplete essential definition. If it is by the proximate genus and the , it is called a complete descriptive definition. If it is by the remote genus and the proprium, or by the proprium alone, it is called an incomplete descriptive definition. An example of the incomplete essential definition is defining human as rational body, or as rational only; of the complete descriptive definition, defining human as laughing animal; and of the incomplete descriptive definition, defining it as laughing body, or as laughing alone. The has no place in definitions, because it does not give distinction.
A is sometimes real (ḥaqīqī), as we have described, and sometimes verbal (lafẓī): one intended to explain what a word signifies, as when they say “Saʿdāna is a plant” and “Ghaḍanfar is the lion”. With this the discussions of , I mean of the defining statement, are complete.
· p. 22
II
Part two: the argument (al-bāb al-thānī fī al-ḥujja)
البابُ الثّانِي فِي الحُجَّةِ
Lesson 10 · The proposition: kinds, parts and quantity
القَضِيَّةُ قَوْلٌ يَحْتَمِلُ الصِّدْقَ وَالكَذِبَ، وَقِيلَ: هُوَ قَوْلٌ يُقالُ لِقائِلِهِ إِنَّهُ صادِقٌ فِيهِ أَوْ كاذِبٌ. وَهِيَ قِسْمانِ: حَمْلِيَّةٌ وَشَرْطِيَّةٌ؛ أَمّا الحَمْلِيَّةُ فَهُوَ ما حُكِمَ فِيها بِثُبُوتِ شَيْءٍ لِشَيْءٍ أَوْ نَفْيِهِ عَنْهُ، كَقَوْلِكَ: «زَيْدٌ قائِمٌ» وَ«زَيْدٌ لَيْسَ بِقائِمٍ»؛ وَأَمّا الشَّرْطِيَّةُ فَما لا يَكُونُ فِيهِ ذٰلِكَ الحُكْمُ، وَقِيلَ: الشَّرْطِيَّةُ ما يَنْحَلُّ إِلَى قَضِيَّتَيْنِ، كَقَوْلِنا: «إِنْ كانَتِ الشَّمْسُ طالِعَةً فَالنَّهارُ مَوْجُودٌ» وَ«لَيْسَ البَتَّةَ إِذا كانَتِ الشَّمْسُ طالِعَةً فَاللَّيْلُ مَوْجُودٌ»؛ فَإِذا حُذِفَ الأَدَواتُ بَقِيَ «الشَّمْسُ طالِعَةٌ» والنَّهارُ مَوْجُودٌ. والحَمْلِيَّةُ لا يَنْحَلُّ إلى قَضِيَّتَيْنِ، بل يَنْحَلُّ إمّا إلى مُفْرَدَيْنِ كقَوْلِكَ: «زَيْدٌ هو قائِمٌ»، فإنّكَ إذا حَذَفْتَ الرّابِطَةَ أعني «هو» بَقِيَ «زَيْدٌ» و«قائِمٌ» وهما مُفْرَدانِ؛ وإمّا إلى مُفْرَدٍ وقَضِيَّةٍ كما في قَوْلِكَ: «زَيْدٌ أبُوهُ قائِمٌ»، فإذا حَلَّلْتَهُ بَقِيَ «زَيْدٌ» وهو مُفْرَدٌ، و«أبُوهُ قائِمٌ» وهو قَضِيَّةٌ.
A is a statement that admits truth and falsehood. It has also been said: it is a statement of whose speaker it is said that he is truthful in it or lying. It is of two kinds, and . The categorical is one in which it is judged that one thing holds of another, or is denied of it, as when you say “Zayd is standing” and “Zayd is not standing”. The conditional is one in which there is no such judgement. It has also been said: the conditional is what resolves into two propositions, as when we say “If the sun has risen, it is day” and “It is never the case that, when the sun has risen, it is night”: if the particles are removed, there remain “the sun has risen” and “it is day”. The categorical does not resolve into two propositions. Rather, it resolves either into two [terms] (mufrad), as when you say “Zayd is standing” (Zayd huwa qāʾim): if you remove the copula, I mean “is” (huwa), there remain “Zayd” and “standing”, and these are two simple [terms]; or into a simple [term] and a proposition, as when you say “Zayd, his father is standing”: when you analyse it, there remain “Zayd”, which is simple, and “his father is standing”, which is a proposition.
الحَمْلِيَّةُ ضَرْبانِ: مُوجَبَةٌ وهي الّتي حُكِمَ فيها بثُبُوتِ شَيْءٍ لشَيْءٍ، وسالِبَةٌ وهي حُكِمَ فيها بنَفْيِ شَيْءٍ عن شَيْءٍ، نحوُ: «الإنْسانُ حَيَوانٌ» و«الإنْسانُ لَيْسَ بفَرَسٍ».
The is of two kinds: , in which it is judged that one thing holds of another, and , in which it is judged that one thing is denied of another, as in “Man is an animal” and “Man is not a horse”.
The is made up of three parts. The first is what is judged about, and it is called the (mawḍūʿ); the second is what is judged of it, and it is called the (maḥmūl); and the third is what signifies the link, and it is called the copula (rābiṭa). So in your saying “Zayd is standing” (Zayd huwa qāʾim), “Zayd” is what is judged about and the subject, “standing” is what is judged of it and the predicate, and the word “is” (huwa, literally “he”) is the relation and the copula. The copula is sometimes dropped in the wording, though not in what is meant, and one says “Zayd standing” (Zayd qāʾim).
The also has parts. Its first part is called the (muqaddam) and its second part the (tālī). So in your saying “If the sun has risen, it is day”, your words “If the sun has risen” are the antecedent, your words “it is day” are the consequent, and the copula is the judgement between the two.
وقد تَنْقَسِمُ القَضِيَّةُ باعْتِبارِ المَوْضُوعِ: فالمَوْضُوعُ إنْ كانَ جُزْئِيًّا وشَخْصًا مُعَيَّنًا سُمِّيَتِ القَضِيَّةُ شَخْصِيَّةً ومَخْصُوصَةً كقَوْلِكَ: «زَيْدٌ قائِمٌ». وإنْ لم يَكُنْ جُزْئِيًّا بل كانَ كُلِّيًّا فهو على أنْحاءٍ؛ لأنّها إنْ كانَ الحُكْمُ فيها على نَفْسِ الحَقِيقَةِ تُسَمّى القَضِيَّةُ طَبْعِيَّةً نحوُ: «الإنْسانُ نَوْعٌ» و«الحَيَوانُ جِنْسٌ»، وإنْ كانَ على أفْرادِها فلا يَخْلُو إمّا أنْ يَكُونَ كَمِّيَّةُ الأفْرادِ فيها مُبَيَّنًا أو لم يَكُنْ، فإنْ بُيِّنَ كَمِّيَّةُ الأفْرادِ تُسَمّى القَضِيَّةُ مَحْصُورَةً كقَوْلِكَ: «كُلُّ إنْسانٍ حَيَوانٌ» و«بَعْضُ الحَيَوانِ إنْسانٌ»، وإنْ لم يُبَيَّنْ تُسَمّى القَضِيَّةُ مُهْمَلَةً نحوُ: «الإنْسانُ في خُسْرٍ».
A is also divided with regard to the . If the subject is a , a specific individual, the proposition is called (shakhṣiyya) or specified (makhṣūṣa), as when you say “Zayd is standing”. If it is not a particular but a , there are several cases. If the judgement in it is about the itself, the proposition is called natural (ṭabʿiyya), as in “Man is a ” and “Animal is a ”. If it is about its individuals, then either the quantity of the individuals is stated in it or it is not. If the quantity of the individuals is stated, the proposition is called (maḥṣūra), as when you say “Every human is an animal” and “Some animal is human”. If it is not stated, the proposition is called (muhmala), as in “Man is in loss” [Qurʾān 103:2].
The are four. The first is the , as when you say “Every human is an animal”; the second the , as in “Some animal is black”; the third the , as in “No Zanjī [black African] is white”; and the fourth the , as in “Some human is not black”.
That by which the quantity of the individuals is stated, whether all or some, is called the (sūr). It is taken from the wall (sūr) of a town. The quantifier of the is “every” (kull) and the lām of comprehensiveness (lām al-istighrāq). That of the is “some” (baʿḍ) and “one” (wāḥid), as in “One of the bodies is inanimate”. That of the is “no” (lā shayʾ) and “not one” (lā wāḥid), as in “No crow is white” and “Not one fire is cold”, and also an noun falling under a , as in “There is no water but it is wet”. That of the is “not some” (laysa baʿḍ), as when you say “Not some animal is a donkey” [that is, some animal is not a donkey], and “some … not” (baʿḍ … laysa), as you say “Some fruit is not sweet”. Know that every language has quantifiers of its own. In Persian, the word “هر” (har) [“every”] is the quantifier of the universal affirmative, as the poet says in a verse: “هر آنکس که در بند حرص اوفتاد * دهد خرمن زندگانی بباد” [“Whoever falls into the bonds of greed gives the harvest of his life to the wind”].
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Lesson 11 · Predication, further divisions and modal propositions
قد جَرَتْ عادَةُ المِيزانِيِّينَ أنّهم يُعَبِّرُونَ عنِ المَوْضُوعِ بـ«ج» وعنِ المَحْمُولِ بـ«ب»، فمَتى أرادُوا التَّعْبِيرَ عنِ المُوجَبَةِ الكُلِّيَّةِ يَقُولُونَ: «كُلُّ ج ب»، ومَقْصُودُهم مِن ذلك الإيجازُ ودَفْعُ تَوَهُّمِ الانْحِصارِ.
The (al-mīzāniyyūn) have made it their custom to express the by J and the by B. So when they want to express the , they say “Every J is B”. Their aim in this is brevity, and to prevent the impression that [the rule] is confined [to one subject matter].
الحَمْلُ في اصْطِلاحِهِمُ اتِّحادُ المُتَغايِرَيْنِ في المَفْهُومِ بحَسَبِ الوُجُودِ؛ فَفي قَوْلِكَ: «زَيْدٌ كاتِبٌ» و«عَمْرٌو شاعِرٌ» مَفْهُومُ «زَيْدٍ» مُغايِرٌ لمَفْهُومِ «كاتِبٍ» لكنّهما مَوْجُودانِ بوُجُودٍ واحِدٍ، وكذا مَفْهُومُ «عَمْرٍو» و«شاعِرٍ» مُتَغايِرانِ وقَدِ اتَّحَدا في الوُجُودِ. ثُمَّ الحَمْلُ على قِسْمَيْنِ؛ لأنّه إنْ كانَ بواسِطَةِ «في» أو «ذُو» أوِ اللّامِ كما في قَوْلِكَ: «زَيْدٌ في الدّارِ» و«المالُ لِزَيْدٍ» و«خالِدٌ ذُو مالٍ» يُسَمّى الحَمْلَ بالاشْتِقاقِ، وإنْ لم يَكُنْ كذلك بل يُحْمَلُ شَيْءٌ على شَيْءٍ بلا واسِطَةِ هذه الوَسائِطِ يُقالُ لَهُ: الحَمْلُ بالمُواطاةِ، نحوُ: «عَمْرٌو طَبِيبٌ» و«بَكْرٌ فَصِيحٌ».
Predication (ḥaml), in their terminology, is the union, in existence, of two things that differ in . So in your saying “Zayd is a writer” and “ʿAmr is a poet”, the concept of “Zayd” differs from the concept of “writer”, but the two exist by one existence; likewise the concepts of “ʿAmr” and “poet” differ, yet they are united in existence. Predication, further, is of two kinds. If it is by means of “in” (fī), “possessor of” (dhū) or the lām [“belonging to”], as when you say “Zayd is in the house”, “The wealth belongs to Zayd” and “Khālid is possessed of wealth”, it is called predication by derivation (bi-l-ishtiqāq). If it is not so, but one thing is of another without these intermediaries, it is called predication by concordance (bi-l-muwāṭāt), as in “ʿAmr is a physician” and “Bakr is eloquent”.
تَقْسِيمٌ آخَرُ لِلْحَمْلِيَّةِ: مَوْضُوعُ الحَمْلِيَّةِ إنْ كانَ مَوْجُودًا في الخارِجِ وكانَ الحُكْمُ فيها باعْتِبارِ تَحَقُّقِ المَوْضُوعِ ووُجُودِهِ في الخارِجِ كانَتِ القَضِيَّةُ خارِجِيَّةً، نحوُ: «الإنْسانُ كاتِبٌ»، وإنْ كانَ مَوْجُودًا في الذِّهْنِ وكانَ الحُكْمُ باعْتِبارِ خُصُوصِ وُجُودِهِ في الذِّهْنِ كانَتْ ذِهْنِيَّةً، نحوُ: «الإنْسانُ كُلِّيٌّ»، وإنْ كانَ الحُكْمُ باعْتِبارِ تَقَرُّرِهِ في الواقِعِ مَعَ عَزْلِ النَّظَرِ عن خُصُوصِيَّةِ ظَرْفِ الخارِجِ أوِ الذِّهْنِ سُمِّيَتِ القَضِيَّةُ حَقِيقِيَّةً، نحوُ: «الأرْبَعَةُ زَوْجٌ» و«السِّتَّةُ ضِعْفُ الثَّلاثَةِ».
Another division of the : if the of the categorical exists in the external world, and the judgement in it is made with regard to the subject's being realised and existing in the external world, the is external (khārijiyya), as in “Man is a writer”. If it exists in the mind, and the judgement is made with regard to its existence in the mind specifically, it is mental (dhihniyya), as in “Man is a ”. If the judgement is made with regard to its being established in fact (fī l-wāqiʿ), setting aside the container, whether the external world or the mind, the proposition is called real (ḥaqīqiyya), as in “Four is even” and “Six is double three”.
القَضِيَّةُ المُوجَبَةُ وكذا السّالِبَةُ تَنْقَسِمانِ إلى مَعْدُولَةٍ وغَيْرِ مَعْدُولَةٍ؛ فالمَعْدُولَةُ ما يَكُونُ فيه حَرْفُ السَّلْبِ جُزْءًا مِنَ المَوْضُوعِ أو مِنَ المَحْمُولِ أو كِلَيْهِما. مِثالُ الأوَّلِ قَوْلُنا: «اللّاحَيُّ جَمادٌ»، مِثالُ الثّاني: «زَيْدٌ لا عالِمٌ»، مِثالُ الثّالِثِ: «اللّاحَيُّ لا عالِمٌ»؛ هذا في الإيجابِ. أمّا في السَّلْبِ فمِثالُ الأوَّلِ: «اللّاحَيُّ لَيْسَ بعالِمٍ»، ومِثالُ الثّاني: «العالِمُ لَيْسَ بلا حَيٍّ»، ومِثالُ الثّالِثِ: «اللّاحَيُّ لَيْسَ بلا جَمادٍ». وغَيْرُ المَعْدُولَةِ بخِلافِها، ويُسَمّى غَيْرُ المَعْدُولَةِ في المُوجَبَةِ بالمُحَصَّلَةِ، وفي السّالِبَةِ بالبَسِيطَةِ.
The , and likewise the , divides into metathetic (maʿdūla) and non-metathetic. The metathetic is one in which the particle of negation is part of the , or of the , or of both. An example of the first is our saying “The non-living is inanimate”; of the second, “Zayd is non-learned”; of the third, “The non-living is non-learned”. That is in the affirmative. In the negative, an example of the first is “The non-living is not learned”; of the second, “The learned is not non-living”; and of the third, “The non-living is not non-inanimate”. The non-metathetic is the opposite of this. The non-metathetic is called positive (muḥaṣṣala) in the affirmative and (basīṭa) in the negative.
وقد يُذْكَرُ الجِهَةُ في القَضِيَّةِ فيُسَمّى مُوَجَّهَةً ورُباعِيَّةً أيْضًا. والمُوَجَّهاتُ خَمْسَةَ عَشَرَ: ثَمانِيَةٌ مِنْها بَسِيطَةٌ، وسَبْعَةٌ مِنْها مُرَكَّبَةٌ. أمّا البَسائِطُ فأحَدُها الضَّرُورِيَّةُ المُطْلَقَةُ، وهي الّتي حُكِمَ فيها بضَرُورَةِ ثُبُوتِ المَحْمُولِ لِلْمَوْضُوعِ أو سَلْبِهِ عنه ما دامَ ذاتُ المَوْضُوعِ مَوْجُودَةً، كقَوْلِكَ: «الإنْسانُ حَيَوانٌ بالضَّرُورَةِ» و«لَيْسَ بحَجَرٍ بالضَّرُورَةِ». والثّانِيَةُ الدّائِمَةُ المُطْلَقَةُ، وهي الّتي حُكِمَ فيها بدَوامِ ثُبُوتِ المَحْمُولِ لِلْمَوْضُوعِ أو سَلْبِهِ عنه، كقَوْلِكَ: «كُلُّ فَلَكٍ مُتَحَرِّكٌ بالدَّوامِ» و«لا شَيْءَ مِنَ الفَلَكِ بساكِنٍ بالدَّوامِ». والثّالِثَةُ المَشْرُوطَةُ العامَّةُ، وهي الّتي حُكِمَ فيها بضَرُورَةِ ثُبُوتِ المَحْمُولِ لِلْمَوْضُوعِ أو نَفْيِهِ عنه ما دامَ ذاتُ المَوْضُوعِ مَوْصُوفًا بالوَصْفِ العُنْوانِيِّ، والوَصْفُ العُنْوانِيُّ عِنْدَهم ما عُبِّرَ بِهِ عنِ المَوْضُوعِ، كقَوْلِنا: «كُلُّ كاتِبٍ مُتَحَرِّكُ الأصابِعِ بالضَّرُورَةِ ما دامَ كاتِبًا» و«لا شَيْءَ مِنَ الكاتِبِ بساكِنِ الأصابِعِ بالضَّرُورَةِ ما دامَ كاتِبًا». والرّابِعَةُ العُرْفِيَّةُ العامَّةُ، وهي الّتي حُكِمَ فيها بدَوامِ ثُبُوتِ المَحْمُولِ لِلْمَوْضُوعِ أو سَلْبِهِ عنه ما دامَ ذاتُ المَوْضُوعِ مُتَّصِفًا بالوَصْفِ العُنْوانِيِّ، كقَوْلِنا: «بالدَّوامِ كُلُّ كاتِبٍ مُتَحَرِّكُ الأصابِعِ ما دامَ كاتِبًا» و«بالدَّوامِ لا شَيْءَ مِنَ النّائِمِ بمُسْتَيْقِظٍ ما دامَ نائِمًا». والخامِسَةُ الوَقْتِيَّةُ المُطْلَقَةُ، وهي الّتي حُكِمَ فيها بضَرُورَةِ ثُبُوتِ المَحْمُولِ لِلْمَوْضُوعِ أو نَفْيِهِ عنه في وَقْتٍ مُعَيَّنٍ مِن أوْقاتِ الذّاتِ، كما تَقُولُ: «كُلُّ قَمَرٍ مُنْخَسِفٌ بالضَّرُورَةِ وَقْتَ حَيْلُولَةِ الأرْضِ بَيْنَهُ وبَيْنَ الشَّمْسِ» و«لا شَيْءَ مِنَ القَمَرِ بمُنْخَسِفٍ بالضَّرُورَةِ وَقْتَ التَّرْبِيعِ». والسّادِسَةُ المُنْتَشِرَةُ المُطْلَقَةُ، وهي الّتي حُكِمَ فيها بضَرُورَةِ ثُبُوتِ المَحْمُولِ لِلْمَوْضُوعِ أو نَفْيِهِ عنه في وَقْتٍ غَيْرِ مُعَيَّنٍ مِن أوْقاتِ الذّاتِ، نحوُ: «كُلُّ حَيَوانٍ مُتَنَفِّسٌ بالضَّرُورَةِ وَقْتًا ما» و «لا شَيْءَ مِنَ الحَجَرِ بمُتَنَفِّسٍ بالضَّرُورَةِ». والسّابِعَةُ المُطْلَقَةُ العامَّةُ، وهي الّتي حُكِمَ فيها بوُجُودِ المَحْمُولِ لِلْمَوْضُوعِ أو سَلْبِهِ عنه، أي في أحَدِ الأزْمِنَةِ الثَّلاثَةِ، كقَوْلِكَ: «كُلُّ إنْسانٍ ضاحِكٌ بالفِعْلِ» و«لا شَيْءَ مِنَ الإنْسانِ بضاحِكٍ». والثّامِنَةُ المُمْكِنَةُ العامَّةُ، وهي الّتي حُكِمَ فيها بسَلْبِ ضَرُورَةِ الجانِبِ المُخالِفِ، كقَوْلِكَ: «كُلُّ نارٍ حارَّةٌ بالإمْكانِ العامِّ» و«لا شَيْءَ مِنَ النّارِ ببارِدٍ بالإمْكانِ العامِّ».
The mode (jiha) is sometimes mentioned in a , and it is then called modal (muwajjaha), and also four-part (rubāʿiyya). The modal propositions are fifteen: eight of them are and seven compound. Of the simple ones, the first is the absolute necessary (ḍarūriyya muṭlaqa): one in which it is judged that the 's holding of the , or its being denied of it, is necessary as long as the of the subject exists, as when you say “Man is an animal by necessity” and “[Man] is not a stone by necessity”. The second is the absolute perpetual (dāʾima muṭlaqa): one in which it is judged that the predicate's holding of the subject, or its being denied of it, is perpetual, as when you say “Every celestial sphere is moving, always” and “No celestial sphere is at rest, always”. The third is the general (mashrūṭa ʿāmma): one in which it is judged that the predicate's holding of the subject, or its being denied of it, is necessary as long as the essence of the subject is described by the descriptive title (waṣf ʿunwānī). The descriptive title, for them, is that by which the subject is expressed. [Examples are] our saying “Every writer is moving his fingers, by necessity, as long as he is writing” and “No writer has his fingers at rest, by necessity, as long as he is writing”. The fourth is the general conventional (ʿurfiyya ʿāmma): one in which it is judged that the predicate's holding of the subject, or its being denied of it, is perpetual as long as the essence of the subject is qualified by the descriptive title, as in our saying “Always, every writer is moving his fingers as long as he is writing” and “Always, no sleeper is awake as long as he is asleep”. The fifth is the absolute temporal (waqtiyya muṭlaqa): one in which it is judged that the predicate's holding of the subject, or its being denied of it, is necessary at a specific one of the times of the essence, as you say “Every moon is eclipsed, by necessity, at the time the earth comes between it and the sun” and “No moon is eclipsed, by necessity, at the time of quadrature”. The sixth is the absolute spread (muntashira muṭlaqa): one in which it is judged that the predicate's holding of the subject, or its being denied of it, is necessary at an unspecified one of the times of the essence, as in “Every animal is breathing, by necessity, at some time” and “No stone is breathing, by necessity”. The seventh is the general absolute (muṭlaqa ʿāmma): one in which it is judged that the predicate belongs to the subject, or is denied of it, that is, at one of the three times [past, present or future], as when you say “Every human is laughing, actually” and “No human is laughing”. The eighth is the general possible (mumkina ʿāmma): one in which it is judged that necessity on the opposite side is negated, as when you say “Every fire is hot by general possibility” and “No fire is cold by general possibility”.
المُرَكَّبَةُ قَضِيَّةٌ رُكِّبَتْ حَقِيقَتُها مِن إيجابٍ وسَلْبٍ، والاعْتِبارُ في تَسْمِيَتِها مُوجَبَةً أو سالِبَةً لِلْجُزْءِ الأوَّلِ؛ فإنْ كانَ الجُزْءُ الأوَّلُ مُوجَبًا كقَوْلِكَ: «بالضَّرُورَةِ كُلُّ كاتِبٍ مُتَحَرِّكُ الأصابِعِ ما دامَ كاتِبًا لا دائِمًا» سُمِّيَتْ مُوجَبَةً، وإنْ كانَ الجُزْءُ الأوَّلُ سالِبًا كقَوْلِنا: «بالضَّرُورَةِ لا شَيْءَ مِنَ الكاتِبِ بساكِنِ الأصابِعِ ما دامَ كاتِبًا لا دائِمًا» سُمِّيَتْ سالِبَةً. ومِنَ المُرَكَّباتِ المَشْرُوطَةُ الخاصَّةُ، وهي المَشْرُوطَةُ العامَّةُ مَعَ قَيْدِ اللّادَوامِ بحَسَبِ الذّاتِ، ومَرَّ مِثالُها إيجابًا وسَلْبًا. ومِنْها العُرْفِيَّةُ الخاصَّةُ، وهي العُرْفِيَّةُ العامَّةُ مَعَ قَيْدِ اللّادَوامِ بحَسَبِ الذّاتِ، كما تَقُولُ: «دائِمًا كُلُّ كاتِبٍ مُتَحَرِّكُ الأصابِعِ ما دامَ كاتِبًا لا دائِمًا» و«دائِمًا لا شَيْءَ مِنَ الكاتِبِ بساكِنِ الأصابِعِ ما دامَ كاتِبًا لا دائِمًا». ومِنْها الوُجُودِيَّةُ اللّاضَرُورِيَّةُ، وهي المُطْلَقَةُ العامَّةُ مَعَ قَيْدِ اللّاضَرُورَةِ بحَسَبِ الذّاتِ، كقَوْلِنا: «كُلُّ إنْسانٍ كاتِبٌ بالفِعْلِ لا بالضَّرُورَةِ» في الإيجابِ، و«لا شَيْءَ مِنَ الإنْسانِ بكاتِبٍ بالفِعْلِ ولا بالضَّرُورَةِ» في السَّلْبِ. ومِنْها الوُجُودِيَّةُ اللّادائِمَةُ، وهي المُطْلَقَةُ العامَّةُ مَعَ قَيْدِ اللّادَوامِ بحَسَبِ الذّاتِ، كقَوْلِكَ في الإيجابِ: «كُلُّ إنْسانٍ ضاحِكٌ بالفِعْلِ لا دائِمًا»، وقَوْلِكَ في السَّلْبِ: «لا شَيْءَ مِنَ الإنْسانِ بضاحِكٍ بالفِعْلِ لا دائِمًا». ومِنْها الوَقْتِيَّةُ، وهي الوَقْتِيَّةُ المُطْلَقَةُ إذا قُيِّدَ باللّادَوامِ بحَسَبِ الذّاتِ، كقَوْلِنا: «بالضَّرُورَةِ كُلُّ قَمَرٍ مُنْخَسِفٌ وَقْتَ حَيْلُولَةِ الأرْضِ بَيْنَهُ وبَيْنَ الشَّمْسِ لا دائِمًا» و«بالضَّرُورَةِ لا شَيْءَ مِنَ القَمَرِ بمُنْخَسِفٍ وَقْتَ التَّرْبِيعِ لا دائِمًا». ومِنْها المُنْتَشِرَةُ، وهي المُنْتَشِرَةُ المُطْلَقَةُ المُقَيَّدَةُ باللّادَوامِ بحَسَبِ الذّاتِ، مِثالُها: «بالضَّرُورَةِ كُلُّ إنْسانٍ مُتَنَفِّسٌ في وَقْتٍ ما لا دائِمًا» و«بالضَّرُورَةِ لا شَيْءَ مِنَ الإنْسانِ بمُتَنَفِّسٍ وَقْتًا ما لا دائِمًا». ومِنْها المُمْكِنَةُ الخاصَّةُ، وهي الّتي حُكِمَ فيها بارْتِفاعِ الضَّرُورَةِ المُطْلَقَةِ عن جانِبَيِ الوُجُودِ والعَدَمِ جَمِيعًا، كقَوْلِكَ: «بالإمْكانِ الخاصِّ كُلُّ إنْسانٍ ضاحِكٌ» و«بالإمْكانِ الخاصِّ لا شَيْءَ مِنَ الإنْسانِ بضاحِكٍ».
A composite (murakkaba) [modal] is a whose is composed of an and a . Whether it is named affirmative or negative depends on the first part. If the first part is affirmative, as when you say “By necessity every writer has moving fingers as long as he is a writer, not always”, it is called affirmative; if the first part is negative, as when we say “By necessity no writer has still fingers as long as he is a writer, not always”, it is called negative. Among the composites is the special : the general conditional with the restriction of non-perpetuity with respect to the ; its example, affirmative and negative, has already been given. Among them is the special conventional: the general conventional with the restriction of non-perpetuity with respect to the essence, as you say: “Always every writer has moving fingers as long as he is a writer, not always” and “Always no writer has still fingers as long as he is a writer, not always”. Among them is the non-necessary existential: the general absolute with the restriction of non-necessity with respect to the essence, as when we say “Every human is a writer actually, not by necessity” for the affirmative, and “No human is a writer actually, and not by necessity” for the negative. Among them is the non-perpetual existential: the general absolute with the restriction of non-perpetuity with respect to the essence, as when you say for the affirmative “Every human is laughing actually, not always”, and for the negative “No human is laughing actually, not always”. Among them is the temporal: the absolute temporal when it is restricted by non-perpetuity with respect to the essence, as when we say “By necessity every moon is eclipsed at the time the earth comes between it and the sun, not always” and “By necessity no moon is eclipsed at the time of quadrature, not always”. Among them is the spread: the absolute spread restricted by non-perpetuity with respect to the essence; its example: “By necessity every human breathes at some time, not always” and “By necessity no human breathes at some time, not always”. Among them is the special possible: one in which it is judged that absolute necessity is removed from both sides together, existence and non-existence, as when you say “By special possibility every human is laughing” and “By special possibility no human is laughing”.
اللّادَوامُ إشارَةٌ إلى مُطْلَقَةٍ عامَّةٍ، واللّاضَرُورَةُ إشارَةٌ إلى مُمْكِنَةٍ عامَّةٍ؛ فإذا قُلْتَ: «كُلُّ إنْسانٍ مُتَعَجِّبٌ بالفِعْلِ لا دائِمًا» فكأنّكَ قُلْتَ: «كُلُّ إنْسانٍ مُتَعَجِّبٌ بالفِعْلِ، ولا شَيْءَ مِنَ الإنْسانِ بمُتَعَجِّبٍ بالفِعْلِ»، وإذا قُلْتَ: «كُلُّ حَيَوانٍ ماشٍ بالفِعْلِ لا بالضَّرُورَةِ» فكأنّكَ قُلْتَ: «كُلُّ حَيَوانٍ ماشٍ بالفِعْلِ، ولا شَيْءَ مِنَ الحَيَوانِ بماشٍ بالإمْكانِ».
Non-perpetuity points to a general absolute, and non-necessity points to a general possible. So if you say “Every human is wondering actually, not always”, it is as if you had said “Every human is wondering actually, and no human is wondering actually”; and if you say “Every animal is walking actually, not by necessity”, it is as if you had said “Every animal is walking actually, and no animal is walking by possibility”.
قد عَرَفْتَ مَعْنى الشَّرْطِيَّةِ، وهي الّتي تَنْحَلُّ إلى قَضِيَّتَيْنِ، والآنَ نَهْدِيكَ إلى أقْسامِها، ونُرْشِدُكَ إلى أحْكامِها؛ فاعْلَمْ أيُّها الفَطِنُ اللَّبِيبُ والذَّكِيُّ الأرِيبُ أنّ الشَّرْطِيَّةَ قِسْمانِ: أحَدُهما المُتَّصِلَةُ، وثانِيهِما المُنْفَصِلَةُ. أمّا المُتَّصِلَةُ فهي الّتي حُكِمَ فيها بثُبُوتِ نِسْبَةٍ على تَقْدِيرِ ثُبُوتِ نِسْبَةٍ أُخْرى في الإيجابِ، وبنَفْيِ نِسْبَةٍ على تَقْدِيرِ نَفْيِ نِسْبَةٍ أُخْرى في السَّلْبِ، كقَوْلِنا في الإيجابِ: «إنْ كانَ زَيْدٌ إنْسانًا كانَ حَيَوانًا»، وقَوْلِنا في السَّلْبِ: «لَيْسَ البَتَّةَ إذا كانَ زَيْدٌ إنْسانًا كانَ فَرَسًا». ثُمَّ المُتَّصِلَةُ صِنْفانِ: إنْ كانَ ذلك الحُكْمُ لِعَلاقَةٍ بَيْنَ المُقَدَّمِ والتّالِي سُمِّيَتْ لُزُومِيَّةً كما مَرَّ، وإنْ كانَ ذلك الحُكْمُ بدُونِ العَلاقَةِ سُمِّيَتِ اتِّفاقِيَّةً، كقَوْلِكَ: «إذا كانَ الإنْسانُ ناطِقًا فالحِمارُ ناهِقٌ». والعَلاقَةُ في عُرْفِهم عِبارَةٌ عن أحَدِ الأمْرَيْنِ: إمّا أنْ يَكُونَ أحَدُهما عِلَّةً لِلْآخَرِ أو كِلاهُما مَعْلُولَيْنِ لِثالِثٍ، وإمّا أنْ يَكُونَ بَيْنَهُما عَلاقَةُ التَّضايُفِ. والتَّضايُفُ هو أنْ يَكُونَ تَعَقُّلُ أحَدِهِما مَوْقُوفًا على تَعَقُّلِ الآخَرِ كالأُبُوَّةِ والبُنُوَّةِ؛ فإذا قُلْتَ: «إنْ كانَ زَيْدٌ أبًا لِعَمْرٍو كانَ عَمْرٌو ابْنًا لَهُ» يَكُونُ شَرْطِيَّةً مُتَّصِلَةً بَيْنَ طَرَفَيْها عَلاقَةُ التَّضايُفِ. وأمّا المُنْفَصِلَةُ فهي الّتي حُكِمَ فيها بالتَّنافِي بَيْنَ شَيْئَيْنِ في مُوجَبَةٍ، وبسَلْبِ التَّنافِي بَيْنَهُما في سالِبَةٍ.
You have already learnt what a is: one that can be broken down into two . Now we shall guide you to its kinds and direct you to its rules. Know, then, perceptive and discerning reader, sharp-witted and skilled, that the conditional is of two kinds: the first is the , the second the .
The connective is one in which it is judged, in the , that a relation holds on the supposition that another relation holds, and, in the , that a relation is negated on the supposition that another relation is negated; as when we say in the affirmative “If Zayd is a human, he is an animal”, and in the negative “Never at all: if Zayd is a human, he is a horse”. The connective is then of two sorts. If that judgement is made because of a connection (ʿalāqa) between the and the , it is called implicative (luzūmiyya), as [in the example] just given; if that judgement is made without a connection, it is called coincidental (ittifāqiyya), as when you say “If man is rational, the donkey brays”. In their usage, connection means one of two things: either one of the two is the cause of the other, or both are effects of a third; or there is between them the connection of correlation (taḍāyuf). Correlation is when understanding one of the two depends on understanding the other, like fatherhood and sonship. So if you say “If Zayd is ʿAmr's father, ʿAmr is his son”, this is a connective conditional between whose two sides there is the connection of correlation.
The disjunctive is one in which it is judged, in an affirmative, that two things are incompatible, and, in a negative, that the incompatibility between them is denied.
الشَّرْطِيَّةُ المُنْفَصِلَةُ على ثَلاثَةِ أضْرُبٍ؛ لأنّها إنْ حُكِمَ فيها بالتَّنافِي أو بعَدَمِهِ بَيْنَ النِّسْبَتَيْنِ في الصِّدْقِ والكَذِبِ مَعًا كانَتِ المُنْفَصِلَةُ حَقِيقِيَّةً، كما تَقُولُ: «هذا العَدَدُ إمّا زَوْجٌ أو فَرْدٌ»، فلا يُمْكِنُ اجْتِماعُ الزَّوْجِيَّةِ والفَرْدِيَّةِ في عَدَدٍ مُعَيَّنٍ ولا ارْتِفاعُهُما. وإنْ حُكِمَ بالتَّنافِي أو بعَدَمِهِ صِدْقًا فَقَطْ كانَتْ مانِعَةَ الجَمْعِ، كقَوْلِكَ: «هذا الشَّيْءُ إمّا شَجَرٌ أو حَجَرٌ»، فلا يُمْكِنُ أنْ يَكُونَ شَيْءٌ مُعَيَّنٌ حَجَرًا وشَجَرًا مَعًا، ويُمْكِنُ أنْ لا يَكُونَ شَيْئًا مِنْهُما. وإنْ حُكِمَ بالتَّنافِي وسَلْبِهِ كَذِبًا فَقَطْ كانَتْ مانِعَةَ الخُلُوِّ، كقَوْلِ القائِلِ: «إمّا أنْ يَكُونَ زَيْدٌ في البَحْرِ أو لا يَغْرَقَ»، فارْتِفاعُهُما بأنْ لا يَكُونَ زَيْدٌ في البَحْرِ ويَغْرَقَ مُحالٌ، ولَيْسَ اجْتِماعُهُما مُحالًا بأنْ يَكُونَ في البَحْرِ ولا يَغْرَقَ.
The is of three sorts. If incompatibility, or its absence, is judged between the two relations in truth and in falsity together, the disjunctive is real (ḥaqīqiyya), as you say: “This number is either even or odd”; evenness and oddness cannot be together in a specified number, nor can both be absent. If incompatibility, or its absence, is judged in truth only, it excludes being together (māniʿat al-jamʿ), as when you say “This thing is either a tree or a stone”: a specified thing cannot be a stone and a tree at once, but it can be neither of them. If incompatibility, or its denial, is judged in falsity only, it excludes being absent together (māniʿat al-khuluww), as when someone says “Zayd is either in the sea or not drowning”: for both to be absent, with Zayd not in the sea and drowning, is impossible; but for both to be together, with him in the sea and not drowning, is not impossible.
المُنْفَصِلَةُ بأقْسامِها الثَّلاثَةِ قِسْمانِ: عِنادِيَّةٌ واتِّفاقِيَّةٌ؛ والعِنادِيَّةُ عِبارَةٌ عن أنْ يَكُونَ فيها التَّنافِي بَيْنَ الجُزْأَيْنِ لِذاتِهِما، والاتِّفاقِيَّةُ عِبارَةٌ عن أنْ يَكُونَ فيها التَّنافِي بمُجَرَّدِ الاتِّفاقِ.
The , in all three of its kinds, is of two sorts: oppositional (ʿinādiyya) and coincidental (ittifāqiyya). The oppositional is one in which the incompatibility between the two parts is due to the parts themselves; the coincidental is one in which the incompatibility is by mere coincidence.
اعْلَمْ أنّه كما يَنْقَسِمُ الحَمْلِيَّةُ إلى الشَّخْصِيَّةِ والمَحْصُورَةِ والمُهْمَلَةِ، كذلك الشَّرْطِيَّةُ تَنْقَسِمُ هذه الأقْسامَ، إلّا أنّ القَضِيَّةَ الطَّبْعِيَّةَ لا تُتَصَوَّرُ هٰهُنا. ثُمَّ التَّقادِيرُ في الشَّرْطِيَّةِ بمَنْزِلَةِ الأفْرادِ في الحَمْلِيَّةِ؛ فإنْ كانَ الحُكْمُ على تَقْدِيرٍ مُعَيَّنٍ ووَضْعٍ خاصٍّ سُمِّيَتِ الشَّرْطِيَّةُ شَخْصِيَّةً، كقَوْلِنا: «إنْ جِئْتَنِي اليَوْمَ أكْرَمْتُكَ»، وإنْ كانَ الحُكْمُ على جَمِيعِ تَقادِيرِ المُقَدَّمِ سُمِّيَتْ كُلِّيَّةً، نحوُ: «كُلَّما كانَتِ الشَّمْسُ طالِعَةً كانَ النَّهارُ مَوْجُودًا»، وإنْ كانَ الحُكْمُ على بَعْضِ التَّقادِيرِ كانَتْ جُزْئِيَّةً، كما في قَوْلِنا: «قد يَكُونُ إذا كانَ الشَّيْءُ حَيَوانًا كانَ إنْسانًا»، وإنْ تُرِكَ ذِكْرُ التَّقادِيرِ كُلًّا وبَعْضًا كانَتْ مُهْمَلَةً، نحوُ: «إنْ كانَ زَيْدٌ إنْسانًا كانَ حَيَوانًا».
Know that, just as the is divided into , and , the is divided into these same kinds; only a natural cannot be here. In the conditional, the situations (taqādīr) stand in place of the individuals in the categorical. If the judgement is made on one specified situation and a state, the conditional is called singular, as when we say “If you come to me today, I will honour you”. If the judgement is made on all the situations of the , it is called , as in “Whenever the sun has risen, it is day”. If the judgement is made on some of the situations, it is particular, as in our saying “Sometimes, if a thing is an animal, it is a human”. If mention of the situations, whether all or some, is left out, it is indefinite, as in “If Zayd is a human, he is an animal”.
سُورُ المُوجَبَةِ الكُلِّيَّةِ في المُتَّصِلَةِ لَفْظَةُ «مَتى» و«مَهْما» و«كُلَّما»، وفي المُنْفَصِلَةِ «دائِمًا». وسُورُ السّالِبَةِ الكُلِّيَّةِ في المُتَّصِلَةِ والمُنْفَصِلَةِ «لَيْسَ البَتَّةَ». وسُورُ المُوجَبَةِ الجُزْئِيَّةِ فيهما «قد يَكُونُ». وسُورُ السّالِبَةِ الجُزْئِيَّةِ فيهما «قد لا يَكُونُ»، وبإدْخالِ حَرْفِ السَّلْبِ على سُورِ الإيجابِ الكُلِّيِّ. ولَفْظَةُ «لَوْ» و«إنْ» و«إذا» في الاتِّصالِ، و«إمّا» و«أوْ» في الانْفِصالِ، تَجِيءُ في الإهْمالِ.
The of the in the is the word matā (“when”), mahmā (“whatever time”) or kullamā (“whenever”), and in the dāʾiman (“always”). The quantifier of the in the connective and the disjunctive is laysa al-battata (“never at all”). The quantifier of the in both is qad yakūnu (“sometimes”). The quantifier of the in both is qad lā yakūnu (“sometimes not”), and also putting the particle of before the quantifier of the universal affirmative. The words law (“if it were”), in (“if”) and idhā (“when”) in connection, and immā (“either”) and aw (“or”) in disjunction, are used in [conditionals].
طَرَفا الشَّرْطِيَّةِ ـ أعْنِي المُقَدَّمَ والتّالِيَ ـ لا حُكْمَ فيهما حِينَ كَوْنِهِما طَرَفَيْنِ، وبَعْدَ التَّحْلِيلِ يُمْكِنُ أنْ يُعْتَبَرَ فيهما حُكْمٌ؛ فطَرَفاها إمّا شَبِيهَتانِ بحَمْلِيَّتَيْنِ، أو مُتَّصِلَتَيْنِ، أو مُنْفَصِلَتَيْنِ، أو مُخْتَلِفَتَيْنِ. عَلَيْكَ باسْتِخْراجِ الأمْثِلَةِ.
The two sides of a , I mean the and the , contain no judgement while they are its sides; after analysis, a judgement can be considered in them. So its two sides either resemble two , or two , or two , or they are mixed. It is up to you to work out the examples.
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 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 and the conversions. Let us, then, devote sections to explaining them and set out some basic principles in them.
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.
is the difference of two in and 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 propositions is eight unities; without them it does not hold: unity of , unity of , 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.
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 between two , the two must differ in quantity, I mean universality and particularity: if one is , the other is . 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 is more general. For contradiction between modal , 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 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 modals. The contradictories of the composite ones are a that alternates between the contradictories of their simple [components]. The details are to be sought in the longer works of the discipline.
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 [ or ] and in [implicative, oppositional and so on] and differ in quality. So the of an implicative connective is a 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”.
العَكْسُ المُسْتَوِي، ويُقالُ لَهُ العَكْسُ المُسْتَقِيمُ أيْضًا، وهو عِبارَةٌ عن جَعْلِ الجُزْءِ الأوَّلِ مِنَ القَضِيَّةِ ثانِيًا والجُزْءِ الثّانِي أوَّلًا مَعَ بَقاءِ الصِّدْقِ والكَيْفِ. فالسّالِبَةُ الكُلِّيَّةُ تَنْعَكِسُ كنَفْسِها، كقَوْلِكَ: «لا شَيْءَ مِنَ الإنْسانِ بحَجَرٍ» يَنْعَكِسُ إلى قَوْلِكَ: «لا شَيْءَ مِنَ الحَجَرِ بإنْسانٍ»، بدَلِيلِ الخُلْفِ؛ تَقْرِيرُهُ أنّه لو لم يَصْدُقْ «لا شَيْءَ مِنَ الحَجَرِ بإنْسانٍ» عِنْدَ صِدْقِ قَوْلِنا: «لا شَيْءَ مِنَ الإنْسانِ بحَجَرٍ» لَصَدَقَ نَقِيضُهُ، أعْنِي قَوْلَنا: «بَعْضُ الحَجَرِ إنْسانٌ»، فنَضُمُّهُ مَعَ الأصْلِ ونَقُولُ: «بَعْضُ الحَجَرِ إنْسانٌ، ولا شَيْءَ مِنَ الإنْسانِ بحَجَرٍ»، يُنْتِجُ: «بَعْضُ الحَجَرِ لَيْسَ بحَجَرٍ»، فيَلْزَمُ سَلْبُ الشَّيْءِ عن نَفْسِهِ، وذلك مُحالٌ. والسّالِبَةُ الجُزْئِيَّةُ لا تَنْعَكِسُ لُزُومًا؛ لجَوازِ عُمُومِ المَوْضُوعِ في الحَمْلِيَّةِ والمُقَدَّمِ في الشَّرْطِيَّةِ، مَثَلًا يَصْدُقُ «بَعْضُ الحَيَوانِ لَيْسَ بإنْسانٍ» ولَيْسَ يَصْدُقُ «بَعْضُ الإنْسانِ لَيْسَ بحَيَوانٍ». والمُوجَبَةُ الكُلِّيَّةُ تَنْعَكِسُ إلى مُوجَبَةٍ جُزْئِيَّةٍ، فقَوْلُنا: «كُلُّ إنْسانٍ حَيَوانٌ» يَنْعَكِسُ إلى قَوْلِنا: «بَعْضُ الحَيَوانِ إنْسانٌ»، ولا يَنْعَكِسُ إلى مُوجَبَةٍ كُلِّيَّةٍ؛ لأنّه يَجُوزُ أنْ يَكُونَ المَحْمُولُ والتّالِي عامًّا كما في مِثالِنا، فلا يَصْدُقُ «كُلُّ حَيَوانٍ إنْسانٌ». وهٰهُنا شَكٌّ، تَقْرِيرُهُ أنّ قَوْلَنا: «كُلُّ شَيْخٍ كانَ شابًّا» مُوجَبَةٌ كُلِّيَّةٌ صادِقَةٌ، مَعَ أنّ عَكْسَهُ «بَعْضُ الشّابِّ كانَ شَيْخًا» لَيْسَ بصادِقٍ. وأُجِيبَ عنه بأنّ عَكْسَهُ لَيْسَ ما ذَكَرْتَ، بل عَكْسُهُ «بَعْضُ مَن كانَ شابًّا شَيْخٌ». وقد يُجابُ بوَجْهٍ آخَرَ، وهو أنّ حِفْظَ النِّسْبَةِ لَيْسَ بضَرُورِيٍّ في العَكْسِ، فعَكْسُهُ «بَعْضُ الشّابِّ يَكُونُ شَيْخًا»، و هو صادِقٌ لا مَحالَةَ. والمُوجَبَةُ الجُزْئِيَّةُ تَنْعَكِسُ إلى مُوجَبَةٍ جُزْئِيَّةٍ، كقَوْلِنا: «بَعْضُ الحَيَوانِ إنْسانٌ» يَنْعَكِسُ إلى قَوْلِنا: «بَعْضُ الإنْسانِ حَيَوانٌ». وقد يُورَدُ على انْعِكاسِ المُوجَبَةِ الجُزْئِيَّةِ كنَفْسِها إيرادٌ، وهو أنّ «بَعْضَ الوَتِدِ في الحائِطِ» صادِقٌ، وعَكْسَهُ أعْنِي «بَعْضَ الحائِطِ في الوَتِدِ» غَيْرُ صادِقٍ. والجَوابُ أنّا لا نُسَلِّمُ أنّ عَكْسَ هذه القَضِيَّةِ ما قُلْتَ مِن «بَعْضِ الحائِطِ في الوَتِدِ»، بل عَكْسُهُ «بَعْضُ ما في الحائِطِ وَتِدٌ»، ولا مِرْيَةَ في صِدْقِهِ. وباقِي مَباحِثِ العُكُوسِ مِن عَكْسِ المُوَجَّهاتِ والشَّرْطِيّاتِ فمَذْكُورٌ في المُطَوَّلاتِ.
(al-ʿaks al-mustawī), also called straight conversion (al-ʿaks al-mustaqīm), is making the first part of a the second and the second part the first, while truth and quality remain. The converts as itself: as when you say “No human is a stone”, which converts to your saying “No stone is human”. [This is shown] by the of reductio (dalīl al-khulf). It runs as follows: if “No stone is human” were not true when our statement “No human is a stone” is true, its , our statement “Some stone is human”, would be true. We join this to the original and say: “Some stone is human, and no human is a stone”, which produces “Some stone is not a stone”. Then the of a thing from itself follows, and that is impossible.
The does not necessarily convert, since the in a , and the in a , may be more general. For example, “Some animal is not human” is true, but “Some human is not an animal” is not true.
The converts to a : our statement “Every human is an animal” converts to our statement “Some animal is human”. It does not convert to a universal affirmative, because the , or the , may be more general, as in our example; so “Every animal is human” is not true. Here there is a doubt, which runs as follows: our statement “Every old man was a young man” is a true universal affirmative, and yet its converse, “Some young man was an old man”, is not true. The answer given is that its converse is not what you have said; rather, its converse is “Some of those who were young men are old men”. Another answer is sometimes given: keeping the relation [exactly as it was] is not required in conversion, so its converse is “Some young man will be an old man”, and that is true without doubt.
The particular affirmative converts to a particular affirmative, as when we say “Some animal is human”, which converts to our statement “Some human is an animal”. An objection is sometimes raised against the particular affirmative converting as itself: “Some peg is in the wall” is true, but its converse, I mean “Some wall is in the peg”, is not true. The answer is: we do not grant that the converse of this proposition is what you have said, “Some wall is in the peg”; rather, its converse is “Some of what is in the wall is a peg”, and there is no doubt that this is true. The rest of the discussions of conversion, the conversion of modal propositions and of conditionals, are given in the longer works.
عَكْسُ النَّقِيضِ هو جَعْلُ نَقِيضِ الجُزْءِ الأوَّلِ مِنَ القَضِيَّةِ ثانِيًا، ونَقِيضِ الجُزْءِ الثّانِي أوَّلًا، مَعَ بَقاءِ الصِّدْقِ والكَيْفِ؛ هذا أُسْلُوبُ المُتَقَدِّمِينَ. فتَنْعَكِسُ المُوجَبَةُ الكُلِّيَّةُ بهذا العَكْسِ كنَفْسِها، كقَوْلِنا: «كُلُّ إنْسانٍ حَيَوانٌ» يَنْعَكِسُ إلى قَوْلِنا: «كُلُّ لا حَيَوانٍ لا إنْسانٌ». والمُوجَبَةُ الجُزْئِيَّةُ لا تَنْعَكِسُ بهذا العَكْسِ؛ لأنّ قَوْلَنا: «بَعْضُ الحَيَوانِ لا إنْسانٌ» صادِقٌ، وعَكْسَهُ أعْنِي «بَعْضُ الإنْسانِ لا حَيَوانٌ» كاذِبٌ. والسّالِبَةُ الكُلِّيَّةُ تَنْعَكِسُ إلى سالِبَةٍ جُزْئِيَّةٍ؛ تَقُولُ: «لا شَيْءَ مِنَ الإنْسانِ بفَرَسٍ»، وتَقُولُ في عَكْسِهِ بهذا العَكْسِ: «بَعْضُ اللّافَرَسِ لَيْسَ بلا إنْسانٍ» إلى جُزْئِيَّةٍ، ولا تَقُولُ: «لا شَيْءَ مِنَ اللّافَرَسِ بلا إنْسانٍ» لصِدْقِ نَقِيضِهِ، أعْنِي «بَعْضُ اللّافَرَسِ لا إنْسانٌ» كالجِدارِ. والسّالِبَةُ الجُزْئِيَّةُ تَنْعَكِسُ إلى سالِبَةٍ جُزْئِيَّةٍ، كقَوْلِكَ: «بَعْضُ الحَيَوانِ لَيْسَ بإنْسانٍ» تَنْعَكِسُ إلى قَوْلِكَ: «بَعْضُ اللّاإنْسانِ لَيْسَ بلا حَيَوانٍ» كالفَرَسِ. وعُكُوسُ المُوَجَّهاتِ مَذْكُورَةٌ في الكُتُبِ الطِّوالِ. وهٰهُنا قد تَمَّ مَباحِثُ القَضايا وأحْكامِها.
(ʿaks al-naqīḍ) is making the of the first part of a the second, and the contradictory of the second part the first, while truth and quality remain; this is the method of the earlier . By this the converts as itself: as when we say “Every human is an animal”, which converts to our statement “Every non-animal is non-human”. The does not convert by this conversion, because our statement “Some animal is non-human” is true, while its converse, I mean “Some human is non-animal”, is false. The converts to a : you say “No human is a horse”, and in its converse by this conversion you say “Some non-horse is not non-human”, [converting it] to a ; you do not say “No non-horse is non-human”, because its contradictory, I mean “Some non-horse is non-human”, like the wall, is true. The particular negative converts to a particular negative: as when you say “Some animal is not human”, which converts to your saying “Some non-human is not non-animal”, like the horse. The conversions of modal propositions are given in the long books. With this the discussions of propositions and their rules are complete.
وإذْ قد فَرَغْنا عن مَباحِثِ القَضايا والعُكُوسِ الّتي كانَتْ مِن مَبادِئِ الحُجَّةِ، فحَرِيٌّ بنا أنْ نَتَكَلَّمَ في مَباحِثِ الحُجَّةِ؛ فنَقُولُ: الحُجَّةُ على ثَلاثَةِ أقْسامٍ: أحَدُها القِياسُ، وثانِيها الاسْتِقْراءُ، وثالِثُها التَّمْثِيلُ؛ فلْنُبَيِّنْ هذه الثَّلاثَةَ في ثَلاثَةِ فُصُولٍ.
Now that we have finished the discussions of and of the conversions, which were among the principles of , it is fitting for us to speak about the discussions of argument. So we say: argument is of three kinds: the first is the , the second , and the third . Let us, then, explain these three in three sections.
It is a statement composed of from which another statement follows once those propositions are granted. If the or its is stated in it, it is called (istithnāʾī), as when we say “If Zayd is a human, he is an animal; but he is a human”, which produces “so he is an animal”; and “If Zayd is a donkey, he brays; but he does not bray”, which produces “that he is not a donkey”. If neither the conclusion nor its contradictory is stated, it is called (iqtirānī), as when you say “Zayd is a human, and every human is an animal”, which produces “Zayd is an animal”.
It is of two kinds: and . The of the in a is called the , because it mostly has fewer individuals; and its is called the , because it usually has more individuals. A made part of a syllogism is called a ; the premise containing the minor term is called the , and the one containing the major term the . The part repeated between them is called the . The joining of the minor premise with the major is called a combination (qarīna) and a mood (ḍarb); and the form that results from the way the middle term is placed with respect to the minor and major terms is called a (shakl). The figures are four. The way to establish this is to say: the middle term is either the predicate of the minor premise and the subject of the major, as when we say “The world is changing, and everything changing came to be”, which produces “The world came to be”: this is the first figure. If it is the predicate in both, it is the second figure, as you say: “Every human is an animal, and no stone is an animal”, so the conclusion is “No human is a stone”. If it is the subject in both, it is the third figure, as in “Every human is an animal, and some human is a writer”, which produces “Some animal is a writer”. If it is the subject in the minor premise and the predicate in the major, it is the fourth figure, as when we say “Every human is an animal, and some writer is human”, which produces “Some animal is a writer”.
The noblest of the four is the first. For that reason its production [of a ] is evident and self-evident: in it the mind runs ahead to the conclusion naturally, with no need for thought and . It has conditions and . The conditions are two: the first is that the be , the second that the be . If both are missing, or one of them, the conclusion does not follow, as becomes clear on reflection. The moods are four. For the possibilities in each figure are sixteen, since the minor premise is of four kinds and the major premise also of four, I mean the , the , the and the []; and four times four is sixteen. The conditions of the first figure drop twelve: the universal negative minor premise with the four major , and the minor premise with those four, which makes eight; and the particular affirmative and particular negative major premise with the particular and universal affirmative minor premise, which makes four. So four moods remain. The first mood is composed of a universal affirmative minor premise and a universal affirmative major premise, and produces a universal affirmative, as in “Every J is B, and every B is D”, which produces “[Every] J is D”. The second mood is made up of a universal affirmative minor premise and a universal negative major premise, and produces a universal negative, as in “Every human is an animal, and no animal is a stone”, which produces “No human is a stone”. The third mood is formed of a particular affirmative minor premise and a universal affirmative major premise, and the conclusion is a particular affirmative, as in “Some animal is a horse, and every horse neighs”, which produces “Some animal neighs”. The fourth mood is paired from a particular affirmative minor premise and a universal negative major premise, and produces a particular negative, as when we say “Some animal is rational, and nothing rational brays”, so the conclusion is “Some animal does not bray”.
إنْتاجُ المُوجَبَةِ الكُلِّيَّةِ مِن خَواصِّ الشَّكْلِ الأوَّلِ، كما أنّ الإنْتاجَ لِلنَّتائِجِ الأرْبَعَةِ أيْضًا مِن خَصائِصِهِ، والصُّغْرى المُمْكِنَةُ غَيْرُ مُنْتِجَةٍ في هذا الشَّكْلِ فَقَطْ. ووَضَحَ بما ذَكَرْنا أنّه لا بُدَّ في هذا الشَّكْلِ كَيْفًا إيجابُ الصُّغْرى، وكَمًّا كُلِّيَّةُ الكُبْرى، وجِهَةً فِعْلِيَّةُ الصُّغْرى.
Producing a is one of the properties of the first , just as producing all four kinds of is also one of its distinctive features; and a possible is unproductive in this figure only. What we have said makes clear that in this figure the minor premise must be , as to quality; the must be , as to quantity; and the minor premise must be actual (fiʿliyya), as to mode.
ويُشْتَرَطُ في إنْتاجِ الشَّكْلِ الثّانِي بحَسَبِ الكَيْفِ ـ أي الإيجابِ والسَّلْبِ ـ اخْتِلافُ المُقَدِّمَتَيْنِ؛ فإنْ كانَتِ الصُّغْرى مُوجَبَةً كانَتِ الكُبْرى سالِبَةً، وبالعَكْسِ؛ وبحَسَبِ الكَمِّ ـ أي الكُلِّيَّةِ والجُزْئِيَّةِ ـ كُلِّيَّةُ الكُبْرى، وإلّا يَلْزَمِ الاخْتِلافُ المُوجِبُ لعَدَمِ الإنْتاجِ، أي صِدْقُ القِياسِ مَعَ إيجابِ النَّتِيجَةِ تارَةً ومَعَ سَلْبِها أُخْرى. ونَتِيجَةُ هذا الشَّكْلِ لا يَكُونُ إلّا سالِبَةً، وضُرُوبُهُ النّاتِجَةُ أيْضًا أرْبَعَةٌ: أحَدُها مِن كُلِّيَّتَيْنِ والصُّغْرى مُوجَبَةٌ، يُنْتِجُ سالِبَةً كُلِّيَّةً، كقَوْلِنا: «كُلُّ ج ب، ولا شَيْءَ مِن ا ب»، «فلا شَيْءَ مِن ج ا». والدَّلِيلُ على هذا الإنْتاجِ عَكْسُ الكُبْرى؛ فإنّكَ إذا عَكَسْتَ الكُبْرى صارَ «لا شَيْءَ مِن ب ا»، وبانْضِمامِها إلى الصُّغْرى انْتَظَمَ الشَّكْلُ الأوَّلُ، ويُنْتِجُ النَّتِيجَةَ المَطْلُوبَةَ. الضَّرْبُ الثّانِي مِن مُوجَبَةٍ كُلِّيَّةٍ كُبْرى وسالِبَةٍ كُلِّيَّةٍ صُغْرى، كقَوْلِنا: «لا شَيْءَ مِن ج ب، وكُلُّ ا ب» يُنْتِجُ: «لا شَيْءَ مِن ج ا». والدَّلِيلُ على الإنْتاجِ عَكْسُ الصُّغْرى وجَعْلُها كُبْرى ثُمَّ عَكْسُ النَّتِيجَةِ. الضَّرْبُ الثّالِثُ مِن مُوجَبَةٍ جُزْئِيَّةٍ صُغْرى وسالِبَةٍ كُلِّيَّةٍ كُبْرى، يُنْتِجُ سالِبَةً جُزْئِيَّةً، كقَوْلِكَ: «بَعْضُ ج ب، ولا شَيْءَ مِن ا ب»، «فلَيْسَ بَعْضُ ج ا». الضَّرْبُ الرّابِعُ مِن سالِبَةٍ جُزْئِيَّةٍ صُغْرى ومُوجَبَةٍ كُلِّيَّةٍ كُبْرى، يُنْتِجُ سالِبَةً جُزْئِيَّةً؛ تَقُولُ: «بَعْضُ ج لَيْسَ ب، وكُلُّ ا ب»، «فبَعْضُ ج لَيْسَ ا».
For the second to produce, it is required, with respect to quality (that is, and ), that the two differ: if the is affirmative, the is negative, and the reverse. With respect to quantity (that is, universality and particularity), it is required that the major premise be . Otherwise there follows the discrepancy (ikhtilāf) that entails sterility, that is, the being true at one time with the affirmative and at another with it negative. The conclusion of this figure is only ever negative. Its are also four. The first is made of two universals, the minor premise being affirmative; it produces a , as when we say: “Every J is B, and no A is B”, “so no J is A”. The proof of this productivity is the of the major premise: if you convert the major premise, it becomes “No B is A”; joined to the minor premise, it makes up the first figure, and this produces the conclusion sought. The second mood is made of a major premise and a universal negative minor premise, as when we say: “No J is B, and every A is B”, which produces “No J is A”. The proof of its productivity is converting the minor premise and making it the major premise, then converting the conclusion. The third mood is made of a minor premise and a universal negative major premise; it produces a , as when you say: “Some J is B, and no A is B”, “so not some J is A”. The fourth mood is made of a particular negative minor premise and a universal affirmative major premise; it produces a particular negative. You say: “Some J is not B, and every A is B”, “so some J is not A”.
شَرْطُ إنْتاجِ الشَّكْلِ الثّالِثِ كَوْنُ الصُّغْرى مُوجَبَةً، وكَوْنُ أحَدِ المُقَدِّمَتَيْنِ كُلِّيَّةً؛ فضُرُوبُهُ النّاتِجَةُ سِتَّةٌ: أحَدُها «كُلُّ ب ج، وكُلُّ ب ا، فبَعْضُ ج ا»، وثانِيها «كُلُّ ب ج، ولا شَيْءَ مِن ب ا، فبَعْضُ ج لَيْسَ ا»، وثالِثُها «بَعْضُ ب ج، وكُلُّ ب ا، فبَعْضُ ج ا»، ورابِعُها «بَعْضُ ب ج، ولا شَيْءَ مِن ب ا، فبَعْضُ ج لَيْسَ ا»، وخامِسُها «كُلُّ ب ج، وبَعْضُ ب ا، فبَعْضُ ج ا»، وسادِسُها «كُلُّ ب ج، وبَعْضُ ب لَيْسَ ا، فبَعْضُ ج لَيْسَ ا».
The condition for the third to produce is that the be and that one of the two be . So its are six. The first: “Every B is J, and every B is A, so some J is A.” The second: “Every B is J, and no B is A, so some J is not A.” The third: “Some B is J, and every B is A, so some J is A.” The fourth: “Some B is J, and no B is A, so some J is not A.” The fifth: “Every B is J, and some B is A, so some J is A.” The sixth: “Every B is J, and some B is not A, so some J is not A.”
وشَرائِطُ إنْتاجِ الشَّكْلِ الرّابِعِ مَعَ كَثْرَتِها وقِلَّةِ جَدْواها مَذْكُورَةٌ في المَبْسُوطاتِ، فلا عَلَيْنا لو تَرَكْنا ذِكْرَها، وكذا شَرائِطُ سائِرِ الأشْكالِ بحَسَبِ الجِهَةِ لا يَتَحَمَّلُ أمْثالُ رِسالَتِي هذه لِبَيانِها.
The conditions for the fourth to produce, many as they are and of little use, are set out in the extensive works, so there is no blame on us if we leave them unmentioned. Likewise the conditions of the other figures with respect to modality (jiha): a treatise such as this one of mine cannot bear setting them out.
ولَعَلَّكَ عَلِمْتَ مِمّا ألْقَيْنا عَلَيْكَ أنّ النَّتِيجَةَ في القِياسِ تَتْبَعُ أدْوَنَ المُقَدِّمَتَيْنِ في الكَيْفِ والكَمِّ، والأدْوَنُ في الكَيْفِ هو السَّلْبُ، وفي الكَمِّ هو الجُزْئِيَّةُ؛ فالقِياسُ مِن مُوجَبَةٍ وسالِبَةٍ يُنْتِجُ سالِبَةً، والمُرَكَّبُ مِن كُلِّيَّةٍ وجُزْئِيَّةٍ إنّما يُنْتِجُ جُزْئِيَّةً. وأمّا المُرَكَّبُ مِنَ الكُلِّيَّتَيْنِ فرُبَّما يُنْتِجُ كُلِّيَّةً، وقد يُنْتِجُ جُزْئِيَّةً.
Perhaps you have learned from what we have put before you that the of a follows the weaker (adwan) of the two in quality and in quantity. The weaker in quality is , and in quantity particularity. So a syllogism made of an and a negative produces a negative, and one composed of a and a produces only a particular. As for one composed of two universals, it may produce a universal, and it may produce a particular.
وحالُها في انْعِقادِ الأشْكالِ الأرْبَعَةِ والضُّرُوبِ المُنْتِجَةِ والشَّرائِطِ المُعْتَبَرَةِ كحالِ الاقْتِرانِيّاتِ مِنَ الحَمْلِيّاتِ سَواءً بسَواءٍ. مِثالُ الشَّكْلِ الأوَّلِ في المُتَّصِلَةِ: «كُلَّما كانَ زَيْدٌ إنْسانًا كانَ حَيَوانًا، وكُلَّما كانَ حَيَوانًا كانَ جِسْمًا» يُنْتِجُ: «كُلَّما كانَ زَيْدٌ إنْسانًا كانَ جِسْمًا». مِثالُ الشَّكْلِ الثّانِي: «كُلَّما كانَ زَيْدٌ إنْسانًا كانَ حَيَوانًا، ولَيْسَ البَتَّةَ إذا كانَ حَجَرًا كانَ حَيَوانًا» يُنْتِجُ: «لَيْسَ البَتَّةَ إنْ كانَ زَيْدٌ إنْسانًا كانَ حَجَرًا». مِثالُ الثّالِثِ مِنْها: «كُلَّما كانَ زَيْدٌ إنْسانًا كانَ حَيَوانًا، وكُلَّما كانَ زَيْدٌ إنْسانًا كانَ كاتِبًا» يُنْتِجُ: «قد يَكُونُ إذا كانَ زَيْدٌ حَيَوانًا كانَ كاتِبًا». وأمّا الاقْتِرانِيُّ الشَّرْطِيُّ المُؤَلَّفُ مِنَ المُنْفَصِلاتِ فمِثالُهُ مِنَ الشَّكْلِ الأوَّلِ: «إمّا كُلُّ ا ب أو كُلُّ ج د، ودائِمًا كُلُّ د ه أو كُلُّ د ز» يُنْتِجُ: «دائِمًا إمّا كُلُّ ا ب أو كُلُّ ج ه أو كُلُّ د ز». وأمّا الاقْتِرانِيُّ الشَّرْطِيُّ المُرَكَّبُ مِن حَمْلِيَّةٍ ومُتَّصِلَةٍ فكقَوْلِنا: «كُلَّما كانَ ب ج فكُلُّ ج [د]، وكُلُّ [د] ا» يُنْتِجُ: «كُلَّما كانَ ب ج فكُلُّ ج ا». وعلى هذا القِياسِ باقِي التَّرْكِيباتِ.
Their state in forming the four , in the and in the conditions that count, is exactly like that of the syllogisms made of . An example of the first figure with : “Whenever Zayd is a human, he is an animal; and whenever he is an animal, he is a body”, which produces “Whenever Zayd is a human, he is a body.” An example of the second figure: “Whenever Zayd is a human, he is an animal; and never at all, if he is a stone, is he an animal”, which produces “Never at all, if Zayd is a human, is he a stone.” An example of the third of them: “Whenever Zayd is a human, he is an animal; and whenever Zayd is a human, he is a writer”, which produces “Sometimes, if Zayd is an animal, he is a writer.” As for the conjunctive composed of , its example in the first figure is: “Either every A is B or every J is D; and always, every D is H or every D is Z”, which produces “Always, either every A is B or every J is H or every D is Z.” As for the conjunctive conditional syllogism composed of a categorical and a connective, it is as when we say: “Whenever B is J, then every J is [D]; and every [D] is A”, which produces “Whenever B is J, then every J is A.” The remaining combinations go by this .
It is composed of two , that is, two , one of them and the other , with the particle of exception, I mean “illā” (“except”) and its sisters, coming between them; for this reason it is called . If the conditional is a , affirming the itself produces the itself, and affirming the of the consequent produces the removal of the antecedent. As you say: “Whenever the sun is up, it is day; but the sun is up”, which produces “so it is day”; [or] “but it is not day”, which produces “so the sun is not up”. If it is a real , affirming one of the two [parts] itself produces the contradictory of the other, and the reverse [holds too]. In one excluding being together (māniʿat al-jamʿ), the first case produces, not the second; and in one excluding being absent together (māniʿat al-khuluww), the second case produces, not the first.
Here the discussions of the have come to an end, in summary form; the details are left to the long books. Now we shall mention some of what attaches to the syllogism.
· p. 42
Lesson 19 · Induction, analogy, reductio, matter and form
الاسْتِقْراءُ هو الحُكْمُ على كُلِّيٍّ بتَتَبُّعِ أكْثَرِ الجُزْئِيّاتِ، كقَوْلِنا: «كُلُّ حَيَوانٍ يُحَرِّكُ فَكَّهُ الأسْفَلَ عِنْدَ المَضْغِ»؛ لأنّا اسْتَقْرَيْنا ـ أي تَتَبَّعْنا ـ الإنْسانَ والفَرَسَ والبَعِيرَ والحَمِيرَ والطُّيُورَ والسِّباعَ فوَجَدْنا كُلَّها كذلك، فحَكَمْنا بَعْدَ تَتَبُّعِ هذه الجُزْئِيّاتِ المُسْتَقْرِيَةِ أنّ كُلَّ حَيَوانٍ يُحَرِّكُ فَكَّهُ الأسْفَلَ عِنْدَ المَضْغِ. والاسْتِقْراءُ لا يُفِيدُ اليَقِينَ، وإنّما يُحَصِّلُ الظَّنَّ الغالِبَ؛ لجَوازِ أنْ لا يَكُونَ جَمِيعُ أفْرادِ هذا الكُلِّيِّ بهذه الحالَةِ، كما يُقالُ: إنّ التِّمْساحَ لَيْسَ على هذه الصِّفَةِ، بل يُحَرِّكُ فَكَّهُ الأعْلى.
(istiqrāʾ) is judging about a by examining most of its , as when we say: “Every animal moves its lower jaw when chewing”; for we have inducted, that is, examined, the human, the horse, the camel, donkeys, birds and beasts of prey and found all of them to be so, and so, after examining these inducted particulars, we judged that every animal moves its lower jaw when chewing. Induction does not yield certainty; it brings about only preponderant opinion (ẓann ghālib), since it is possible that not all the individuals of this universal are in this state. As is said, the crocodile does not have this attribute: it moves its upper jaw.
(tamthīl) is establishing a judgement in one because it exists in another particular, on account of a uniting factor (maʿnā jāmiʿ) shared by the two, as when we say: “The world is composite, so it has come to be, like a house.” To establish that the shared factor is the cause of the judgement mentioned, they have many methods, set out in the principles of jurisprudence (uṣūl). The chief of them are two. The first is co-variation (dawarān), as the later scholars call it; the earlier ones used to call it presence and absence together (al-ṭard wa-l-ʿaks). It is that the judgement turns with the shared factor in existence and non-existence: when the factor is found, the judgement is found, and when the factor is absent, the judgement is absent. So co-variation is evidence that what it turns on (madār), I mean the factor, is the cause of what turns (dāʾir), that is, the judgement. The second method is probing and division (al-sabr wa-l-taqsīm). It is that they enumerate the attributes of the base case (aṣl), then establish that everything apart from the shared factor is unfit to require the judgement, because those attributes are found in another place where the judgement fails to follow. For example, in the example mentioned they say: the cause of the house's having come to be is either contingency, or existence, or being a substance, or being a body, or being composite; and none of these except being composite is fit to be the cause of having come to be; otherwise everything contingent, every substance, everything existent and every body would have come to be, whereas the Necessary [Being], exalted is He, the separate substances and the ethereal bodies are not so.
Among the compound syllogisms is one called the reductio (qiyās al-khulf). It comes down to two syllogisms. The first is a composed of two . The second is an , one of whose is implicative (luzūmiyya), I mean the of the first syllogism, while the other premise is one in which the of the is affirmed. It is set out as follows: the claim holds; for if the claim did not hold, its contradictory would hold; and whenever its contradictory holds, the absurd holds. This produces: if the claim did not hold, the absurd would hold. This is the first of the two syllogisms. Then we make this conclusion the and say: “If the claim did not hold, the absurd would hold”, and we join to it an exceptive and say: “But the absurd does not hold.” So, necessarily, the claim holds; otherwise both contradictories would be removed. If you wish to grasp this in a example, you say: “Every human is an animal” is true; for if it were not true, “Some human is not an animal” would be true; and whenever “Some human is not an animal” is true, the absurd follows. This produces: whenever the claim is not true, the absurd follows. But the absurd does not hold; so the claim's not holding does not hold; so the claim holds.
It should be known that every must have a form (ṣūra) and a matter (mādda). The form is the arrangement that arises from ordering the and placing some of them next to others. You have come to know the four and have learned their conditions of productivity; what remains is the matter. The earlier scholars, up to and including the Shaykh al-Raʾīs [Ibn Sīnā], were most concerned with setting out the matters of syllogisms in detail and making them clear, and gave most care to the inquiry into expanding and refining them. That is because knowing this is of fuller benefit and wider return to those who seek the . But the later scholars have spoken at length on explaining the forms of syllogisms and expanded on them to the utmost, especially on syllogisms made of and conditionals, though these discussions are of little use; and they cast aside the matter, confining themselves, in explaining it, to giving the definitions of the five arts. I do not know what led them to this, or what motive drew them there. The perceptive, intelligent [student] must devote the utmost care to these discussions, which are of great standing and of dazzling proof, and seek this great goal and lofty aim in the books of the skilled ancients and the writings of the earliest masters, those enchanters [of the art]. So, dear son, you must listen to my counsel and not forget my advice. I shall set before you only fragments of what concerns these arts, relying on the One who suffices for every concern.
Hear, then, that the syllogism, with respect to its matter, divides into five kinds, which are called the five arts: the first is the demonstrative, the second the dialectical, the third the rhetorical, the fourth the poetic and the fifth the sophistical.
Know that is a composed of , whether self-evident (badīhī) or ones that end in them. The matter is not as has been claimed, that demonstration is composed only of self-evident .
The self-evident premises are six. The first is (awwaliyyāt): in which the intellect is decisive merely by turning to them and [their terms], without needing an intermediary, as when you say: “The whole is greater than the part.”
The second is innate premises (fiṭriyyāt): those that need an intermediary which is never absent from the mind. These propositions are also called “propositions that carry their proofs with them”, as in “Four is even”; for whoever conceives the concept of four, and conceives the concept of even as that which divides into two equal [parts], judges self-evidently that four is even. And as when we say: “One is half of two”; for the intellect judges this once it has considered the concept of half of two and of one.
The third is premises (ḥadsiyyāt). [Intuition] is the starting points appearing all at once, without any movement of thought there. The difference between intuition (ḥads) and thinking (fikr) is that thinking requires two movements of the soul, unlike intuition. For the mind, after the thing sought has come to it in some respect, moves among the stored meanings and hidden starting points, seeking what is related to the thing sought, until it finds known items that suit it; here the first movement is complete. Then it turns back and moves a second time, ordering the stored known items it has found, step by step, until it reaches the thing sought; and the second movement is complete. The two movements together are called thinking. For example: if you have conceived the human in some respect, such as the writer and the laughing [being], and then come to seek the of the human, you move your mind towards the meanings stored with you and find animal and rational suited to what you seek; so the first movement is complete, its starting point being the thing sought, known in one respect, and its end animal and rational. Then you order animal and rational by putting animal, which is the , before rational, which is the , and say: “rational animal”. Here the second movement ends and the thing sought is obtained. In intuition, by contrast, the mind passes from the thing sought to the starting points all at once, and from them to the thing sought likewise. Intuition most often comes after longing and effort, though it may come without them. People differ in intuition: some are strong and abundant in intuition, so that most of what they seek comes to them by intuition, such as one supported by the holy power (al-quwwa al-qudsiyya), like the philosophers, the saints and the prophets; some have little and weak intuition; and some have no intuition at all, like one extreme in dullness. From this it is known that being self-evident and being acquired differ with persons and times: many an intuitive [proposition] is acquired for one who lacks the holy power and self-evident for one who has it.
The fourth is (mushāhadāt): propositions judged by means of observation and sensation. They divide into two kinds. The first is what is observed by one of the outer senses, which are five: sight, hearing, smell, taste and touch; this kind is called sensory premises (ḥissiyyāt). The second is what is perceived by the perceiving faculties among the inner senses, which are also five: the common sense (al-ḥiss al-mushtarak), which perceives forms; imagination (khayāl), which is its storehouse; estimation (wahm), which perceives individual and meanings; memory (ḥāfiẓa), which is the storehouse of particular meanings; and the compositive faculty (mutaṣarrifa), which works on forms and meanings by separating and combining. This kind is called introspective premises (wijdāniyyāt). What the pure intellect perceives, I mean , does not fall under this kind. An example of the second kind: as when we judge that we have hunger or thirst.
The fifth is premises (tajribiyyāt): propositions that the intellect judges with a universal judgement by means of repeated observation and [the effect] never failing to follow, like the judgement that drinking scammony purges bile.
The sixth is premises (mutawātirāt): propositions judged by means of reports from a group whose agreeing on a lie the intellect deems impossible. They differ on the least number of this group: it has been said that the least is four, or ten, or forty. The likeliest view is that the number varies with the state of those who report and with the event [reported], so no number is fixed; the rule is that it reaches a point that yields certainty.
These six are the starting points of demonstrations, where proof comes to rest and certainty reaches its end.
Some have claimed that transmitted (naqliyya) are not used in a demonstrative , supposing that error and mistake creep into transmission in many ways: how, then, could they be starting points of a demonstrative syllogism, which yields certainty? This supposition is a sin, for transmission very often yields certainty when certain conditions are observed in it and the intellect is joined to it. Yes, if it were said that bare transmission, without the intellect being joined to it, is not taken into account and yields nothing, that would have some ground.
is of two kinds: limmī and innī. The limmī is the one in which the is the cause of the holding of the in , just as it is the intermediary in the judgement; it is so called because it gives the limmiyya [the “why”], that is, the cause. The innī is the one in which the middle term is the cause of the judgement in the mind only, and is not the cause in reality; rather, it may be its effect. An example of the limmī is your saying: “Zayd is feverish, because his humours are putrefied; and everyone whose humours are putrefied is feverish; so Zayd is feverish.” Just as in this the middle term is the cause of fever being established for Zayd in your mind, so it is the cause of the fever's existing in reality. An example of the innī is your saying: “Zayd's humours are putrefied, because he is feverish; and everyone feverish has putrefied humours; so Zayd's humours are putrefied.” The existence of the fever is the cause, in your mind, of its being established that his humours are putrefied, but it is not the cause in the thing itself (nafs al-amr); rather, in reality the matter may well be the reverse.
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Lesson 21 · Dialectic, rhetoric, poetics and sophistry
The dialectical is a syllogism composed of that are widely accepted (mashhūra) or conceded (musallama) by the opponent, whether they are true or false. The first are those on which the views of a people agree: either because of a common interest, as in “Justice is good”, “Injustice is bad” and “Killing the thief is obligatory”; or out of tenderness of heart, as in the saying of the people of India: “Slaughtering animals is blameworthy”; or because of affections of character or temperament. For temperaments and customs have a great share in beliefs: people of fierce temperament regard taking revenge on evildoers as good, and people of gentle temperament regard forgiveness as better. That is why you see people differing in customs and usages; every people has widely accepted premises of its own, and so does every . Among the widely accepted premises of the grammarians are: “The agent is in the nominative, the object in the accusative, and the second term of a genitive construction in the genitive”; and among those of the scholars of legal theory (uṣūliyyūn): “A command indicates obligation.” The second are those composed of what is conceded between the two disputants. Widely accepted premises resemble ; freeing the mind [of such influences] and careful tell them apart. The purpose of the art of is to bind the opponent [to a concession] and to protect one's view.
The rhetorical is a syllogism that yields opinion (ẓann). Its are either accepted premises (maqbūlāt), taken from people of whom one thinks well, like the saints and the philosophers. Those taken from the prophets, upon them and upon our Prophet be blessings and peace, are not , because they are true reports from a truthful reporter whose truthfulness is shown by the miracle; there is no room in them for estimation such that error and defect could creep into them. So a syllogism composed of them is demonstrative, with premises that are certain. Or [its premises are] probable premises (maẓnūnāt), judged on account of their preponderance. Under these fall , and premises that have not reached the level of firm conviction, because the cause is not perceived or because the number of reporters has not reached the extent of wide transmission (tawātur). This has great benefit in ordering the affairs of this life and arranging the rulings of the life to come, either by using it or by guarding against it. That is why the great philosophers use this art often and admonish great crowds with rhetorical speech. The premises used in it must be persuasive to the listeners and useful to those who admonish.
The poetic is a syllogism composed of (mukhayyalāt), true or false, impossible or possible, that affect the soul with contraction or expansion. The soul yields to imaginative evocation (takhyīl) as it yields to , and even more. The purpose of this is that the soul be moved by deterrence and enticement. It is stipulated in poetry that the speech run according to the rules of the language and contain fine, pleasing metaphors and elegant, excellent similes, so that it affects the soul in a wondrous way and produces in it a state that brings sorrow or joy. Moreover, the use of true is not allowed in it, and the use of false imaginative premises is considered good, as the gnostic of Ganja [Niẓāmī] said, addressing his son, his own flesh and blood (literally “the piece of his liver”), in a verse: “در شعر مپیچ و در فن او * چون اکذب اوست احسن او” [“Do not get entangled in poetry and its craft, / since the most false of it is the finest of it”]. And as in the words of one who describes old wine: “لَها البَدْرُ كَأْسٌ وَهْيَ شَمْسٌ يُدِيرُها * هِلالٌ، وَكَمْ يَبْدُو إِذا مُزِجَتْ نَجْمُ” [“The full moon is her cup, and she is a sun that a crescent passes round; / and how many a star appears when she is mixed!”]. And the poet said, in verse: “لا تَعْجَبُوا مِنْ بِلَى غِلالَتِهِ * قَدْ زُرَّ أَزْرارُهُ عَلَى القَمَرِ” [“Do not wonder that his shirt wears through: / its buttons have been fastened over the moon”]. He likened the beloved to the moon and said: do not wonder that his shirt splits, because he is a moon over whom the shirt has been buttoned, and every moon of that kind has its shirt split; this produces: the beloved's shirt splits. It may even produce the coming together of two contradictories, as in: “I conceal my needs with my tongue and reveal them with my tears; everyone who conceals his needs is silent, and everyone who reveals them speaks”, which produces “I am silent and speaking.” Metre is not a condition of poetry for the masters of the balance [the ], though it does lend it beauty. When poetic speech is recited with a pleasing voice, its effect on souls increases, until excess of delight sometimes knocks the turbans off heads. The first of the Greek philosophers were the most devoted of people to poetry.
The sophistical is a syllogism composed of false (wahmiyyāt), invented by estimation, like judging what is not sensible by with what is sensible, as in “Everything existent can be pointed to.” Estimative premises bear a strong resemblance to ; were it not that the intellect and the revealed law reject the judgement of estimation, the confusion between them would last. Or [it is composed] of false premises that resemble true ones (mushabbahāt): the intellect believes to be first principles, or widely accepted, or accepted, or conceded, because they resemble these in wording or in meaning, and so they lead into error. This is false and counterfeit, not useful in itself, though useful incidentally: one who has it neither errs nor is led into error, and he is able to lead others into error and to test them with it or contend against them. If one who has this art opposes the philosopher [with it], he is called a sophist (sūfisṭāʾī), and this art is sophistics (safsaṭa), that is, a counterfeit, glossed-over philosophy (ḥikma); otherwise he is called a wrangler (mushāghibī), and this is wrangling (mushāghaba). On either assumption the one who has it is himself in error and leads others into error, and his art is (mughālaṭa). It is a corrupt syllogism, either on the side of matter only, or on the side of form only, or both.
Know that the causes of error, many as they are, come back to two things: the first is mere misunderstanding, and the second is false [] being mistaken for true ones. The first comes about only through the soul's immersion in the darkness of estimation, until it takes false propositions to be certainly true, or even necessary, as in: “Everything that is not visible is not a body, so air is not a body.” As for the second, it has a detailed account, as will come. One of the verifying scholars said: they come back to a single thing, namely failing to distinguish between a thing and what resembles it, and nothing else.
Failing to distinguish between a thing and what resembles it divides into what concerns and what concerns meanings. The first kind, I mean what concerns utterances, is of two kinds: the first concerns utterances not with respect to their composition, and the second concerns them with respect to composition. Then what concerns utterances not with respect to composition is of two kinds. The first concerns the utterances themselves: the utterances differ in what they signify, so that confusion arises about what is meant. An example is the error that arises because an utterance is equivocal (mushtarak lafẓī) between two or more meanings, or because one of its meanings is literal and the others figurative; under this fall metaphor and the like, and all of this is called equivocity (al-ishtirāk al-lafẓī). As when you say of a spring of water: “This is an ʿayn, and by every ʿayn the world is lit; so by this ʿayn the world is lit”; or you say: “Zayd is a lion, and every lion has claws; so Zayd has claws.” The error in the first is that the word ʿayn is equivocal between a spring of water and the sun; in the second, that applying the word “lion” to Zayd is figurative, while applying it to the predatory animal is literal. The second concerns utterances because of their morphology (taṣrīf), like the confusion that arises in the word mukhtār: when it has the sense of the active participle, its underlying form is mukhtayir, with i on the yāʾ, and when it has the sense of the passive participle, its underlying form is mukhtayar, with a on it. Or [it arises] because of dotting and case endings, as when someone says “غلام حسن” (ghulām ḥasan) without case endings, and it is taken at one time as a noun with its adjective [“a handsome boy”] and at another as a genitive construction [“Ḥasan's boy”].
What concerns utterances with respect to composition is either due to a difference in what [a pronoun] refers back to, as in “Whatever the philosopher knows, he acts on what he knows”: if the pronoun refers back to the philosopher, it is true; otherwise it is false. Or it is due to separating what is compound, as in “The bitter orange is sweet-sour”, which is true; but if it is separated and one says “This is sweet, and [it is] sour”, it is not true. Or it is due to combining what is separate, as in “Zayd is a physician, and [he is] skilled”, which is true; but if it is combined and one says “[He is] a skilled physician”, it is false.
These too are of several kinds, for they arise either from the matter or from the form. Those that arise from the matter: as when [an ] is such that, if the meanings in it are arranged in a way that makes it true, it is not a , and if they are arranged in a way that makes it a syllogism, it is not true. For example: “Human is rational insofar as it is rational, and nothing rational, insofar as it is rational, is an animal; so no human is an animal.” For if the qualification “insofar as it is rational” is kept, the is false; if it is dropped from it, the is false; and if it is dropped from the minor premise and kept in the major, the form of the syllogism breaks down, because [the ] is not shared. Those that arise from the form: as when [an argument] has a form that does not produce [a ]; all of that is faulty composition (sūʾ al-taʾlīf). For example, someone's saying: “Time encompasses events, and the celestial sphere also encompasses them”, producing “So time is the celestial sphere.” This is the second , and the condition that the two differ in and is missing in it, since here both are affirmative. Now we mention some of the fallacies (mughālaṭāt) whose cause is a defect in the form. We say: among the formal fallacies is begging the question (al-muṣādara ʿalā l-maṭlūb), as in “Zayd is a human, because he is a human being (bashar), and every human being is a human.” Among them is taking what is so accidentally (bi-l-ʿaraḍ) in place of what is so essentially (bi-l-dhāt), as in “The one sitting in the ship is moving, and nothing that moves stays fixed in one place.” Among them is the middle term's not being repeated in full, as when it is said: “Human has hair, and all hair grows [like a plant]”, producing “Human grows [like a plant].” For the middle term is “has hair”, and it was not made, in full, the of the major premise. Among them is the middle term's not being the same in the two premises, because it differs as to potentiality and actuality, as in “The silent one is a speaker, and the speaker is not silent”, producing “The silent one is not silent.” Among them is a flaw in the construction arising from a doubt whether a qualification belongs to the subject or to the , as in their saying: “Human alone is laughing, and everything laughing is an animal”, producing “Human alone is an animal.” The error arose only from imagining that the word “alone” is part of the subject. Had it been made part of the predicate, so that one said: “Human is: that which alone is laughing; and everything that alone is laughing is an animal”, the conclusion would be true, because it would then be “Human is an animal.” So the error in this example comes from a faulty view of the predication. Among them is the 's not being predicated, in the major premise, of all the individuals of the middle term, as when you say: “Every human is an animal, and animal is general, or a , or said of many that differ in their ”, which produces “Every human is general, or a genus, or said of many that differ in their realities.” That is certainly false. The cause of the error is only the neglect of the universality of the major premise: the major premise is a natural (ṭabīʿiyya), so the judgement does not pass on [to the individuals]. Among them is [the error] that occurs because the copulas come before or after the negations, and likewise because the modality (jiha) comes before or after the negations: as in “Zayd is not standing” (Zayd laysa huwa bi-qāʾim) and “Zayd is not-standing” (Zayd huwa laysa bi-qāʾim); “necessarily it is not” and “it is not necessarily”; and “it is not required that it be” [as against] “it is required that it not be”. The multiplying of negations also belongs to this chapter: the even degrees, such as the negation of a negation, and the negation of the negation of the negation of a negation, are affirmation; and the odd ones, such as the negation of the negation of a negation, and so on, are negation. Among them is taking mental considerations (iʿtibārāt dhihniyya) and intellectual predicates as things in external reality: as when it is said “Human is ”, and one supposes that it is so in external things. That supposition is not correct, for universality attaches to things only in the mind, not outside it. Through this verification another fallacy (ughlūṭa) is resolved. It is set out as follows: “The impossible exists; for if something were impossible outside [the mind], its impossibility would obtain outside, and so the impossible would exist outside.” So the existence of the impossible would follow, which is certainly false. The way it is resolved: impossibility is a mental consideration; a thing's being qualified by it does not require that [impossibility] exist outside, so as to require that what is qualified by it exist outside. Among them is taking the image (mithāl) of a thing in place of the thing, as when you say of an image of fire: “It is fire, and all fire burns, so it burns.” This confusion is what the deniers of mental existence argued from, when they said: if things were present [in the mind] in themselves, the mind would have to burn when it fire, be pierced when it conceives a mountain, and be qualified by whiteness and blackness when it conceives them, and so on. Its resolution is that it belongs to taking what is so accidentally in place of what is so essentially. That is, burning, piercing and the like are among the accidents that attach to a thing when it exists with original, external existence; they are not among the accidents of shadow, mental existence (al-wujūd al-ẓillī al-dhihnī). Among them is taking part of the cause in place of the cause: as when seventy men carry a heavy stone seventy parasangs, say, and one imagines that one of them alone would carry it one parasang. Among them is applying the argument from priority (awlawiyya) where [the two cases] differ, as when you say: “Human has no more claim than the sparrow to receive the rational soul, since the two share in animality.” Among them is what arises from carelessness about the respects (ḥaythiyyāt) [in which something is said] and from not attending to them, as in someone's saying: “Every white thing has whiteness entering into its reality, and Zayd is white”, so that whiteness would have to enter into his reality. The source of the error here is that whiteness is in the concept of “white” insofar as it is white, not insofar as it is an animal and a human. Among them is their saying: the like of a like is a like; as in “Human is like the palm tree, and the palm tree is like the stone in not having a soul”, so it would follow that Zayd is inanimate. What misleads here is that the palm tree's likeness to human is in one thing, say tallness, and its likeness to the stone is in something else. Among the things that lead into error is taking the privation that is opposed to possession (al-ʿadam al-muqābil li-l-malaka) in place of the contrary and the . Such is rest: it is the absence of motion in what is apt to move; and such is blindness: it is the absence of sight in what is apt to see. So one supposes that the stone is at rest and the wall is blind. Among the well-known fallacies is their saying: an unknown cannot be . For when that unknown is obtained, by what would it be known that it is what you were seeking? So either the ignorance must remain, or the [of it] must exist beforehand so that you recognise that it is the one; and on either supposition acquiring it is impossible: on the first, because it is impossible to recognise it when it is found; on the second, because it is impossible to acquire what has already been acquired. The answer is that what is sought is known in one respect and unknown in another. So after the unknown is obtained, it is known, through the known respect that singles it out, that it is what was sought. This is like a runaway slave when he is found: he was known in his person and unknown in his whereabouts, so once he was found you recognised, by what you already knew of his person and his appearance, that he was your runaway.
If no were true, “Zayd is standing” would not be true; and whenever “Zayd is standing” is not true, its , I mean “Zayd is not standing”, is true. This produces: whenever no proposition is true, “Zayd is not standing” is true; and yet it is one of the propositions. The resolution: the suppositions (taqādīr) taken in the , I mean your words “Whenever ‘Zayd is standing’ is not true, its contradictory, I mean ‘Zayd is not standing’, is true”, are either actual (wāqiʿiyya) or more general. If they are actual, its truth is granted, but [the 's case] is not included under it: for the judgement in the minor premise is only on hypothetical, non-actual suppositions, necessarily so, since that no proposition at all is true is among the impossible things. It is necessarily so because our saying “The Necessary [Being] exists”, or “is hearing”, or “is seeing” is necessarily true, so its not being true is impossible. If the suppositions of the major premise are more general, we do not grant its universality: for the falsity of a thing entails the truth of its contradictory only in actuality, since on an impossible supposition both contradictories may be false together, because the impossible may entail another impossible. Close to this fallacy is the fallacy of general application, by which any claim you like can be proved, whether true or false. We say: the claim holds; for if the claim did not hold, its contradictory would hold; and whenever its contradictory holds, something holds. This produces: if the claim did not hold, something would hold. By (ʿaks al-naqīḍ) this to: if nothing held, the claim would hold; and yet [the claim] is something. This is absurd (khulf). Thinkers have been perplexed in resolving it. Some say: we do not grant that this converts by this conversion into that conditional. How could it, when the “thing” in the original and in the converse differ in generality and specificity? Rather, the converse of this conditional is our saying: “Whenever that thing does not hold, the claim holds”, and that is true. Or, if you like, put it another way: the converse of that conditional is “If nothing held within the contradictory of the claim, the claim would hold.” Others answer that the in the converse is impossible, and the impossible may entail its contradictory; so nothing absurd follows. This chapter has been treated at length because the handbooks written in this which it is customary to read in this time of mine lack a detailed treatment of the chapter on (mughālaṭa). So I saw fit to adorn this treatise of mine with it, so that it may benefit learners and be useful to students.
It must be known that if one of the two of a is not demonstrative, but is dialectical, rhetorical, poetic or something else, the syllogism too is not demonstrative; and the same holds for the dialectical syllogism and its counterparts. In short, what is composed of the stronger and the weaker is weaker. Here the discussion of the is complete, and with it the aims of the art in both its kinds are complete, I mean what leads to and what leads to .
Every science has three things. The first is the (mawḍūʿ): that whose accidents, which attach to it, are investigated in the science; like the human body for medicine, the word and speech for grammar, continuous magnitude for geometry, and what is known by and what is known by for this of mine. It should be known that neither the existence of the subject nor its is investigated in the science of which it is the subject. So the physician does not investigate the human body insofar as it is existent, a growing body, or a rational animal; nor does the grammarian investigate the of the word and of speech. Hence, since the subject of natural science is body as such, and the master of this discipline sets out the discussions of prime matter (hayūlā) and form in the natural sciences, the difficulty was raised against him that prime matter and form are among the parts and constituents of body: so how can he set out these discussions in the natural sciences? The excuse offered on his behalf is that these discussions are digressions. The second is the principles (mabādī). The principles are what the questions are built on. They are either conceptual, that is, definitions given of the subject of the art, of its parts, its and its essential accidents; or assent-related, namely the of which its syllogisms are composed. These are either (badīhī), and are called axioms (al-ʿulūm al-mutaʿārafa); or not immediate but and granted. If they are granted out of good opinion of the one who put them forward, they are called posited principles (uṣūl mawḍūʿa); if they are granted with reluctance, [such a premise] is called a postulate (muṣādara). The third is the questions (masāʾil): what the science contains, and which it tries to establish by proof.
Know that the ancients used to mention eight things at the beginnings of books, and called them the eight headings. The first is the aim, I mean the final cause, so that the reader does not act in vain. The second is the benefit, so that the hardship of acquiring [the science] is made easier for him. The third is the name, I mean the title of the science, so that the reader has a summary of what the aim sets out in detail. The fourth is the author, so that the learner's heart may be at rest. The fifth is the rank it holds, so that it is known which science it must come before and which it must come after. The sixth is which science it belongs to, so that what befits it may be sought. The seventh is the division, that is, the chapters of the science and of the book. The eighth is the modes of instruction: division, analysis, and , so that it is known whether the book contains all of them or some. I say, I being Muḥammad Faḍl-i Imām al-Khayrābādī: this is the end of what we wished to gather and compose in this treatise from the books of the ancients and the words of the later scholars. The aim of this composition is nothing but the instruction of beginners and making things easy for students. So if this hasty work benefits you even a little, O eager student, do not forget me in a prayer for a good end and for deliverance from al-Ḥāṭima [the Crushing Fire]. May God bless our master Muḥammad, the Seal of the Prophets, first and last, outwardly and inwardly; and praise be to God, Lord of the worlds.