al-Sullam al-munawraq ʿAbd al-Raḥmān al-Akhḍarī

Praise be to God, who has brought forth the results of thought for people of understanding, and has removed from them, from the sky of the intellect, every veil of the clouds of ignorance, until the suns of knowledge appeared to them and they saw its hidden brides unveiled.

We praise Him, exalted is He, for His favour — the gift of faith and of Islam — who singled us out with the best of those ever sent, the best of those who attained the highest stations: Muḥammad, master of all who are followed, the Arab, the Hāshimī, the chosen one. May God bless him as long as the mind wades into the depths of the sea of meanings, and his family and companions, people of guidance, who were likened to stars to be guided by.

Now then: logic is to the mind what grammar is to the tongue. It guards thought against the error of mistakes and lifts the veil from subtle understanding. So here are rules from its foundations, gathering benefits from its branches.

I have named it al-Sullam al-munawraq, the Embellished Ladder, by which one climbs to the sky of the science of logic. I hope from God that it will be purely for His noble face, not falling short, and that it will benefit the beginner, so that by it he finds his way to the longer works.

There is disagreement about whether one may busy oneself with it, in three views: Ibn al-Ṣalāḥ and al-Nawawī forbade it; some said it ought to be learnt;

and the well-known, correct view is that it is permitted for someone of sound mind who is practised in the Sunna and the Book, so that he is guided by it to what is right.

Perceiving a single thing is known as conception; perceiving a relation is called assent. Put the first first when setting out, because it comes first by nature.

The theoretical is what needs reflection, and its opposite is the necessary, the evident. What leads to a conception is called an explanatory phrase — so take note; and what is used to reach an assent is known among the wise as a proof.

The signification of a word on what it fits exactly they call correspondence; on its part, inclusion; and on what is bound to it, implication — if the binding is made by the intellect.

Words in use, wherever they occur, are either composite or single. The first is that whose part signifies a part of its meaning; the opposite of this is what follows.

The single, I mean, is of two kinds wherever it is found: universal or particular. What conveys sharing is the universal, like “lion”; its opposite is the particular.

First, ascribe it to the essence if it is included in it, or to an accident if it lies outside. The universals are five, nothing missing: genus, differentia, accident, species and property. The first is of three kinds, no exaggeration: near genus, far, or in between.

The relation of words to meanings is of five kinds, nothing lacking: univocal, graded, distinct, equivocal, and its opposite, synonymous.

Speech is either a request or a report. The first is of three kinds, to be named: a command, with superiority; its opposite, a supplication; and between equals it is called a request (iltimās).

The whole is our judgement on the totality, as in “all of that did not happen”; and wherever a judgement is made on each individual, it is a universal judgement, as is known. A judgement on some is the particular one, and the part is plain to know.

The definer is divided into three: real definition, description and verbal definition, as is known. The real definition is made of genus and differentia together, and the description of genus and property together. The incomplete definition is by the differentia alone, or together with a far genus, not a near one.

The incomplete description is by the property alone, or joined with a farther genus. What is known among them as verbal is replacing a word by a better-known synonym.

The condition of each is that it be seen to hold wherever the defined holds and the reverse, clear, not more obscure, nor equal in obscurity, nor figurative without a sign that guards against error, nor by what is known only through the defined, nor equivocal without a sign.

Among what they reject is bringing judgements into definitions. In definitions “or” may not be mentioned, but it is allowed in a description — so know what they have handed down.

What can be true in itself is called among them a proposition and a report. Propositions, among them, are of two kinds: conditional and categorical; and the second is universal or personal, and the first is either quantified or neglected.

The quantifier is found universal and particular, and its kinds are four wherever it occurs: with “every”, with “some”, with “no”, and with “not some” or the like, as is clear. And all of these are affirmative and negative, so they come to eight.

The first part in a categorical is the subject, the last the predicate, in the same way. If in it the judgement is made on a condition, it is a conditional, and it too divides into a connective conditional and, like it, a disjunctive conditional.

Their two parts are the antecedent and the consequent. As for the account of the connective: it is one that requires the two parts to go together; and the disjunctive, without falsehood, is one that requires them to be incompatible. Its kinds are three, so know them: excluding being together, excluding being absent, or both — and that is the real disjunctive, the narrowest, so know it.

Contradiction is the difference of two propositions in quality, such that the truth of one follows. If it is personal or neglected, its contradictory is made by changing the quality; if it is quantified with a quantifier, contradict it with the opposite of its quantifier.

If it is a universal affirmative, its contradictory is a particular negative; if it is a universal negative, its contradictory is a particular affirmative.

Conversion is turning round the two parts of the proposition, while truth, quality and quantity remain — except the universal affirmative, whose replacement is the particular affirmative. Conversion holds for all but those in which the two weaknesses meet, so be moderate;

and like it is the neglected negative, because it has the force of the particular. Conversion is in what is ordered by nature, not in what is ordered by convention.

The syllogism is composed of propositions and entails of itself another statement. The syllogism, among them, is of two kinds: one is called conjunctive, which points to the conclusion potentially and is limited to categoricals.

If you want to build it, put together its premises as is required: order the premises and look, testing the sound from the unsound, for what follows from the premises comes according to the premises.

The premise that is the minor must fall under the major. The one with the minor term is the minor of the two, and the one with the major term the major; the minor term is the one that falls under, and the middle term is dropped in the conclusion.

The figure, among these people, is said of the two propositions of a syllogism without regard to the quantifiers, for with those it is called a mood. The premises have only four figures, according to the middle term.

Predicate in the minor and subject in the major is called the first figure, as is known; predicate in both is known as the second; subject in both is called the third; and the fourth of the figures is the reverse of the first. They come in order of perfection, so wherever this arrangement is departed from, the arrangement is unsound.

As for the first, its condition is affirmation in its minor and that its major be universal. For the second, that they differ in quality, with the universality of the major: this is its condition. For the third, affirmation in the minor and that one of the two be universal.

For the fourth, that the two weaknesses not be joined, except in one form, which you will find: its minor a particular affirmative and its major a universal negative.

So the first produces four moods, like the second; then the third, six; and the fourth produces by five; anything other than what I have mentioned will not produce. The conclusion follows the weaker of those premises: so it is known.

These figures belong to the categorical, not to the conditional. A premise or the conclusion may be left out when it is known. And the premises end in what is necessary, because of the circle or the endless regress that would otherwise follow.

Another kind is called the exceptive, known as the conditional syllogism without doubt: it is the one that shows the conclusion or its contrary in actuality, not potentially.

If the conditional is connective, affirming the antecedent produces the affirmation of the consequent, and denying the consequent the denial of the antecedent; it does not follow in the reverse of these, as has become clear.

If it is disjunctive, affirming this produces denying that, and the reverse likewise — that is in the narrowest, the real one. Then, if it excludes being together, by affirming this the denial of that is known, without the reverse; and when it excludes absence, it is the reverse of this.

Another kind they call the compound, because it is built from several proofs. Build it, if you want to know it, and turn a conclusion into a premise: from putting it with another, a conclusion follows, and so on. With its conclusions stated or left out, all is the same.

If one argues from particulars to a universal, this is understood among them as induction; the reverse is called the logical syllogism, the one I have set out, so be sure of it. And wherever one particular is judged by another because of something they share, that is made an analogy. Induction and analogy do not give certainty by their proof.

Proof is transmitted or rational; the kinds of the latter are five, clear: rhetoric, poetry, demonstration, dialectic, and the fifth, sophistry — you have reached your hope. The noblest of them is demonstration: what is composed of premises joined to certainty,

from first principles, things witnessed, things tested by experience, things reported by many, things grasped by intuition and things sensed: these are all the certain premises. On how premises point to the conclusion there is disagreement: rational, customary, by generation, or necessary — and the first is the one supported.

An error in a demonstration, wherever it is found, lies in the matter or in the form. The first is in the wording, like equivocation, or like taking as distinct what is synonymous; and in the meanings, through a false premise being confused with a true one — so understand what is said:

like treating the accidental as the essential, or taking the conclusion as one of the premises, or judging the genus by the judgement of the species, or treating the uncertain as certain. The second is like leaving its figures, or leaving out a condition of producing from its completeness.

This completes the intended aim among the mothers of praiseworthy logic. By the praise of the Lord of the daybreak, what I sought from the science of logic is finished. The lowly, needy servant put it in verse, in need of the mercy of the great, mighty Master: al-Akhḍarī, ʿAbd al-Raḥmān, hoping from his generous Lord

for forgiveness that covers all sins and lifts the veil from hearts, and that He reward us with the high Garden, for He is the most generous of those who give.

Be lenient, my brother, with the beginner, and be a sincere helper in setting right what is wrong. Set right what is wrong after reflection, and do not change things on first sight, for it has been said: how many have found fault with what is sound only because their understanding was poor! And say to whoever does not do my purpose justice: the excuse is a right owed to the beginner,

and for a youth of twenty-one years an excuse is accepted and fitting, above all in the tenth century, the age of ignorance, corruption and strife. The writing of this ordered rajaz was at the beginning of Muḥarram of the year forty-one after nine hundred.

Then blessing and peace for ever on the Messenger of God, the best who ever guided, and his family and trustworthy companions, who travel the paths of salvation, as long as the sun of the day crosses the constellations and the shining full moon rises in the dark.