Sullam al-ʿulūm: the book

1The title and the date

Sullam means a ladder. In the preface the author names the book and states its subject: ‘This is a treatise on the science of the balance [i.e. logic]. I have called it the Ladder of the Sciences. Lord, make it among base texts like a sun among stars!’ The commentators read this short prayer as answered. Mullā Mubīn (d. 1225/1810) explains that when the sun rises the stars can no longer be seen, and that God granted the prayer: scholars wrote commentaries on the book, it spread among the students of the madrasas, ‘and other base texts came to be obscured’.

The text carries no date. Asad Q. Ahmed, whose study and English translation (2022) are the main modern work on it, places it in the second half of the eleventh/seventeenth century and before 1109/1698, the year in which al-Bihārī wrote his book on legal theory, Musallam al-thubūt; the TDV İslâm Ansiklopedisi notes that al-Bihārī refers to his own Sullam in the logical parts of the Musallam. It was probably written in Lucknow or Delhi, where its author served the Mughal emperor Awrangzīb. The book spread fast: what may be the first full commentary, by al-Sāʾinpūrī, was finished in the first half of 1119/1707, the year of the author’s death, and already describes the Sullam as well known.

2A short book in the shape of the great handbooks

Before the Sullam, according to Ahmed, the three most widely read logic books in India were al-Kātibī’s Shamsiyya, read with the commentary of Quṭb al-Dīn al-Rāzī (al-Taḥtānī) and al-Jurjānī’s glosses; al-Taftāzānī’s Tahdhīb al-manṭiq, read with the commentaries of ʿAbd Allāh al-Yazdī and al-Dawānī and Mīr Zāhid al-Harawī’s gloss on al-Dawānī; and al-Urmawī’s Maṭāliʿ al-anwār. The Sullam follows their order of topics, and even the space it gives each topic is in proportion to theirs. Its structure matches the Tahdhīb most closely, which Ahmed explains by the Tahdhīb’s dominance in India just before the Sullam appeared.

Like those books it has two parts: ‘conceptualizations’ (taṣawwurāt), the part on concepts, words, universals and definition, and ‘assents’ (taṣdīqāt), the part on propositions and arguments. A proem, a preface and an introduction on knowledge come first; a one-sentence ‘final thought’ and a one-sentence conclusion close the book. Ahmed’s translation divides the text into fifty-two numbered paragraphs. It is short, but every line is compressed, and the later tradition read it almost always through its commentaries; from the late twelfth/eighteenth century many commentaries went only as far as the section on conditional propositions (see ‘The commentaries’).

3Contents

The introduction defines knowledge as conception (taṣawwur), ‘what is present for the one who apprehends’, and adds that it is among the most evident things, ‘like light and happiness’, though its reality is hard to examine. It then divides knowledge into conception and assent and at once raises a ‘well-known doubt’: if knowledge and the thing known are one, then conceiving an assent would make the two one, although they are said to be distinct. The author offers a solution ‘that I am unique in offering’. The introduction goes on to prove that not all knowledge can be acquired by reasoning, since that would lead to circularity or an infinite regress; it answers ‘a doubt which was addressed to Socrates’, the old puzzle of how one can seek what one does not already know; and it defines logic as a body of rules that protects the mind from error, whose subject is ‘intelligibles insofar as they lead to conception and assent’. A short section lists the four basic questions: what, which, whether and why.

The part on conceptualizations opens with the puzzle of the ‘absolutely unknown’ (al-majhūl al-muṭlaq), about which, it seems, nothing can be judged. It then treats signification (by correspondence, inclusion and implication), simple and compound expressions, particles and verbs (with the remark that forms such as ‘I walk’ are verbs for the grammarians but not for the logicians, because they can be true or false), universals and particulars, homonyms and other kinds of words, literal and figurative speech, synonyms, statements and propositions (where the liar paradox appears), the contradictories of universals, the five universals and their nature, the logical, natural and mental universal, and definition.

The part on assents covers judgment and the parts of a proposition, the kinds of propositions, conditionals, the subject term and quantification, predication, modal propositions, conditional propositions in detail, contradiction, conversion and ‘contradictory conversion’ (ʿaks al-naqīḍ). The theory of argument follows: the definition, kinds and conditions of the syllogism, modal, conditional, exceptive and compound syllogisms, induction and analogy, the principles and kinds of demonstration, and the remaining four ‘arts’: dialectic, rhetoric, poetics and sophistics. The ‘final thought’ states that an argument made of stronger and weaker premises falls into the weaker class; the conclusion, that ‘the parts of the sciences are [only] the problems’, while the principles are among the means of solving them.

4A text that asks for commentary

Ahmed describes the Sullam as a concise teaching text that holds the earlier tradition inside its own sentences. It does not summarize named authorities, as an abridgement would; it builds a new and consistent position out of a ‘patchwork’ of earlier texts, sometimes quoted word for word, and it is ‘laden with puzzles, obscure points, insolubles, hints, and gestures’. Many of its statements answer debates in the commentaries on the Shamsiyya and the Tahdhīb without naming them, and Mīr Dāmād’s al-Ufuq al-mubīn forms what Ahmed calls an undercurrent of some of its solutions. The author’s own glosses on the book did not remove these difficulties; in Ahmed’s reading they were meant to guide later commentators toward solutions rather than to supply them.

The commentators said the same in their own way. Qāḍī Mubārak (d. 1162/1749) calls the book ‘a heavenly book (ṣaḥīfa malakūtiyya), from which the rivers of the real disciplines flow’, and speaks of its ‘knots’ and ‘obscurities’. Mullā Mubīn calls it ‘among the most subtle and precise of base texts written in logic’ and ‘utterly inaccessible’, and complains that earlier commentators added new investigations of their own instead of explaining it. Ḥāfiẓ Darāz (d. 1263/1847), who glossed Mubārak, says that the lemmata of the Sullam ‘are like the sun among the stars’. This difficulty was part of the book’s purpose. The madrasa course associated with Mullā Niẓām al-Dīn of Farangī Maḥall was known for reading the hardest books of each subject; Francis Robinson describes Niẓām al-Dīn’s method as teaching ‘the two most difficult books in each subject’, on the grounds that the rest would then present few problems.

5The liar paradox (al-jadhr al-aṣamm)

The most famous passage of the Sullam comes in the section on propositions. A proposition is defined, as in the older handbooks, as a statement that can be true or false. Al-Bihārī then adds a problem that none of those handbooks raises: ‘One may say that “This speech of mine is false” is not a statement, because a report about itself is nonsensical. The truth is that when this statement is taken, with all its parts, as the subject, the relation in it is considered in compressed form (ijmālan), so that it is that about which there is a report; and insofar as a statement is generated by means of the relation, the relation is considered in expressed form (tafṣīlan), so it is a report. So the difficulty is resolved in all its manifestations.’ He compares the sentence ‘Every praise is for God’, which is itself a praise and so falls under ‘every praise’, and ends: ‘So ponder this! For this is an irrational root (jadhr aṣamm).’

The problem is the ancient liar paradox: if the sentence is true, it is false, and if it is false, it is true. The Arabic name al-jadhr al-aṣamm (Ahmed vocalizes it jidhr) means ‘the irrational root’, literally ‘the deaf root’. According to David Sanson’s survey of the liar in Arabic philosophy, al-Taftāzānī (d. 793/1390) gave the paradox this name without explaining it, and later authors could only guess why. Ahmed notes that the expression comes from mathematics and may mean that the problem runs on without end; Mullā Mubīn says that aṣamm is used in its literal sense, ‘deaf’, because one never hears a solution to the problem.

Ahmed traces the background of the passage. The view the Sullam rejects first, that such a sentence is no statement at all because a report and what it reports on must be distinct, is al-Dawānī’s, from his commentary on the Tahdhīb; al-Dawānī compared it to a sketch that claims to be a sketch of itself and so cannot be wrong. The distinction between the ‘compressed’ and the ‘expressed’ consideration of a proposition comes from another debate, in al-Jurjānī’s and al-Siyālkūtī’s glosses on Quṭb al-Dīn al-Rāzī’s commentary on the Shamsiyya, about how to tell predicative propositions from conditional ones. The example ‘Every praise is for God’ is aimed at al-Dawānī: Mubīn explains that al-Dawānī accepted that sentence as a statement, so he would have to accept the Sullam’s solution for the liar as well.

The passage gave rise to a large literature. The early commentator al-Sāʾinpūrī distinguished three things the words ‘this speech’ might refer to and discussed a two-sentence version of the paradox (on Thursday someone says ‘What I say on Friday is true’, and on Friday ‘What I said on Thursday was false’). Fīrūz b. Maḥabba held that a distinction made only by the mind is enough and that al-Dawānī’s requirement of a real distinction was a mistake. Kamāl al-Dīn al-Sihālawī wrote a commentary on difficult parts of the Sullam ‘such as the liar paradox’, and Khalīl al-Raḥmān al-Muṣṭafābādī wrote a separate treatise on it, printed in 1268/1851–52. Modern studies of these debates include Hassan Rezakhany’s article on al-Dawānī’s solution and its reception by Qāḍī Mubārak and Mullā Mubīn (2018); Sanson’s survey notes that the liar ‘was widely discussed within the Indo-Muslim tradition’.

6Other puzzles and a common method

The liar is only one of many puzzles in the book. Ahmed lists the subjects on which the Sullam inspired separate treatises: the liar paradox, ‘copular existence’ (al-wujūd al-rābiṭī), the ‘absolutely unknown’, the nature of knowledge, simple and compound ‘making’ (jaʿl basīṭ and murakkab), and the ‘paradox of entailment’ (shubhat al-istilzām). These problems had been discussed before, but in India they were often approached through the Sullam and its commentaries. On the absolutely unknown, for example, the Sullam answers that it is ‘known per se and absolutely unknown per accidens’, so that affirming and denying a judgment about it concern two different considerations; ʿAbd al-Ḥayy al-Laknawī (d. 1304/1887) wrote his treatise Ḥall al-mughlaq on this point when one of his students reached it.

Ahmed sees one method behind the solutions. Again and again the Sullam resolves a paradox by showing that two different ways in which the mind considers the same thing (iʿtibār, mental consideration) have been confused: knowledge as a form that arrives in the mind is the thing known, and as a form that subsists in the mind it is knowledge; Zayd conceived in many minds is not a universal, because a universal is defined by the possibility of many instances outside the mind; an apparent infinite regress of ‘concomitances’ stops when the mind stops considering. Its commentators quote the maxim ‘Were it not for considerations, philosophy would be falsified’. The same concern leads them into the question of what it means for a mental consideration to be true ‘in itself’ (fī nafs al-amr).

This orientation explains why the commentaries on the Sullam reach so far into metaphysics and theology. Ahmed quotes Bakhtiyār Ḥusayn Ṣiddīqī’s Urdu study of the old Arabic madrasas of the subcontinent (Lahore, 1982): Mullā Ḥasan, Ḥamd Allāh and Qāḍī Mubārak ‘are books on logic’, yet most of their investigations concern divine knowledge, simple and compound making, the existence of the natural universal outside the mind, mental existence and similar questions. In Ahmed’s view these subjects belong to the Sullam’s own concern with puzzles about what the subject of a proposition can refer to.

7Reading the Sullam today

There is no critical edition. Ahmed based his translation on the text printed with Muḥammad Barakat Allāh’s gloss Iṣʿād al-fuhūm, because that lithograph is easy to obtain and widely used in South Asian madrasas, and he explains its sense mainly from Mullā Mubīn’s commentary Mirʾāt al-shurūḥ. He calls a proper edition ‘a desideratum’, but adds that in a commentary tradition, where the wording of the text grew and shrank from one commentary to the next, a historical edition that shows these changes would be more useful than one that tries only to recover the author’s autograph. The commentaries themselves, the transmission of the book and its place in teaching today are described in the following articles.