Al-Mirqāt: the book

1The title and the purpose

Mirqāt (Arabic al-mirqāh or al-mirqāt) means a ladder or a step: something one climbs. The book is also catalogued as al-Mirqāt al-mīzāniyya, ‘the ladder of the balance’, because Faḍl-i Imām, like many Indian logicians, calls logic ʿilm al-mīzān, ‘the science of the balance’. In Urdu it is simply Mirqāt.

The author states his aim in two places. The short preface presents the book as ‘a number of chapters on the science of the balance, which anyone of intelligence who wants to remember must memorise and master’. At the end he names himself and explains: ‘This is the end of what we wanted to gather and compose in this treatise from the books of the ancients and the words of the later scholars. The purpose of this composition is nothing but to teach beginners and to make things easy for students; that is why we did not write in an extremely concise style.’ He closes by asking the student who has profited from ‘this hasty piece’ to pray that he may die well.

The book is therefore meant as a second step: longer and more discursive than the very short primers, but still a book for beginners. Today it is usually read after a first primer (often Taysīr al-manṭiq, or al-Abharī’s Īsāghūjī) and before al-Taftāzānī’s Tahdhīb al-manṭiq; see ‘Al-Mirqāt in the madrasa’.

2Structure

The text consists of about ninety-five short chapters, almost all headed simply faṣl (‘section’), a few called fāʾida (‘useful note’) or tanbīh (‘remark’). The lithographs also group them into larger parts: after an introduction, a first part leads from the kinds of knowledge to definition, and a second part, headed ‘on the argument (ḥujja) and what belongs to it’, begins with propositions and runs to the end. A conclusion (khātima) on the parts of a science and the ‘eight headings’ closes the book.

In print the matn fills about thirty lithographed pages: the Delhi lithograph of 1286/1869 has the text on pages 2–32, and the British Library’s Delhi edition of 1886 has 32 pages in all. This makes it several times longer than al-Abharī’s Īsāghūjī, though far shorter than the handbooks read later in the course.

3Contents: knowledge, words and universals

The book begins with knowledge itself. It lists five meanings of the word ʿilm (the occurrence of a form in the mind, the form itself, what is present to the knower, the soul’s reception of the form, and the relation between knower and known), divides knowledge into conception (taṣawwur) and assent (taṣdīq), and sets out the dispute between ‘the philosophers’, for whom assent is the judgement alone, and ‘the Imām’ Fakhr al-Dīn al-Rāzī, for whom it is the sum of three perceptions. It then explains what reasoning (naẓar) is, why a set of rules is needed to keep reasoning from error, and what the definition, subject and aim of logic are.

The next chapters deal with words: why the logician must discuss them at all, the three kinds of verbal signification (by correspondence, inclusion and implication), simple and composite expressions, and the kinds of simple words. A separate chapter warns against confusing the logicians’ ‘word’ (kalima) with the grammarians’ verb: a verb like aḍribu (‘I hit’) is a single verb in grammar but a composite expression in logic, because a part of it signifies a part of its meaning. There are chapters on homonyms, transferred words, literal and figurative use and synonyms, and on complete and incomplete composite expressions.

The core of the first part is the theory of universals: universal and particular, the four relations between two universals, the five universals (genus, species, differentia, proprium, common accident), the ordering of genera and species from the highest to the lowest, and the division of accidentals into the inseparable and the separable. Unlike the Īsāghūjī, al-Mirqāt also lists the ten highest genera, the categories: substance and the nine kinds of accident. Its notes explain that this is strictly a topic of philosophy, which the early logicians included to give students examples and which the author kept for that reason. The part ends with definition: the complete and incomplete essential and descriptive definitions, and the merely verbal definition.

4Contents: propositions and arguments

The second part begins with propositions. It covers categorical propositions and their three parts, singular, quantified and unquantified propositions and the quantifiers, the conventions of writing ‘J’ and ‘B’ for subject and predicate, what predication is, propositions about existing and about merely supposed subjects, ‘metathetic’ propositions with a negated term, and a long treatment of modality: fifteen modal propositions, eight simple and seven compound. Conditional propositions follow, connective and disjunctive, with their kinds and quantifiers.

Then come the ‘secondary’ topics: contradiction, with its conditions for quantified, modal and conditional propositions; simple conversion; and contraposition, where the book sets the procedure of ‘the earlier’ logicians beside that of ‘the later’ ones. The conversion of modal and conditional propositions it leaves, explicitly, to ‘the long books’.

The theory of argument (ḥujja) names three kinds of argument, syllogism, induction and analogy, and opens with the syllogism. The book defines the conjunctive (iqtirānī) syllogism and its four figures, with the conditions under which the second, third and fourth figures produce a conclusion; for the fourth figure it refers the student to longer works. It adds conjunctive syllogisms made of conditional propositions, the exceptive (istithnāʾī) syllogism, induction, analogy (with the method later scholars call dawarān), compound syllogisms and the reductio, or ‘syllogism of the absurd’ (qiyās al-khalf).

5Contents: the five arts, fallacies and the eight headings

The last third of the book is unusually generous to what the logicians call the ‘matter’ of arguments, as distinct from their form. The author explains why. The ancient logicians, ‘even al-Shaykh al-Raʾīs’ (Ibn Sīnā), took great care over the matter of syllogisms, which is the more useful knowledge; ‘but the later scholars lengthened the discussion of the form of syllogisms, especially conditional ones, though these discussions are of little use, and neglected the matter, contenting themselves with the definitions of the five arts. I do not know what led them to this.’ He then turns to the reader: ‘So you, dear son, must listen to my advice and not forget my counsel’, and asks him to seek this subject in the books of the ancients.

The five arts (ṣināʿāt) follow: demonstration (burhān), built from certain premises, with the six kinds of self-evident premises and the distinction between demonstration ‘why’ (limmī) and ‘that’ (innī); dialectic; rhetoric; poetics; and sophistry. Two further chapters classify the causes of error (asbāb al-ghalaṭ), first those that come from words and then those that come from meanings, and a last chapter of the part notes that an argument with even one non-demonstrative premise is no longer a demonstration. ‘With this’, the author writes, ‘the aims of the art in both its kinds, what leads to conception and what leads to assent, are complete.’

The conclusion explains what every science has: a subject, principles (definitions, axioms and postulates) and problems. The very last chapter gives the ‘eight headings’ (al-ruʾūs al-thamāniya) with which, the author says, the ancients used to open their books: aim, use, name, author, rank among the sciences, the science to which it belongs, division into parts, and methods of teaching. Putting this traditional preface at the end of the book is one of al-Mirqāt’s peculiarities.

6How it teaches

Al-Mirqāt is written in plain didactic prose. Most chapters give a definition, divide it, and illustrate it with the familiar school examples: ‘every human is an animal’, ‘the world changes, and everything that changes is originated, so the world is originated’, a number that is even or odd. The author often speaks to the student directly, with ‘know that…’ (iʿlam), ‘beware of thinking that…’ (iyyāka wa-an taẓunna), and in the passage on the five arts with personal advice.

Unlike the Īsāghūjī, it names positions and disputes: the philosophers against al-Rāzī on assent, the earlier against the later logicians on contraposition, and the critique of the later logicians’ neglect of the matter of arguments. These remarks are short, but they give the commentators their starting points. The notes in modern editions draw mainly on two commentaries, that of the author’s grandson ʿAbd al-Ḥaqq Khayrābādī and the gloss al-Mirḍāt of ʿAbd al-Ḥakīm Sharaf Qādirī; see ‘Commentaries, glosses and translations’.