Logic in the Islamic Legacy: a General Overview

Domains of Logic

The Subject Matter of Logic

Al-Farabi, in his Ihsa' al-'ulum (Enumeration of the Sciences), defines logic as an instrumental, rule-based science aimed at directing the intellect towards the truth and safeguarding it from error in its acts of reasoning. He states:

The subject matters (mawdû‘ât ) of logic are the things for which [logic] provides the rules, namely, intelligibles in so far as they are signified by expressions, and expressions in so far as they signify intelligibles.

He defends the need for such a science of reasoning on the grounds that it is possible for the mind to err in at least some of its acts, for example, in those in which the intelligibles sought are not innate, but are rather attained discursively and empirically 'through reflection and contemplation'. Al-Farabi compares logic to tools such as rulers and compasses, which are used to ensure exactness when we measure physical objects subject to the errors of sensation. Like these tools, logical measures can be employed by their users to verify both their own acts of reasoning and the arguments of others. Indeed, logic is especially useful and important to guide the intellect when it is faced with the need to adjudicate between opposed and conflicting opinions and authorities.

Al-Farabi's view of logic as a rule-based science which governs the mind's operations over intelligibles forms the foundation for Ibn Sina's later refinements. In the opening chapters of hisal-Madkhal (Introduction), the first logical book of his encyclopedic workal-Shifa' (Healing), Ibn Sina describes the purpose of logic as one of enabling the intellect to acquire 'knowledge of the unknown from the known'. He defends the need for logic by arguing that the innate capacities of reasoning are insufficient to ensure the attainment of this purpose, and thus they require the aid of an art. While there may be some cases in which innate intelligence is sufficient to ensure the attainment of true knowledge, such cases are haphazard at best; he compares them to someone who manages to hit a target on occasion without being a true marksman. The most important and influential innovation that Ibn Sina introduces into the characterization of logic is his identification of its subject matter as 'second intentions' or 'secondary concepts', in contrast to 'first intentions'. This distinction is closely linked in Ibn Sina's philosophy to his important metaphysical claim that essence or quiddity can be distinguished from existence, and that existence in turn can be considered in either of its two modes: existence in concrete, singular things in the external world; or conceptual existence in one of the soul's sensible or intellectual faculties.

Inal-Madkhal , Ibn Sina argues that logic differs from the other sciences because it considers not conceptual existence as such (this would be psychology), but rather the accidents or properties that belong to any quiddity by virtue of its being conceptualized by the mind. These properties, according to Ibn Sina, include such things as essential and accidental predication, being a subject or being a predicate, and being a premise or a syllogism. It is these properties that allow the mind to connect concepts

together in order to acquire knowledge of the unknown; they provide the foundation for the rules of reasoning and inference that logic studies. They are moreover formal properties in the sense that, as properties belonging to all concepts in virtue of their mental mode of existence, they are entirely independent of the content of the thought itself; they are indifferent to the intrinsic natures of the quiddities which they serve to link together.

In theIlahiyyat (Metaphysics) of al-Shifa', Ibn Sina introduces the terminology of first and second 'intentions' or concepts in order to express the relation between the concepts of these quiddities themselves - which are studied in the theoretical sciences - and the concepts of the states and accidents of their mental existence which logic studies: 'As you know, the subject matter of logical science is second intelligible intentions (al-ma'ani al-ma'qula al-thaniyya) which are dependent upon the primary intelligible intentions with respect to some property by which they lead from the known to the unknown' (Ilahiyyat Book 1, ch. 2,). For example, the second intentions of 'being a subject' and 'being a predicate' are studied in logic independently of whatever first intentions function as the subject and predicate terms in a given proposition, for example, 'human being' and 'rational animal' in the proposition 'a human being is a rational animal'. The logical second intentions depend upon the first intentions because the first intentions are the conceptual building blocks of the new knowledge which second intentions link together: but logic studies the second intentions in abstraction from whatever particular first intentions the logical relations depend upon in any given case.

Secondary Intelligibles

A more careful statement is provided by Avicenna. Concepts like “horse”, “animal”, “body”, correspond to entities in the real world, entities which can have various properties. In the realm of the mental, concepts too can acquire various properties, properties they acquire simply by virtue of existing and being manipulated by the mind, properties like being a subject, or a predicate, or a genus. These are the subject matter of logic, and it seems it is only mental manipulation that gives rise to these properties:

If we wish to investigate things and gain knowledge of them we must bring them into Conception (fî t-tasawwur ); thus they necessarily acquire certain states (ahwâl ) that come to be in Conception: we must therefore consider those states which belong to them in Conception, especially as we seek by thought to arrive at things unknown from those that are known. Now things can be unknown or known only in relation to a mind; and it is in Conception that they acquire what they do acquire in order that we move from what is known to what is unknown regarding them, without however losing what belongs to them in themselves; we ought, therefore, to have knowledge of these states and of their quantity and quality and of how they may be examined in this new circumstance.

These properties that concepts acquire are secondary intelligibles; here is an exposition of this part of Avicennan doctrine by Râzî:

The subject matter of logic is the secondary intelligibles in so far as it is possible to pass by means of them from the known (al-ma‘lûmât) to the unknown (al-majhûlât) not in so far as they are intelligible and possess

intellectual existence (an existence) which does not depend on matter at all, or depends on an incorporeal matter).. The explanation of “secondary intelligibles” is that man Conceives the realities of things (haqâ'iq al-ashyâ’ ) in the first place, then qualifies some with others either restrictively or predicatively (hukman taqyîdiyyan aw khabariyyan ). The quiddity's being qualified in this way is something that only attaches to the quiddity after it has become known in the first place, so it is a second-order [consideration] (fî d-darajati th-thâniya ). If these considerations are investigated, not absolutely, but rather with respect to how it is possible to pass correctly by means of them from the known to the unknown, that is logic. So its subject matter is certainly the secondary intelligibles under the consideration mentioned above (Râzî (1381 A. H.) Mulakhkhas 10.1-10.8).

In identifying the secondary intelligibles, Avicenna is able to place logic within the hierarchy of the sciences, because it has its own distinct stretch of being which is its proper subject matter.

So much for the first problem in Alfarabi's formulation of what the subject matter of logic is; finding it to be secondary intelligibles preserves the topic-neutrality of logic. Avicenna also has a view on the second problem, the question of whether or not expression is essential to a definition of logic and its subject matter.

There is no merit in what some say, that the subject matter of logic is speculation concerning the expressions insofar as they signify meanings… And since the subject matter of logic is not in fact distinguished by these things, and there is no way in which they are its subject matter, (such people) are only babbling and showing themselves to be stupid.

Conceptions and Assents

Khûnajî argued in the second quarter of the thirteenth century that the subject matter of logic was Conceptions and Assents:

A thing is knowable in two ways: one of them is for the thing to be merely Conceived (yutasawwara) so that when the name of the thing is uttered, its meaning becomes present in the mind without there being truth or falsity, as when someone says “man” or “do this!” For when you understand the meaning of what has been said to you, you will have conceived it. The second is for the Conception to be [accompanied] with Assent, so that if someone says to you, for example, “every whiteness is an accident,” you do not only have a Conception of the meaning of this statement, but [also] Assent to it being so. If, however, you doubt whether it is so or not, then you have Conceived what is said, for you cannot doubt what you do not Conceive or understand… but what you have gained through Conception in this [latter] case is that the form of this composition and what it is composed of, such as “whiteness” and “accident,” have been produced in the mind. Assent, however, occurs when there takes place in the mind a relating of this form to the things themselves as being in accordance with them; denial is the opposite of that.

Note that an Assent is not merely the production of a proposition by tying a subject and predicate together; “Assent, however, occurs when there takes place in the mind a relating of this form to the things themselves as being in accordance with them.” All knowledge, according to Avicenna, is

either Conception or Assent. Conception is produced by definition, Assent by proof. All Avicennan treatises on logic are structured in accordance with this doctrine: a first section deals with definition, which conduces to Conception, a second with proof, which conduces to Assent.

Later logicians in the line of Fakhraddîn ar-Râzî made Conceptions and Assents the subject matter of logic. We know that Khûnajî was the first to do this thanks to a report in the Qistâs al-Afkâr of Shamsaddîn as-Samarqandî (d. c. 1310). Samarqandî says:

This is the view adopted by the verifying scholars (al-muhaqqiqûn), but Khûnajî (sâhib al-kashf ) and the people who follow him differed from them and said: Logic may investigate the universal and the particular and the essential and the accidental and the subject and the predicate; they are among the questions [of the science]. You [Avicennan logicians] are taking the subject matter of logic as more general than the secondary intelligibles so that the secondary intelligibles and (especially) the secondary intelligibles you have mentioned and what follows after them may come under it as logic. It would be correct for you to say that the subject matter of logic is known Conceptions and Assents (al-ma‘lûmât at-tasawwuriyya wa-t-tasdîqiyya ) not in so far as they are [what they are] but in so far as they conduce to what is sought (al-matlûb ) …

Two logicians who followed Khûnajî on this were Abharî and Kâtibî. Here is Abharî's statement:

The subject matter of logic, I mean, the thing which the logician investigates in respect of its concomitants in so far as it is what it is, are precisely Conceptions and Assents. [This is] because [the logician] investigates what conduces to Conception and what the means [to Conception] depends upon (for something to be universal and particular, essential and accidental, and such like); and he investigates what conduces to Assent and what the means to Assent depends upon, whether proximately (like something being a proposition or the converse of a proposition or the contradictory of a proposition and such like) or remotely (like something being a predicate or a subject). These are states which inhere in Conceptions and Assents in so far as they are what they are. So certainly its subject matter is Conceptions and Assents (Tûsî (1974b) Ta‘dîl 144.14-20).

Here is part of Tûsî's rejection:

If what he means by Conceptions and Assents is everything on which these two nouns fall, it is the sciences in their entirety, because knowledge is divided into these two; whereupon what is understood from [his claim] is that the subject matter of logic is all the sciences. Yet there is no doubt that they are not the subject matter of logic…

The truth is that the subject matter for logic is the secondary intelligibles in so far as reflection on them leads from the known to the unknown (or to something similar, as do reductive arguments or persuasive arguments [146] or imaginative arguments and the like). And if they are characterised by the rider mentioned by the masters of this craft, Conceptions and Assents are among the set of secondary intelligibles in just the same way as definition and syllogism and their parts, like universal and particular and subject and

predicate and proposition and premise and conclusion (Tûsî (1974b) Ta‘dîl 144.21-u, 145.pu-146.3).

It is hard to know precisely what is being disputed. What we can note at this stage is that one point at issue has to do with the claim that Avicenna's identification of secondary intelligibles as logic's subject matter is inaccurate, and too narrow to achieve what he hopes it can.

Arguments aim to bring about Assent; more precisely, when Conceptions have been gained that produce in the mind both the meaning of the terms in a given proposition, and the form of composition of these terms, Assent “occurs when there takes place in the mind a relating of this form to the things themselves as being in accordance with them…” In fact, different kinds of discourse can bring about one or other kind of Assent, or something enough like Assent to be included in a general theory of discourse..

Since Avicenna had finished explaining the formal andquasi -formal aspects of syllogistic, he turned to its material aspects. With respect to these, syllogistic divides into five kinds, because it either conveys an Assent, or an Influence (ta‘aththur) of another kind (I mean an Imagining or Wonder). What leads to Assent leads either to an Assent which is Truth-apt (jâzim) or to one which is not. And what is Truth-apt is either taken [in the argument] as True (haqq), or is not so taken. And what is taken as True either is true, or isn't.

That which leads to true truth-apt Assent is Demonstration; untrue truth-apt Assent is  Sophistry. That which leads to truth-apt Assent not taken as true or false but rather as (a matter of) Common Consent*(‘umûm al-i‘tirâf* ) is - if it's like this - Dialectic (jada l), otherwise it's Eristic (shaghab ) which is, along with Sophistry (safsata ), under one kind of Fallacy Production (mughâlata ). And what leads to Overwhelming though not Truth-apt Assent is Rhetoric; and to Imagining rather than Assent, Poetry (Tûsî (1971) Sharh al-Ishârât 460.1-461.12).

Tûsî immediately goes on to lay out grounds for Assent to propositions, for example, because they are primary, or because they are agreed for the purposes of discussion. Propositions to be used as premises for Demonstration make the most irresistible demands for our Assent; premises for lower kinds of discourse make weaker demands.