Al-Farabi, Syllogism: An Abridgement of Aristotle's Prior Analytics

Saloua Chatti, Wilfrid Hodges, Saloua Chatti, Wilfrid Hodges

• Publisher: Bloomsbury Academic
• Year: 2020
• ISBN:
  9781350127036
• Edition: 1
• Topic: Philosophy
• Subtopic: Ancient & Classical Philosophy

The philosopher Abu Nasr al-Farabi (c. 870-c. 950 CE) is a key Arabic intermediary figure. He knew Aristotle, and in particular Aristotle's logic, through Greek Neoplatonist interpretations translated into Arabic via Syriac and possibly Persian. For example, he revised a general description of Aristotle's logic by the 6th century Paul the Persian, and further influenced famous later philosophers and theologians writing in Arabic in the 11th to 12th centuries: Avicenna, Al-Ghazali, Avempace and Averroes. Averroes' reports on Farabi were subsequently transmitted to the West in Latin translation. This book is an abridgement of Aristotle's Prior Analytics, rather than a commentary on successive passages. In it Farabi discusses Aristotle's invention, the syllogism, and aims to codify the deductively valid arguments in all disciplines. He describes Aristotle's categorical syllogisms in detail; these are syllogisms with premises such as 'Every A is a B' and 'No A is a B'. He adds a discussion of how categorical syllogisms can codify arguments by induction from known examples or by analogy, and also some kinds of theological argument from perceived facts to conclusions lying beyond perception. He also describes post-Aristotelian hypothetical syllogisms, which draw conclusions from premises such as 'If P then Q' and 'Either P or Q'. His treatment of categorical syllogisms is one of the first to recognise logically productive pairs of premises by using 'conditions of productivity', a device that had appeared in the Greek Philoponus in 6th century Alexandria.

Introduction

Wilfrid Hodges

1 A brief guide to categorical syllogisms

We begin our discussion of al-Fārābī’s book Syllogism [66] with a short description of Aristotle’s theory of syllogisms as al-Fārābī will have known it from the Arabic sources available to him.

1.1 Categorical sentences

There are four main kinds of quantified categorical sentence, as in the following examples:

Universal affirmative Every human is an animal.

Universal negative No human is a horse.

Particular affirmative Some animal is a human.

Particular negative Some animal is not a horse. Or, Not every animal is a horse.

These sentences all happen to be true, but of course there are false categorical sentences too, like ‘Every human is a horse’.

The noun immediately after the quantifier expression ‘Every’, ‘No’, ‘Some’ or ‘Not every’ is known as the subject, and the noun at the end of the sentence is known as the predicate. In the examples above, the subject comes before the predicate, or as we will say, the sentences are written in SP ordering. But al-Fārābī was aware that some logicians wrote the sentences in PS ordering, i.e. with predicate before subject. The PS ordering is almost as artificial in Arabic as it is in English. Al-Fārābī illustrates it with sentences that we translate as:

Animal is true of every human.

Animal holds of every human.

Animal is in every human.

There are similar examples for the other categorical forms. As PS versions of ‘Not every animal is a horse’ al-Fārābī writes sentences that we translate as

Horse doesn’t hold of every animal.

Horse fails to hold of some animal.

Horse is absent from some animal.

These three sentences are read as synonymous – so the scope of ‘some’ in the last two is the whole sentence.

The subject and predicate of a categorical sentence are called its terms. Aristotelian logic is relaxed about the syntactic form of terms. For example the sentence ‘Every philosopher laughs’ is acceptable as a universal affirmative sentence with ‘laughs’ as predicate. If you want to you can paraphrase it as ‘Every philosopher is a laugher’, so as to replace the verb by a noun. In PS form that becomes ‘Laugher is true of every philosopher’. Al-Fārābī observed (22,11f) that in logic Aristotle generally replaced the term words and phrases by single letters of the alphabet: ‘No B is an A’ and so on.

Aristotle recognized two kinds of categorical sentence that have no quantifier. One is singular sentences with a proper name subject, such as ‘Zayd is an animal’. The other, called indeterminate sentences, would be illustrated by ‘Horse is animal’ if English allowed such a sentence. Al-Fārābī believes that indeterminate sentences have a role to play in explaining how arguments that are not logically valid can still have a limited form of cogency; see the discussion of Tolerance in Section 3.21 below. Otherwise sentences with no quantifier play a very minor role in Syllogism.

1.2 Syllogisms

When we take two categorical sentences, we sometimes find ourselves committed to a third sentence. If this happens, we say that the first two sentences are premises, the third is the conclusion, and the premises form a syllogism.

For example the pair of premises ‘Every human is an animal’ and ‘Every animal is sentient’ produces the conclusion ‘Every human is sentient’. But the pair of premises ‘Every human is an animal’ and ‘Some animals fly’ has no conclusion and doesn’t form a syllogism.

What exactly does it mean to say that if we ‘take’ a certain pair of sentences then we are ‘committed to’ a third sentence? Aristotelian logicians tended to treat this relationship between premises and conclusion as undefined but recognizable from examples, so that part of the task of logic was to build up a description of the properties of the relationship by studying examples. Al-Fārābī believed that Aristotle and the other Greek philosophers had bequeathed two main kinds of example.¹

In the first kind of example we have a scientific or philosophical question which we want to answer, for example ‘Is it the case or not that the moon is spherical?’ Al-Fārābī calls a two-way question of this kind an objective (maṭlūb). A scholar will try to resolve the question by finding a fact already known about the moon, and a fact already known about sphericity, such that when these two facts are put together they prove either that the moon is spherical or that it is not spherical. Resolving the question in this way is called ‘verifying the objective’ (taṣḥīḥ al-maṭlūb), or ‘proving the objective’ (bayān al-maṭlūb). Al-Fārābī takes from Aristotle the point that the already known facts could be either things previously proved by syllogisms, or self-evident things. In order for anything to be known at all, some things must be self-evident; al-Fārābī has his own catalogue of the ways in which a thing can be self-evident (cf. Part 7). Al-Fārābī also notes that if a syllogism uses facts proved by other syllogisms, then the syllogisms involved can be combined into a compound syllogism (cf. Part 18b).

The second kind of example occurs when two people find that they disagree about something. Disagreements are resolved by debate according to an established protocol. The two debaters are respectively the Questioner and the Responder. The Questioner begins the debate by posing an objective, which is a two-way question as in the previous paragraph. The Responder is required to choose one of the two answers to the objective, an action called concession or commitment (both taslīm), since it concedes a proposition to the Questioner and commits the Responder to trying to defend the conceded proposition against attacks by the Questioner. For example the Questioner can attack by inviting the Responder to make two further commitments, to premises of a syllogism whose conclusion is incompatible with the chosen proposition. Or the Responder can do the same in reverse, enticing the Questioner to commit to the premises of a syllogism which has the chosen proposition as its conclusion. Ideally this to-and-fro will eventually lead the two debaters to an agreement about which arm of the objective is true; when this happens, the debate is again said to verify the objective. (The objective may also be posed as a single sentence which the Responder can accept or reject. This sentence is said to be ‘put up for consideration’ (mafrūḍ).)

Al-Fārābī observes that in the first kind of case the outcome is new knowledge, ideally knowledge with certainty (which he calls demonstrative knowledge and studies in his book Demonstration [71]). In the second kind of case the outcome is only the resolution of a dispute, and the proposition that the debaters come to agree on could well be false. Nevertheless both contexts use the same rules about what propositions do or don’t follow from what other propositions, rules which al-Fārābī believes were known to Plato but formalized by Aristotle. Before the rules of debate were established, the best that one could do by way of arguments was to use rhetorical devices that had the power to persuade people...

Table of contents

• Cover
• Half-Title Page
• Series Page
• Title Page
• Dedication
• Contents
• Preface
• Conventions
• Acknowledgements
• Introduction
• Textual Emendations
• Translation Saloua Chatti and Wilfrid Hodges
• Notes
• Bibliography
• English–Arabic–Greek glossary
• Arabic–English index
• Index of Passages from Aristotle
• Subject Index
• Copyright Page