Compound Indication

What is this Tutorial About?

Introduction to Logic introduced the concepts of تصور (concept) and تصديق (assent) and revealed that the science of Logic is concerned with definitions with respect to concepts and with proofs with respect to assent. Indication then outlined the role that speech plays in indicating on the concepts and assents in the mind.

We have already focused on تصور (concepts) in the two tutorials Simple Indication and Indicated Concept, and that section of logic culminated in the discussion on Definitions. We now focus on تصديق (assent). In this focus, we need to briefly study the speech that indicates on assent in the mind, and subsequently the assents themselves in order to study proofs. This tutorial deals with the speech that indicates on assent.

Categorizing Informative Sentences to Facilitate
The Different Variations of Proof

In logic, the term “informative sentence”/“clause” (قضية ج. قضايا) refers to the speech which indicates on the mental idea. And the idea itself is called a “statement”/”assent” (تصديق). Note: “statement” is another word for “assent”, not another word for “sentence”. Logicians divide informative sentences into three categories as follows.

1.       حملية (atomic clause) – an informative sentence in which the predicate is claimed either positively or negatively for the subject; or, alternatively, an informative sentence that cannot be split up to form two or more informative sentences

·         شرطية (hypothetical clause) – an informative sentence that splits up to form two or more informative sentences

2.       شرطية متصلة (composite clause) – two informative sentences where one is made the result of the other by way of conditional elements (e.g. the word “if”); a شرطية متصلة is made of two حملية

3.       شرطية منفصلة (compound clause) – two informative sentences compounded by means of a disjunction; a شرطية منفصلة is made of two حملية, as in “it is night or it is day” or as in “it is either night or day”

The Atomic Clause

The subject of a clause is known in Logic as the موضوع. The copula is known as the رابط, but since Arabic is a Zero Copula language, this is not always present in speech. And the predicate is called the مجمول. Sometimes the subject is also called the محكوم عليه, the copula is called the جكم, and the predicated is called the محكوم به. Below is a simple example; an expletive pronoun has been added to illustrate the copula.

Categorization Based on Equation

Now, clauses can be categorized based on the nature and purpose of the copula. If the subject and predicate are being equated directly, then this is known as حمل بالمواطاة (equation). For example, “Zaid is a human,” “humans are animals”, “I am not an animal,” “I am tired,” “the bucket is full”. If, however, the subject and predicate are not being directly equated, then this is known as حمل بالإشتقاق(non-equation). Examples of this include “Zaid is in the house,” “the house belongs to Zaid,” “I’m not in it for the money.”

Notice that, in the first set of examples, one entity is being equated with another. But in the second set of examples, no such equation is taking place. When we say “Zaid is in the house,” for instance, we are not claiming that Zaid is or is not some entity – “Zaid is the house” would have been an equational sentence. Instead, we are claiming something about the whereabouts of Zaid. In effect, what we are saying is “Zaid’s location is the location of the house,” or something to that effect.

Hence a sentence is equational if the predicate directly asserts that the subject is or is not something. If that is not the case, then the sentence is non-equational. Non-equational sentences are usually ones whose predicates begin with a particle, but that need not be the case.

Categorization Based on the Subject

Clauses are also categorized based on their subjects. If the subject is a particular, then the sentence is termed جزئية or شخصية (singular). And if the subject is a universal, the sentence is termed كلية (general). Examples of the former include “I am sick” and “Zaid is annoying.” And examples of the latter include “Mankind is technologically advanced” and “some lions are ferocious.” In the former two examples, “I” and “Zaid” are both particulars, and in the latter two examples, both “Mankind” and “lions” are universals.

If a sentence is general, then the judgement made by the predicate may apply to the entire universal the subject represents, or to its members. For instance “Mankind” is a word that applies to an entire universal and there is no consideration of any individual members. But “some lions” is clearly an application on the members of a universal and not on the universal itself.

An even clearer example of this is the Al of جنس versus the Al of استغراق known from grammar. The Al of جنس makes it so that the noun on which it enters refers to the entire universal it represents, as in “Mankind was born to build,” and the Al of استغراق makes it so that the noun on which it enters refers to the individuals of the universal it represents, as in “every human was born to build.” Although both of these statements encompass each human being, the distinction to be noted here is that the Al of جنس has achieved this encompassment by applying itself to the universal Human, whereas the Al of استغراق has achieved this by applying itself to the individuals of that universal at a collective level.

A general clause (one whose subject is a universal) in which the subject refers to the entire universal is termed كلية طبعية (non-quantified). And a clause in which the subject refers to the members of the universal subdivides; if it is mentioned whether all or some of the members are intended, then the sentence is termed محصورة (explicitly quantified), and if no such distinction is made, then the sentence is termed مهملة (esoterically quantified).

Exercise: For each example below, determine the following.

        I.            whether the sentence is شخصية or كلية

      II.            if it is كلية, whether it is كلية طبعية or not

    III.            if it is not, whether it is محصورة or مهملة

    IV.            if it is محصورة, whether the quantification is affirmative-existential, negative-existential, affirmative-universal, or negative-universal

Categorization Based on Affirmativeness

Naturally, a clause is either موجبة (affirmative) or سالبة (negative). What determines whether a clause is affirmative or negative is the parity of the copula. We would say, for instance, that “Zaid is handsome” or that “Zaid is not handsome.” In order to achieve the affirmation and negation in these sentences, the copula was toggled between “is” and “is not”. In Arabic, affirmative speech would be achieved by default, and negative speech would be achieved by negating the main verb in a verbal sentence and by introducing a negative copula such as ليس in a nominal sentence.

But apart from the main parity of the sentence, the subject and the predicate may in and of themselves be negated. For example, “Zaid is a non-scholar” is an example of a clause that, although affirmative, contains negation in its predicate. And similarly, “non-humans are uncivilized” is an example of a clause that, again, although affirmative, contains negation in its subject.

Clauses with this type of internal negation are known as معدولة (internally negated). If the subject is internally negated, the clause is termed معدولة الموضوع. If the predicate is internally negated, the clause is termed معدولة المحمول. And if both are negated, then the clause is termed معدولة الموضوع والمحمول. If there is no internal negation and the clause is affirmative, it is termed مخصلة. And if there is no internal negation and the clause is negative, it is termed بسيطة.

The chart below gives examples for each of the six methods of internally negating a clause, as well as the two types of clauses in which there is no internal negation (shaded).

Categorization Based on Modality

In a given sentence, the predication of the predicate to the subject may be valid conditional to some tertiary stipulation. For example, the claim that “Zaid is standing” is either true or false. Let’s assume that it’s true. Despite the fact that it is true currently, it may not remain as such indefinitely. In other words, the predicate “is standing” may not always apply to “Zaid”; he may eventually sit down.

What dictates the validity of the predication is what we are calling modalities. For instance, “Zaid is standing as long as he’s not sitting or lying down.” In this clause, “as long as he’s not sitting or lying down” is a modality which stipulates the parameters under which the predication is valid. Now these parameters always exist whether they are mentioned explicitly in the sentence or not. If they are mentioned, the clause is termed موجهة (moderated), and if they are not mentioned, the clause is termed غير موجهة (un-moderated).

There are several modalities – whether we mention them explicitly or not – and they have been summarized in the table below.

Examples

1.       “Water is dry.” This is impossible

2.       “The water is hot.” This is possible, but not necessarily true.

3.       “Dry is not wet.” Not only is this statement necessarily true, but the concept of “dry” doesn’t even have to exist in order for it not to be “wet”. Only the concept of “wet” is equal to the concept of “wet”; every other concept is “not wet”.

4.       “A human is an animal.” This is necessarily true. But, unlike the statement “dry is not wet” where “dry” didn’t even have to exist for this to be true, as soon as the human ceases to exist, the validity of this statement is voided. Put another way, if humans didn’t exist, they wouldn’t be called animals. Or, when a human being dies, he is no longer an animal.

5.       “Everything that moves, changes.” It is necessarily the case that something that moves, insofar as it is moving, it is also changing. As soon as it stops moving, however, it may not necessarily be changing.

6.       “The moon is blocked from sunlight during its eclipse.” This is necessarily true; after all, this is what it means for the moon to be eclipsed. But this statement is only valid as long as the temporal condition “during its eclipse” holds.

7.       “Humans exhale.” This is necessarily true, but during certain, unspecified moments in time.

8.       “Every planet orbits its star.” This is not necessarily true because, if a planet were to discontinue its orbit, we would still consider it a planet. Perpetual orbit is not constitutive for planets. However, it is something that we observe to be continuous.

9.       “Every writer moves his fingers.” This is not necessarily true because moving of the fingers is not constitutive of writing. However, it is true that a writer does continuously move his fingers insofar as he is a writer. This is different from (8) inasmuch as “writer” is a quality attributed to an entity whereas “planet” is in itself an entity. And this is also different from (5) inasmuch as moving of the fingers is not constitutive for writing, but changing is constitutive for moving.

Exercises

Identify the mistakes in the following analyses, if any.

The Hypothetical Clauses

The composite and compound clauses are collectively called the hypothetical clauses. The composite clause is a hypothetical in which there is a conditional element. For example, “if Socrates stands then I will sit,” or “I am sitting because Socrates is standing.” Notice that this type of clause is a combination of two atomic clauses connected by way of conditional elements which cause one of the two to become the result of the other. The condition is known as the مقدم (protasis), and the clause is known as the تالٍ (apodosis).

Similarly, a compound clause is a hypothetical in which two atomic clauses are connected by the medium of a disjunction. For example, “Socrates is either sitting or standing.” The unabridged version of this clause would be “Socrates is sitting, or Socrates is standing.” Like the composite clause, the first part of a compound clause is known as the مقدم (conjunct), and the seconds part is known as the تالٍ (also, conjunct).

Now, just as the قضية حملية (atomic clause) was either شخصية (singular) or كلية (general), so too is the قضية شرطية (hypothetical clause) also either شخصية or كلية. But the sense here is different. A شرطية شخصية (restricted hypothetical) is a hypothetical in which the hypothesis is restricted. For example, “if Socrates sits right now, then I will also sit.” Here the condition “right now” is a restriction on the conditional nature of “if Socrates sits”. Another example is “at this moment, either Socrates is sitting, or he is standing.” Again, “at this moment” is a restriction of the disjunctive nature of “either sitting or standing.”

A شرطية كلية (universal hypothetical), on the other hand, is a hypothetical in which the hypothesis is not restricted. For example, “whenever Socrates sits, I will also sit.” And “it is always the case that either Socrates is sitting or he is standing.”

Notice the sentence “whenever Socrates sits, I will also sit.” Both atomic clauses in this hypothetical are actually شخصية (singular), yet we are calling it a كلية (universal). This is because of the “whenever”; it is this quantifier that determines whether the hypothetical is restricted or universal.

Furthermore, if the quantifier is mentioned explicitly in a شرطية كلية, then it is termed محصورة (explicitly quantified), and if that is not the case, then it is termed مهملة (esoterically quantified).