Mulla Sadra and the Reduction of All Propositions to Necessary

 Universal Affirmative Categorical Propositions

 

By:Ahad Faramarz Qaramaliki

Introduction

 

In al-Tanqih Mulla Sadra introduces the reduction of propositions to necessary universal affirmative categorical ones as an Illuminative (Ishraqi) principle and employs it in simplifying a great number of logical discussions. This issue has a variety of dimensions.

Reducing conditional propositions to categorical ones or viewing them as being so, was always a topic for dialogs and disputes among early logicians. However, it seems that the returning of particular and indefinite propositions to universal ones, negative propositions to affirmative ones, and modal propositions to necessary ones is among Shaykh al-Ishraq’s (550 – 587 A.H) innovations. In addition to some scattered discussions in this regard, he has devoted an independent chapter to this issue, entitled ‘Ishraqi Philosophy on the Reduction of all Propositions to Necessary Affirmative Ones’.[1]

The writer of this article believes that Mulla Sadra is the first logician who, in addition to confirming Shaykh al-Ishraq’s approach in reducing all propositions into necessary universal affirmative categorical ones, compiled his scattered notes and writings in this regard and presented them in a full chapter entitled Lam‘a Ishraqiyyah (Ishraqi gleam). The reduction of all logical propositions to necessary universal affirmative categorical ones can be divided into four types:

1. Conditional reduction (conjunctive and disjunctive)

2. Reduction of negative propositions into affirmative ones

3. Reduction of particular and indefinite propositions into universal ones

4. Reduction of modal propositions into necessary ones

The methods and reasons of these four-fold types are different from each other. Ibn Sina’s arguments on the reduction of conditional propositions to categorical ones have been analyzed and criticized previously,[2] and Shaykh al-Ishraq’s views concerning the other three types have been extensively discussed elsewhere. [3]

 

Reduction of conditional propositions to categorical ones

 

The reduction of conditional propositions to categorical ones seems to be inevitable in the Aristotelian system of logic, and Ibn Sina, relying on the conditional categorical syllogism, has made it a common tradition to view conditional propositions as categorical ones. He has a short statement which represents Muslim logicians’ common view in this regard: “And you should regard all the rules of categorical propositions, including those related to restriction, indefiniteness, inconsistency, and conversion, as applicable to conjunctive (conditional) propositions as well, for the antecedent and consequent of conjunctive propositions are, respectively, the same as the subject and predicate of categorical ones”. [4]

There are two related but distinct issues in this discussion: 1) reducing conditional propositions to categorical ones, and 2) viewing conditional propositions as categorical ones. Both of these issues are rooted in the centrality of categorical syllogisms (logic of predicates) upon which conditional syllogisms (logic of propositions) are based. According to Aristotle’s followers, the principle here is the categorical syllogism, and any other inference should be based on this principle.[5] In the Aristotelian system, the theory of syllogism is based on quantified categorical propositions and decomposing them into subject and predicate. Therefore, in such a system, the conditional syllogism can be based on a categorical one only if the conditional proposition is reduced to a categorical one. In order to do this, due to the presence of the conditional connective, we should firstly view the antecedent and the consequent as concepts rather than propositions. Second, we should pass a judgment as to whether the antecedent necessitates or implies the consequent or is inconsistent with it. For example, in order to change the conjunctive conditional proposition into a categorical one, one can say:

1. Conjunctive conditional proposition: If the sun rises, it is daytime.

2. The equivalent categorical proposition of the above: The rising of the sun implies daytime.

The reduction of the disjunctive proposition into a categorical one is as follows:

3. Disjunctive conditional proposition: Either the sun has risen or it is night.

4. The equivalent categorical proposition of the above: Sunrise is inconsistent with night.

A conditional proposition consisting of two components (antecedent and consequent in the conjunctive proposition and components in the disjunctive proposition) changes into a categorical one consisting of a subject and a predicate. This simple method of reduction has led some to assume that a conditional proposition is basically the same as a categorical one which has been misinterpreted. In other words, a conditional proposition has in fact no specific identity; it is, rather, the same as a categorical proposition which has not been correctly phrased with respect to its structure. Viewing conditional propositions as categorical ones can be explained by, for example, changing statement (5) to statement (6), as follows:

5. At all times, a student’s being hardworking implies his being successful.

6. If a student is hard working, he will be successful.

Shaykh al-Ishraq believes in this view, and Mulla Sadra, too, has confirmed it. He stipulates that a conditional proposition is basically a misinterpreted categorical one in which the emphasis on implication and inconsistency has been replaced by incorporating conjunction and disjunction markers.

Khwajah Nasir al-Din Ěęsi (598-672 A.H) poses the problem in a completely different way and provides a more convincing response to it. He asks: Does the distinction between categorical and conditional propositions lie in their kind or in their class? Unlike Shaykh al-Ishraq, he is interested in details. If we consider the structure of the content of propositions as the criterion, Shaykh al-Ishraq’s analysis as to viewing conditional propositions as categorical ones is acceptable; however, if we consider their formal structure as the criterion, categorical and conditional propositions are distinct in kind and cannot be reduced to each other. This is because the formal structure of categorical propositions consists of a first grade combination while that of a conditional proposition consists of a second grade one.[6]

The reduction of conditional propositions to categorical ones, according to Shaykh Ishraq and Mulla Sadra, is based on two issues: 1) The antecedent and consequent of conditional syllogisms should not be propositions; 2) Conjunction and disjunction relations should be changed to implication and inconsistency. Both of these issues deserve analysis and inspection, as presented below.

1. Most Aristotelian logicians maintain that the use of condition markers changes the status of the antecedent and consequent from being propositions. They try to demonstrate this by arguing that, first, the conditional relation is not the same as “this is that”, since the predication of one proposition upon another is meaningless;[7] second, the truth of a conditional syllogism is defined in terms of the truth of its components, while truth and falsity are secondary to the proposition itself.

2. The reduction of the conjunction relation to the concept of implication is based on a fallacy originating from terminological commonality and the ambiguity involved in the meaning of implication. Implication is commonly employed in the following three senses: 1) nafs al-amr (the thing as it is itself) or the world of affirmation  (this meaning of implication is accompanied by the concept of causality in the common trend of philosophical thought); 2) material implication or a value function established between two propositions according to which the syllogism is interpreted as a conditional one; 3) a logical implication established between the premises and the consequent in one form of the argument which is, accordingly, interpreted as a deductive one. Therefore replacing implication (in its ontological sense) by condition markers (implication of value function) in viewing conditional propositions as categorical ones is based on confusing application with reference.

3. The reduction of conditional propositions with false antecedents to categorical ones is problematic. This is because in such cases, the conditional proposition is true, while the categorical proposition, due to absence of the condition of the truth of the affirmative predicate, is false.

7) If a cat is human, it is rational.

8) A cat’s being human implies its being rational.

4. Neither implication nor inconsistency is among the concepts which have a clear-cut place in Aristotelian logic of ‘subject, predicate, and copula’. Rather, they are of the type of relation. Moreover, categorical propositions including relations are basically problematic in Aristotelian logic, as in the case of equality syllogisms.

 

Reduction of negative propositions to affirmative propositions

 

The distinction between negative and positive propositions is essentially an Aristotelian one, and there is no trace of the reduction of negative propositions to affirmative ones in Muslim logicians’ works until Ibn Sina’s time. When the general conditions for the syllogism are established, Ibn Sina criticizes the inconclusiveness of the two premises of a negative syllogism or that of the first form which includes the minor premise of such a syllogism. In his view, there are some cases of composite modal propositions in which the negative proposition can be changed into an affirmative one. In such cases, there is, in fact, no difference between particular contingent and existential propositions, whether they are written in a negative or affirmative form.[8]

9) A is B through particular contingency.

10) A is not B through particular contingency.

11) A is B temporarily.

12) A is not B temporarily.

For the same reason, Ibn Sina emphasizes that the contingent negative proposition is other than the negation of possibility, and that the temporary negative existential proposition is other than the negation of temporary existence. [9]

Here, Shaykh al-Ishraq poses two arguments. Firstly, a negative proposition is essentially based on affirmation; in other words, at the heart of each negation, there is hidden an affirmation. “A negative proposition is a rational judgment, and since it issues a judgment as to negation, this is an affirmation itself. [10]

Secondly, negative propositions can be reduced to affirmative ones. In conclusion, in line with Ibn Sina’s view, we should say that the canceling of the condition of being affirmative is at least one of the premises of the syllogism. Shaykh al-Ishraq suggests the method of obversion for reducing negative propositions to affirmative ones. In this method, through using negative markers in the predicate, the negative proposition is transformed into an affirmative obverted proposition, and the negation of the predicate changes to the predication of negation. This is done in the form of the proposition by replacing the markers of relation with those of negation.

The method of obversion can be analyzed from two perspectives: truth and meaning. This issue is commonly analyzed by logicians from the perspective of truth. They believe that a negative proposition, because of its truth in the case of being negated, is more general than an affirmative proposition concerning its truth. Therefore, not every true negative proposition can be changed into a true affirmative one. Shaykh al-Ishraq pays attention to this criticism and, in response, states that the fact that a definite negative proposition is more general than an obverted affirmative proposition in terms of truth only holds true with respect to individual prepositions; however, there is no difference between them in this regard when dealing with restricted propositions.[11] This view of Shaykh al-Ishraq should be explained on the basis of the reduction of particular propositions to universal ones. In fact, he means that with regard to universal propositions, definite negative propositions and obverted affirmative ones are of the same value. This idea can be defended in the light of the particular analysis made of the semantic structure of a universal proposition, as well as the relation between its subject and predicate.

In discussing this issue, Mulla Sadra does not refer to any new points in Shaykh al-Ishraq’s explanation, nor does he speak of any other method for reducing negative propositions to affirmative ones except for the method of obversion.

The reduction of negative propositions to positive ones can be explored from the perspective of their semantic structure. This, of course, requires an introduction. According to Aristotelian logicians, in real sciences, a valid proposition has a specific semantic structure so that therein the predicate is inherent in the subject in the sense of being inherent in the proof. Term and proof are defined as atoms of logic, and the logic of proof lies in the predicate’s being inherent in the subject in propositions and the defined thing’s being inherent in the definiendum in definitions.

The use of indefinite concepts is not consistent with the system of the logic of quiddities. That is why al-Farabi (260- 339 A.H) consciously tries to analyze Aristotle’s famous statement in Perihermeneis concerning indefinite names (16612-15) against its surface meaning.[12] This is because an indefinite name in the sense used in such sentences and exemplified by a word such as non-human completely alters the logic of quiddities. ‘Non-human’ is neither accidental nor essential, neither constitutive nor necessary, and neither can it be contained in the Isagogic system, nor can it be a predicate of demonstrative issues. [13]

Considering the introduction given above, the logical defect of the obversion method in Aristotelian system becomes apparent, since, according to this method, an indefinite concept becomes the predicate of the proposition. Besides, such a predicate has not been defined in the Isagogic system, unless, through considering indefinite names as privation versus possession, we reduce them to definite names and, for example, instead of ‘non-seeing’, write ‘blind’. The defect of this method is clearer than that of obversion.

 

Reduction of particular and indefinite propositions to universal ones

 

As mentioned before, the basis for reducing conditional propositions to categorical ones was that conditional propositions are essentially categorical, and the one for the reduction of negative propositions to affirmative ones was that affirmation lies at the heart of negation. However, the basis for the reduction of particular propositions and what is considered their judgment (indefinite propositions) to universal propositions is the validity of the universal proposition in different sciences.

The invalidity of individual propositions in real sciences is one of the evident principles of earlier epistemology. Dinani has explained this issue as a philosophical principle in detail.[14] According to Ikhwan al-Safa (360-421 A.H), indefinite propositions are not specified in terms of their truth or falsity. Therefore, they are misleading and lack validity in those branches of science employing precision of expression. [15]

Shaykh al-Ishraq propounds the same analysis with regard to particular propositions, too, and calls them partial indefinite propositions. Accordingly, it can be said that a valid proposition in real sciences must be a universal proposition. [16]

An indefinite proposition can be regarded as a particular one which is reducible to a universal proposition following the necessitation method. In this method, the collection of the subject’s referents qualified by the predication assumes a single, common, and comprehensive concept. Later this single and universal concept becomes the subject of the same predicate and, therefore, another proposition is formed which, in terms of truth, is as valid as the first one. Pay attention to the following examples:

13) Some humans worship the One God (particular).

14) Every monotheist worships the One God (universal proposition equivalent to particular proposition)

In his discussion of reducing particular propositions to universal ones, Mulla Sadra suffices to Shaykh al-Ishraq’s analysis and does not criticize any of his views in this regard.

The necessitation method can be criticized from different aspects. First, according to Muslim logicians and all modern logicians, the content structures of particular and universal propositions are basically different. In a particular proposition, the subject and predicate have been combined through conjunction, and, more precisely stated, they have incidental symmetry; however, in universal propositions, the conjunction of the subject and predicate is necessary.

Second, through necessitation, a particular proposition turns into a pseudo-universal rather than into a truly universal one. To put it more clearly, in such a universal proposition, we use ‘all’ rather than ‘every’ since the common comprehensive concept, as Shaykh al-Ishraq explains, is not a reality or nature which can be inevitably predicated on each and every of its individuals. Rather, it is a name that refers to all the members of the collection (rather than a natural universal common to all the individuals).

Third, concerning the example given above, we should say that the reduction of common predication to primary predication or the reduction of all propositions to necessity, which is conditioned by predicate, will be necessary. This is because proposition (13) is a common technical proposition; however, in proposition (15), the subject clearly depends on the predicate, or the predicate is considered in it.

Fourth, Shaykh al-Ishraq’s criterion for reducing particular propositions to universal ones, that is, having validity in real (demonstrative) sciences, indicates that two universal concepts have been mixed with each other; in other words, he does not make a distinction between universality in truth, which is taken into consideration in demonstrative problems and real sciences, and which is applied to an individual proposition, such as ‘Aristotle is man’, and universality in relation or quantitative universality.

 

Reduction of modal propositions to necessary ones

 

 The criterion determined by Shaykh al-Ishraq and Mulla Sadra for reducing modal propositions to necessary ones, like that for the reduction of particular propositions to universal ones, is the validity of the proposition in real sciences. They maintain that the issues in demonstrative sciences are necessary ones, and, accordingly, try to find a way to reduce all modal propositions to necessary ones. Their suggested method is to consider the modality in the predicate. [17] In this way, contingent propositions can be reduced to necessary ones.

15) Contingent proposition: Every man exists through possibility.

16) Necessary proposition equivalent to contingent proposition: Every man is a contingent existent through necessity.

The method adopted by Shaykh al-Ishraq is expressed as a principle in the 5^th system of the new logic of modals. [18]

ŕ Asymbol 224 \f "Wingdings" \s 12ŕ  ٱ ŕ A

The lack of distinction between the modality of relation and the modality of truth in the reduction of propositions to necessary ones demands some hesitation. The possibility in proposition (15) means the quality of the relation between existence and man. However, in proposition (16), necessity means the quality of judging man as being existent through contingency. Therefore, in this reduction, the modality of relation is reduced to the modality of judgment.

 

Table of the reduction of all propositions to necessary universal affirmative categorical propositions

 

No	Proposition	Example	Reduction method	Reduced	Example
1	Conjunctive conditional	If the sun rises, it is daytime.	Negating the prepositional identity of the antecedent and consequent and reducing conjunction markers to the concept of implication.	Categorical	Sunrise implies the daytime.
2	Disjunctive conditional	Either the sun has risen or it is night.	Negating the prepositional identity of components and reducing disjunction to the concept of inconsistency.	Categorical	Sunrise is inconsistent with night.
3	Negative	No scorpion is seeing	The replacement of negative markers and copula or negating the predicate.	Affirmative	Every scorpion is blind.
4	Particular	Some men worship the One God	Considering a common comprehensive concept for the collection of subject’s referents which are qualified by the predicate.	Universal	Every monotheist worships the One God.
5	Unnecessary modals	Man exists through possibility	Considering modality in the predicate.	Necessary	Every man is a possible existent through necessity.

 

 

The advantages of the theory of reduction

 

The reason for Mulla Sadra’s emphasis on Shaykh al-Ishraq’s reductionist view and confirming it is that through such a reduction a lot of logical principles, such as contradiction, transposition, and combined syllogisms, can be simplified. [19]

Mulla Sadra’s reason for simplifying logical principles is to provide a simple instructional text for teaching logic. However, with respect to its applications, the question is whether such an inclination is justified or not.

A functionalist approach to teaching logic which is necessitated by its instrumental and organic identity leads us to the discussion of contradiction, transposition, and other logical principles in detail so that one could identify the ambiguities involved in such issues and does not fall in the trap of logical fallacies. That is why Mulla Sadra, with respect to the necessary unities between two contradictory propositions, does not agree with the minimalist theory of Farabi and Fakhr al-Din Razi (reducing the unities to the unity of the subject and predicate) and, in addition to confirming his own maximalist approach, adds the unity of predicate to it. [20]

The emergence of the reductionist theory reveals lack of growth in sciences. In an epistemological atmosphere, where the common explanations in natural sciences are restricted to Aristotelian naturalist interpretations, and where sciences are limited to problems which are inherent predicates of subjects, there is no need to any proposition except for necessary universal affirmative categorical ones.

 

 

 

Notes

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