How did the modalities improve in Avicenna’s logics?

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Mufid University, Ghom, Iran

How did the modalities improve in Avicenna's logics?

Jabbehdari M.

Аннотация

modality logic avicenna

В данной статье рассматриваются вопросы проявления и развития модальностей в логике Авиценны.

Проанализированы особенности арабоязычной философии в общем и арабоязычной логики в частности. Также указаны на некоторые характеристики религии Ислама в качестве контекста возникновения интереса к логической мысли.

На основе проведенного исследования автором показано, что именно математическое знание Авиценны вместе с его знакомством с аристотелевской философией служились причиной использования им современных модальностей. Также показана важная роль, которую играли современные модальности в обосновании теологических идей Авиценны.

Ключевые слова: Авиценна, Аристотель, арабоязычная логика, модальность, современная модальность.

Abstract

Modality among Muslim logicians was first introduced by Avicenna. The modal logic and all modalities have always played an important role in Avicenna logicians' opinions. Avicenna has specially shown a great deal of attention to Time Modalities Theories improvement have designed a precise Inference System. Usage and improvement of modal propositions by Avicenna, not only was affected by his familiarity with Aristotelian logic, but also by his scientific knowledge including his dominance over Mathematics, since his knew this science and its branches specially Algebra were well and study of his logic shows that since he knew the parallelism of Mathematics and Logic, not only used Mathematics examples in his logic discussions skillfully, but also, used the Mathematics science to improve his logics system and specially in modality dispute. In fact, Avicenna solved the issues relative to proof or propositional truth into a special structure of Islamic theology and Mathematics science which reached its pick in his modal lessons. After Avicenna also the spirit he had revived in Arab logics has always provided opportunities to spread and improve Logics science in general and modality discussions specifically.

Keywords: Avicenna, Aristotle, Arabic logic, Modality, Temporal modality.

In the first centuries of Islam emergence, though the ideological pillars of the society were shaped based on the religious lessons, the philosophy and logic inherited from Greece had its tracks on knowledge seekers thought, had indirectly its effect on those lessons indirectly. Such effects naturally were manifested in the opinions of those scientists who tended to Greek philosophy, as, for example, if in order to solve the issue of world creation, Theologians and Mu'tazilites as fans of Islamic theology were determined that God existed before the world was created and has created the world in a second [23, P. 72], Avicenna the philosopher did not accept the idea of world creation in a second following Aristotle in his metaphysical opinions and considered the time of God existence and material the same [23, P. 72]. Avicenna developed Aristotle's logic, physics and metaphysics and criticizing Sufism, he emphasized the unity of rational thought and experience, reason and experiment. He believed that logic determines the rules of right reasoning, so that structures and categories of logic must match real-world objects.

Hence, in his religious-philosophical system, God and all the world make a single united total which of course in reference to religious believes, God as a start point of this total, is different and outstanding from the other elements.

In Avicenna Ontological Scheme, all the existence element are located on one line and what completed this linear scheme was the explanation of connection between the existence and nature of these element. In this way Avicenna used his knowledge of logics. Avicenna in the Treatise of Logic called logics as the laws and the forms of thought that come from nature and do not depend on any specific context. Logic in his view, like science, is about the truth and studies the statement and proof process.

In Avicenna's view, logic, along with physics and mathematics, is a part of philosophy and analyzes four main issues: concept, judgment, argumentation and proof.

In this way Avicenna studied the relation between general and partial as well as the subject and the predicate in the sentence and emphasized the unity of rational thought and experience, reason and experiment.

The relation between nature and existence could be different based on different objects and Avicenna lessons also exactly responded to how nature of an object is related to its existence: the relationship between each creature and the nature attributed to it is recognized either by necessity or possibility, hence, the relative objects regarding their Ontological role and position were divided to necessary, possible and impossible objects and God who has a totally necessary nature as the beginning of existence collection and the cause of its own existence, unlike other elements of the mentioned collection existed on and by its own and its existence is derived from the situation of its nature necessity [3, Chapters 1, 2, 3 and 4 from the Forth Nahj]. As a result, in Avicenna system like Aristotle, modalities more than anything, had ontological points of view, as division of sentences according to modalities, in fact was division of “ranks and degrees” of the existence [12, P. 160].

As pointed out in Introduction in Islamic theology the non-eternal nature of the world did not require explanation, as for theologians who recognized every change existing in world resulting from God's will, there was no problem in determining the existence system. However, Avicenna the philosopher who relied majorly on Aristotle's lessons in presenting his metaphysical opinions and specially those explaining existence system and God's nature believed in worlds eternity and inevitably had to explain the “Potentialities” existing in eternal causes function, since if he believed an absolutely unchangeable cause can end to a necessary and eternal effect and this effect itself also in a way can cause the next existence and also the existence of cause, necessarily ends to existence of the effect, hence he should have explained why I spite of eternity of the first cause and its effects, still, all the possible happenings have not occurred in the world [19, p. 72-73]. In order to solve this problem, Avicenna in interpretation of world Cause and Effect Rules, relying on Aristotle's metaphysics, following him announced a cause becomes a cause “Actively” if it is in a suitable “situation”, as otherwise even its existence does not lead to creation of an effect.

In Aristotle metaphysics, God was cause of everything and the first principle, to the extent that metaphysics itself which talked about all causes, in Aristotle's opinion was a science either belonged only to God or God was higher than all necessary creatures of it:

“If, then, God is always in that good state in which we sometimes are, this compels our wonder; and if in a better this compels it yet more. And God is in a better state. And life also belongs to God; for the actuality of thought is life, and God is that actuality; and God's self-dependent actuality is life most good and eternal. We say therefore that God is a living being, eternal, most good, so that life and duration continuous and eternal belong to God; for this is God” [28, metaphysics P. 2209-2210].

“So the necessity that there should be motion continuously requires that there should be a first movement that is unmoved even accidentally” [28, P. 827].

“For some of the older philosophers thought that `what is' must of necessity be `one' and immovable” [28, physics, 987].

Aristotle parallel to dynamic and non-dynamic objects, considered a third object which though moves, is not dynamic. This non-dynamic motive is God which is not mixed with substance and in reality is the exact form of eternity and complete actuality. He is an absolute spirit which is the absolute wisdom and everything in the world is searching for it as Ideal. Therefore, God is the ultimate cause of all activities [23, P. 142]. In Aristotle's view who believed in God the individual and common distinction vanish completely, the world itself was also considered as a “Whole”:

“ `A whole' means (1) that from which is absent none of the parts of which it is said to be naturally a whole, and (2) that which so contains the things it contains that they form a unity; and this in two senses - either as being each severally one single thing, or as making up the unity between them. For (a) that which is true of a whole class and is said to hold good as a whole (which implies that it is a kind whole) is true of a whole in the sense that it contains many things by being predicated of each, and by all of them, e.g. man, horse, god, being severally one single thing, because all are living things” [28, P. 2326].

Aristotle also believes that “These are of necessity the only ways in which the numbers can exist. And of those who say that 1 is the beginning and substance and element of all things, and that number is formed from the 1 and something else, almost everyone has described number in one of these ways: only no one has said the units are in associable”[28, P. 2498].

Necessity in mathematics is in a way similar to necessity in things which come to be through the operation of nature. Since a straight line is what it is, it is necessary that the angles of a triangle should equal two right angles but not conversely; though if the angles are not equal, to two right angles, then the straight line is not what it is either. But in things which come to be for an end, the reverse is true [28, P. 651].

Though these ideas of Aristotle could be used as a solid basis in founding Islamic theological philosophy by Avicenna there was a contradiction in Aristotle's theory: this theory did not determine the transformation of existence from God (Whole Existence) to Existence World (Multiple Existence). Avicenna in order to complete Aristotle indefensible theory of God, inspired by Neo-Platonist theory of existence, introduced the non-substantial wisdom release from Whole Existence and his theory of existence, like those of his former Muslim philosophers had gracefully aspect: from self-existence God only the first wisdom is released, since from the Whole existence and absolutely comprehensive only one creature is released. However, since this wisdom, is not self-existence by its own and is considered as possible to exist, its possibility is actualized by God, it does not have an absolutely comprehensive nature and as a result of this dual nature of its own which is dominant over the whole world of creatures creates two creatures, namely Second Wisdom (in association with its higher aspect which is actuality) and the First and Higher Doom (in association with its lower aspect which is natural possibility) and release of these two aspects continues to the lowest and the tenth wisdom which manages earth world [23, P. 685].

This was the first theory using which the Avicenna could not only by repeating Greek philosophy create a reasonable system, but also the theory itself was so close to the belief of Muslims in angles existence and using it they could bring perfection and solidity to Islamic Tradition, since according to it, though God is self-existence and above creatures world, between necessity and absolute eternity which is God on one hand and the entire world of possibility on other hand, there were middle rings with mediators [23, P. 685].

But, does not the theory of release destroy the necessary and important distance between the creator and the creature and does not lead to emergence of Unity of Absolute Existence belief which Islam like other major religions stand firmly against? [23, P. 685] here, another theory of Avicenna, his famous doctrine of Existence and Nature which was introduced to complete Aristotle's theory and also to persuade rational and religious needs of its time, prevented this jeopardy [23, P. 686].

According to Avicenna, only God is absolutely comprehensive in its existence and all other objects have a dual nature. Comprehensiveness of God is as His nature and existence are not two elements of one existence, but, it is a comprehensive non-componence element in a whole existence, as in reality, its existence is united with its identity. But, this property does not apply to any other existence, since existence and nature are not the same in other existences. The result of this discussion is God's existence is necessary and other objects' existence is possible and is released from God's existence, as assumption of God's nonexistence causes contradiction, no other case results the same. God's creation happens through a rational necessity: God's wisdom surpasses all other happenings. Therefore, though whole world is a possible thing, but, assuming God's nonexistence and necessities graced by God, it becomes necessity (necessity due to other) [23, P. 686]. And since, substance has been the casual cause of existence, it provides the external properties of plurality and substance and form are continuously released by God, world eternally exists along God [23, P. 691].

Although, this theory does not comply with true Islam, but, Avicenna's purpose to introduce the mentioned theory was to be fair to religion and reason and on the other hand, by introducing this theory, he avoided bringing forth philosophy of atheistic materialism according to which the world always existed without God. Introducing such theory, Avicenna presented the world as an eternal existence, being a possible thing in its nature, in its eternity or antiquity needed God and is permanently depending on Him [23, P. 713].

But what could more than anything help Avicenna to structure his philosophical-theological system was the modalities dispute, using which the distinction between miscellaneous existences was possible perfectly. Modalities logic and modality propositions discussion were among the latest branches entering to Muslim Logicians thinking by Avicenna and in chapters One, Two, Three and Four of Forth Nahj in the book “Hints and Punishments”, chapter Four of Article Two, Phrase Section, Chapters Four and Five of Article One, Analogy Section and Chapter One of Article Two, Argument Section in the book “Healing” and also in Chapter Four in the Logic book “Salvation”, he discusses modality propositions.

Achieving the main structure of modalities from Aristotle and logicians after him, Avicenna first divided propositions in regards to modality to two kinds of necessary and possible, explained them, then began to introduce innovations of his own in this field and specially combination of modalities to time. In chapter Two of Forth Nahj in the book “Hints and Punishments” he divided propositions of necessity into six categories, first of which is completely relative to God, therefore it is absolutely eternal and the other five categories are conditional. The definition of these six categories of necessity is as following:

Proposition of Eternal Necessity: It is a proposition which indicates the necessity of predicts proof for the subject, while the subject is not conditioned by any constraint. This specific necessity is a proposition whose subject is necessary nature and whose predict is existence or other properties of it. Therefore, this proposition can only be used for God, as the saying is “God exists as necessary and is wise and capable as necessary”.

Proposition of Nature Necessity: It is a proposition indicating the necessity of predict proof for the subject conditioned by existence of nature, for example “Number for is even as necessary”.

Proposition of General Conditional: It is a proposition indicating the necessity of predicts proof for the subject under the condition that the namely description of the subject is constant for the subject nature, for example: “Every motile is changeable”.

Proposition of Predict Conditional Necessity: It is a proposition indicating the necessity of predicts proof for the subject conditioned by the existence of predict, for example: “Zaid is necessarily walking, until he can walk”.

Proposition of Absolute Time: It is a proposition indicating the necessity of predicts proof for the subject conditioned by determined time, for example: “The moonlight is determined necessarily at a time”.

Proposition of Absolute Published: It is a proposition indication the necessity of predict for the subject conditioned by undetermined time, for example: “Necessarily every human breathes”.

Along with proposition of necessity, Avicenna argues another proposition and it is the Proposition of Permanence which is a proposition indication that though predict is permanently constant for the subject, reason approves the separation of predict and subject. The name of such a relation is Permanence and the Proposition of Permanence is divided to categories of Absolute Permanence and General Costume:

Proposition of Absolute Permanence: It is a proposition indication the permanence of predicts proof for the subject conditioned by the existence of subject nature, for example: “Moon is dynamic until it is moon”.

Proposition of General Costume: It is a proposition indicating the permanence of predict proof for the subject under the condition that the subject nature is descriptive by a namely description, for example; “Every motile while moving, permanently is changeable”.

In Chapter Three of the Forth Nahj of the book “Hints and Punishments”, Avicenna introduces four categories for Possibility:

General Possibility, Specific Possibility, Special Possibility, Acceptance Possibility. Hence, Avicenna, clearly names twelve Modified Propositions all in a way combined with time.

Theory of Modified Time Analogies in Avicenna's logic and following him in Arabic logics in general, as Nicolas Rasher introduces, indicate the relationship between predict and subject in the four propositions of predict mainly through a special method: each of the four enclosures A, E, I and O can accept one of the four modalities of “Necessity”, “Permanence”, “Actuality (Prediction)” and “Possibility” which in four previously mentioned modalities, the modality is General Possibility from Actualization, General Actualization from Permanence, General permanence from Necessity, meaning that Necessity is the strongest modality and Possibility is the weakest one. Therefore, in order to describe the Simple Modified Propositions, two properties are combined:

A modality of the four: 1 - Necessity, 2 - Permanence, 3 - Actualization, 4 - Possibility

A “Time Tense” of the four tenses: 1- Eternal (E): As long as the subject exists meaning at the time of subject existence. 2- Permanently Describable (C): As long as the subject exists and it is conditioned to the description of the subject. 3- In a Determined Time (T): When the subject exists in a determined and specific time meaning in a specific and determined period of the subject existence (for example in Youth). 4- In an Undetermined Time (S): When the subject exists in an undetermined and unspecified time, meaning in an undetermined and unspecified period of the subject existence (17). The propositions including the four time tenses can be called respectively “Existential”, “Conditional”, “Timely” and “Published” and the four tenses (E, C, T and S) intensity order depends on their combination with the modality (17).

Among the four modalities above and mentioned time tenses, all time modalities and as a result, all simple propositions are extractable (4*4=16), as this method was also used, improved and modified after Avicenna by other logicians such as Katebi and Shirvani who are the latest logicians studying modified propositions using Avicenna's method.

For example, in his book “A Complete Description of Logic”, Shirvani points to fourteen forms of modified propositions and the reason for not mentioning the other two remaining of the sixteen forms might be that the modality “Permanence” along the time tense “Determined Time” (or Undetermined Time” makes no sense. The fourteen above mentioned forms of Modified Propositions are as following (17):

After this brief introduction of the method of Avicenna and logicians following him in presenting modalities discussion, we will go through the reasons Avicenna combined modalities with time. Generally, entrance of modalities discussion to Islamic logics was not only the result of Avicenna following Aristotle's logic, but also was the result of his approach to two sciences of Logics and Mathematics. Avicenna knows them as resembling sciences whose main difference was Abstract Elements of Logics opposing the Objects studied by Mathematics which do not exist in nature. But, when Mathematics studies the sensible and changing objects, Logics comes to our help in the phase of authentication and mutually the specific value of Mathematics science is clarified in its relation to Logics which is the proof or analogy about a permanent object in time or necessary synthetic or in other words, about objects studied by Mathematics.

Before Avicenna, the first Muslims talking about Mathematics and the necessity of learning it, were those scientists famous as “Safa Brothers” who introduced different sciences including Logics, Mathematics and Physics in their Encyclopedia of 52 theses, advising that after learning religious sciences one should go to earthly sciences such as grammar, poetry and history and only after that one can begin to learn philosophy which should itself begin with mathematics. In Safa Brothers' mathematics the major attention is paid to Pythagorean doctrines and numerical mysticism of India and they believed that science of numbers makes the beginning, middle and end of philosophy, as even geometry which is also concerned with shape of objects prepares us for the science of calculation that is a real and pure science [16, P. 158].

After Safa Brothers gradually mathematics was much more common among Muslims to the extent that while the geometric interpretation of the spherical trigonometry by Ancient Greeks, including Ptolemy made its practical use difficult, the more abstract form of this science, Algebra, which Arabs had learnt very well in medieval times, was improved by Muslims. This provided them the opportunity to have access to more extensive information [11, P. 158]. Familiarization of a well-knowledge physician, philosopher and scientist like Avicenna with Mathematics and its branches was an obvious thing, as his dominance over Mathematics is clearly manifested in his logic books and it would definitely be said not only almost all proof discussion of the book “Healing” is weaved with mathematics and geometry, but also the two books “Encyclopedia” and “Hints and Punishments” are also full of descriptions and examples of mathematics.

Avicenna first by presenting descriptions of Mathematics, priories this science and its branches from other:

“Propositions principles are not used in every science, but some of which only using priorities and limits such as calculating, however, in geometry all these principles are used and in natural sciences also sometimes all these principles based on habits are used mixed and not defined [3, P. 117].

“The ignorance opposing science means ignorance which not only destroys science, but also leads to belief in anti-science, as we have seen in the second form of the two forms of being nonscientific and non-geometric - such things seldom happen in Mathematics: [3, P. 268].

“Imagination in nonmathematical sciences is often misleading, but, in mathematics, it is guiding and guideline. As a result, teaching mathematics unless with shapes marked by alphabets is hard, since this is a help to imagination and empowers it, since in mathematics, contrary to other sciences, there is no fear of imagination”[3, P. 270].

Along the book Healing, Avicenna in pages 11-21 of the book Encyclopedia also first divides sciences to Practical and Theoretical and among Theoretical sciences introduces Mathematics as: “and the other one is Mathematics science and in it there is not much anxiety and disagreement, since it is far from change and movement and its subject in general is “quantity” and in detail is “size and number” and sciences of geometry, calculation, universe, music, debate, reality, dynamics, solution and others alike belong to it” and then discusses about geometry, different angles and also fracture and cohesion [4, P. 6].

Avicenna tries to along distinguishing mathematics from other sciences and introducing it, shows its precision: “Mathematics science in most cases use the first form, and from multiplication, use the first multiplication and sometimes the second. Hence, in these sciences few mistakes might happen through synopsis” [3, P. 272]. He also introduces the subject of Mathematics sciences: “And sometimes in each of these sciences (Calculation and Geometry) other proofs are used. But, in this case what is used for analogy is not prior to any of them (Calculation and Geometry), however, Absolute Quantity is prior for it, with the difference that in Calculation and Geometry Namely Quantity is not used and it is not overpassed” [3, P. 181].

After describing properties and precision of Mathematic science, Avicenna with introducing examples in this field, attends to prove his logical reasons. Mathematical examples of Avicenna, not only have the responsibility to complete training, but also they are used to describe and show the logical positions and characteristics of verification of predicts - that according to him are functions of how objects studied exist meaning they are subject of predicts [7, P. 39].Avicenna trying to manifest the relationship between objects whether as reality elements or subjects studied by logics in a better way with the help of mathematical examples, on the contrary with examples of natural reality such as:

“It is possible that Zaid is in the house or Omer is” [2, P. 23]

“If the sun is rising, hence, there exists day” [2, P. 20]

“Either Zaid is in the sea or he will not drown” [2, P. 26]

In which using natural and non-mathematical objects, he shows compound predicts with non-strict season, clearly he points to different possibility situation of the object, using mathematical examples as:

“This number is either even or odd” [2, P. 20]

If you look at the number unconditionally, hence, you will not find impossibility in its nature, since if it was impossible it never existed. But, when you look at four conditioned as two multiplied two, it becomes a necessary number and when you look at four conditioned that it cannot be the result of two multiplied two, then it is impossible” [2, P. 126]

“Also, when we know this number is not even, immediately we know it is odd and this is science of certainty and it is not destroyed and it is not resulted from a cause, since not being even does is not the cause of being odd, but, being odd itself is the cause of not being even and this is something out of odd nature, since its value is different from being odd” [3, P. 79].

Introduces compound predicts with non-strict season, discusses objects having one necessary property or do not have it, in a way that this property considered in mathematical aspect, has a necessary nature, using which it can be said that relative to which objects, the mentioned predict definitely belongs to the subject or not, as no number can be both even and odd, to the extent that if an object exists which can be both even and odd at the same time, hence, that object is not a number and the necessary nature of mathematical objects is hidden in this.

The two predicts he uses respectively to describe more precisely the continuous and non-continuous conditional meaning:

“If a line crosses two parallel lines, the exterior angles are equal to interior angles” (3, P. 19)

“This angle is either [3, P. 20]

Take us toward two properties in the mentioned objects: First, these objects show us the necessary substance of predict which means the properties discussed, are always pertinent to mathematical objects mentioned and this pertinent nature is unconditional. Second, they show that the necessity for these mathematical objects existence is conditional as a function to time and permanence function. Therefore, considering that these two examples describe synthetically necessary nature, we should write them with moderator operator as following:

Along mentioned examples which show Avicenna's approach to mathematics and its objects, studying his ideas about mathematics also proves this science position and importance in his thinking system. According to Avicenna, since mathematics studies absolutely abstract objects through mental review, it is categorized among those theoretical sciences which have philosophical value, since presents objects definition is a way that they can be studies without considering their changes and separate from sensual substance, hence, the sensual characteristics of objects can be ignored and an abstract recognition of them can be achieved. This abstract characteristic of mathematical objects is paid attention to by Avicenna more than all:

“For example, Calculation science is considered an individual science since it has a specific subject which is number. And Calculation science intrigue studies excuses of number applicable to it, since it is a number. If the intrigue of Calculation science in number looks into quantity or intrigue of Geometry in amount looks into quantity, the subject of both sciences will be quantity, neither number, nor amount” [3, P. 156]. Also, this characteristic of Mathematics attracted attention of Avicenna completely to counting, as in the book Encyclopedia he writes: “But each existence being even, odd, round, three-sided or long is not due to existence, since at first it should be counted, then it should be even or odd and first it should be measured to be round, three-sided or long” [2, P. 7].

The importance of counting attracts Avicenna's attention to “Odd” and its importance, as in response to the question “What is the meaning of subject in sciences and disputes?” declares the subject of positive propositions in sciences and disputes as each of the immediate individual subjects and in his different books declares this reality that subject of propositions in science, are each one of the immediate individual subjects [19, P. 81].

Avicenna does not stop here and following that introduces his main principle based on that each clear and distinguished concept must comply with a specific example or case. This is the main principle which later Descartes used as pillar of his theory of duality of spirit-object [10, P. 684].

These counted individuals are those elements which nowadays are presented with “N” in Mathematical induction and are presented with “X” to describe four enclosures:

Going back to modalities and time, we study the reasons Avicenna combined modalities with time. As you could see, Avicenna's philosophical system and parallel to it, his logical system, considering the metaphysics he believed in, needs to justify and explain all existing elements in a linear collection of God and His creatures. Since, these elements are limited to the real world and happenings in it, Mathematics with its synthetically necessary nature of its own can provide needs of logic and metaphysics to successive elements of existence. However, on the other hand, Avicenna in order to relate cohesion or in other words the successive counting of Mathematics to miscellaneous elements of existence, goes to logics, find the solution in it: Modalities and Time Modalities were introduced to logics long ago before Avicenna and he could use them again to complete his lessons. modalities by themselves considering the necessity degrees they related to everything (including Necessity, Possibility and Impossibility), helped categorization of existence elements, but their combination with time could complete the order of existence elements much stronger and in a very precise and detailed manner, to the extent that no element was ignored, all individuals or Xs were considered. Avicenna, using time, showed the difference between different individuals with different moments of time, as looking closely to his method of combining modality to time, we realize that after separating God as the static existence in all moments of time, he categorizes the rest of existence elements depending on how much they go along the element of time. With this method, Avicenna uses every moment of time as a basis for the Xs. Each X is overlapping a moment of time, all combinations of modality and time, cover all existence elements.

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