Islamic Studies

Andrey Smirnov

[437] The problem of truth was raised in medieval Islamic philosophy within the framework of discussions starting from the question of whether our knowledge corresponds to the "actuality of affairs." The notion of validity thus elaborated was comprehended as a quality of knowledge established through a comparison with "matters of fact." What was intended is not coincidence with what is and has existence. Existence (wujud) was generally understood in Islamic thought as one of the attributes (sifa) that a thing might or might not possess while still being "a thing" (shay'), and since our knowledge embraces things independently of their accidental attributes, the question about truth was placed on a wider footing. Validity, from that point of view, testifies that our knowledge conforms with reality in the immediate meaning of the term — thing-ness. This notion of reality (shayiyya) does not necessarily exclude Divinity, for God in Islamic sciences is often comprehended as The Thing, although different in every respect (except that of thing-ness) from all other things. The concept of "thing" serves to introduce some thing into the current of intellectual discourse rather than to state anything definite about it; to be a thing — that is, fixed and established — means to enter the field of discussion.

Validity as affirmation of conformity with reality was referred to as sidq (veracity, truth) or tasdiq (certification of truth). The "actuality of affairs" to which our knowledge conforms was comprehended also as a sort of "authenticity," and the corresponding term haqiqa may be rendered into English as "truth" as well. Thus verification is carried out by comparing our knowledge to the "truth of things," and if the result is positive, knowledge is "true (sadiq); if not, it is "false" (kadhib). Knowledge is valid by virtue of its coincidence with the truth of things, while the truth of the latter needs no verification. It follows from the fact of their "being affirmed": they just "are there" as "fixed" and "true." The ideas of truth, fixity and thing are closely linked in Arabic. The term "thing" (shay') is usually explained as "something that is established" (thabit), and the root h-q-q, from which "truth" (haqiqa) is derived, renders the same meaning. (For example, haqq means both "true" and "unshakable.")

The problem of truth was raised rather early in Islamic thought, and already the al-Rawafid discussed it. As al-Ash'ari informs us, most of them maintained that all human knowledge is "necessitated" (idtirar). From their point of view, a person is not free to acquire true knowledge or to reject the false; moreover, knowledge about the falsity or validity of our knowledge also cannot be obtained at our will. This [438] argument proceeded from the general assumption that all human deeds are "forced" (idtirar). At the same time, some of the al-Rawafid considered the human mind able to receive true knowledge independently, for example, to learn of God's unity (tawhid) before the prophets inform people of it. Knowledge gained independently, they argued, is obtained with the help of qiyas (literally "co-measuring"). The term designates rational epistemological procedures that produce new knowledge "by measure" of the old one and was used not only in Kalam, but in other sciences as well, denoting analogous judgment in fiqh (Islamic jurisprudence) and the syllogism in logic. However, al-Rawafid who affirmed the independent ability of reason to gain new knowledge were in the minority (al-Ash`ari, 1980, pp. 51-3).

The discussion of truth was deepened by the Mu'tazila. First, they were concerned with determining the types of propositions that can be true or false. These are statements containing "denial and affirmation" (al-nafy wa al-ithbat), "praise and reprobation" (al-madh wa al-dhamm) as well as "wonder" (ta`ajjub), while "question" (istifham), "order and interdiction" (al-'amr wa al-nahy), "regret" ('asaf), "hope" (tamanni) and "request" (mas'ala) are neither true nor false (al-Ash'ari, 1980, p. 444). The Mu`tazila seem to have been little occupied with how true knowledge is reached, and this is perhaps due to the fact that they discussed truth in connection with the reliability of prophetic sayings — which is not an art to be taught. The Mu"tazila had different opinions as to whether a proposition can be called true or false if its author was ignorant of the "actuality of affairs." (The question here is whether unintended deception can be called a lie, or whether a statement that incidentally happened to be exact can be called truth). When the relevant "actuality of affairs" does not exist (for example, if the event has not yet occurred) or is unknown to a person, the verification procedure that compares a proposition to the "truth of things" cannot be executed — for objective and subjective reasons respectively — and such a proposition is to be regarded as neither true nor false. This argument, however, was not generally accepted by the Mu"tazila.

As for Aristotelian logic, it took root in medieval Islamic thought above all due to peripatetism. This school gave much more sophistication to what the Mutakallimun said about truth and the possible ways of acquiring it. Many elements of Aristotelian logic introduced by the Islamic peripatetics became indisputable patterns of reasoning for Islamic thinkers, and no school of medieval philosophy seriously challenged the syllogism as a paradigm for the preservation of truth in argumentation. What was disputed was the sphere in which the syllogistic method is relevant. This method appears to have gained less favor among Islamic thinkers than it did among ancient or medieval Western thinkers, and in philosophy per se we find even among the peripatetics great reservations in this respect.

Elements of Aristotelian logic were rather well known to Islamic scholars from translations of Aristotle's works as well as from writings of his great commentators, among which must be mentioned in particular Porphyry's Eisagoge. There also existed quite a number of logical treatises of educational and propadeutical character composed in Arabic, many of which belong, or are ascribed to, al-Farabi.

[439] According to the peripatetics, the purpose of logic is to gain true knowledge. Such knowledge is twofold, consisting of "notions" (tasawwur) and "certifications of truth" (tasdiq), which are both accessible only on the basis of some a priori know ledge. As for "notions" (that is, understanding what the thing is), this knowledge in the final analysis is based on the units of meaning that definitions, later used in arguments, are composed of. In "certifications of truth" this primary knowledge is represented by "principles of intellect" (awa'il al-`aql), that very intellect with the help of which, as al-Farabi interprets Aristotle, we perceive the "certainty (yaqin) of necessary and true general presuppositions" (al-Farabi, 1890, p. 40) with no prior investigation or argument.

This is how Ibn Sina expresses the point in his concise Book of Remarks and Admonitions:

The purpose of logic is to provide a canonical tool (ala qanuniyya) that prevents aberration of thought. By "thought" (fikr) I mean here what takes place when a person, having pulled himself up, passes from what is present in his mind, what he has a notion of or what he is certain of... to what is not [present] there. This transition has a certain order and figure that might be correct and might happen to be incorrect. The incorrect often looks correct or makes you believe that it is correct. So logic is a science that studies ways of transition from what is present in the human mind to what it acquires, ... the correct modes of ordering this transition and its figures, as well as the kinds of incorrect ones. (Ibn Sina, 1960. Pt I, pp. 167-78)

Atomic "individual meanings" (ma'ani mufrada), from which complex logical structures are produced by "ordering" (tartib) and "composing" (ta'lif), constitute the basis for all logical operations (Ibn Sina, 1960. Pt 1. pp. 179-80). These meanings entirely correspond to the things in question. The correspondence is based on what is established by the language-giver who assigns certain "meanings" (ma'ani) to certain "sounds" (alfaz): this correspondence is therefore called "established" (bi al-wad`). For example, the sound "human" corresponds to the meaning "animal endowed with speech." The sound and its meaning are the two elements that make up a "word" (kalima); the relation of "denotation" (dalala) exists between the first and the second. What is denoted by the "sound" is that very "meaning" that constitutes the "truth" (haqiqa) of things. Thus logic, dealing with sounds and their meanings, deals in fact with things — as long as the denotation originally established in language is preserved.

In order to acquire the correct notion of a thing, one must arrive at a "clarifying saying" (qawl sharih) about it. This can be achieved, first, in a "definition" (hadd) of the thing. The construction of definitions is described in every detail as a procedure of answering the question what is it? by providing its genus (jins) and specific difference (fasl) to produce a definition of the species (naw') that informs us of the quiddity (mahiya) of the thing in question. Besides a definition, a "description" (rasm) can also be given to clarify the notion of a thing, although this does not deal with thing's quiddity. A description has to be given to those tools that serve us in setting out definitions — that is, notions of genus, species and specific difference — as well as to the highest genera that have no genus above them (and, consequently, [440] for which no definition can be given). Second, a description may be given to the things that have quiddity; for example, "animal endowed with laughter" serves as a description for "human."

As for arguments, they are composed in the form of syllogisms. Aristotelian syllogistic doctrine was exposed in Islamic peripatetism in every detail, accompanied by the examination of possible errors, mistakes and sophisms. The validity of conclusions reached through syllogisms is based on the accuracy with which we establish true meanings in definitions.

A great project of the unification and hierarchization of sciences was advanced in Islamic peripatetism. The hierarchization was to be based on differences in the degrees of generality of the various sciences' subjects. What is proved in the more general sciences may serve as non-provable principles for the more particular ones. From that point of view, sciences form a pyramid of axiomatically subordinated branches of knowledge. AI-Farabi, in Kitab al-milla, al-Kindi, in Kitab al-falsafa al-'ula, Ibn Sina, in al-Burhan (part of Kitab al-shifa') (to give only examples, and not an exhaustive list) speak about such subordination of the more particular to the more general sciences. This structure of knowledge is conceived as corresponding to the universe, which is ordered along the same lines of generality-particularity.

Logic is an important instrument of cognition. This does not mean, however, that the peripatetics tend to exaggerate its significance. Besides knowledge acquired by means of logic, direct, intuitive (hadsiyy) knowledge is possible. This is granted as immediate manifestation, in which the thing unconditionally and completely expresses itself as such.

Knowledge of our ego serves as a paradigm of intuitive cognition, Ibn Sina introduces this thesis in his famous fragment about the "flying person" in his Book of Remarks and Admonitions:

Look at your soul and answer: when you are in sound health, or even not, but correctly perceive things, did it ever happen that you were ignorant of your self(dhat) or didn't ascertain your soul? ... Imagine that your self has just been created: assume that it is in its right mind and figure, sees none of its parts and its members don't feel each other, but it is spread and suspended at some moment in pure air. Then you will find that it notices nothing: however it observes fixity of its egoness (ana'iyya). (Ibn Sina. 1957, Pt 2, pp. 319-20)

The ego is always manifest to itself, and this manifestation is the primary fact of our consciousness. It depends on nothing and, furthermore, no sophisticated proof is needed to understand it: it suffices to imagine the situation described above for the fact of the ego's manifestation to itself to become clear.

Immediate manifestation can be considered a sort of completion for the logical form of cognition. This concluding step, however, already transcends the path that it completes and opens fundamentally new horizons. According to Ibn Sina, Ibn Tufayl and other authors, a person acquires complete and true knowledge through union with Active Intellect — the last of the Cosmic Intellects, repository of all forms and governor of the sublunar world. This full contact with the source of forms that [441] are the subject of logical inquiry no longer presupposes any necessity of transition from the already-present to the yet-unknown, and thus places one outside the framework of logical reasoning. Certainly, not everyone is able to achieve this union; only if the soul is pure, Ibn Sina argues, can it be inflamed by Active Intellect and directly imprinted with the forms of all possible knowledge. It is the same intention of achieving immediately manifest self-evidence that speaks for itself in these cases, as also when these authors abandon philosophical jargon and talk about directly witnessing the Divine world. It is also obvious that the patency of our ego for itself guarantees its ability to reach absolutely complete and true knowledge by witnessing the Divinity, for the two kinds of evidential witnessing differ with respect to their subject, rather than in their essence.

The exposition of the peripatetic doctrine of truth is in no way complete before Ibn Rushd's work Kitab fasl al-maqal wa taqrir ma bayna al-shari`a wa al-hikma min al-ittisal (or "Decisive Saying Establishing the Connection between Law and Wisdom") is mentioned. Despite its title, the chief idea of this little treatise is that the spheres of "wisdom" (that is, philosophy) and "Law" (the theoretical postulates followed in religious life as well as its practical prescriptions) may be separated. The work attempts to fix independent rights of reason for obtaining the truth that -within the limits defined for it — no one can violate. It is noteworthy that Ibn Rushd had predecessors among the Mutakallimun in the differentiation of what falls under the Law, which is established and can be revised under no circumstances, and what reason is permitted to discuss and decide. "What is known by reason and what is known only through Law," a chapter in Usul al-din ( Principles of Religion), a book by an Ash'arite author, Abu Mansur al-Baghdadi, bears a resemblance to Averroes's treatise not only by its title. Al-Baghdadi definitely states that only Divine prescriptions, either direct or transmitted through prophets, constitute the domain of Law, whereas problems of the world's origin and similar questions involve theories that human reason elaborates.

Isma`ilism may to a certain degree be regarded as a successor of peripatetism with respect to the theory of knowledge and truth. Isma`ili theoreticians, on the one hand, have no doubt concerning reason's capability of knowing the truth; more over, cognition of the truth is, in their view, indispensable for the person who wants to reach salvation. On the other hand, they give up the syllogistic method as the principal means of cognition. The Universe, in their estimation, is not a unified structure arranged in the hierarchical (generality-particularity) order that the peripatetics described. It is rather a system of structures that stand with respect to each other in relations of similarity, isomorphism and correspondence. This ontology presupposes a special method of cognition.

This is how Hamid al-Din al-Kirmani. the most prominent Isma`ili theoretician, expresses these theses. Any science, he argues, has its own "laws" (qawanin) — that is to say, criteria by which knowledge is tested in order to determine whether it really corresponds to the "true order" (nizam al-haqq) of the subject of study. And if the peripatetics strive to achieve their aim, that is, "knowledge of the meanings of existence" (ma`ani al-wujud), by means of logic. Isma`ili philosophers employ a different method.

[442] Its basic premise can be expressed as follows: anything in the world belongs to some structure and may correctly be comprehended only within that structure, through its place in the overall framework and its structural role. Thus the preliminary step for cognition is to single out the universal structures that, being completely "balanced" (mutawazina) and "isomorphic" (mutashakila), form the created world. In their mutual conformity universal harmony is embodied, expressing the highest wisdom of their creation and giving evidence to the perfection of our world, which is the best of all possible worlds.

The principle of hierarchical harmony, penetrating the Universe, can be traced on different levels. As Isma`ili works show, this can be done with great accuracy and amazing sophistication. There are four basic structures to be identified; the metaphysical world, the religious community, the natural world, and the human being. It is of fundamental importance that knowledge of any of these structures allows us to know all of the others with the help of special rules of interstructural translation of meaning, since corresponding elements of different structures have a similar structural place, function and essence.

Had all the structures of the Universe been manifest to us, no special cognitive procedures would be necessary. However, universal structures fall into two classes. Some of them are "obvious" (zahir), while others are "latent" (batin). Isma`ili theory of knowledge proceeds from the premise that "latent" structure (as a whole, as well as any of its separate elements) can be known only through the "obvious." Since it is the structure of Isma`ili community (or as al-Kirmani prefers to say, the "world of religion") that is known to us in every detail, all new knowledge is acquired on this basis. This method is referred to as finding "balance" (muwazana) and "correspondence" (mutabaqa). Isma`ili community structure is harmoniously balanced with all other structures in the world (this is a postulate of Isma`ili philosophy, not a conclusion to be proved), and knowing it we can arrive at knowledge of anything. Besides, numeric structures are widely used in search of mutual structural correspondences. Using this method, al-Kirmani consistently and in every detail describes the metaphysical world (the hierarchy of Cosmic Intellects) as well as the natural world and the microcosm.

Structural correspondence is for al-Kirmani not only a method of finding new knowledge, but also a criterion for the verification of existing knowledge. Only that is valid which has a correct structure. "This criterion is such that what agrees with it. is true, and what disagrees, is false; it is this criterion that is so attractive for the intellect that seeks to know with its help what is given to it as well as what escapes it" (al-Kirmani, 1983, p. 236). In cognitive procedures the structure of the "religious world" (which means the Isma`ili community) is taken as a paradigm, but that structure too is verified by correspondence to "God's creation." The perfection of the manifest structure and its undoubted validity is proved for al-Kirmani by the fact that it disagrees with the Universe in no detail (al-Kirmani, 1983, p. 237).

Certainly, the person who would endeavor to apply this method of cognition in his own research will hardly succeed. This method serves well in the exposition and structuring of already acquired knowledge, but in spite of what al-Kirmani maintains, not in the search for new knowledge. The author of Rahat al-'aql leaves us [443] ignorant of the most interesting and important detail of his method — those inter structural semantic translation procedures that fill the unknown structure with new meanings so that it balances the structure manifest to us. In this respect what al-Farabi said on another occasion seems to be relevant. In this critique of astrologers, the "Second Teacher" argues that in the world one can single out diverse "sets" (kathra) of things, like animals' movements, the voices of birds, written signs, and so on, in order to put them in correspondence with the multitude of events that we experience; such a procedure, however, produces "only occasional, instead of necessary [truth] that reason should have accepted" (al-Farabi, 1890, p. III).

Illuminative philosophy is another successor to peripatetism with respect to the theory of truth. It is no exaggeration to say that Ibn Sina is the greatest authority for the most prominent representative of this school, Shihab al-Din Yahya al-Suhrawardi. The affinity of these two thinkers is surprising, in view of the disagreements between their teachings caused by al-Suhrawardi's adherence to a metaphysics of light and darkness; on the subject of the theory of truth, however, the disagreements between them are minimal.

Like Ibn Sina, al-Suhrawardi speaks about two kinds of true knowledge: immediate intuitive knowledge and logical knowledge. The first he also calls "truthful witnessing" (mushahada haqqiya), and the second "research" (bahth). Knowledge of the ego. or, as al-Suhrawardi himself calls it, ego-ness (ana'iyya), serves for him. as it did for Ibn Sina, as an archetype of the direct cognition of truth. But since the majority of people are unable to experience the completeness of truth immediately, they have to resort to indirect logical cognition, which starts with basic unquestionably valid premises and proceeds from them to the unknown (al-Suhrawardi, 1952, p. 18).

Al-Suhrawardi considers the elementary sensual perceptions "simple meanings." logical atoms from which the construction of concepts begins. These perceptions are simple, absolutely evident and self-identical; they are the principal elements known by anyone who has healthy organs of perception. Sensual perception is absolutely adequate, al-Suhrawardi argues: we perceive exactly what is there in the things perceived. Finally, basic sensual perceptions, being elements of knowledge, have no logical definition (al-Suhrawardi, 1952, p. 104). This sensualism of the celebrated mystic agrees well with his radical nominalism: according to al-Suhrawardi, no general concepts exist independently of our minds. On this basis he argues that quiddity is constituted not only by substantial features, as the peripatetics maintained, but also by accidental features. For the shape of a house, for example, is accidental with respect to the clay from which it is constructed, and nevertheless we say, in response to the question "what is it?" that it is a "house," rather than "clay" (al-Suhrawardi, 1952, pp. 85-6). Given Suhrawardi's metaphysics of light and darkness, he denies that the first matter is universal substance, and consequently is compelled to look for a different basis of individuation. For him it is not matter that is "responsible" for the multiplicity of individuals which all have the same quiddity and which therefore are, logically speaking, one and the same, but rather the degree of perfection (kamal) or degree of completeness by which this or that "universal meaning" is represented in the individual (al-Suhrawardi, 1952, [444] p. 87). This concept of individuality as a degree of perfection will later be elaborated in Sufism by Ibn 'Arabi.

As for the syllogistic method, the importance that al-Suhrawardi attaches to it is testified to by the fact that the first half of his chef-d'oeuvre, Hikmat al-ishraq (Wisdom of illumination), is solely devoted to its exposition. Al-Suhrawardi points out that it is a necessary propaedeutic for the second, metaphysical and mystical, part of his book. In his analysis of syllogisms accompanied by a detailed study of possible errors and sophisms, al-Suhrawardi strives to prove that all modes of syllogism can be reduced to a single positive categorical mode, which, in his estimation, makes knowledge of all the subtleties of the other modes superfluous.

As for the complete and perfect witnessing of truth, it is reached, according to al-Suhrawardi, in the state of "illumination" (ishraq). "Illumination" is the central concept of al-Suhrawardi's philosophy. It signifies direct irradiation of the soul by superior, metaphysical lights. The soul itself is a light that has descended from the world of light" into the "world of darkness" and is yet impotent to return to its original abode. This congeneity of human soul and the highest principles of being constitutes the ontological foundation for the possibility of such irradiation. Illumination discloses the truth (haqq) immediately and needs no verification (tasdiq). Logical instruments that verify the correctness of "transition" procedures are of no use when no such transition takes place.

The Sufi doctrine of the truth and the ways of acquiring it differs in its central point from any of the doctrines that we have hitherto discussed. No matter how truth is understood in Kalam, peripatetism, Isma`ilism, or the philosophy of illumination, all of these schools have in common an explicit or implicit understanding of true knowledge as something unhesitatingly established: the term "certainty" (yaqin) generally serves to express this fixity. Such certainty is understood as "quiescence" (itmi'nan), the same idea of quietude reached through complete and true knowledge is expressed by the title of al-Kirmani's magnum opus Rahat al-'aql — Peace of mind) on the basis of the generally accepted notion of the "perfect" (kamil) and "complete" (tamm) as immobile. The true. by virtue of its completeness, needs nothing external to be accomplished and, consequently, no movement is necessary for it. Against this understanding of truth as a state of clear certainty, Sufism opposes the doctrine of the truth being witnessed in its completeness in a state of "abashment" and "confusion" (hayra) that presupposes constant restlessness.

Although in this respect Sufism stands in opposition to other trends of medieval Islamic philosophy, there is doubtless continuity in the way Sufi theoreticians arrive at the above conclusion. Peripatetism, Isma`ilism and the philosophy of illumination understand the achievement of truth, at least in its logical form, as "transition" (intiqal) from what a person possesses as established truth to what he or she currently does not possess: as for mystical revelation, it also provides a sort of finally established and unequivocally valid knowledge. "The unknown — against the known," Ibn Sina writes (Ibn Sina, 1960. Pt 1. p. 181): all things are divided into two classes that stand to each other in a relation of exact mutual correspondence; everything is truly known after it has been unknown. Dividing things [445] into the "unseen" (batin) and the manifest" (zahir) was commonplace in medieval Islamic thought, and these concepts remain fundamental in Sufi epistemology as well, where cognition is often referred to as "making [the unseen] manifest" (izhar).

This substantial departure from traditional Islamic thinking in the final conclusion of Sufi epistemology (that is, the cognition of truth as "confusion" instead of as "fixed certainty") in spite of common intention of finding the solution (truth as unseen made manifest) is explained by a basic feature of this philosophy that may be defined as interiorization. Both Sufi ontology (see Causality and islamic thought) and epistemology are deeply marked by it. Just as the cause and effect relation is an inner division of the same essence rather than an external relation between two different essences, so the inner and the outside (the "hidden" and the "manifest") are not two different and definite aspects of things, but rather one and the same. What other schools of philosophy consider as occurring between, Sufi philosophy regards as taking place inside.

However, Sufi philosophy does not deny other points of view. As the doctrines of Ibn Sina and al-Suhrawardi demonstrated, logic may be regarded as an incomplete version of immediate and perfect truth-witnessing, rather than as its alternative. Ibn 'Arabi, the greatest of Sufi philosophers, adopts the same position. In this sense his theory of truth is inclusive rather than exclusive, for he regards non-Sufi ways of cognition as also true — within their limits, however, and not absolutely.

For example, the knowledge obtained through correct syllogisms is certainly true, and there is no doubt about its scientific results, like our knowledge of the sun's size or the rules of mathematics (Ibn 'Arabi, 1980. pp. 102-4). The intuitive "witnessing" (mushahada) gives true knowledge as well: the "inner sight" (basira) discovers immediately behind things their causes and thus discloses the inner essence of things hidden under their manifest outwardness. The cause of things and of their inner essence thus discovered is God, or The Truth (al-Haqq) — each time seen in one of His infinite aspects. However, the "witnessing" first brings into sight the thing, and then behind it, or inside it, discovers God. The two are still divided and differentiated, and the all-encompassing Truth that constitutes the core of everything is not found as the thing's outwardness. The highest stage of truth is to see things in God. to notice the sameness and equality of the different, to be unable to differentiate. This is the ability of the "heart" (qalb). Intellect, inner sight, and heart form an ascending hierarchy of organs with their corresponding methods of cognition.

Rational knowledge is acquired by moving "from" premises "to" a conclusion, by going along "the stretched path," as Ibn `Arabi puts it (Ibn 'Arabi, 1980, p. 73). The intuitive witnessing of God as the inner essence of things spheres this line. But only when the sphered line becomes equal to its center (see CAUSALITY AND ISLAMIC THOUGHT) does "confusion" come, and the person sees the hidden as manifest and the manifest as hidden, sees God as His creation and the creation as God Himself. Total oneness and sameness, the transcendence of any differentiation and the non-fixity of any definiteness and any limit (the results of logical cognition included) — this is what such a way of seeing the truth boils down to. The Sufi [446] understanding of truth undermines well established stereotypes of dichotomizing divisions. The fundamental ontological sameness of God and His creation entails the sameness of any pair of opposed categories. The law of excluded middle is irrelevant for this point of view: what it points to is but a step that should inevitably be overcome. Truth turns out to be a transcendence of dichotomic divisions — a transcendence which, however, presupposes that each of them is fixed — but only as a step in an unceasing movement, equal to any other of its infinite steps.

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