Renaissance interpretation of dialectics. Nikolai Kuzansky and the principle of the coincidence of opposites
Siberian State University communication lines
Department of Philosophy
PHILOSOPHICAL VIEWS OF NICHOLAS OF CUSANUS
Essay
In the discipline "Philosophy"
Supervisor:
Associate Professor A.N. Bystrova
Developed by:
Student gr. U-213 Belova V.A.
year 2012
Content
Introduction
Nicholas of Cusa was the greatest and most original philosopher of the Renaissance. Originally from southern Germany (the town of Kuza). Cardinal of the Catholic Church. He combined in his works and activities the cultures of the Middle Ages and the culture of humanism. On the one hand, he is an active hierarch of the Catholic Church, on the other hand, he is a member of the humanist circle.
Nowadays, the philosophical work of Nicholas of Cusa is of great interest and occupies a strong place in the history of philosophy: not a single historian of philosophy analyzing the worldview of the Renaissance can ignore philosophical teaching Nicholas of Cusa, since it is the philosophy of Cusa that demonstrates the path of transition from the Middle Ages to Renaissance ideas.
However, in order to better understand the significance of Cusan's philosophical work in the history of the Renaissance, one should consider and explore not only his philosophy, but also the circumstances of his personal life, his relationships with various layers of the society of that time.
The purpose of this work is to study philosophical sources dedicated to the legacy of Nicholas of Cusa.
1. Main features philosophical ideas N. Kuzansky
1.1. Cusanus' concept of God
The concept of God Cusanus, despite his affiliation with the Catholic Church, had pantheism. For him, God is not the personality of Christianity, but an infinite single principle that contains all opposites. God, according to Cusanus is at the same time an absolute. maximum and abs. minimum. On the one hand, God is the whole world, i.e. an endless variety of things. But, on the other hand, God is something absolute. simple and united, since in infinity, as Kuzan says, all opposites coincide. To prove this idea, he uses examples from geometry. If the radius of the circle increases, the circle will tend to coincide with the line. The same applies to the triangle. If you continue the side to infinity, the triangle will also tend to the straight line. Thus, at infinity, opposites coincide. God, therefore, is the coagulation of opposites and their coincidence. And, conversely, nature is the result of the unfolding of God.
1.2. Anthropology of N. Kuzansky
“God is the macrocosm, man is the microcosm.” Man is created in the image and likeness of God. Since God is the absolute maximum and the absolute minimum, then man, or rather his soul, or even more precisely, the mind, is both the absolute maximum and the absolute minimum. The human mind, on the one hand, is something simple and united, on the other hand, it includes an infinite number of images. In this sense, man, just like God, includes the whole world. In addition, just as God has many potential options for the development of the universe, so man has an infinite number of options for his own development - a conclusion that is extremely important for humanism. From all this it follows that man, in the words of Cusan, is a “second God.” Here we clearly see how medieval theocentrism is being replaced by humanistic anthropocentrism.
2. Dialectics of Nicholas of Cusa
2.1. Unity and struggle of opposites
The dialectics of Nicholas of Cusa is rooted in his understanding of God and the world, it is manifested in the doctrine of God as infinite and one (and therefore the focus of the unity of opposites), generating the world, positing the finite from the infinite, the many from the one, parts from the whole. It also manifests itself in Nicholas’s teaching about existence as a dialectical combination of opposites. On this basis, he developed the dialectical concept of man as a microcosm and the dialectical concept of knowledge, combining truth and error - the two main opposites, comprehending the unity of the plural, the infinity of the finite, the burden of the opposites of the world of concrete, finite things.
Further, V.V. Sokolov points out that Nikolai sought to solve the problem of God in the spirit of negative theology, believing that positive theology brings the creator too close to creation, and does not elevate him above it. Negative theology interprets God as one and actually infinite, for, according to it, “there is neither father, nor son, nor holy spirit, but there is only the infinite. Infinity, as such, does not generate, is not generated, does not come from anything."
Denial of the persons of the divine trinity and transition to abstract understanding God, as one, as the principle of unity, a very bold, essentially “heretical” step, for which in the next century Catholic Church severely punished.
From my point of view, Cusansky anticipated his time in this matter, since later the church itself came to such an understanding of God.
The pathos of unity and infinity is a defining feature in Nicholas’s interpretation of God. Theology insisted on the unknowability of the divine being, and Nicholas consistently continued this line, which asserted the existence of a “hidden god.” Having taken it to its logical conclusion, he essentially completely depersonalized God. Even in terminology, he does not always mention the name of God, systematically calling him in “Learned Ignorance” “the absolute maximum” and simply “the absolute.” In subsequent works, this impersonal, abstract god is referred to as the Non-Other, and as Being-possibility, and as Possibility Itself, or simply as possibility. Interpreted so abstractly, God is not divorced from nature and man, but is in every possible way close to them. It becomes the main expression of the unity of nature itself, understood pantheistically. “The Creator and creation,” writes Nikolai, “are one and the same”; “God is in all things, as they are all in him.” The naturalistic tendency clearly takes precedence over the mystical one in Nicholas, and the “Book of Nature” interests him much more than the “Book of Grace” Holy Scripture.
Unity not only expresses, according to Nicholas, the very essence of God, but is also interpreted as a form of the relationship of a single God to a plural world. The Divine absolute, acting from certain depths of nature, of course, does not dissolve completely in things and phenomena. But, although it constitutes something completely special - an absolute, it is by no means indifferent to the world of things, phenomena and beings. This world is not a scattered and external collection of individuals. Since “God is the only simplest basis of the entire Universe,” his most important function is that he brings unity to the motley diversity of the world. The enormous, one might say, primordial dialectical problem that arose in this connection isthe problem of an infinite and at the same time single, integral world.
I think that such a deep understanding of the structure of the universe is quite surprising for XIV century, and speaks of the high degree of talent for generalizations of Nicholas of Cusa.
The interpretation of the world as a single whole in the era under review was based primarily on analogies between the organism and the world.
Nicholas says: “The movement of love carries all things towards unity in order to form from them all one and only Universe.”
As already noted, the pathos of unity in the understanding of God was combined in Nicholas with the pathos of infinity. Kuzan, in the spirit of the mystical tradition, sees in actual, complete, once forever given infinity a synonym for unknowability, inaccessibility to any, primarily mathematical, concepts of the human mind. “The Infinite, which escapes like the Infinite from all proportion, is unknown.”
At the same time, the full approach of the absolute to nature leads Cusanto to radical changes in the interpretation of the latter in comparison with the traditional religious-medieval worldview. Of course, for a pantheist, even a naturalistic one, the world cannot be infinite in the same sense in which only the divine absolute is infinite. But the world is no longer considered as finite, representing a kind of unity of opposites - actual infinity and finitude. Although “the world is not infinite, it still cannot be considered finite because it does not have boundaries between which it is enclosed.” So, before us the concept arisespotential infinity, or limitlessness,expressing the impossibility of finding any real boundary in nature and at the same time the possibility of crossing any predetermined limit.
The interpretation of infinity inevitably led Nicholas to the dialectic of the finite and the infinite, and the interpretation of unity just as inevitably led (when considering the relationship of God to the world of things) to the dialectic of the one and the many.
2.2. The principle of emanation
In the same connection stands the concept developed by Nikolaidialectics of the whole and parts. Resuming the principle of “all in all,” Kuzanets emphasizes that the whole “is directly in any member through any member, just as the whole is in its parts in any part through any part.” True, this process is based on the “soul of the world,” which “is entirely in the whole world and in every part of it,” but the most significant thing is that it is the whole that determines the direction of movement of its constituent parts, for “every movement of a part is directed toward the whole as perfection."
As an absolute maximality, God is interpreted by Nicholas as the absolute possibility of everything that exists. In this regard, instead of the principle of creation, Kuzanets puts forward the principle restrictions absolute maximum, thanks to which all the infinite diversity of the concrete world arises. Only a consistent limitation of a comprehensive whole leads to the emergence of corresponding parts, for “all limited objects are between the maximum and the minimum.” It is not for nothing that the philosopher called one of his works “On Being-Possibility.” This name is formed from two Latin words: posse “to be able” and esse “to be”, it denotes the coincidence of the opposites of possibility and reality in God. But it is possibility, the potential side of divine omnipotence, that explains the “eternal birth” of all things and beings. The Divine maximum as an absolute unity contains in itself in a “collapsed” form all the infinite diversity of the world of nature and man. Therefore, its generation is a kind of “unfolding”.
The direct source of this most important idea of Nicholas’s ontology and dialectics is the principle of emanation, through which the entire concrete multitude of bodily objects gradually emerges from a spiritual and extranatural unity. Indirectly, this idea goes back to the Heraclitean-Stoic teaching about the strict universal rhythm of the emergence of the world from fire and its return after thousands of years to the same fiery element. The principle of emanation is a purely idealistic principle, but from the end of antiquity and throughout the Middle Ages it was the main and, in essence, the only antipode of monotheistic creationism.
The idea of “collapsing” and “unfolding” the world from some single and the only basis, from the absolute, introduced dynamics into nature and led to the idea of development, at least in organic nature. The following statement by Cusan is very eloquent in this regard: “Vegetable life itself, in its darkness, hides spiritual life.” The same idea is formulated even more expressively in another work: “The power of the elements is hidden in chaos, in the power of development lies the sensual, and in it the imaginative power, and in it the logical, or the power of reason, and in the power of reason the power of understanding, in the power of understanding spiritually seeing and in the spiritually seeing the power of forces, i.e. unity.” At the same time, “in sensual nature life is nobler than in plant life, and even nobler in rational nature.”
From my point of view, it is obvious that the interpretation of God as one and infinite, the transfer of the principles of unity, infinity, dynamism to the world gave rise to a whole complex of dialectical ideas in Nicholas’s philosophy - the dialectics of the one and the many, the infinite and the finite, the whole and the part, a kind of idea of development .
The traditional formula of pantheism, according to which God acts as the beginning, middle and end of all things, means the affirmation of not only the principle of the unity of the world, but also the principle of the unity of opposites, immanent in God. “Since God is everything,” states Kuzan, “he is also nothing,” for “he is everywhere and nowhere.” Essentially, the properties of both being and non-being are simultaneously attributed to God. Likewise, the world, everything that exists, consists of opposites. “All things are composed of opposites in varying degrees, having sometimes more of this, sometimes less of the other, revealing their nature from two contrasts by the predominance of one over the other.” Nikolai draws examples of such a coincidence primarily from mathematics: as the radius increases, the circle coincides more and more with the tangent to it, and therefore “infinite curvature is infinite straightness.” In a similar way, the triangle turns into a straight line as the angle opposite the base decreases, i.e., as the height of the triangle increases endlessly, as a result of which its sides merge into a straight line. The unity of opposites also represents the divine being: as containing the whole world, it is the absolute maximum, and as being in any, even the most insignificant object, it is the absolute minimum. By focusing his interest not only on infinitely large relations, but also on infinitely small ones, Kuzanets thereby acted as one of the forerunners of differential calculus.
2.3. Concept of cognition
The dialectical nature of Nikolai’s concept of God and the world is naturally connected with the dialectical nature of the interpretation of knowledge.
From all that has been said above, it is clear that man is interpreted as a part of nature. But this is a special part. Nikolai often names a personfinite-infinitebeing: he is finite as a corporeal being and infinite as a spiritual being.
Nicholas's turn towards naturalistic pantheism was accompanied by a renewal of the idea of man as a microcosm. “Human nature...,” he writes, “contains the entire Universe in itself: it is a microcosm, a small world, as the ancients called it with good reason. It is such that... in humanity everything is raised to the highest degree.”
And if this is so, then in man, as in the macrocosm, there are contained the same universal characteristics as in the latter, including all dialectical characteristics: man is not only a finite, but also an infinite being due to his connection with the absolute; he is both one and many, and a whole consisting of parts, and one consisting of opposites. Christ, according to Nicholas of Cusa, is the maximum man, but then man is also “the second god,” “the human god.” Nicholas calls man the second god because “just as God is the creator of real things and natural forms, so man is the creator of logical being and artificial forms.” “Just as God unfolds from himself all the diverse wealth of natural things, so the human mind unfolds the concepts enfolded in him.”
However, in the concept of man put forward by Nikolai, we see not only a reproduction of those forms of dialectics that were found in the concept of God and the world, but also something new - the dialectics of interpretation of the process of cognition, one of the most profound achievements, at the dawn of modern times, anticipating criticism of the metaphysical, rational way of thinking and the development of a dialectical way of thinking as thinking through contradictions.
The human mind (or spirit), Nikolai taught, is a complex system of abilities. Basically there are three of them: feeling together with imagination, reason and reason. “Man is formed from feeling and reason, connected through reason, which serves as a mediator for them.
These cognitive abilities were repeatedly recorded in the Platonic-Aristotelian tradition and are well known to scholasticism.
However, Kuzanets gives his deeply substantiated specification of each of these abilities, not only in their separateness, which is precisely characteristic of scholasticism, but also in unity, in interaction. This feature of Nikolai’s epistemology is certainly dialectical, for only interaction cognitive powers leads to real truth. He explains the unity of human consciousness with a simple organic analogy: “Just as in the body the head, arms and legs have different functions, so in the soul the mind is the head, reason arms, feelings legs.” This formula expressed a very productive view of the characteristics and connection of all three cognitive functions.
At the basis of the cognitive hierarchy are feelings, for “the power of the mind... cannot proceed to its functions unless it receives stimulation... through sensory representations.” But sensory knowledge gives only partial knowledge. The results obtained by feeling are distinguished and ordered by reason, without the influence of which the activity of feeling is impossible. Kuzanets subscribes to the formula according to which “there is nothing in the intellect that did not previously exist in sensation.” How stronger Nikolai emphasized the unknowability of God for reason, since God eludes all rational definitions, all the more so he insisted on the knowability of the world. Reason realizes this knowledge primarily in mathematics, the most reliable of all sciences, for number is the prototype of all the concepts of our mind and without it nothing can be understood or created.
2.4. The role of mathematics in the philosophy of N. Kuzansky
Having come to the conviction that all natural phenomena are based on mathematical proportions and relationships, the author of “Scientific Ignorance” seeks to explain the most difficult concepts of his philosophy with mathematical examples. Thus, Kuzanets likens the absolute unity of God to a point. The point enfolds all forms of the visible world into itself, being present in each of them, and any number expands from one. Likewise, Movement represents the unfolding of rest, A time unfolding of the present moment.
The highest theoretical ability is reason. These philosophers considered reason as a means of comprehending the highest and final foundations of being and consciousness, the main tool of metaphysics (in the sense of “first philosophy”). This interpretation of reason is also inherent in Nicholas, who believes that “reason... cognizes only the universal, incorruptible and continuous”, comprehends the actual-infinite, absolute. In the Neoplatonic tradition, this highest cognitive ability of the human spirit was interpreted as intuition, not associated with discursive thinking and representing the main means of “comprehension” of the divine absolute. We also find a mystical interpretation of reason in Nicholas. It is expressed in the provisions about the unknowability of the divine absolute, in the agnostic statement according to which “the essence of things, which is the truth of being, is incomprehensible in its purity.”
Particularly important here is the thesis about the incomprehensibility of reason itself. It turns the mind into mystical intuition. Above the discursive side of the mind, facing the understanding, rises a purely mysterious absolute contemplative power. The philosopher calls it true vision, or intellectual intuition.
He going into further details, we emphasize that it is the mind that, according to Nikolai, is the focus of man’s dialectical ability, serves as an organ dialectical thinking: as the highest theoretical ability of the human spirit, thinking the infinite, reason not only comprehends opposites in their unity, but also perceives their identity. It is in connection with the characterization of the dialectical nature of reason that Nikolai anticipates criticism of the metaphysical nature of the activity of the mind. Reason, deprived of the infinite power of reason, “stumbles”, “cannot connect the contradictions separated by infinity” in this connection, he criticizes the metaphysics of the scholastic followers of Aristotle: they adhere only to the “affirmative method”, think in finite concepts, do not understand how it is possiblecoincidence of opposites. And it is possible precisely because, as we have seen, God, the world, and man contain opposites. The mind, thinking of the infinite and the one, comprehends the world in opposites. Infinity “forces us to completely overcome all opposition.” But the comprehension of the identity of opposites merging in actual infinity is no longer a matter of the discursive, but of the intuitive, mystical side of the human mind. It is she who identifies the subject with the object. This is where “deification”, the deification of man, is achieved.
2.5. Truth and the knowability of the world
At the same time, the doctrine of the knowledge of the coincidence of opposites is closely related to the deepdialectics of truth,developed by the author of “Scientific Ignorance”. Its essence lies in the position according to which truth is inseparable from its opposite - from error. Error is as inseparable from truth as shadow is from light. After all, even " upper world has light, but not without darkness; in the lower world darkness reigns, but also not without light.”
Knowability of the worldis implemented against the backgroundthe unknowability of God, the absolute.Its unattainability means that the human mind should not consider any of its truths as final and unshakable. “Divine paths are precisely unattainable. However, we create assumptions about them, some more vague, others more clear.” The truths of mathematics are the clearest, but even they, being considered as fragments of infinity, are only assumptions “accurate knowledge of the truth is impossible.”
The dialectics of truth developed by Cusan also explains the seemingly paradoxical title of his main work, “Scientific Ignorance.” In contrast to the Areopagitica and the subsequent mystical-theological tradition, which persistently pointed to human ignorance determined by the absolute mystery of the divine being, Nicholas constantly emphasizes that, although human ignorance is inevitable, it is necessary to always remain in this very ignorance scientists. Therefore, in the field of science, knowledge is always more important than ignorance. However, even the deepest learning cannot hide from the mind of a true philosopher the fact that in a number of respects it does not eliminate ignorance. Actually, the deeper the scholarship, the stronger this awareness. Dogmatically, metaphysically reasoning reason, which essentially exhausted the wisdom of scholasticism, reason, devoid of understanding the coincidence of opposites, is inclined to consider each of its provisions as true in the last instance. The mind is completely devoid of this limitation. It is “as close to the truth as a polygon is to a circle; for the greater the number of angles of an inscribed polygon, the closer it will come to a circle, but it will never become equal to the circle even if the angles are multiplied to infinity, unless it becomes identical to the circle.”
The philosophy of Nicholas of Cusa and his ideas had a significant impact on the further development of the philosophy of the Renaissance and Modern times. Bruno, who deeply appreciated the “divine Cusan,” was directly influenced by the ideas of Nicholas of Cusa. The influence of Cusan's philosophy can be found in Descartes. Many of his ideas, and in particular the idea of the unity of opposites and the possibility of its knowledge through reason, overcoming the metaphysical limitations of rational knowledge, are revived in German classical idealism.
Conclusion
We can conclude that the main content of Nikolai Kuzansky’s work was fruitful and progressive for the development of philosophy.
The progressive significance of his work is determined by the role that Kuzanets played in the history of dialectics.
It was the dialectical teaching of Nicholas of Cusa about the coincidence of opposites that found its continuation and development in the philosophy of German classical idealism late XVIII - early XIX centuries. The dialectical nature of Nicholas of Cusa's philosophy allowed him to take steps towards materialism.
These steps, not being consistent, led the philosopher to pantheism, which contained a well-known materialist tendency.
It is the understanding of God as a “collapsed” and the world as an “unfolded” maximum that found its continuation in the materialistic pantheism of B. Spinoza.
An equally important role was played by the cosmology of Nicholas of Cusa, which was based on the dialectical-pantheistic worldview of the philosopher. The revolutionary idea of the infinity of the Universe, the idea of the absence of a center and a circle, a top and a bottom in the Universe, was perceived and developed by Giordano Bruno.
Kuzantz also made a great contribution to the development of epistemological problems. In accordance with the needs of the bourgeoisie, Kuzanets tried to solve the problem of the most effective knowledge of nature. He introduced mathematical and natural science methods into knowledge, which makes him related to the future.
Nikolai Kuzansky was one of the first among philosophers to express the idea of the inconsistency of the process of cognition, the guess that “cognition is an eternal, endless approach of thinking to an object,” which was for him infinity, understood as a coincidence of opposites.
Objectively, Kuzan's ideas contradicted feudal ideology and undermined it. It was in his teaching that the natural philosophy of the Renaissance originated. Therefore, based on the above, Nicholas of Cusa can be considered one of the outstanding representatives of culture.
Bibliography
1. Raevskaya D. N. Philosophy of the Renaissance St. Petersburg, 2007
2. Sokolov V.V. Nikolai Kuzansky // History of dialectics of the XIV-XVIII centuries. / Ed. Col.: Kamensky 3.A., Narsky I.S., Oizerman T.I. M.: Mysl, 1974. - 356 p. P.35-51.
The key figure in the philosophical thought of the Renaissance was Nicholas of Cusa (1401-1464) , born Nikolai Krebs (he acquired a name that went down in the history of philosophy at the place of his birth - the small village of Kuza, on the banks of the Moselle, in Southern Germany). His father was a fisherman and winemaker. Political, scientific and philosophical activity N. Kuzansky is closely connected with Italy, which allows us to consider his philosophical work within the framework of Italian philosophy.
Having been educated at the Universities of Heidelberg, Padua and Cologne, Cusanus became a clergyman and subsequently a cardinal of the Roman Catholic Church.
Philosophical and social activity Nicholas of Cusa, despite his religious rank, actively contributed to the secularization of public consciousness in general and philosophical consciousness in particular. Many ideas of humanism were close to him. Being the greatest scientist of his time, he seriously studied mathematics, astronomy, medicine, and geography.
One of the central places in the philosophy of Cusanus is occupied by teaching about God. In accordance with the medieval scholastic tradition, he argues that divine existence plays a decisive role in the formation of the natural world and the human world. However, Kuzanets departs from orthodox scholastic ideas in the interpretation of God and develops ideas close to ancient pantheism, depersonalizes God, who appears to him as “non-other,” “being-possibility,” “possibility itself,” and most often as “absolute maximum,” actual infinity. The world is a “limited maximum,” potential infinity.
Cusansky comes to the idea of the inconsistency of God, which is due to the fact that the absolute maximum, being infinity, does not suffer from any finite operations. Being indivisible, it is also the absolute minimum, and thus represents unity of opposites- absolute maximum and absolute minimum. The coincidence of maximum and minimum allows us to conclude, firstly, that God is in everything (“all is in all”) and the recognition of a world outside of God is inconsistent; that, secondly, God is the unity of cause and effect, i.e. the creator and the created; and, finally, thirdly, the essence of visible things and God coincides, and this testifies to the unity of the world. Understanding God as a unity of opposites weakens his creative personal functions, brings the infinite God and the finite world closer together, and leads to a departure from the principle of creationism.
idea genesis of the universe Cusanus develops in accordance with the Neoplatonic principle emanations. The Divine principle, being the unlimited possibility of all things and absolute unity, contains within itself all the infinite diversity of the natural and human world in a collapsed form; the emergence of the world is the result of its unfolding from the divine depths. There is an “eternal generation” of the unlimited limited, the single multiple, the abstractly simple, the concretely complex, the individual. The return of the diverse, individual world of nature and man to God represents a kind of “collapse” process.
Thus, without completely breaking with the theistic views of medieval scholasticism, Nikolai Kuzansky puts forward the idea mystical pantheism, identifying the creator and the creation, dissolving the creation in the creator. He neglects the idea of the gap between the divine and the natural, the earthly and the heavenly, characteristic of scholastic thinking. Arguing that “the existence of God in the world is nothing other than the existence of the world in God,” Cusansky formulates the principles inherent in cultural and philosophical tradition the Renaissance, striving to understand the spiritual world and the earthly world as a single whole.
The pantheistic and dialectical ideas of Nicholas of Cusa found their further expression in cosmology and natural philosophy. Having reduced the infinity of God into nature, Cusansky puts forward the idea of the infinity of the Universe in space. He claims that the sphere of fixed stars is not a circle enclosing the world: “... the machine of the world will seem to have a center everywhere and a circle nowhere. For its circumference and center is God, who is everywhere and nowhere.” The Universe is homogeneous, the same laws prevail in different parts of it, every part of the Universe is of equal value, not a single stellar region is devoid of inhabitants.
The starting points of Cusanus's cosmology were the basis for the assertion that the Earth is not the center of the Universe, it has the same nature as other planets and is in constant motion. Such a view contradicted the prevailing idea in the Middle Ages about the finitude of the universe in space and about the Earth as its center. Cusansky in a speculative form rethought the Aristotelian-Ptolemaic picture of the world and was a harbinger of the heliocentric view of the universe. He anticipated with his concept the conclusions of Copernicus, who “by moving the Earth, stopped the Sun” and limited the Universe to the sphere of fixed stars.
The cosmological ideas of Cusanus had a great influence on G. Bruno, who overcame the narrow views of Copernicus, relying on the deep dialectical ideas of Cusanus.
The natural world, according to Kuzantz, is a living organism animated by the world soul. All parts of this world are in common connection and exist in constant dynamics. Nature is contradictory, acts as a unity of opposites. “All things,” writes Cusanus in “Learned Ignorance,” “are composed of opposites... revealing their nature from two contrasts by the predominance of one over the other.” He usually draws examples of the coincidence of opposites from mathematicians , because he believes that mathematical principles underlie all phenomena. Extension of the principle of the unity of opposites to the real natural world allowed Kuzansky to take a prominent place in the history of the development of dialectics.
Particular attention in the philosophy of Nicholas of Cusa is paid teaching about man. Cusansky abandons the Christian idea of creationism in the interpretation of man and returns to the ideas of antiquity, viewing man as a kind of microcosm. Trying to connect the microcosm with the divine essence, he introduces the concept "small world" those. the man himself, « big world» , i.e. universe and "maximum peace"- the divine absolute. According to Cusanus, the small world is a similarity to the large one, and the large world is a similarity to the maximum one. This statement necessarily leads to the conclusion that the small world, man, not only reproduces the multifaceted natural world around him, but is also a similarity to the world of the maximum God.
A superficial analysis gives the impression that by likening man to God, Nicholas of Cusa does not go beyond the framework of medieval orthodoxy. However, upon deeper examination, it becomes clear that he does not so much liken man to God, but rather comes to his deification, calling man "human God" or "to the humanized Gods". Man, from the point of view of Cusanus, is a dialectical unity of the finite and the infinite, a finite-infinite being. Ontologically, man stands above all other creations of God, with the exception of angels, and is as close as possible to God. “Human nature is a polygon inscribed in a circle, and the circle is divine nature,” states Cusansky in his Treatise on Learned Ignorance.
By deifying man, Kuzansky expresses the idea of his creative essence. If the absolute, God, is creativity, then man, like God, is also an absolute, represents a creative principle, i.e. has complete free will.
Naturalistic, close to anthropocentrism, tendencies in the philosophy of Nicholas of Cusa were strengthened in later humanistic concepts Italian Renaissance XV century
The doctrine of Cusanus about man is closely connected with epistemological problems and solving the question of human cognitive capabilities. Cusansky sees the main task of knowledge in the elimination of scholastic faith in authorities. “No one’s authority guides me, even if it encourages me to move,” he writes in the dialogue “The Simpleton about the Mind,” and in the dialogue “The Simpleton about Wisdom,” Cusansky compares the scholastic, shackled by faith in authority, with a horse, which is free by nature , but is tied by a bridle to the feeder and cannot eat anything other than what is served to him. Cusansky believes that man, as a microcosm, has a natural ability to perceive nature. His cognitive capabilities are realized through crazy, likened to the divine, creative mind. The mind is individual, which is due to the different bodily structure of people. There are three faculties, three types of mind: feeling (sensations plus imagination), reason and reason.
The identification of sensory cognition as one of human cognitive abilities indicates that Cusansky does not deny the need for an experimental-empirical study of reality, and this goes beyond the medieval tradition. However, he considers sensory knowledge to be the most limited type of mind, inherent even in animals. Sensory cognition human being is subordinated to the discriminating and ordering principle of reason. But neither feelings nor reason are capable of knowing God. They are a tool for understanding nature. Kuzansky does not doubt the possibility of knowledge of nature, the methodological core of which is mathematics.
Reason is the highest cognitive ability of a person. “The mind cannot comprehend anything that is not already within itself in a reduced, limited state.” The mind is completely isolated from sensory-rational activity, being a purely speculative, purely spiritual essence, the creation of God himself. He is able to think of the universal, incorruptible, permanent, thereby approaching the sphere of the infinite and absolute. The understanding of infinity inherent in the mind leads it to an understanding of the meaning of opposites and their unity. This is the superiority of reason over reason, which “stumbles because it is far from this infinite power and cannot connect the contradictions separated by infinity.”
Considering the basic cognitive capabilities of a person in their interaction, Cusansky comes to the idea that the process of cognition is the unity of opposite moments - knowable nature and the unknowable God, the limited abilities of feeling and reason and the higher possibilities of the mind.
The problem of the truth of knowledge is solved dialectically by Cusanus. The doctrine of truth is based on the following proposition: truth is inseparable from its opposite - error, just as light is inseparable from shadow, without which it is invisible. A person in cognitive activity is only capable of a more or less accurate idea of the essence of the world, for the divine ways are incomprehensible, they cannot be comprehended accurately and consistently. The inconsistency of “scientific” ignorance can only be understood by reason, which thereby approaches the truth. However, “our mind... never comprehends the truth so precisely that it cannot comprehend it more and more accurately without end, and relates to the truth like a polygon to a circle: being inscribed in a circle, the more similar it is to it, the more angles it has, but even when its angles are multiplied to infinity, it is never equal to a circle.” As for reason, it is dogmatic, inclined to consider each of its provisions as the ultimate truth. Cusansky believes that the mind needs to constantly overcome the dogamtic self-confidence of the mind regarding the final truth of judgments, thereby promoting the understanding of truth as a process of ever-increasing deepening of knowledge on the path to the unattainable absolute.
The philosophical views of Nicholas of Cusa played a significant role in overcoming the scholastic tradition in philosophy and in the development of the ideas of the late Renaissance
FEDERAL AGENCY FOR EDUCATION
FEDERAL STATE EDUCATIONAL INSTITUTION OF HIGHER PROFESSIONAL EDUCATION " VOLGOGRAD ACADEMY OF PUBLIC SERVICE"
Faculty of State Municipal Administration
Department of Philosophy and Cultural Studies
THE CONCEPT OF INFINITY IN THE PHILOSOPHY OF NICHOLAS OF CUSANUS
Course work
in the discipline "Philosophy"
Performed
student of group UP-100
Kvitsinia Shyaiza Khadjaratovna
Scientific director
Candidate of Philosophy, teacher
Sivkov Denis Yurievich
Volgograd
Chapter I The Doctrine of Infinity……….. …………………...4
1.1 About the incomprehensibility of truth………………………...4
1.2 About the coincidence of opposites………….….........5
Conclusion……………………………………………………..11
Chapter II “Collapse-expandability”………………………..13
2.1 About the relationship between God and the world.………………….13
2.2 The Universe of Cusanus…………………………………….15
Chapter III Man as a microcosm…………………………….17
Conclusion……………………………………………………20
INTRODUCTION
Nikolai Kuzansky is one of the greatest European thinkers of the 15th century. He is one of the most prominent humanists of the Renaissance and is considered the founder of Italian natural philosophy. Nicholas of Cusa (1401-1464, born in Germany, studied in Padua). Coming from a family of winemaker and fisherman, he went through all the levels of the priesthood, working his way up to papal cardinal and bishop. His activities as a philosopher, socio-political figure and minister of the church largely contributed to the secularization that was brewing at that time.
The treatise “On Learned Ignorance” was written in 1440 and was the first philosophical book of Nicholas of Cusa. Cusanus is usually called the first thinker of the Renaissance due to the original doctrine of “scientific ignorance” that he developed and proposed and, accordingly, the special concept of man that follows from it.
The purpose of our course work is to study the treatise “On Learned Ignorance”, and specifically to study the concept of infinity in the philosophy of Nicholas of Cusa.
Cusanus’s treatise “On Learned Ignorance” consists of three main components:
1. The doctrine of infinity
2. The doctrine of man as a microcosm
3.The idea of the interconnection of all phenomena
In our work, consisting of an introduction, three chapters and a conclusion, we will dwell in detail on all the main topics of “scientific ignorance”.
1. The doctrine of infinity.
1.1 On the incomprehensibility of truth
At the beginning of his work, Nikolai Kuzansky sets out the reason for writing it - the desire to comprehend the truth. The author connects the process of cognition with the activity of the mind, and the path of such research or cognition is based on comparison and juxtaposition, since a judgment about something unknown always begins with its comparison using certain relationships with what is known in advance. Our finite mind, based on similarities, does not have the ability to accurately comprehend the truth of all things. It is impossible to find in nature two or more objects so similar or equal that there would not exist even more similar things in an infinite number. There will always be differences, no matter how equal the measures and measured objects are. Truth is by nature indivisible and incapable of perceiving more or less. Anything that is not in itself true cannot accurately measure truth. Therefore reason, which is not truth in itself, is not capable of apprehending truth with such precision that it could not be more accurately apprehended through infinity.
The cognitive attitude—scientific ignorance—is based on the understanding of the radical disproportion between the finitude of the human mind and the infinity that it wants to embrace. Kuzan says that everything that we want to know is our ignorance. “Our finite mind, moving through comparisons, cannot therefore accurately comprehend the truth of things. After all, truth cannot be more or less, it lies in something indivisible and, except by the truth itself, cannot be accurately measured by anything, just as a circle, the existence of which consists in something indivisible, cannot be measured by a non-circle . Not being the truth, our mind also never comprehends the truth so accurately that it can no longer comprehend it more and more accurately without end, and relates to truth like a polygon to a circle: being inscribed in a circle, the more similar it is to it, the more angles it has, but even if its angles are multiplied to infinity, it will never become equal to the circle unless it resolves into identity with it.” (chapter 3 book 1)
1.2 On the coincidence of opposites
In his work, Cusansky introduces the concept of maximum, which he defines as the infinite existence of God. There is nothing greater than the maximum, because it is all that there is, but there is nothing less than the maximum, because it is all that there is. Thus, something less than ALL cannot exist and at the same time not be involved in everything that exists. The maximum is devoid of any gradations, this is what is beyond the limit of any measure, it is absolute simplicity, all differences in which are in a collapsed state. The maximum is incomprehensible; among finite things the maximum does not exist. The maximum is the diversity of everything that exists in reality and everything that currently exists only in possibility. The maximum is the combination in unity of all opposites and differences. Based on this concept of the maximum, Cusansky in his own way substantiates the concept of infinity, an infinity inherent only in the existence of God. Absolute unity or the highest fullness of being is a maximum that is inherent only in deity.
God is absolute unity in the sense of the maximum fullness of being. “God, that is, absolute maximality itself, is light” and “God is as much maximum light as minimal light.” After all, if absolute maximum were not infinite, if it were not a universal limit, not determined by anything in the world, it would not be the relevance of everything possible.” (chapter 4, book 1)
Being as an absolute unity contains both maximum and minimum, and they are opposites in their essence, hence the conclusion follows that this infinite being is a coincidence of opposites, like a coincidence of completeness and simplicity.” Infinity according to Kuzantz is the maximum being, the absolute unity or integration of all differences and opposites.
Nikolai Kuzansky considers infinity as a kind of figured construction, which is subject to the principle of ordering. In chapter five of his treatise, Cusansky is extremely clear, so that his reasoning does not raise any doubts, shows us that if in the system natural numbers start moving from one finite number to another, then we will not be able to stop anywhere. Indeed, in the series of natural numbers, each finite number is possible only if there is an even larger number, even if it is only larger by one. Thus, moving from one number to another, we understand that there is an infinite number that we cannot obtain by adding one to one or another finite number, no matter how large it is. And we can neither increase nor decrease this infinity, nor multiply, nor divide.
Infinity +1 is still infinity, infinity – 1 is also infinity, infinity multiplied by any finite number will remain infinity. And infinity divided by one number or another will give us the same infinity as a result. From this we can conclude that there is an absolute maximum, which cannot be changed by any finite operations, but being indivisible, it is also an absolute minimum, thus, the absolute maximum and the absolute minimum are one and the same.” The absolute maximum is in full actuality, being all that it can be, and for the same reason that it cannot be more, it cannot be less: for it is all that can exist. But that which nothing can be less than is the minimum. This means that since the maximum is as stated, it obviously coincides with the minimum.” (Chapter 4, paragraph 2, book 1)
“And since the absolute maximum is the absolute actuality of everything that can be, and so without any opposition that it coincides with the minimum, it is equally higher than any affirmation and any negation. Everything that we think about him, he is no more than he is not, and everything that we do not think about him, he is no more not than he is: he is just like everyone else, and he is so everything is like nothing; and most of all he is precisely this thing, so that together and least of all it is” (chapter 4, book 1). That is, we can say that Kuzanets concludes that infinity is absolute perfection, the absolute fullness of being, which is beyond any degrees and differences. Kuzansky writes: “we see that the absolute maximum is infinity, to which nothing opposes and with which the minimum coincides.” (chapter 4, ab. 5, book 1)
This is one of the reasons why, in order to know finite things, in knowledge we must begin with the infinite, and not with the finite and in this sense determinate.
Thus, since the human mind cannot comprehend infinity, it means that it comes closest to it when it encounters something absurd, unthinkable from a human point of view. According to Cusansky, this is, first of all, the “coincidence of opposites.” Cusansky’s doctrine of the “coincidence of opposites” is fundamental to his philosophy: the maximum contains BOTH AND THE OTHER opposite to it, at the same time there IS BOTH. In the words of Cusanus, “the absolute maximum is in full actuality, being all that it can be.”
Cusansky begins his argument “On Learned Ignorance” with the assertion that the process of human cognition arises through a comparison of the known and the unknown.
Popular philosophy Gusev Dmitry Alekseevich
§ 27. Coincidence of opposites (Nicholas Kuzansky)
Another outstanding representative of Renaissance philosophy was the German thinker Nikolai Kuzansky. Like Giordano Bruno, he was a pantheist and argued that the infinite universe is God, who is in everything that exists, everywhere and therefore nowhere in particular, fused with everything. God is everything in general – Being itself or "maximum of Being", as Kuzansky said. All things, objects and bodies of the universe are a deity embodied in something concrete and corporeal. The Universe is an expanded God, and God is the Universe rolled up into a single one.
As a result, any thing is a manifestation of God, his realization, his embodiment in a certain object. In other words, God represents a certain single, homogeneous basis of everything, an ideal and infinite essence that reveals itself through material, finite, separate things. There is one God, and there is a huge multitude of objects in the world around us, which is the deployment or manifestation, or otherness (that is, existence in another form) of a single deity, identical to the entire universe. The things we see around us are completely different and unlike each other. But this is only from the point of view of these things themselves.
If you look at them from the point of view of the infinite God, then it follows that all things are one and the same, since any of them is only the embodiment of God, his form, mode, particle, his manifestation. This idea is not new. Let us remember how the Milesian philosophers said that behind the visible diversity of the world lies its invisible unity, all things are only different shapes or the state of some homogeneous world substance (water, air, etc.) and therefore, by and large, we must talk not about the difference between things, but about their similarity and even identity.
Nikolai Cusansky declares the pantheistic impersonal principle - the infinite God - to be the world basis of all things and says that things that seem different to us from the point of view of everyday life and common sense, are actually identical, since they are all manifestations of this pantheistic principle. However, the differences between them are erased and disappear if they are perceived not as separate objects, but considered in God, that is, from the point of view of infinity. Everyday Thinking, states Cusansky, can never comprehend how different things can be the same, how opposites can merge into one whole and cease to be opposites. Ordinary consciousness thinks of everything on a finite, limited scale and cannot look at things from a global point of view. Philosophical thinking, on the contrary, can quite break away from the usual reality, perceive infinity, and therefore it has access to what seems paradoxical and incredible - the coincidence of opposites. It is only necessary to emphasize once again that the different are identified only in infinity, merge into one only in the single and eternal basis of everything that exists - even if it is some kind of world substance or some kind of spiritual principle.
To illustrate this point, Nikolai Kuzansky gives several mathematical examples. Let's imagine a circle and a straight line passing next to it. Obviously they are completely different geometric figures. If you increase the radius of the circle, the curvature in each specific section will decrease. As the radius increases to infinity(!), the circle will turn into a straight line, that is, it will cease to be itself.
In a similar way, you can consider a triangle and a straight line. If you decrease the angles at the base of a triangle to infinity, it will become straight. Let's imagine that a polygon is inscribed in a circle. If you increase the number of its sides or faces to infinity, it will turn into a circle. Finally, we will show that from the point of view of infinity, 2 and 5, 3 and 7, 9 and 15 and any two other quantities are the same thing, that the differences between them are erased and disappear. Let's say that in front of us there are two segments of 10 cm each. We will divide one into parts of 5 cm, and the other into parts of 2 cm. The first, thus, will split into 2 parts, and the second into five parts. It turns out that we divided the same segments into different sizes (5 cm and 2 cm) and therefore got different results, therefore, the difference between five and two is obvious. But 5 and 2 differ from each other only on a finite, limited scale - we considered two segments. Now let’s imagine that in front of us are two straight lines (endless lines). Divide the first straight line into segments of 5 cm, and the other into segments of 2 cm. How many parts will there be on the first straight line? How many parts will the second straight line split into? In both the first case and the second, the number of resulting parts will be infinite. Thus, we divided two infinite lines into different quantities, but the result was the same.
The only thing that follows from this is that the difference between two and five disappears at infinity, just as the differences between any two other quantities invariably disappear at infinity. Although mathematical examples are the most obvious, the coincidence of opposites at infinity can be seen in completely different areas. For example, if a person were an immortal (that is, infinite) being, would the question about the meaning of life arise in his mind? No. So in this case, questions about the purpose of man, about his duty and responsibility would automatically disappear; goals, objectives, aspirations and desires would disappear. In the face of infinity, everything is lost, lost and disappears.
According to Kuzansky, the task philosophical knowledge lies not in the consistent study of individual things and objects of the surrounding world, but in the comprehension of infinity, a single world essence, which is everything. But if it is quite possible to obtain certain knowledge about each specific thing, it is completely impossible to comprehend infinity, there can only be ignorance about it. However, this fact does not at all mean a refusal of metaphysical knowledge, of the desire to discover the incomprehensible. Philosophy is the love of wisdom, trying to accomplish what seems in principle incredible, to do the impossible, to strive for the unthinkable.
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Based on discoveries and technological progress during the Renaissance, a peculiar natural philosophy(philosophy of nature).
The largest representatives of natural philosophy are Nicholas of Cusa, Giordano Bruno, Nicolaus Copernicus, Leonardo da Vinci, Galileo Galilei. Summarizing their views, we can formulate main provisions, inherent in their teachings.
1. Natural philosophy was often pantheistic in nature, that is, without directly denying God, it identified him with nature. 2. Knowledge of God the Universe goes through the following stages: sensory perception; reason separating opposites; the mind that composes them; intuition.
At the same time, the sensual and rational merge and become united in the knowledge of the surrounding nature.
Nikolai Kuzansky one of the greatest European thinkers of the 15th century. He is one of the most prominent humanists of the Renaissance and is considered the founder of Italian natural philosophy. Nicholas of Cusa (1401-1464, born in Germany, studied in Padua). Coming from a family of winemaker and fisherman, he went through all the levels of the priesthood, working his way up to papal cardinal and bishop.
N. Kuzansky expressed deeply dialectical ideas in his teaching about God as infinity in space - the “absolute maximum.”
Nikolai Kuzansky considers infinity as a kind of figured construction, which is subject to the principle of ordering. If in the system of natural numbers we begin to move from one finite number to another, then we will not be able to stop anywhere. Indeed, in the series of natural numbers, each finite number is possible only if there is an even larger number, even if it is only larger by one. Thus, moving from one number to another, we understand that there is an infinite number that we cannot obtain by adding one to one or another finite number, no matter how large it is. And we can neither increase nor decrease this infinity, nor multiply, nor divide.
Infinity +1 is still infinity, infinity - 1 is also infinity, infinity multiplied by any finite number will remain infinity. And infinity divided by one number or another will give us the same infinity as a result. From this we can conclude that there is an absolute maximum, which cannot be changed by any finite operations, but being indivisible, it is also an absolute minimum, thus, the absolute maximum and the absolute minimum are one and the same.” The absolute maximum is in full actuality, being all that it can be, and for the same reason that it cannot be more, it cannot be less: for it is all that can exist. But that which nothing can be less than is the minimum. This means that since the maximum is as stated, it obviously coincides with the minimum.
Being as an absolute unity contains both maximum and minimum, and they are opposites in their essence, hence the conclusion follows that this infinite being is a coincidence of opposites, like a coincidence of completeness and simplicity.” Infinity according to Cusanus is the maximum being, the absolute unity or integration of all differences and opposites.
God is absolute unity in the sense of the maximum fullness of being. “God, that is, absolute maximality itself, is light” and “God is as much maximum light as minimal light.” After all, if absolute maximum were not infinite, if it were not a universal limit, not determined by anything in the world, it would not be the relevance of everything possible.”
Pantheism by J. Bruno.
Giordano Bruno (1548-1600) - Italian philosopher, in whose views the philosophical thought of the Renaissance found its full expression. Creator of the religion of the cosmos. He preached his ideas at universities in England, Germany, France, and Switzerland. Sentenced to death by the Inquisition for heretical religious messianism. Burned at the stake in Rome.
Bruno's teaching. - specific poetic pantheism, based on the latest achievements of natural science (especially the heliocentric system of Copernicus) and fragments of Epicureanism, Stoicism and Neoplatonism. He viewed the world around us as one, in which matter and form are fused together. The Universe, according to Bruno, is one, infinite and motionless. There are constant changes and movements in it, but on the whole it does not move, because it fills everything around us. The universe is the coincidence of God and nature, matter and form, unity and multiplicity. The idea of the One permeates all the main provisions of Bruno's philosophy. For Bruno, the One is both the essence of being and the form of its existence. The One is a category that, according to Bruno, explains everything in the world - both its variability and its constancy. All contradictions and opposites can be explained by the fact that the Universe is one. .The infinite universe as a whole is God. He is in everything and everywhere, not “outside” and not “above,” but as “most present.”
Bruno emphasizes that in the Universe, spiritual and bodily substances have one being, one root. Matter has the property of divinity. By this, Bruno rejected the idea of creation and the conditioning of nature by God as an external source of its existence. Thus, Bruno stood on the position of radical pantheism. Bruno considered matter as consisting of atoms, following in this regard the ancient atomists. Everything in nature, according to Bruno, consists of indivisible particles, atoms, which determine the unity of all things. Bruno formulates the atomic understanding of nature in the form of the concept of the minimum: there is nothing in the world except the minimum, which determines everything in the world, the entire maximum. The minimum contains all the power, and therefore it represents the maximum of things. The minimum determines the maximum. The absolute minimum in the Universe is an atom, in mathematics it is a point, in the sphere of metaphysics it is a monad. The minimum or monad forms everything that defines the maximum and the whole. The monad reflects all the properties of nature. Here Bruno stands on the position of a dialectical coincidence of opposites. In his dialectics, Bruno follows Nicholas of Cusa, but extends this dialectic to all of nature. According to Bruno, the entire Universe is animated, it is characterized by an internal life principle, which he calls the “world soul.” Bruno used universal animation to explain the reasons for movement in nature, which has the property of self-motion. Recognizing all nature as animate, Bruno thereby took the position of hylozoism, which at that time, under the dominance of scholasticism and theology, played a progressive role, since it recognized man as a part of nature. Bruno developed questions of cosmology, relying on the heliocentric theory of Copernicus. He argued that the Universe is infinite, that there is only one Universe around us and there are countless worlds in it. The number of individual things is also infinite, although each thing represents a finite quantity. Recognition of the existence of one Universe excludes for Bruno the presence of an external God who created the world. Bruno rejects creationism and believes, following his pantheism, that nature is God in things, matter is the divine being in things. God is contained in things as an active principle. Nature and God are one and the same, they have the same single principle: this is the same order, the law that determines the course of things. Bruno identifies God with nature, understood as a set of patterns of movement and development that are inherent in the world around us. Moreover, Bruno identifies God-nature with matter. Nature is matter. Thus, for Bruno, God is another name for the natural world around us. Closely related to Bruno’s pantheism is the concept of panpsychism, namely, that spiritual substance determines all the diversity of the manifestation of things.
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