The Problem of Docta ignorantia as a Intellectual Modesty by Nicholas of Cusa
Abstract: In the present study the author focuses attention to the problem of learned ignorance by Nicolas of Cusa. The author analyses Cusanus limits of human cognition (borders of linguistic concepts, paradox of infinity and mind limits). He shows the history of invention of the problem of learning and explanation in renaissance and problem of intellectual modesty of learning. The study is dedicated to the wide public as a compendium of Cusanus noetic work.
Keywords: attitudes toward computer, students, questionnaire, computer enjoyment, computer anxiety
The life and work of Nicholas of Cusa raises lots of different approaches and interpretations in the history of European culture. For some historians, Cusanus is still a prototype of late-scholastic scholar and representative of late medieval time with its typically theocentric and logically elaborated structure. The others see him mainly as a cardinal and modern minister of the Catholic Church in the period of its fragmentation (De maioritate auctoritatis sacrorum conciliorum supra auctoritatem papae); or as a very important negotiator and peacemaker in the area of denomination (Opusculum contra Bohemorum errorem: De usu communionis). Except the above mentioned, he has been credited with mathematic genius (De arithmeticis complementis, De mathematica perfectione), with unusual use of new – mathematic method of thinking (De geometricis transmutationibus) and its application in the search for truth and knowledge. Because of his considerable advance in the area of methodology of knowledge, Cusanus is considered by many others to be the first expressive representative and the main instigator of the philosophy of the transition stage between Medieval Age and Renaissance and is regarded even as an ancestor of modern science and experimental investigation (Idiota de staticis experimentis). (Cusanus is credited with first inquiries into the growth of plants, first modern formal experiments in biology and considerations about the weight of the air,... and mainly with remarkable reflections and opinions on cosmology, noetic, and anthropology.)
However, there’s no doubt that the work and philosophical message of Nicholas of Cusa makes up an important part of heritage of European thinking. Cusanus’s idea of inter-religious tolerance, Christian ecumenism (De concordantia catholica) and his cosmological contemplations about the Earth (De figura mundi) were a few centuries ahead of their time, we are able to recognize the very impact of them only after some lapse of time. One of the biggest and more and more valued contribution of Cusanus’s thinking is his conception of intellectual modesty which, in my opinion, results from the change of his philosophical thinking.
Presented study tries to focus an attention to the problem of learning, education or ignorantia and limitation of knowledge through analyses of Cusanu’s philosophical texts. Through the thematisation (or view) of main points of Cusanu’s thinking it is possible to present this philosopher’s heritage to the wide public and show some renaissance inspirations for later Erasmus and Comenius work.
It seems that Cusanus’s conception of cognition comes out of the deep tradition of medieval thinking. The Medieval school adopted an approach towards the problem of cognition characteristic with its faith in knowability knowledge of the world and possibility of reaching the truth through our cognition. Scholastic scholars were convinced that God has created the world and man in His own image. That meant, that though "imago Dei" man was capable of adequate and truthful cognition. The guarantee for the truthfulness of cognition was God Himself 1. God has given us the ability to know the world and ourselves in the moment of our creation and He made accessible to us what originally belonged only to Him – His own knowledge. He accessed it to us in three ways. The first one was the possibility of getting the idea of Him in the depths of our soul presented by neoplatonic, Augustin’s stream. The second way – revealing God´s Providence from orderliness and excellence of the universe – His Creation (Thomas Aquinas) and the third one – the Revelation on its own by which God has revealed.
The basic problem of theological dialogues was the designation of primacy between the sources mentioned of knowledge accessible for us (God’s Word vs. intellectus). Initially, the main tool for truthful cognition has been faith. Although none of the theologians would admit that intellect had bigger cogency than the Revelation 2 at the beginning, it seems that it was just intellect, which took (in the course of time) 3 the leadership 4 in inquiry into the world and God. Knowing the world and so knowing God who has created it was for scholastics not even possible, but was essential for their salvation (Summa theologiae). God has given us the reason (lux naturale) to reveal through its relationship to lux aeterna the order, that He put into this world and thus to know Him, too. In this way they have subordinated God to an intellect 5.
Cusanus trusts this scholastic view; he believes that visible things are really the reflection of invisible ones and that it is possible to know Creator through His creations. He gives us notice at the same time, that God is an absolute infinity, and the inquiry into Him from the view of ultimate being and finite infinity (universe) is fairly limited. Cusanus clearly sees the difference between subject and object. He knows that the measure and what is measured significantly differ, so however close they could be (Zigo 1979; p. 27), our understanding of the infinity will be always problematic. The mirror presents just the reflexion of God, not God himself – it is finite on its own. The intellect, which is not the truth itself, will never understand the truth completely so that the movement to infinity could not enable us to understand the truth more correctly (Kuzánsky, 1979; 37). That is why we have no other choice than to dwell upon metaphoric knowledge, or to find such a method that would be able us to eliminate all mirror deformations when reflecting infinity. Cusanus found this method of inquiry in mathematics - according to a model of the Thinkers of Antiquity and thanks to Proklos.
According to Cusanus, it is just the mathematic (in his view mainly geometric) way of thinking that enables us to think about uncertain things with certainty. By using the deductive way of thinking it is possible to deduce conclusions about the unknown from things that are known and even to deduce them with indisputable evidence (Kuzánský, 1979; 50). The exceptional advantage of mathematical system of thinking resides also in the fact that it uses as an object if its inquiry finite symbols (figures and numbers) which are then appropriately transferred to infinite figures and relations, even to absolute infinity (limits - apeiron). At the end it means that mathematical symbols by their nature reflect the relation of finite to infinite and so they can be used for formulation of the relations between finite – man and infinite – God and for disclosing infinity, too. Cusanus uses for grasping the phenomenon behind the horizon of commonly accessible knowledge the analogy in the way that Kant does. His examples with infinite line, circle, sphere and triangle belong to classical examples of such grasping of infinity. With this method he manages to exceed the horizon of his own finality and comes to revelation of infinity (De docta ignorantia Liber I. cap. XVI-XXIV). What is important, he also discovers that all particulars meet in infinity (or behind the horizon of finality) and in this way he comes to coincidentia oppositorum and paradoxically also to the conception of intellectual modesty.
Thanks to mathematics Cusanus managed to exceed the horizon of infinity 6 . But at the same time he realized that to walk on this horizon or even behind it is not very safe. “Unsafety” in this area was not so much in limitless boundlessness of new space or unacquaintance of its hidden obstacles, awe, and respect for infinity, but rather in sudden loss of orientation in what we have known before reaching the horizon. Loosing the horizon we somehow loose a reference scope for our assessment, too. Infinite triangle stops to be triangle in infinity. In infinity, the circle becomes quadratic, the triangle becomes the line and there is no difference between the sphere and something else. In infinity, we loose concrete shapes of thinking and all our terms are devaluated. That is the reason why Cusanus uses negation of any affirmations in theology.
It is very interesting, that the truthfulness of our knowledge about the finite entities did not loose anything from its validity in the empire of infinity at the same time. The truthfulness of singular positive affirmations has not been limited at all but was relativised and completed with new knowledge – knowledge from other aspects yet unseen (e.g. that an absolute triangle is the circle).
Cusanus realised that it is impossible for man to grasp the truth in its integrity and totality in spite of all sureness of mathematical knowledge. There were many others before Cusanus there who did realize this fact, too, but they reasoned it mainly by the argument of our absolute finality and imperfectness of knowledge.
The classical interpretation of limited competences of human knowledge originated from the idea of cognition drawing from reflections of what is known - from the Creation. Cusanus says in this situation, that to know the being of creation is more difficult than to know the being of the first (De docta ignorantia Liber II. cap. II), so the knowledge of infinity only by imperfect finite things cannot be very precise and is also deformed by the imperfection of things. This is the reason why mediaeval thinkers, when interpreting the extent of knowledge, drew mainly from the hierarchy levels of all creations. They supposed that entities existing in this hierarchy closest to God gain its knowledge in the best and the most adequate way 7 . In Idiota de mente (cap.XIV) Cusanus even says about the nine levels of angel beings with several levels of knowledge only after which follows the knowledge of man (Kusánský in: Floss, 1977;337).
It could be said that the problem of unattainability of absolute truth is in insufficiency of our cognition and imperfection or looseness of its observation. According to Cusanus the real problem of our cognition is not in the intensity or an extension of our cognition, but rather in its inner disposition. Terms that we use loose their foundation behind the horizon of finality. They meet others and are not unchangeable at all (unlike the angel’s ones). So if we talk about the infinity that it is like this or that, we never grasp it by our terms (De Deo abscondito). Infinity stays ungraspable, because the terms through which we try to do so are finite. The terms we use are the measure for our thinking about things (Idiota de mente) and in this way we are also the measure of things about which we think at the same time. The nature of the mind resides in measurement (Mens – mensurare). Knowledge of absolute Truth in its integrity and totality is not possible, because every our grasp of a whole is always determined by getting known the whole through some specific and subjectively set point of view (Floss, 1977; 114). The reason for Cusanus’s intellectual modesty does not reside in looseness and insufficiency of our cognition in its reflection of the world, but rather in pointing out that our cognition is confined in its own boundaries, that it is just our cognition not the grasp of eternal and noumenonal contents – God himself. The heart of the matter of learned ignorance is in kind pointing to the boundary of our knowledge by knowing ourselves. And this is the core of the problem of Cusanus’s intellectual modesty that can be seen from two levels.
It seems that the base of Cusanus’s conception of negative theology and learned ignorance is in his distinction between senses, ratio and intellectus. He pays attention to this distinction in several works of his philosophical inquiry (De coniecturis, Idiota de mente, De beryllo). He clarifies there, that senses on their own are not the ones that are able to make a distinction; they are only the carrier of the matter (the barrier) that should be distinguished. Our senses are able to see, but they do not know what they see – they are actually nothing on their own. According to his anatomically very interesting and not wholly straying theory, substantial matter happens only after their revival by ratio that grasps perceived matter on receptors and “assigns” it through imagination (fantasy). The problem is that distinguishing ratio distinguishes matter in senses by assigning a kind of immaterial picture or terms. The substance of every picture of term is its border. Ratio synthesizes the matter from senses, but at the same time it closes it into limited and final terms. Things or entities we meet in ratio are always the ones they really are only because of their borders with others (that means they are concrete); by this they are mutually defined. And this is the problem of competencies of ratio.
Rational knowledge is always knowledge in terms and images. By its substance it is predetermined for inquiry hic et nunc, for mutual definitions and comparisons. Distinguishing ratio is then the “empire of other”; it analyses and compares separate contents, but always from the point of view of concrete term and so from the own specific point of view, too. For discursive way of thinking using borders it is not possible to enable us to grasp the truth as a whole. That is why we may consider Cusanus’s intellectual modesty rather as modesty rational. Modesty, that results in discovering the borders of our ratio 8.
Cusanus exceeds these borders. He exceeds the horizon of the finite world through the mathematical way of thinking and sees infinity in its whole. It is intellect that enables him to do this. Intellect sees things from a higher perspective and on the point where ratio makes the division, intellect finds hidden and so far unseen integrity (Floss, 1977;114). Intellect sees the integration of finality in infinity; it is even able to see infinity itself. It seems then, that after all on the higher stage of cognition Cusanus believes in revelation of Infinity. And that is the reason why he writes about it so courageously (compared to idea of negative theology). Cusanus knows that in infinity the opposites fade away.
He neither disputes about the existence of outer world, nor about the existence of God and it even looks as if he reveals His attributes 9. He knows which attributes belong to God, but at the same time he knows that everything that is said about God does not give a true picture of Him. Neoplatonic tradition believed in the possibility of exceeding the borders and in joining or at least grasping God in ecstasy. Anyway, the problem of expressing what was seen 10 does not disappear. That is why there follows his use of the principle of negative theology. The real substance of it is then in the character and structure of our thinking – that means in rational (not intellectual) modesty. It is just this level (as I see) that creates the basic background of Cusanus’s idea of tolerance and interreligious dialogue as a possibility of mutual revelation of aspects of truth, which is accessible to us. In addition to this level he presents the second one – the level of limitation of our knowledge, too.
According to neoplatonists Cusanus believes that our mind is a kind of enfolded reflection of God’s mind. He sees the mind as a diamond which reflects shapes of things and finds them in its own centre (Kusánský in: Floss, 1977; 303). It could be possible - from the precise grasp of one idea in mind - to develop knowledge of everything about everything 11. However, this does not happen. Nobody can ever have precise knowledge about anything. Knowledge we have does not come from perfect reflection of God (none of the reflections could ever be perfect) but rather from our own mind 12. Unlike neoplatonists, Cusanus believes that what the mind sees in itself, it sees in limits only of its own essence 13 . The reasons for this are not moral, but noetic. Man does not grasp the world passively; he is the creator of entium rationalium (De beryllo). “The originality of Cusanus theory of cognition consists in this stress of assimilation. He does not conceive of the knower and the known, but as a production of a “similitudo”, by which the mind mediates itself to the objects. By producing such mediations, the mind is able to reach an approximate cognition of the objects”. (Sato in: Yamaki, 2002, p. 79) Terms that he uses are not absolute terms and his view of things is not the view from nowhere. Our knowledge of the world is always essentially human; it is knowledge that does not enable us to see noumentalities of the world (Kant). It is knowledge determined by our point of view (De coniecturis). Absolute infinity stays ungraspable for us not because of intensity or extension of possible knowledge, but because of the type of our cognition.
While (from the point of view of ratio) the learned ignorance resides in the character of conceptual thinking, the second level of Cusanus’s modesty uncovers own borders of intellect; uncovers the fact of the unexceedability of antropocentrical character of our thinking. Our knowledge is essentially human and so cannot reveal whole absolute truth, because it does not dispose of God’s “absolute” perspective. In this meaning our cognition can be only probable and therefore always dependent on faith in its essence. From this reason Cusanus then appeals to tolerance and humility of human research.
It seems that Cusanus’s concept of learned ignorance as intellectual modesty with its conclusions stands back in the Middle Ages, the thinking of modern times. Through this work Cusanus created a modern interest for knowing and the process of his creation, which have been analysed by Descartes and Locke and the whole modern period.
The second important aspect of Cusanus heritage is the creation of new attention to learning and teaching in the modern age, mainly because of his conception of mind as a mensurare, that became very important for creating a new conception of mind and education.
1. This consideration is relevant for Descartes and Leibniz, too.
2. Tertulianus: Credo, qua absurdum est.
3. Anselm of Cantenbury: Credo, ut inteligam.
4. Aquinas’s proofs of God’s existence.
5. see: Vopěnka, P.: Úhelný kámen evropské vědy a vzdělanosti. Práh, Praha 2001.
6. On history of mathematic infinity see: McFarlane, T.J.: Nicolas of Cusa and he Infinity. online: http://www.integralscience.org/cusa.html [2009-06-21]
7. see e.g. R.Lullus: Ars Generalis Ultima
8. see: Kremer, K.: Gröβe und Grenzen der Menschlichen Vernunft (intelectus) nach Cusanus. In: YAMAKI, K. (ed.): Nicholas of Cusa. A Mediaeval Thinker for the Modern Age. Richmond, UK: Curzon Press, 2002, p. 5-34.
9. Cusanus says that the original name for God was Theoro – I see.
10. Compare with the problem ratio-intuition in Bergson.
11. see: Cusanus; compare Leibniz’s teaching about monads and preestablished harmony
12. Compare with the problem ratio-intuition in Bergson.
13. see Aquinas’s teaching about species and contractibility
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