Mathematics as Art: The Missing Standard

1999 ◽  
Vol 92 (4) ◽  
pp. 284-285
Author(s):  
James R. Rogers

Mathematics, rightly viewed, possesses not only truth, but supreme beauty—a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry. What is best in mathematics deserves not merely to be learnt as a task, but to be assimilated as a part of daily thought, and brought again and again before the mind with ever-renewed encouragement. Real life is, to most men, a long second-best, a perpetual compromise between the ideal and the possible; but the world of pure reason knows no compromise, no practical limitations, no barrier to the creative activity embodying in splendid edifices the passionate aspiration after the perfect from which all great work springs. Remote from human passions, remote even from the pitiful facts of nature, the generations have gradually created an ordered cosmos, where pure thought can dwell as in its natural home, and where one, at least, of our nobler impulses can escape from the dreary exile of the actual world.

2019 ◽  
Vol 26 (3) ◽  
pp. 31-46
Author(s):  
Krzysztof Wałczyk

Nikifor Krynicki (Epifaniusz Drowniak, 1895-1968) was one of the most popular non-academic Polish painters worldwide. To show the biblical inspiration in his creative output I chose two categories from various thematic aspects: self-portraits and landscapes with a church. There are plenty of Nikifor’s paintings showing him as a teacher, as a celebrating priest, as a bishop, or even as Christ. A pop­ular way to explain this idea of self-portraits is a psychological one: as a form of auto-therapy. This analysis is aims to show a deeper expla­nation for the biblical anthropology. Nikifor’s self-portraits as a priest celebrating the liturgy are a symbol of creative activity understood as a divine re-creation of the world. Such activity needs divine inspira­tion. Here are two paintings to recall: Potrójny autoportret (The triple self-portrait) and Autoportret w trzech postaciach (Self-portrait in three persons). The proper way to understand the self-identification with Christ needs a reference to biblical anthropology. To achieve our re­al-self we need to identify with Christ, whose death and resurrection bring about our whole humanity. The key impression we may have by showing Nikifor’s landscapes with a church is harmony. The painter used plenty of warm colors. Many of the critics are of the opinion that Nikifor created an imaginary, ideal world in his landscapes, the world he wanted to be there and not the real world. The thesis of this article is that Nikifor created not only the ideal world, but he also showed the source of the harmony – the divine order.


2020 ◽  
Author(s):  
Vasil Penchev

“Super-humans” is usually to be linked to Nietzsche or to Heidegger’s criticism to Nietzsche, or even to the ideology of Nazism. However, they can be properly underlain by philosophical and scientific anthropology as that biological species who will originate from humans eventually in the course of evolution. There is a series of more or less well-established facts in anthropogenesis, which would be relevant to the philosophical question about the “super-humans”: bipedalism, cooling by sweating, specific hair or its lack, omnivorous-ness, thumb opposition and apposition, vocal system of speech production, human brain, long childhood; our species is evolutionary young (about 200 000 years old), but it is the last survived descendant being genetically exceptionally homogenous (<00,01% genetic differences) of the genus “homo” (about 6 000 000 old). All this generates a few main features of our population: society, technics, language, and mind, which guarantee the contemporary absolute domination of mankind. The society has reached a natural limitation of earth. The technics depends on how much energy is produced. The mind is restricted by its carrier, i.e. by the brain. Thus only the language seems to be the frontier of any future development inducing a much better use of the former three. The recent informational technologies suggest the same. Language is defined as symbolic image of the world doubling it by an ideal or virtual world, which is fruitful for creativity and any modeling of the real world. Consequently, a gap between the material and the ideal world produces language. The language increases that gap in turn. Furthermore, the ideal world is secondary and derivative from the material world in origin and objectivity: Language serves for the world to be ordered. Thus language refers to the philosophical categories of ‘being’ and ‘time’. Any “super-language” should transcend some of those definitive borders of language and be a generalization. The involving of infinity can extend the language. Any human language is finite and addresses some finite reality. Thus the gap between reality and any model in language can be seen as that between infinity and its limitation to any finite representation: Finite representations dominate over society, technics, and the mind use. A “super-language” as an “infinite language” can be approached in a few reference frames: Husserl’s “Back to the things themselves!” if “phenomenon” in his philosophy is thought as the ‘word’ of the language of consciousness; the semantic and philosophical theory of symbol: from consciousness and language to reality; the concept of infinity in mathematics and its foundation: set or category theory; quantum mechanics and information: the coincidence of the quantum model and reality; quantum computer. Mankind is approached the problem of infinite language as the language of nature


Author(s):  
Evgenii M. Dmitrievskii ◽  

The article analyzes the ideal from the position of antipsycholo- gism (objectivism), which is opposed to psychologism. The proponents of psy- chologism attributed the ideal only to the mind of an individual. Objectivists considered the existence of the ideal not only in the mind of a separate indivi- dual, but also outside of it, as a rule, allocating their own area for it in reality. But the objectivists also understood the objective existence of the ideal differ- ently. E. Husserl connected the ideal with the pure laws of logic and mathema- tics, comprehended intuitively. G. Frege extended the ideal, including the laws of nature, linking it with the meaning of the sentence. He also formulated the concept of three regions of reality, including the ideal. K. Popper extended the ideal to cultural objects and also introduced the principles of evolutionism into the world of the ideal. M. A. Lifshits connected the ideal with all objects, both the natural and cultural. He pointed to the activity of the ideal in relation to the subject. E.V. Ilyenkov understood the ideal not as an abstract image, but as a form (scheme) of human activity in the rational transformation of the reality objects revealed in social practice. He believed that the ideal exists objectively in the forms of social consciousness.


Author(s):  
Thomas Baldwin

McTaggart was one of the last of the ‘British Idealists’, the group of British philosophers, such as B. Bosanquet and F.H. Bradley, who took their inspiration from Hegel. In his early writings from the 1890s, McTaggart gave a critical exposition of themes from Hegel’s logic before advancing his own distinctive idealist positions concerning time, the mind, and reality in general. But in his writings from 1910 he developed an independent account of the structure of existence from which he then argued for the same idealist positions as before. The thesis for which McTaggart is now most famous is that of the unreality of time; what is even more difficult to come to terms with is his thesis that the ultimate reality of the world comprises a community of selves wholly constituted by their loving perceptions of each other. This thesis is a manifestation of a mysticism that is an essential element in McTaggart’s philosophy; yet this mysticism is combined with a rationalist determination, reminiscent of Spinoza, to vindicate mystical insights by the light of pure reason alone.


2020 ◽  
Author(s):  
Vasil Dinev Penchev

“Super-humans” is usually to be linked to Nietzsche or to Heidegger’s criticism to Nietzsche, or even to the ideology of Nazism. However, they can be properly underlain by philosophical and scientific anthropology as that biological species who will originate from humans eventually in the course of evolution. There is a series of more or less well-established facts in anthropogenesis, which would be relevant to the philosophical question about the “super-humans”: bipedalism, cooling by sweating, specific hair or its lack, omnivorous-ness, thumb opposition and apposition, vocal system of speech production, human brain, long childhood; our species is evolutionary young (about 200 000 years old), but it is the last survived descendant being genetically exceptionally homogenous (&lt;00,01% genetic differences) of the genus “homo” (about 6 000 000 old). All this generates a few main features of our population: society, technics, language, and mind, which guarantee the contemporary absolute domination of mankind. The society has reached a natural limitation of earth. The technics depends on how much energy is produced. The mind is restricted by its carrier, i.e. by the brain. Thus only the language seems to be the frontier of any future development inducing a much better use of the former three. The recent informational technologies suggest the same. Language is defined as symbolic image of the world doubling it by an ideal or virtual world, which is fruitful for creativity and any modeling of the real world. Consequently, a gap between the material and the ideal world produces language. The language increases that gap in turn. Furthermore, the ideal world is secondary and derivative from the material world in origin and objectivity: Language serves for the world to be ordered. Thus language refers to the philosophical categories of ‘being’ and ‘time’. Any “super-language” should transcend some of those definitive borders of language and be a generalization. The involving of infinity can extend the language. Any human language is finite and addresses some finite reality. Thus the gap between reality and any model in language can be seen as that between infinity and its limitation to any finite representation: Finite representations dominate over society, technics, and the mind use. A “super-language” as an “infinite language” can be approached in a few reference frames: Husserl’s “Back to the things themselves!” if “phenomenon” in his philosophy is thought as the ‘word’ of the language of consciousness; the semantic and philosophical theory of symbol: from consciousness and language to reality; the concept of infinity in mathematics and its foundation: set or category theory; quantum mechanics and information: the coincidence of the quantum model and reality; quantum computer. Mankind is approached the problem of infinite language as the language of nature.


Author(s):  
Brian Schrag ◽  
Kathleen J. Van Buren

Step 5 helps readers to design a new creative activity or modify an existing activity in a community. It addresses a number of critical issues relevant to developing artistic programs, including community values that affect artistic production; social, material, financial, and spiritual resources required for events; people who need to be involved in the creation process; and possible opportunities and barriers. It also offers guidance on how to develop the following types of sparking activities: commissioning, workshops, showcase events, mentoring, apprenticeship, publications, and creators’ clubs. Finally, Step 5 provides examples of sparking activities that relate to three main issues: identity and sustainability, health and well-being, and human rights. For each of these issues, readers are presented with examples of practical activities for designing artistic programs, real-life case studies from around the world, and relevant resources for further study.


2020 ◽  
Vol 51 (2) ◽  
pp. 113-133 ◽  
Author(s):  
Nandita Chaudhary ◽  
Sujata Sriram

The mind has been the subject of fascination since ancient times, and every cultural tradition has folk theories related to meaning-making, attributions, and explanations about being human. In this sense, the subject of Psychology is as old as humanity, although its rise as a global, scientific discipline is relatively recent, emerging from 20th-century Europe and America. Theoretical ideas and methods generated during the growth of the discipline were aligned with beliefs about human nature and scientific methods specific to Euro-American cultures. Although “preached” and practiced universally as a science, this culturally circumscribed and ideologically bound history of the discipline needs further examination. Rather than “thinking globally” and “acting locally,” the agenda of Psychology has been the reverse; “think locally and act globally,” as critics of mainstream Psychology have pointed out. The predominance of individual, intra-mental, laboratory-tested, quantifiable dimensions of human conduct are based subliminally on Western ideology. The alternative methods of approaching real-life experiences, literature, art, inter-mental phenomena, and other qualitative dimensions of human interactions remain relatively under-explored. The dominant mainstream Psychology is seen as an objective, measurable, and universal science that has had far-reaching consequences for ordinary people around the world. This somewhat sinister side of conventional Psychology is the subject of this article, where we argue that despite significant exceptions and scholarly dissent, the popularity and prevalence of experimental Psychology has marginalized “others” at the expense of its own progress. We use illustrations primarily from teaching, research and practice in Psychology in Indian Universities.


2020 ◽  
Vol 50 (2) ◽  
pp. 177-198
Author(s):  
Anne O’Byrne

Abstract Arendt was famously dismissive of the work of psychologists, claiming that they did nothing more than reveal the pervasive ugliness and monotony of the psyche. If we want to know who people are, she argued, we should observe what they do and say rather than delving into the turmoil of their inner lives; if we want to understand humanity, we would be better off reading Oedipus Rex than hearing about someone’s Oedipus complex. The rejection has a certain coherence in the context of her understanding of public life as the realm of appearance and opinion, but examining it through the specific question of ugliness complicates that understanding. While beauty invites us to contemplate the world and admire it, ugliness repels our attention and sows the seed of a worry that the world might not want to be known. Working with Eichmann in Jerusalem, The Life of the Mind: Thinking, the Kant lectures and a striking Denktagebuch entry in which she reacts with revulsion to Matisse’s Heads of Jeannette, I argue that Arendt’s response to the ugly psyche requires a re-examination of the sensus communis. If the psyche does not want to be known, and if not all points of view are open to imaginative occupation, the ideal and practice of enlarged mentality must reckon with a right to opacity.


Author(s):  
Edward Uzoma Ezedike

This paper focuses extensively on Kant’s critical epistemology as postulated in his Critique of Pure Reason. It grapples with the problem of identifying and harmonizing these borderlines of empirical and rational knowledge with that of metaphysical knowledge. Kant argues that the mind is so structured and empowered that it imposes interpretative categories on our experience so that we do not simply experience the world, as the empiricists claim, but interpret it through the categorizing mechanism of the mind. In ruling out indifference to metaphysical questions, Kant posits that if metaphysics is not science, yet still as natural disposition, human reason is driven on ‘by an inward need’ and not by mere ‘idle desire’ to ask metaphysical questions. Furthermore, Kant posits that what makes skepticism about metaphysics unsustainable is that metaphysics cannot be discarded in isolation from cognition in general. Kant, therefore, is of the view that the very same principles of reasoning as are employed in empirical judgments about physical objects are also used in a purified form, in metaphysical judgments about God, the soul and other non-empirical entities. However, the paper criticizes Kant for being too anxious to prove the subjectivity of space, as an escape route from materialism. Kant was quite averse to the argument that if space is objective and universal, God must exist in space, and hence, be spacial and material in nature. Thus, Kant might have been satisfied with the critical idealism which holds that all reality is known to us as our sensations and ideas.


2020 ◽  
Author(s):  
Vasil Penchev

“Super-humans” is usually to be linked to Nietzsche or to Heidegger’s criticism to Nietzsche, or even to the ideology of Nazism. However, they can be properly underlain by philosophical and scientific anthropology as that biological species who will originate from humans eventually in the course of evolution. There is a series of more or less well-established facts in anthropogenesis, which would be relevant to the philosophical question about the “super-humans”: bipedalism, cooling by sweating, specific hair or its lack, omnivorous-ness, thumb opposition and apposition, vocal system of speech production, human brain, long childhood; our species is evolutionary young (about 200 000 years old), but it is the last survived descendant being genetically exceptionally homogenous (<00,01% genetic differences) of the genus “homo” (about 6 000 000 old). All this generates a few main features of our population: society, technics, language, and mind, which guarantee the contemporary absolute domination of mankind. The society has reached a natural limitation of earth. The technics depends on how much energy is produced. The mind is restricted by its carrier, i.e. by the brain. Thus only the language seems to be the frontier of any future development inducing a much better use of the former three. The recent informational technologies suggest the same. Language is defined as symbolic image of the world doubling it by an ideal or virtual world, which is fruitful for creativity and any modeling of the real world. Consequently, a gap between the material and the ideal world produces language. The language increases that gap in turn. Furthermore, the ideal world is secondary and derivative from the material world in origin and objectivity: Language serves for the world to be ordered. Thus language refers to the philosophical categories of ‘being’ and ‘time’. Any “super-language” should transcend some of those definitive borders of language and be a generalization. The involving of infinity can extend the language. Any human language is finite and addresses some finite reality. Thus the gap between reality and any model in language can be seen as that between infinity and its limitation to any finite representation: Finite representations dominate over society, technics, and the mind use. A “super-language” as an “infinite language” can be approached in a few reference frames: Husserl’s “Back to the things themselves!” if “phenomenon” in his philosophy is thought as the ‘word’ of the language of consciousness; the semantic and philosophical theory of symbol: from consciousness and language to reality; the concept of infinity in mathematics and its foundation: set or category theory; quantum mechanics and information: the coincidence of the quantum model and reality; quantum computer. Mankind is approached the problem of infinite language as the language of nature


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