scholarly journals From the Four-Color Theorem to a Generalizing 'Four-Letter Theorem': A Sketch for 'Human Proof' and the Philosophical Interpretation

2020 ◽  
Author(s):  
Vasil Penchev
Keyword(s):  
Philosophical Interpretation ◽  
Four Color Theorem

scholarly journals From the four-color theorem to a generalizing “four-letter theorem”: A sketch for “human proof” and the philosophical interpretation

2020 ◽  
Author(s):  
Vasil Dinev Penchev
Keyword(s):  
Mathematical Proof ◽  
General Theorem ◽  
Human Capabilities ◽  
Letter Alphabet ◽  
Philosophical Interpretation ◽  
Four Color Theorem ◽  
The Universe

The “four-color” theorem seems to be generalizable as follows. The four-letter alphabet is sufficient to encode unambiguously any set of well-orderings including a geographical map or the “map” of any logic and thus that of all logics or the DNA (RNA) plan(s) of any (all) alive being(s).Then the corresponding maximally generalizing conjecture would state: anything in the universe or mind can be encoded unambiguously by four letters.That admits to be formulated as a “four-letter theorem”, and thus one can search for a properly mathematical proof of the statement.It would imply the “four colour theorem”, the proof of which many philosophers and mathematicians believe not to be entirely satisfactory for it is not a “human proof”, but intermediated by computers unavoidably since the necessary calculations exceed the human capabilities fundamentally. It is furthermore rather unsatisfactory because it consists in enumerating and proving all cases one by one.Sometimes, a more general theorem turns out to be much easier for proving including a general “human” method, and the particular and too difficult for proving theorem to be implied as a corollary in certain simple conditions.The same approach will be followed as to the four colour theorem, i.e. to be deduced more or less trivially from the “four-letter theorem” if the latter is proved. References are only classical and thus very well-known papers: their complete bibliographic description is omitted.

Modality and folk psychology

2019 ◽  
Vol 28 (1) ◽  
pp. 19-27
Author(s):  
Ja. O. Petik
Keyword(s):  
Modal Logic ◽  
Brain Activity ◽  
Formal System ◽  
Philosophy Of Logic ◽  
Psychological States ◽  
Formal Systems ◽  
Modern Psychology ◽  
Philosophical Interpretation ◽  
Important Direction

The connection of the modern psychology and formal systems remains an important direction of research. This paper is centered on philosophical problems surrounding relations between mental and logic. Main attention is given to philosophy of logic but certain ideas are introduced that can be incorporated into the practical philosophical logic. The definition and properties of basic modal logic and descending ones which are used in study of mental activity are in view. The defining role of philosophical interpretation of modality for the particular formal system used for research in the field of psychological states of agents is postulated. Different semantics of modal logic are studied. The hypothesis about the connection of research in cognitive psychology (semantics of brain activity) and formal systems connected to research of psychological states is stated.

Le premier moment de l’art dans À la recherche du temps perdu de Marcel Proust – une « leçon d’idéalisme » ?

2020 ◽  
pp. 25-40
Author(s):  
Larisa Botnari
Keyword(s):  
Essential Role ◽  
Marcel Proust ◽  
The Self ◽  
Philosophy Of Art ◽  
The Novel ◽  
Philosophical Interpretation ◽  
German Philosopher ◽  
Lost Time ◽  
Aesthetic Thinking

Although very famous, some key moments of the novel In Search of Lost Time, such as those of the madeleine or the uneven pavement, often remain enigmatic for the reader. Our article attempts to formulate a possible philosophical interpretation of the narrator's experiences during these scenes, through a confrontation of the Proustian text with the ideas found in the System of Transcendental Idealism (1800) of the German philosopher F. W. J. Schelling. We thus try to highlight the essential role of the self in Marcel Proust's aesthetic thinking, by showing that the mysterious happiness felt by the narrator, and from which the project of creating a work of art is ultimately born, is similar to the experiences of pure self-consciousness evoked and analyzed by Schellingian philosophy of art.

On the possibility/possibilities of the history of philosophy today

2006 ◽  
Vol 49 (1-2) ◽  
pp. 81-95
Author(s):  
Predrag Milidrag
Keyword(s):  
History Of Philosophy ◽  
Philosophy Today ◽  
Philosophical Interpretation ◽  
History Of

The article discusses the philosophical presuppositions of the history of philosophy as a philosophical discipline on the example of the problem of interpreting mutually incoherent claims of a philosopher. The conclusion is that the constitution of these presuppositions is onto-theo-logical. The importance of the criteria of coherence and comprehensiveness for historic philosophical interpretation is analyzed. Finally, the idea of the possibility of a postmetaphysical history of philosophy as a philosophical discipline is exposed, viewed as the accumulation of understandings of various paths - followed and not followed alike -found in past philosophers.

Excursus

2018 ◽  
Author(s):  
Jens Schlieter
Keyword(s):  
Life Review ◽  
Human Consciousness ◽  
Niklas Luhmann ◽  
Search For Meaning ◽  
Thomas Nagel ◽  
Philosophical Interpretation

This chapter, an excursus, embarks on a more philosophical interpretation of consciousness and experience. Building on Thomas Nagel and Niklas Luhmann, it is argued that human consciousness, defined as a process of self-reproduction of never-ending new possibilities, is perplexed by the task of imagining its own nonexistence. Given that consciousness is not equipped for this task, that is to imagine death (its own nonexistence), it will react with a search for meaning, a context for the existential threat. The excursus argues that this leads to the highly accelerated activity of consciousness. It may result in a phenomenon reported by a certain number of near-death experiencers, namely, the life review. In short, then, the life review is a highly accelerated search for meaning. These deliberations are further substantiated by a comparison with “wake-up dreams,” in which a similar structure becomes visible.

Individuality and Beyond

2019 ◽  
Author(s):  
Benedetta Zavatta
Keyword(s):  
Moral Autonomy ◽  
First Line ◽  
Philosophical Interpretation ◽  
Individual Personality ◽  
The World ◽  
Regulative Ideal ◽  
Personal Library ◽  
The Many ◽  
The Individual ◽  
The Impact

Based on an analysis of the marginal markings and annotations Nietzsche made to the works of Emerson in his personal library, the book offers a philosophical interpretation of the impact on Nietzsche’s thought of his reading of these works, a reading that began when he was a schoolboy and extended to the final years of his conscious life. The many ideas and sources of inspiration that Nietzsche drew from Emerson can be organized in terms of two main lines of thought. The first line leads in the direction of the development of the individual personality, that is, the achievement of critical thinking, moral autonomy, and original self-expression. The second line of thought is the overcoming of individuality: that is to say, the need to transcend one’s own individual—and thus by definition limited—view of the world by continually confronting and engaging with visions different from one’s own and by putting into question and debating one’s own values and certainties. The image of the strong personality that Nietzsche forms thanks to his reading of Emerson ultimately takes on the appearance of a nomadic subject who is continually passing out of themselves—that is to say, abandoning their own positions and convictions—so as to undergo a constant process of evolution. In other words, the formation of the individual personality takes on the form of a regulative ideal: a goal that can never be said to have been definitively and once and for all attained.

Neo-Confucian Hermeneutics at Work:Cheng Yi's Philosophical Interpretation of Analects 8.9 and 17.3

2008 ◽  
Vol 101 (2) ◽  
pp. 169-201 ◽  
Author(s):  
Yong Huang
Keyword(s):  
Song Dynasty ◽  
Traditional View ◽  
Philosophical Concept ◽  
The Real ◽  
The Song Dynasty ◽  
Philosophical Interpretation ◽  
Chinese Scholars ◽  
First Time ◽  
The Relationship

In this article, I discuss the Song 宋 Neo-Confucian Cheng Yi's 程頤 (1033–1107) interpretation of two related controversial passages in the Analects, the recorded sayings of Confucius. The term “neo-Confucianism” was coined by Western scholars to refer to the Confucianism of the period from the Song dynasty to the Ming 明 dynasty (and sometimes through the Qing 清 dynasty). Among Chinese scholars, neo-Confucianism is most commonly referred to as the Learning of Principle (li xue 理學). Although before Cheng Yi and his brother Cheng Hao 程顥 (1032–1085) there were three other philosophers who are normally also regarded as neo-Confucians— Shao Yong 邵雍 (1011–1077), Zhou Dunyi 周敦頤 (1017–1073), and Zhang Zai 張載 (1020–1077)—we can justifiably regard the Cheng brothers as the real founders of neo-Confucianism in the sense that principle becomes the essential philosophical concept for the first time in their works. There is no consensus among scholars as to the relationship between the philosophies of these two brothers. The traditional view regards them as substantially different due to the two different schools of neo-Confucianism that developed from their teachings, the realistic school synthesized by Zhu Xi 朱熹 (1130–1200) from the teachings of Cheng Yi and the idealist school culminating in Wang Yangming 王陽明 (1472–1529) from the teachings of ChengHao. I, however, tend to think that the philosophical positions of the two brothers are largely similar. Unfortunately, since Cheng Hao did not live as long as Cheng Yi, there is insufficient material to create a systematic picture of his view of the Analects passages with which this article will deal.

scholarly journals Toward a language theoretic proof of the four color theorem

2012 ◽  
Vol 48 (2) ◽  
pp. 414-431 ◽  
Author(s):  
Bobbe Cooper ◽  
Eric Rowland ◽  
Doron Zeilberger
Keyword(s):  
Theoretic Proof ◽  
Four Color Theorem
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