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45. The Non-Euclidean Geometry

Charles S. Peirce Indiana University Press PDF


The Non-Euclidean Geometry

11 February 1892

The Nation

Geometrical Researches on the Theory of Parallels. By

Nicholaus Lobatchewsky. Translated from the original by

George Bruce Halsted, A.M., Ph.D., ex-Fellow of Princeton

College and Johns Hopkins University, Professor of Mathematics in the University of Texas. Austin: University of Texas. 1891.

Lobachevski’s little book, Geometrische Untersuchungen, marks an epoch in the history of thought, that of the overthrow of the axioms of geometry. The philosophical consequences of this are undoubtedly momentous, and there are thinkers who hold that it must lead to a new conception of nature, less mechanical than that which has guided the steps of science since Newton’s discovery. The book has been published many years,—in fact, the essence of it was set forth before 1830; so long does it take a pure idea to make its way, unbacked by any interest more aggressive than the love of truth. In this case, the idea is lucid, easy, and convincing. Nobody with enough mathematical capacity to be able to understand the first book of geometry need fear the least difficulty in mastering Lobachevski’s tract; and really it is high time that every thinking man and woman should know what is in it.

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10 Ecosophy, Sophophily, and Philotheria

John Llewelyn Indiana University Press ePub

Once upon a time I took part in a trek along a network of valleys to the base camp of the 1970 British expedition to the south summit of Annapurna in the Himalayas. Although our final destination was merely the edge of the Hiunchuli glacier, our sirdar Yong Tenzing acceded to my request that I might proceed on my own to a cairn a little higher up. On top of the cairn was a Norwegian 10-øre coin. Had this been placed there, I mused, by the philosopher and mountaineer Arne Naess with some of whose writings I was familiar? If not, had it been put there by his namesake and nephew, the Arne Naess who has sponsored Himalayan climbs, supporting them financially to the tune of rather more than 10 øre?

In his Ecology, Community, and Lifestyle: Outline of an Ecosophy, Arne Naess senior describes how each thing belongs to a whole and to a plurality of subwholes according to an indefinite range of possible Gestalten in which it may appear as a figure or ground.1 That belonging is not the belonging only of an instance that falls under a concept. Belonging as the belonging of an instance that falls under a concept, the belonging in terms of which rights and justice are defined, itself falls within a notion of justice as concordance that is closer to the idea of justice as expounded in Plato’s Republic and to Anaximander’s notion of dikē as expounded in Heidegger’s “The Anaximander Fragment”2 than it is to the Enlightenment and Kantian idea of justice and injustice determined as cases or maxims falling under or falling foul of a natural or moral law by which they are taken to be covered. However, in the Critical system of Kant this hierarchical idea of justice falls under the regulative Idea of orderedness in an organic whole that has more in common with the Platonic conception of justice as synergic harmony. Instead of prescribing principles entailing conclusions unidimensionally, this conception of justice as balance within a multidimensional whole offers guidelines. Deductive rigor makes way for persuasion, as in the cosmogony outlined in the Timaeus. Instead of a blueprint we have a recipe, instead of a tracing a map. A recipe leaves room for practical judgment and imagination. It therefore leaves room for their misuse. The difference between use and misuse is a difference of phronēsis, practical understanding in our ways of conducting ourselves in the regional ecologies of the world.

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Chapter 12: Education and Integration

J Krishnamurti Krishnamurti Foundation America ePub
Medium 9781934989104

~ Respectability

J Krishnamurti Krishnamurti Foundation America ePub

He asserted that he was not greedy, that he was satisfied with little, and that life had been good to him, though he suffered the usual miseries of human existence. He was a quiet man, unobtrusive, hoping not to be disturbed from his easy ways. He said that he was not ambitious, but prayed to God for the things he had, for his family, and for the even flow of his life. He was thankful not to be plunged into problems and conflicts, as his friends and relations were. He was rapidly becoming very respectable and happy in the thought that he was one of the lite. He was not attracted to other women, and he had a peaceful family life, though there were the usual wrangles of husband and wife. He had no special vices, prayed often and worshiped God. "What is the matter with me," he asked, "as I have no problems?" He did not wait for a reply, but smiling in a satisfied and somewhat mournful way proceeded to tell of his past, what he was doing, and what kind of education he was giving to his children. He went on to say that he was not generous, but gave a little here and there. He was certain that each one must struggle to make a position for himself in the world.

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31. An Essay toward Improving Our Reasoning in Security and in Uberty (1913)

Edited by the Peirce Edition Project Indiana University Press ePub


MS 682. [This text, composed in September–October 1913, a few months before Peirce’s death, belongs to a series of unfinished papers on reasoning.] Written in a retrospective mood, this unfinished work shows Peirce continuing to assess the completeness of his logic and the scope of his pragmatism. We learn that reasoning involves a trade-off between security and uberty (rich suggestiveness), and that, not surprisingly, deductive reasoning provides the most security, but little uberty, while abduction provides much uberty but almost no security. Pragmatism, it seems, falls in on the side of security: “[it] does not bestow a single smile upon beauty, upon moral virtue, or upon abstract truth;—the three things that alone raise Humanity above Animality.” Peirce objects strongly to Francis Bacon’s pessimistic claim that nature is beyond human understanding and repeats his long-held conviction that psychology can offer no significant aid to logic. The essay ends with a reminder that the connection between words and thought is as intimate as that between body and mind.

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