标签：Poincaré

Space and Geometry—Questions for Reflection and Suggestions for Discussion from Teacher Wang’s Lecture

History of Science & Scholarship2010.10.13
Space and Geometry—Questions for Reflection and Suggestions for Discussion from Teacher Wang’s Lecture
http://hps.phil.pku.edu.cn/bbs/read.php?tid=1169 Although Professor Wang’s lecture this time was rather jumpy in content, the reading materials assigned this time are relatively readable. If you read the materials in advance, listening to Professor Wang’s lecture can serve to help the two illuminate each other. I hope everyone will be sure to read the relevant materials, and at the very least must read the second part of *Science and Hypothesis*. In tomorrow’s discussion class, the main speakers and the TAs should discuss more around the materials, and not wander too far afield. Broadly speaking, the issues involved in this lecture and the reading materials are these: 1. What is space? 2. What is…
science Kant space Newton
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2010年10月13日
Later Wittgenstein and the Philosophy of Mathematics of Intuitionism

History of Science & Scholarship2007.05.15
Later Wittgenstein and the Philosophy of Mathematics of Intuitionism
Late Wittgenstein and the Mathematical Philosophy of Intuitionism Abstract: This essay takes intuitionism as its guiding thread to explicate Wittgenstein’s late philosophy of mathematics, with the hope that it may contribute to a grasp of his late philosophy; on the other hand, it also cites Wittgenstein’s philosophical claims to provide support for intuitionism. Thus, this essay attempts both to sort out the mathematical philosophy of Wittgenstein’s later period and, at the same time, to offer a brief critical account of intuitionism. The author discusses separately the views of intuitionism and of late Wittgenstein on themes such as constructivism, empiricism, positivism, Platonism, logicism, formalism, conventionalism, the axiomatization movement, and the development…
philosophy mathematics paper language
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2007年5月15日
Is Non-Euclidean Geometry Favorable to Apriorism?

Philosophy & Thought2007.01.16
Is Non-Euclidean Geometry Favorable to Apriorism?
Non-Euclidean geometry is generally thought to be a “fatal blow” to Kantian transcendental theory. In an earlier article, I expressed doubt about this overly simplistic idea. But recently, as I happened to mull over the question again, an even bolder thought popped into my head — the discovery of non-Euclidean geometry is actually favorable to transcendental theory! It should be noted that Kant’s transcendental theory is neither empiricism nor rationalism. Kant is not saying that if one first finds a few axioms in human a priori intuition, then one can deduce the true state of the objective world. Kant is answering this question: since human experience of this world is…
philosophy Kant space Poincaré
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2007年1月16日
In Defense of Intuitionism

History of Science & Scholarship2006.08.15
In Defense of Intuitionism
In Defense of Intuitionism Abstract: From the perspective of defending intuitionism, the author explains intuitionism’s claims in the philosophy of mathematics and the philosophy of logic. The basic position of intuitionism is that mathematics is a creation of the human mind. Intuitionism rejects assigning any mathematical object a transcendent existence beyond mind and matter; intuition and creation, rather than proof and deduction, are the most important mathematical methods, the life of mathematics; the meaning of mathematics, like that of the other sciences, lies in discovering problems worth studying, touching the mysteries of nature, and ceaselessly pursuing truth. In the first half of this essay, the author sorts out intuitionism’s resistance…
philosophy Aristotle mathematics paper
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2006年8月15日
Preliminary Thoughts on “Intuitionism”

Philosophy & Thought2006.08.07
Preliminary Thoughts on “Intuitionism”
My term paper for my class on logical paradoxes has now been decided: I’m going to write on intuitionism and the foundations of mathematics. At first I had been dead set on writing about inductive logic, and I read a lot of books, but the more I read, the fewer ideas of my own I seemed to have left; in the end they were almost completely buried. Writing an article that simply surveys the various schools of thought isn’t very interesting either, and I also seem unable to sort out any ideas of my own in such a short time, so in the end I had no choice but to…
philosophy mathematics Kant Poincaré
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2006年8月7日
Kant’s Significance for the Philosophy of Science

History of Science & Scholarship2006.07.04
Kant’s Significance for the Philosophy of Science
My own view is that Kant’s philosophy has great heuristic significance for the philosophy of science, but among the group of philosophers of science who continue empiricism in the contemporary era, it has been widely neglected. Of course, Kant’s exalted place in the history of philosophy is something very few philosophers would dare to deny, and philosophers of science are no exception. In writings on the philosophy of science, Kant is still often mentioned. But the problem is this: nine times out of ten, when philosophers of science mention Kant, they refer only to his “transcendental theory.” It seems as though Kant’s contribution to the philosophy of science amounted to…
philosophy science philosophy of science Kant
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2006年7月4日
The Religious Views of Great Scientists: Quotation Piling

Philosophy & Thought2006.03.28
The Religious Views of Great Scientists: Quotation Piling
The Big Scientists’ View of Religion: A Heap of Quotations Einstein: You will have a hard time finding among scientists of deep attainment anyone who does not have his own religious feeling. — “The Religious Spirit of Science,” in The Collected Works of Einstein, vol. 1, p. 67 A person inspired by religion has already, to the greatest possible extent, freed himself from the shackles of selfish desire, and is wholly devoted to thoughts, feelings, and aspirations that possess transpersonal value and which he holds fast to. What I consider important is the power of this content that transcends the individual, and the depth of the belief in its far-reaching…
book reading notes history of science philosophy of science
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2006年3月28日
[Fr.] Poincaré: “Last Thoughts”

History of Science & Scholarship2006.02.09
[Fr.] Poincaré: “Last Thoughts”
[French] Poincaré: “The Last Reflections,” translated by Li Xingmin, proofread by Fan Dainian, Commercial Press, December 1996 Poincaré was such a great, even legendary, figure! Poincaré is widely regarded as the “last all-around mathematical genius,” comparable to Gauss; in fact, it would not be at all excessive to remove even the word “mathematical.” “Poincaré’s achievements in the four main branches of mathematics—arithmetic, algebra, geometry, and analysis—were all pioneering; in particular, he made outstanding contributions to branches such as function theory, algebraic geometry, number theory, the mathematics of strings, differential equations, and algebraic topology.” (p. ii) “In astronomy, Poincaré’s main work fell into three areas: the equilibrium shapes of rotating fluids;…
philosophy book reading notes philosophy of science
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2006年2月9日