refraction
发表于 2025-3-25 06:51:09
The Exact Sciences and Non-Euclidean Logic,totle. Parmenides even questioned the reality of plurality and change. (Einstein’s vision has much in common with Parmenides.) Toward the end of the nineteenth century, an acrimonious exchange took place between Kronecker and Cantor regarding the reality of the actual (as opposed to potential) infin
Deadpan
发表于 2025-3-25 10:26:15
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国家明智
发表于 2025-3-25 12:17:21
Cognitive Networks: Brains, Internet, and Civilizations, civilizations. One motivation for such comparative study is its heuristic value. Attempts to better understand the functioning of “wetware” involved in cognitive activities of the central nervous system by comparing it with a computing device have a long tradition. We suggest that comparison with I
苦涩
发表于 2025-3-25 16:29:32
Reuben Hersh on the Growth of Mathematical Knowledge: Kant, Geometry, and Number Theory, close attention to what mathematicians really do in their research, as they extend mathematical knowledge at the frontier between the known and the conjectured, we see that their work does not only involve deductive reasoning. It also includes plausible reasoning, “analytic” reasoning upward that s
Alcove
发表于 2025-3-25 20:15:00
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半圆凿
发表于 2025-3-26 01:08:23
,School Mathematics and “Real” Mathematics,cs, and fields close to mathematics that we don’t consider to be mathematics, developed in the last century. What do subjects that are considered mathematics have in common, that those that are not part of mathematics lack? As a contribution to this approach, we discuss here the extent to which scho
皱痕
发表于 2025-3-26 08:22:23
What Is Mathematics and What Should It Be?,bert, mathematics is a . activity and culture and its pretensions to absolute truth are unfounded. Mathematics .!. This . was further expanded in the wonderful “sequel” ., also with Davis, and the more philosophical ., written by Reuben all by himself. The fact that mathematics is what (human) mathe
musicologist
发表于 2025-3-26 12:22:42
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Ceramic
发表于 2025-3-26 14:38:45
,The “Artificial Mathematician” Objection: Exploring the (Im)possibility of Automating Mathematical ians would be replaced by computers. Rather than focus on computers . mathematicians, however, our aim is to consider the (im)possibility of human mathematicians being . by “artificial mathematicians” in the proving practice—not just as a method of inquiry but as a fellow inquirer.
overbearing
发表于 2025-3-26 18:46:56
Wittgenstein, Mathematics, and the Temporality of Technique,athematicians, conversely and equally, “no mathematical discovery” can by itself “advance” philosophy in its quest to clarify the forms of our lives and language. It would thus appear . that, for Wittgenstein, the mathematician and the philosopher of mathematics, operating with different methods and