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数学的逻辑基础?

(2019-08-23 20:39:02)

数学的逻辑基础?

   20197月,国家4部委联合发文,要求全国加强数学研究的《通知》。

  该《通知》开宗明义,说:“数学是自然科学的基础。”

   然而,英国逻辑学家罗素认为:逻辑才是数学的基础。为此,罗素花费了十年时间,于1910-13年,发表经典专著“数学原理”,严格论证数学的逻辑基础。由此,我们应该关注数理逻辑学科。

  请见本文附件文章。

袁萌   陈启清  823

附件:

Principia Mathematica

  For Isaac Newton's book containing basic laws of physics, see Philosophiæ Naturalis Principia Mathematica.

Not to be confused with The Principles of Mathematics—another book of Russell published in 1903.

The title page of the shortened Principia Mathematica to 56

 

 

54.43: "From this proposition it will follow, when arithmetical addition has been defined, that 1 + 1 = 2." —Volume I, 1st edition, page 379 (page 362 in 2nd edition; page 360 in abridged version). (The proof is actually completed in Volume II, 1st edition, page 86, accompanied by the comment, "The above proposition is occasionally useful." Τhey go on to say "It is used at least three times, in 113.66 and 120.123.472.")

I can remember Bertrand Russell telling me of a horrible dream. He was in the top floor of the University Library, about A.D. 2100. A library assistant was going round the shelves carrying an enormous bucket, taking down books, glancing at them, restoring them to the shelves or dumping them into the bucket. At last he came to three large volumes which Russell could recognize as the last surviving copy of Principia Mathematica. He took down one of the volumes, turned over a few pages, seemed puzzled for a moment by the curious symbolism, closed the volume, balanced it in his hand and hesitated....

Hardy, G. H. (2004) [1940]. A Mathematician's Apology. Cambridge: University Press. p. 83. ISBN 978-0-521-42706-7.

He [Russell] said once, after some contact with the Chinese language, that he was horrified to find that the language of Principia Mathematica was an Indo-European one

Littlewood, J. E. (1985). A Mathematician's Miscellany. Cambridge: University Press. p. 130.

The Principia Mathematica (often abbreviated PM) is a three-volume work on the foundations of mathematics written by Alfred North Whitehead and Bertrand Russell and published in 1910, 1912, and 1913. In 1925–27, it appeared in a second edition with an important Introduction to the Second Edition, an Appendix A that replaced 9 and all-new Appendix B and Appendix C. PM is not to be confused with Russell's 1903 The Principles of Mathematics. PM was originally conceived as a sequel volume to Russe

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