| 单词 | Type |
| 释义 | TypeWhitehead and Russell (1927) devised a hierarchy of ``types'' in order to eliminate self-referential statements from Principia Mathematica, which purported to derive all of mathematics from logic. A set of the lowest type contained onlyobjects (not sets), a set of the next higher type could contain only objects or sets of the lower type, and so on.Unfortunately, Gödel's Incompleteness Theorem showed that both PrincipiaMathematica and all consistent formal systems must be incomplete. See also Gödel's Incompleteness Theorem
Hofstadter, D. R. Gödel, Escher, Bach: An Eternal Golden Braid. New York: Vintage Books, pp. 21-22, 1989. Whitehead, A. N. and Russell, B. Principia Mathematica. New York: Cambridge University Press, 1927. |
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