| 单词 |
reducibility |
| 释义 |
reduciˈbility
[f. next + -ity.]
a. The fact or quality of being reducible.
1676Collins in Rigaud Corr. Sci. Men (1841) II. 10 The reducibility of Davenant's problem to infinite series. 1842Parnell Chem. Anal. (1845) 89 The easy reducibility of its compounds to the metallic state. 1889Lancet 18 May 1002/1 The complete reducibility of the tumour.
b. spec. in Logic, as axiom of reducibility (see quot. 1952).
1910Whitehead & Russell Principia Math. I. 168 (heading) The hierarchy of types and the axiom of reducibility. Ibid. 174 We assume, then, that every function of one variable is equivalent, for all its values, to some predicative function of the same argument. This assumption seems to be the essence of the usual assumption of classes; at any rate, it retains as much of classes as we have any use for... We will call this assumption the axiom of classes, or the axiom of reducibility. 1930L. S. Stebbing Mod. Introd. Logic xxiii. 463 Ramsey has suggested a reconstruction of the system of Principia Mathematica in which the axiom of reducibility is no longer needed. 1942D. D. Runes Dict. Philos. 266/2 As an indication or rough description of the axiom of reducibility, it may be said that it cancels a large part of the restrictive consequences of the prohibition against impredicative definition..and, in approximate effect, reduces the ramified theory of types to the simple theory of types. 1952S. C. Kleene Introd. Metamath. iii. 44 To escape this outcome, Russell postulated his axiom of reducibility, which asserts that to any property belonging to an order above the lowest, there is a coextensive property (i.e. one possessed by exactly the same objects) of order 0. 1963W. V. Quine Set Theory & its Logic xi. 251 The axiom of reducibility regales us after all with attributes unspecifiable except by quantifying over attributes whose order is as high as their own. |
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