| 释义 |
quantification|ˌkwɒntɪfɪˈkeɪʃən|
[f. quantify v.: see -fication.]
The action of quantifying. Esp. in Logic, as quantification theory: theory concerned with quantifiers or with giving formal expression to the scope of variables in general propositions. Cf. quantifier.
quantification of the predicate: the expression of the logical quantity of the predicate of a proposition, by applying to the predicate the sign all, or some, or an equivalent; a device introduced chiefly by Sir W. Hamilton, and intended to simplify logical processes.
c1840Sir W. Hamilton Logic (1866) II. 297 Because the universal quantification of the predicate is, in this instance, materially false, is such quantification, therefore, always formally illegal? 1864Bowen Logic vii. 181 It is enough that the quantifications of the Middle Term in both Premises, added together, should exceed unity. 1882Piazzi Smith in Nature XXVI. 552 All that we require for the..quantification of watery vapour. 1918C. I. Lewis Survey of Symbolic Logic i. 24 He [sc. Lambert] reconstructs the whole of Aristotelian logic by the quantification of the predicate. 1940Brit. Jrnl. Psychol. Jan. 233 Quantification pertains to a statistical population of persons, assessed or measured for amounts of that particular quality. 1940W. V. Quine Math. Logic p. vi, Quantification theory, like the preceding part of logic, is expounded within the medium of metamathematics; its presentation in any other medium appears disadvantageous, indeed, because of subtleties having to do with the so-called bound and free occurrences of variables. 1949R. K. Merton Social Theory iii. 109 What appears as a tendency in research for quantification (through the development of scales) can thus be seen as a special case of attempting to clarify concepts sufficiently to permit the conduct of empirical investigation. 1950W. V. Quine Methods of Logic (1952) §28. 166 Quantification theory was founded by Frege in 1879. 1962E. W. Beth Formal Methods iii. 50 If a semantic tableau for the sequent Ø/Z is closed, then the formula Z will be called a tautology (of quantification theory). 1966A. D. Biderman in R. Bauer Social Indicators ii. 75 Quantification was not until fairly recently an essential element of the definition of statistics. 1969N. I. Styazhkin Hist. Math. Logic Leibniz to Peano iii. 123 It would not be an exaggeration to say that Lambert's theory of quantification actually contains all the basic results of the studies in quantification made by W. Hamilton in the nineteenth century. 1971World Archaeol. III. 122 Groups of granaries..do not permit quantification of men by compound. 1973J. Hintikka Logic, Language-Games & Information iii. 53 Quantification theory may be characterized from this point of view as the study of the phrases ‘there is’, and ‘for every’ over and above the study of the words ‘not’, and ‘or’, which are already studied in propositional logic plus whatever terms are required to express predication. 1974H. Wang From Math. to Philos. 143 The many attractive properties of the first order or restricted predicate calculus (quantification theory) have suggested the convenient identification of it with first order logic, pure logic, or just logic. 1979Amer. Speech LIV. 9 Scholars have criticized, sometimes effectively, the validity of the prescriptivists' quantifications. 1979Dædalus Summer 77 A quantification of love that would be comic were it not that its effects are so awful. |