finitistadj.n.

1904 W. James Let. 12 June (1920) II. 203 My philosophy..is finitist; but it does not attribute to the question of the Infinite the great methodological importance which you and Renouvier attribute to it.

1914 B. Russell Our Knowl. External World vi. 155 There is no longer any reason to struggle after a finitist explanation of the world.

1931 F. P. Ramsey Found. Math. 243 Provable..means provable in any number of steps, and on finitist principles the number must in some way be limited, e.g. to the humanly possible.

1935 Mind 44 186 These present to the finitist school of mathematicians difficulties.

1940 Mind 49 243 He will use only ‘finitist’ methods.

1966 Math. Rev. Jan. 9/2 F is complete with respect to some distinguished notion of proof, such as finitist or predicative.

1897 B. Russell in Mind VI. 118 When the finitist objects that an infinite collection can never be..really a whole, the infinitist replies that..number itself must be contradictory.

1900 J. Royce World & Indiv. I. 558 Couturat, in his dialectical discussion between the ‘finitist’ and the ‘infinitist’,..gives full room to..these arguments.

1935 Mind 44 186 Denials by the finitists which the formalist and logistic schools contest.

1960 S. Körner Philos. of Math. v. 111 Finitists such as Aristotle, Gauss, and the older and the newer intuitionists, deny all ‘real’ content or even ‘intelligibility’ to such mathematical notions as are not characteristic either of finite aggregates or at most of potentially infinite.

1937 Mind 46 58 Gödel..seemed to have destroyed for ever Hilbert's hope that he would carry out his programme of establishing with finitistic means the non-contradictoriness of mathematics.

1959 E. W. Beth Found. Math. iii. 73 Complete induction ranked high among the forms of argument admitted in finitistic meta-mathematics.