INTENSIONALITY AND PARADOXES IN RAMSEY'S 'THE FOUNDATIONS OF MATHEMATICS'

摘要: In 'The Foundations of Mathematics', Frank Ramsey separates paradoxes into two groups, now taken to be the logical and semantical. But he also revises system developed in Whitehead Russell's Principia Mathematica, particular attempts provide an alternate resolution semantical paradoxes. I reconstruct logic that develops for this purpose, argue it falls well short his goals. then groups identifies are not properly thought as semantical, particular, group normally includes other paradoxes—the intensional paradoxes—which resolved by standard metalinguistic approaches It thus seems if we take Ramsey's interest these problems seriously, deserve more widespread attention than they have historically received. §1. Introduction. (1925) Mathematics' is re- membered almost exclusively distinguishing types paradox: 1 influential distinction was, its statement takes up less a page, while reprinting paper Braithwaite (1931) (and Mellor, 1990, matter) 61 pages long. One might wonder what was doing 60 pages. The title work makes purpose clear: attempting construct foundations mathematics. Specifically, revise Mathematica (Whitehead & Russell, 1910) 2 order avoid saw three major defects. first third concerned with classes identity respectively, will set them aside. second defect is, ultimately, axiom reducibility. Russell employ ramified theory which, among things, requires ranges bound variables restricted only type, but order. Because this, one cannot talk about, instance, all functions from individuals propositions, n propositions. reducibility introduced attempt correct diminished power logic.