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Second‐Order Logic and Set Theory[Note 2. This paper is an attempt to survey, starting from ...]
Author(s) -
Väänänen Jouko
Publication year - 2015
Publication title -
philosophy compass
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.973
H-Index - 25
ISSN - 1747-9991
DOI - 10.1111/phc3.12229
Subject(s) - second order logic , set theory , set (abstract data type) , foundations of mathematics , order (exchange) , universal set , theory , computer science , first order logic , higher order logic , mathematical logic , abstract model theory , mathematics , calculus (dental) , description logic , theoretical computer science , algorithm , programming language , mathematics education , medicine , finance , dentistry , economics , physics , quantum gravity , quantum mechanics , quantum , relationship between string theory and quantum field theory
Both second‐order logic and set theory can be used as a foundation for mathematics, that is, as a formal language in which propositions of mathematics can be expressed and proved. We take it upon ourselves in this paper to compare the two approaches, second‐order logic on one hand and set theory on the other hand, evaluating their merits and weaknesses. We argue that we should think of first‐order set theory as a very high‐order logic.