TY - JOUR AU - WEBER, Z Y2 - 2014/05/22 Y1 - 2010/03 SN - 1755-0203 UR - http://hdl.handle.net/11343/31746 AB - This paper begins an axiomatic development of naive set theory—the consequences of a full comprehension principle—in a paraconsistent logic. Results divide into two sorts. There is classical recapture, where the main theorems of ordinal and Peano arithmetic are proved, showing that naive set theory can provide a foundation for standard mathematics. Then there are major extensions, including proofs of the famous paradoxes and the axiom of choice (in the form of the well-ordering principle). At the end I indicate how later developments of cardinal numbers will lead to Cantor’s theorem, the existence of large cardinals, and a counterexample to the continuum hypothesis. LA - en PB - Cambridge University Press (CUP) KW - Philosophy T1 - TRANSFINITE NUMBERS IN PARACONSISTENT SET THEORY DO - 10.1017/s1755020309990281 IS - The Review of Symbolic Logic VL - 3 IS - 1 SP - 71-92 L1 - /bitstream/handle/11343/31746/281306_150541.pdf?sequence=1&isAllowed=n ER -