green numbers give full details.     |    back to list of philosophers     |     unexpand these ideas

Ideas of Saunders MacLane, by Text

[American, fl. 1949, Professor of Mathematics at Chicago. A founder of Category Theory.]

1986 Mathematics: Form and Function
p.406 p.29 ZFC could contain a contradiction, and it can never prove its own consistency
     Full Idea: We have at hand no proof that the axioms of ZFC for set theory will never yield a contradiction, while Gödel's second theorem tells us that such a consistency proof cannot be conducted within ZFC.
     From: Saunders MacLane (Mathematics: Form and Function [1986], p.406), quoted by Penelope Maddy - Naturalism in Mathematics
     A reaction: Maddy quotes this, while defending set theory as the foundation of mathematics, but it clearly isn't the most secure foundation that could be devised. She says the benefits of set theory do not need guaranteed consistency (p.30).