Jane Frances McDonnell

"1. Mathematics is about the structure of Being."

"2. Mathematics is necessary and true."

"3. Mathematical objects do not exist in a mysterious Platonic heaven totally independent of the physical world. Rather, physical reality is a mental interpretation of a subset of mathematical structure."

"4. Human mathematics is the cultural product of a community of rational beings."

"5. We come to know about mathematics by abstracting structure from the world around us and focusing on the structure of Being mirrored in us."

"6. Mathematics is applicable because it truly describes the fundamental structure of reality."

"7. There are rational beings with mental powers surpassing those of humans who have a deeper insight into mathematics than we do."

"8. Model theory provides the correct picture of how mathematical languages describe mathematical reality."

"9. No mathematics is surplus."

"10. There is one, true mathematics."

"11. There are no absolutely undecidable propositions in mathematics."

"12. Some human mathematics is fiction."

"13. The universe of sets V cannot be Gödel’s L; it must be something like Woodin’s Ultimate L which contains all possible large cardinals and has the semantic resources to witness them."