Jane Frances McDonnell
Jane Frances McDonnell is a philosopher who focuses on the philosophy of mathematics and physics. She obtained her doctorate from Monash University in Victoria, Australia.
The Pythagorean World (2016)
[edit]- McDonnell, Jane (2016). The Pythagorean World: Why Mathematics Is Unreasonably Effective In Physics. Cham, Switzerland: Springer. ISBN 978-3-319-40976-4.
- 1. Mathematics is about the structure of Being.
- p. 206
- 2. Mathematics is necessary and true.
- p. 206
- 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.
- p. 206
- 4. Human mathematics is the cultural product of a community of rational beings.
- p. 206
- 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.
- p. 207
- 6. Mathematics is applicable because it truly describes the fundamental structure of reality.
- p. 210
- 7. There are rational beings with mental powers surpassing those of humans who have a deeper insight into mathematics than we do.
- p. 210
- 8. Model theory provides the correct picture of how mathematical languages describe mathematical reality.
- p. 211
- 9. No mathematics is surplus.
- p. 211
- 10. There is one, true mathematics.
- p. 217
- 11. There are no absolutely undecidable propositions in mathematics.
- p. 217
- 12. Some human mathematics is fiction.
- p. 217
- 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.
- p. 219