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Quotes from The Pythagorean World — Jane Frances McDonnell

← All quotes by Jane Frances McDonnell

13 quotes

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

The Pythagorean World (2016)

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

The Pythagorean World (2016)

11. There are no absolutely undecidable propositions in mathematics.

The Pythagorean World (2016)

1. Mathematics is about the structure of Being.

The Pythagorean World (2016)

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.

The Pythagorean World (2016)

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

The Pythagorean World (2016)

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

The Pythagorean World (2016)

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.

The Pythagorean World (2016)

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.

The Pythagorean World (2016)

12. Some human mathematics is fiction.

The Pythagorean World (2016)

2. Mathematics is necessary and true.

The Pythagorean World (2016)

10. There is one, true mathematics.

The Pythagorean World (2016)

9. No mathematics is surplus.

The Pythagorean World (2016)

Attribution

Quotes and notes from Wikiquote: Jane Frances McDonnell (page history), available under CC BY-SA 4.0.