Views
Beliefs about Belief; meta-philosophy and meta-mathematics.
The Limitations of Logic
Inconsistency
Incompleteness
Gödel "proved it impossible to establish the internal logical consistency of a very large class of deductive systems" (Nagel and Newman).
Randomness
Further Reading
- http://metamath.org/
- The Metamath web site, an online archive of mathematical proofs.
- Meta Math! The Quest for Omega (PDF) and The Limits of Mathematics
- Accessible introductions to the analysis and limitations of formal axiomatic systems by Gregory Chaitin.
Axiomatic Utility
If a particular axiom causes needless suffering, discard the axiom. Balance this by being true to yourself and by accepting others as they are.
Truths and Falsehoods
Great truths can be illustrated through stories that are not literally true.