The Logic of Mathematical Discovery

• "Nobody will doubt that some problems about a mathematical theory can only be approached once it has been formalized, just as some problems about human beings (say concerning their anatomy) can only be approached after their death."
• Dogmatism vs Scepticism
  • Dogmatists believe that with the intellectual capacity of human beings, truth can be achieved/known and it can be known when truth is achieved/known.
  • Sceptics believe that we cannot attain truth at all or even if we do there is no way to know if we have attained it, further, it might be impossible to know whether we can attain it or not.
• A "proof" is the decomposition of a conjecture to many sub-conjectures.