Thesis

My eventual graduate thesis will be on the inconsistency of mathematics, and its implications. Topics will include:

• A proof of the inconsistency of all theories of mathematics in first-order logic.
• The equivalence of truth and provability, via Tarski’s truth schema.
• The equivalence of all first-order theories of mathematics, via the truth schema.
• The consequences of naïve set theory:
  • Properties of the set of all sets, including the combinatoric indescribability of its cardinality.
  • Infinitely deep sets, and a proof of the continuum hypothesis.
  • The existence of various large cardinals.
  • The existence of indefinable sets.
• Whatever I figure out about the “singularity point” of mathematics: the location of the border between consistency and inconsistency in the hierarchy of increasingly strong theories.
• My philosophy of mathematics, including mathematical nondualism: the view that every statement is ultimately true and false. As well as the view that formal proof does not solely dictate what propositions we are to accept.