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.
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