Monday, February 22, 2010

The Vicious Möbius Reference Principle

The Vicious Möbius Reference Principle (VMRP) describes a collection of propositions that together create a contradiction. This collection of propositions has the following properties:
  • The collection consists of a finite number of propositions.
  • Each proposition refers to one other proposition in the collection.
  • The collection contains a finite, odd number of negative references, each of which is a negative statement regarding the proposition to which it refers.
  • The propositions can be chained to form a circular sequence. That is, each proposition refers to the following one and the last one refers to the very first one.
My goal is to accomplish the following:
  • Formal and rigorous definition of the Vicious Möbius Reference Principle. This will provide a definition of a class of paradoxes, such as the famous Liar's Paradox, Russell’s Paradox and the lesser known Hebrew Calendar Paradox. On the other hand, while the Surprise Paradox is self-referential proposition, it does not conform to VMRP.
  • Create a formal exclusionary rule. By excluding any proposition that conforms to the Vicious Möbius Reference Principle it may be possible to create a subset of a formal mathematical system that is free of contradictions.