•  58
    A further reformulation of Naive Set Comprehension related to that proposed in “Resolving Insolubilia: Internal Inconsistency and the Reform of Naive Set Comprehension” is possible in which contradiction is averted not by excluding sets such as the Russell Set but rather by treating sentences resulting from instantiation of such sets as the Russell Set in their own descriptions as invalid. So the set of all sets that are not members of themselves in this further revision is a valid set but the c…Read more
  •  5
    Arithmetic Proof and Open Sentences
    Philosophy Study 2 (1): 43-50. 2012.
    If the concept of proof (including arithmetic proof) is syntactically restricted to closed sentences (or their Gödel numbers), then the standard accounts of Gödel’s Incompleteness Theorems (and Löb’s Theorem) are blocked. In these standard accounts (Gödel’s own paper and the exposition in Boolos’ Computability and Logic are treated as exemplars), it is assumed that certain formulas (notably so called “Gödel sentences”) containing the Gödel number of an open sentence and an arithmetic proof predi…Read more