Self-knowledge and embedded operators

Abstract

Queen Anne is dead, and it is a fallacy to substitute a definite description for another designator of the same object in stating the content of someone's propositional attitudes. The fallacy can take subtle forms, as when Godel's incompleteness theorems are used to argue against mechanistic views of mind. Some instances of the fallacy exemplify a more general logical phenomenon: the set of principles satisfied by one sentential operator can differ from, and even contradict, the set of principles satisfied by another sentential operator coextensive with the first. These notions will be formally defined. The phenomenon will be explored through a series of example, with particular attention to the misapplication of G6del's results. According to the 'KK' principle, if one knows that something is so, then one knows that one knows that it is so. Although the principle, unqualified, is false, appropriately restricted or idealized versions of it may be true. What modes of presentation of oneself to oneself are relevant to such a qualified KK principle? Use the phrase 'singular term' broadly, for definite descriptions as well as names, demonstratives and pronouns, without prejudice to the question whether definite descriptions are quantifiers. For any singular term 't', 't knows that ...' is therefore a sentence operator. Relative to a fixed context, say that 't' fits the KK principle just in case for all P, if t knows that P, then t knows that t knows that P. Suppose (counterfactually) that in the context of its use by me 'I' fits the KK principle. Suppose also that, although I am in fact the man with a hole in his pocket, I do not know that I am the man with a hole in his pocket. In this context, does the definite description 'the man with a hole in his pocket' fit the KK principle? Suppose that the man with a hole in his pocket knows that it is sunny. Does it follow that the man with a hole in his pocket knows that the man with a hole in his pocket knows that it is sunny? It certainly follows that I know that it is sunny. Since 'I' fits the KK principle in this context, it follows that I know that I know that it is sunny. Thus the man with a hole in his pocket knows that I know that it is sunny. However, it does not follow that the man with a hole in his pocket knows that the man with a hole in his pocket knows that it is sunny, or that I know that the man with