Arithmetical self-reference through diagonalization is compared with self-recognition in a mirror, in a series of diagrams that show the structure and main stages of construction of self-referential sentences. A Gödel code is compared with a mirror, Gödel numbers with mirror images, numerical reference to arithmetical formulas with using a mirror to see things indirectly, self-reference with looking at one’s own image, and arithmetical provability of self-reference with recognition of the mirror image. The comparison turns arithmetical self-reference into an idealized model (...) of self-recognition and the conception(s) of self based on that capacity. (shrink)

The notion of interaction and interaction machines, developed by Peter Wegner, includes the comparison between incompleteness of interaction machines and Gödel incompleteness. However, this comparison is not adequate, because it combines different notions and different sources of incompleteness. In particular, it merges syntactic with two senses of semantic completeness, and results about truth with results about provability and their consequences . The comparison also overlooks structural differences in the way diagonalization produces incompleteness. More generally, the comparison is unlikely because interaction (...) incompleteness is supposed to come from a system's involvement with its environment, whereas Gödel incompleteness comes from a system's involvement with itself. (shrink)

Evaluating the usefulness of Davidson's semantics to computational understanding of language requires an examination of the role of a theory of truth in characterizing sentence meaning and logical form, and in particular of the connection between meaning and belief. The suggested conclusion is that the relevance of Davidson's semantics for computational semantics lies not so much in its methods and particular proposals of logical form as in its general orientation towards "desubstantializing" meaning.

Evaluating the usefulness of Davidson's semantics to computational understanding of language requires an examination of the role of a theory of truth in characterizing sentence meaning and logical form, and in particular of the connection between meaning and belief. The suggested conclusion is that the relevance of Davidson's semantics for computational semantics lies not so much in its methods and particular proposals of logical form as in its general orientation towards "desubstantializing" meaning.

The kind of self-reference which Perlis characterizes as strong, as opposed to formal self-reference which he characterizes as weak, is actually already present in standard forms of formal self-reference. Even if formal self-reference is weak because it is delegated, there is no specific delegation of reference for self-referential sentences, and their ‘self’ part is strong enough. In particular, the structure of self-reference in Godel's sentence, with its application of a self-referential process to itself, provides a model of Perlis’ characterization of (...) a self. This structure can also be interpreted visually, in a way relevant to self and consciousness, namely as self-recognition in a mirror. (shrink)