What's in the dictionary (or Is It?)*

Abstract

We develop a formal framework in which to study dictionaries satisfying a seemingly desirable property. A dictionary is said to be closed if every word used in that definition is itself defined (elsewhere in the dictionary). We show that any closed dictionary is degenerate: all words have the same meaning. Implications of this result are discussed, as well as potential remedies.

Acknowledgement

The authors wish to thank an editor for helpful comments on both the structure and presentation of the paper.

Notes

¹We cannot resist mentioning another quote, this from Richard Garnett in 1835: “[T]he only good English dictionary we possess is Dr. Jamieson's.”

²Thus the basic version of our model is akin to some of the simpler methods of lexical disambiguation in computational linguistics.

³A slightly more standard alternate formulation is that every graph has a unique decoration.

⁴It has not escaped the authors' attention that one corollary to the theorem is that this paper could have been written more succinctly: Ω.

⁵Formally, a dictionary is closed if for all entries w _i , TC(w _i ) ∩ D ⫅ D\A. That is, all words in the transitive closure of w _i must be entries in the dictionary.

⁶Altmann & Kind (1983) speculate that the inverse relationship between levels and their size is due to the hierarchical conceptual nature of human memory.