Editorial to the theme issue on metamodelling

摘要

Linguistics, Mathematics, and Computer Science are inherently reflective disciplines. Linguists use language to talk about language. Mathematicians use mathematical methods to study mathematics itself, and Computer Scientists describe descriptions in order to facilitate automation. For instance, one of the most important concepts in computer science, the universal Turing machine, can be regarded as a program that executes other programs.rnAll the above examples of self-application are variations of a common "meta" theme. All of them require care in avoiding paradoxes which may be caused by uncontrolled self-reference. Linguists are faced with associating semantics to sentences like "This statement is false." This self-referencing sentence is commonly referred to as "The Liar" and its semantics refuses assignment into "true" and "false" categories. Linguists, therefore, strictly distinguish between "metalanguage" and "object-language" to avoid the paradoxical nature of such antinomies. Mathematicians had to abandon naive set theory because of Russell's set paradox, which is nothing else but a mathematical version of the aforementioned "Liar". Computer scientists have to deal with both the blessing and curse of self-referencing programs and descriptions. On the one hand, we can use this power to build interpreters which may even be parametrised with a language definition, on the other hand we have to deal with non-terminating programs and potentially inconsistent circular definitions.