formeelformeel

Formeelformeel is a theoretical concept in logic and linguistics that denotes a formal system capable of expressing statements about its own form, including its syntax, rules, and derivations. The term emphasizes meta-level reflection on form rather than content.

Origin and usage: The word is a coined Dutch-language neologism built from formeel (formal) and an intensifying reduplication, used in discussions of self-reference. It is not an established standard term, but appears in speculative or pedagogical contexts to illustrate how a system might internalize its own description.

Core idea: In a formeelformeel framework, there exists an encoding, or arithmetization, that represents the system's rules and symbols inside the system itself. This lets meta-statements about the system be formulated within the same language, enabling self-description and self-analysis while preserving a separation between object-level syntax and meta-level discourse in a single formal apparatus.

Consequences and limits: The construction supports fixed points and self-referential constructs, and it highlights relationships to Gödel's incompleteness phenomena and Kripke–Tarski style truth conditions. In practice, formulating a complete theory that both describes its own rules and proves all their consequences can lead to undecidability or inconsistency if pushed too far.

Applications and examples: The concept is used in thought experiments about self-describing grammars, meta-programming languages, and formal systems that include their own specification as data. A toy example might encode a rule like "the following statement is not provable" within the language and study its consequences.