Publication 3082

Kampis G. (1995) Computability, self-reference, and self-amendment. Special Issue on Self-Reference in Biological and Cognitive Systems Communication and Cognition – Artificial Intelligence 12(1–2): 91–109. Fulltext at https://cepa.info/3082
There exist theories of cognition that assume the importance of self-referentiality and/or self-modification. We argue for the necessity of such considerations. We discuss basic concepts of self-reference and self-amendment, as well as their relationship to each other. Self-modification will be suggested to involve non-algorithmic mechanisms, and it will be developed as a primary concept from which self-reference derives. A biologically motivated mechanism for achieving both phenomena is outlined. Problems of computability are briefly discussed in connection with the definability and describability of self-modifying systems. Finally, the relevance of these problems to applications in semantic problems of cognition is shown. We proceed in the following way. The paper starts with an outline of the evolutionary approach to cognition, as that context where the problems of circularity and recursiveness can be raised. Next, complete and incomplete forms of self-references are discussed. The “causal” theory of self-referentiality is reviewed, and a thought experiment is presented, which points out that no computable model for complete self-reference can exist. On the other hand, constructive definitions are shown to offer a framework where “selfdefining” and self-modifying systems, if such exist in reality, can be formulated. Studying the realization problem, a general abstract model is given, and a “biological computation” mechanism that corresponds to it is outlined. The underlying phenomenon, called “shifting reading frame,” is discussed in relation to how self-referentiality can be achieved through self-modification. The applicability of the approach to the autonomous definition of semantic relations in symbol systems, that may allow for a kind of autonomous “symbol grounding,” is discussed.

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