Equivalence of the Symbol Grounding and Quantum System Identification Problems

Abstract

The symbol grounding problem is the problem of specifying a semantics for the representations employed by a physical symbol system in a way that is neither circular nor regressive. The quantum system identification problem is the problem of relating observational outcomes to specific collections of physical degrees of freedom, i.e., to specific Hilbert spaces. It is shown that with reasonable physical assumptions these problems are equivalent. As the quantum system identification problem is demonstrably unsolvable by finite means, the symbol grounding problem is similarly unsolvable.

Building the Observer into the System: Toward a Realistic Description of Human Interaction with the World

“…The question of whether this semantic relationship can be considered fixed by causal processes and hence unique underlies the "symbol grounding problem" (SGP) [126,127] in cognitive science and AI. As "grounding" a symbol in the external world requires identifying the object, event, or class of objects or events to which it refers, the external SGP is equivalent to the problem of object or system identification [128]. Responses to the SGP range from treating the observer's world as a black box, at least methodologically [129], to considering essentially arbitrary components of the state of the world as components of the observer's cognitive state [130].…”

Equivalence of the Frame and Halting Problems

“…Determining the reference of a symbol and hence "grounding" it on the object(s) to which it refers requires identifying the referred-to object(s). If system identification is undecidable, the question of what object(s) ground any particular symbol is likewise undecidable [23]. While this has long been suspected on philosophical grounds [38], here we see it as a consequence of fundamental physical and information-theoretic considerations.…”

“…If identity over time is regarded as a property of an object or more generally, a system, the problem of re-identifying objects or systems as persistent individuals is equivalent to the FP [22]. If the denotation of a symbol is a persistent object or set of objects, the symbol grounding problem is equivalent to the object identification problem [23] and hence to the FP. Undecidability of the FP renders these problems undecidable.…”

A Model for Information

“…An IA can never be a complete description of a slice. This is the "blind men and the elephant" point discussed, for example, in [20] and [21]. So completeness does not fit well with intrinsic IQ.…”

“…Information is relative in a different sense-it depends on what is measured, how it is measured and the processes which deliver the information to an IE. It is impossible to capture the entire state of a slice (see [20,21]). However, once the information is measured it may be sensed, interpreted, combined and transmitted many times.…”