Informal Concepts in Machines

TL;DR

This paper demonstrates the theoretical existence of machines capable of processing informal concepts like computable functions beyond traditional limits, proposing that such creativity is essential for machine intelligence.

Contribution

It introduces the concept of creative machines that can process informal concepts beyond Turing limits and develops hypotheses on their role in machine intelligence.

Findings

Existence of effective procedures generating non-enumerable functions.

Machines can process informal concepts beyond Turing machine limits.

Hypotheses on self-developing procedures for machine intelligence.

Abstract

This paper constructively proves the existence of an effective procedure generating a computable (total) function that is not contained in any given effectively enumerable set of such functions. The proof implies the existence of machines that process informal concepts such as computable (total) functions beyond the limits of any given Turing machine or formal system, that is, these machines can, in a certain sense, "compute" function values beyond these limits. We call these machines creative. We argue that any "intelligent" machine should be capable of processing informal concepts such as computable (total) functions, that is, it should be creative. Finally, we introduce hypotheses on creative machines which were developed on the basis of theoretical investigations and experiments with computer programs. The hypotheses say that machine intelligence is the execution of a self-developing procedure starting from any universal programming language and any input.