Why Go¨del's theorem cannot refute computationalism
Artificial Intelligence
Ten Years of Hoare's Logic: A Survey—Part I
ACM Transactions on Programming Languages and Systems (TOPLAS)
Computation: finite and infinite machines
Computation: finite and infinite machines
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This article applies mathematical logic to obtain a rigorous foundation for previous inherently nonrigorous results and also extends those previous results. Roughly speaking, our main theorem states: any agent A that comprehends the correctness-related properties of software S also comprehends an intelligence-related limitation of S. The theorem treats the output of S, if any, as an attempt at solving a halting problem. Previous nonrigorous attempts to obtain similar theorems depend on infallibility assumptions on both the agent and the software. The hypothesis that intelligent agents and intelligent software must be infallible has been widely questioned. In addition, recent work by others has determined that well-known previous attempts use a fallacious form of reasoning; that is, the same form of reasoning can yield paradoxical results. Our main theorem avoids infallibility assumptions on both the agent and the software. In addition, our proof is rigorous, in the sense that in principle one can carry it out in Zermelo-Fraenkel set theory. The software correctness framework considered in the main theorem is that of Hoare logic.