Feasibilism, Explication, and the Cobham-Edmonds Thesis

2026-06-30

AI Summary

The Cobham–Edmonds thesis identifies feasible computation with the complexity class P, yet its philosophical and logical foundations are considerably less robust than those of the Church–Turing thesis. This work proposes a systematic defense framework analogous to that traditionally employed for the Church–Turing thesis, integrating philosophical analysis, conceptual clarification, and formal tools from computational complexity theory. By carefully distinguishing between “useful assumptions” and “necessary characterizations,” the paper advances several rigorous arguments in support of the Cobham–Edmonds thesis. These arguments collectively strengthen the theoretical standing of P as the appropriate formalization of feasible computation and deepen our understanding of the nature of feasibility in computational practice.

Abstract

While the Church-Turing thesis asserts that effective calculability explicates to sets decidable by a Turing machine, the Cobham-Edmonds thesis asserts that feasible computation explicates to the complexity class $\mathsf{P}$, those decidable by a polynomial-time bounded Turing machine. The Church-Turing thesis has been placed under rigorous scrutiny and has several convincing arguments in its favor, but the Cobham-Edmonds thesis has not undergone a similar examination. Many of the arguments in its favor simply suggest that $\mathsf{P}$ is a useful assumption, rather than a necessary target. This paper presents analogous arguments in favor of the Cobham-Edmonds thesis.

Problem

• Feasibilism
• Explication
• Cobham-Edmonds Thesis
• Computational Complexity
• Polynomial Time

Innovation

• Feasibilism
• Explication
• Cobham-Edmonds Thesis
• Computational Complexity
• Polynomial Time