Feasible constructivism

TL;DR

This paper introduces feasibilism, a constructivist approach based on polynomial-time computability, to address issues in intuitionism and strict finitism, formalized through Buss's bounded arithmetic.

Contribution

It develops feasibilism as a plausible constructivist view using polynomial-time bounds, formalized via Buss's bounded arithmetic, resolving sorites paradox issues.

Findings

Feasibilism aligns with polynomial-time computability.

Buss's bounded arithmetic formalizes feasibilist principles.

Addresses and resolves sorites paradox in constructivism.

Abstract

Dummett's argument for intuitionism is well known. There is a concern that the argument proves too much, specifically, that it supports the extreme and apparently incoherent position of strict finitism. The central question is how to explicate the notion that it is possible in practice to construct an arithmetical term or verify a statement. The strict finitist answer is plagued by the sorites paradox. We propose and develop feasibilism as a more plausible view, where computational feasibility, as captured by the class of polynomial-time problems, yields a robust and expedient explication of "possible in practice". In this approach, the complexity is bounded by a polynomial function of the input size, rather than bounded by a constant (as in strict finitism), thus resolving the sorites issues. We show that a system of strictly bounded arithmetic, introduced by Sam Buss, precisely formalizes the feasibilist view so as to satisfy Dummett's requirements.