Abstract
Although the formalizations of computability provided in the 1930s have proven to be equivalent, two different accounts of computability may be distinguished regarding computability as an epistemic concept. While computability, according to the epistemic account, should be based on epistemic constraints related to the capacities of human computers, the non-epistemic account considers computability as based on manipulations of symbols that require no human capacities other than the capacity of manipulating symbols according to a set of rules. In this paper, I shall evaluate, both from a logical and physical point of view, whether computability should be regarded as an epistemic concept, i.e., whether epistemic constraints should be added on (physical) computability for considering functions as (physically) computable. Specifically, I shall argue that the introduction of epistemic constraints have deep implications for the set of computable functions, for the logical and physical Church-Turing thesis—cornerstones of logical and physical computability respectively—might turn out to be false according to which epistemic constraints are accepted.
Highlights
Computability historically deals with functions of positive integral arguments with values 0 or 1 that are effectively computable—even though whether an arbitrary function is computable, e.g., on arbitrary strings of symbols, can be investigated
The epistemic account of computability regards computability as an epistemic concept, which should be based on epistemic constraints related to the capacities of human computers
I shall argue that the introduction of epistemic constraints have deep implications for the set of computable functions, for the logical and physical Church-Turing thesis—cornerstones of logical and physical computability respectively—might turn out to be false according to which epistemic constraints are accepted
Summary
Computability historically deals with functions of positive integral arguments with values 0 or 1 that are effectively computable—even though whether an arbitrary function is computable, e.g., on arbitrary strings of symbols, can be investigated. From a logical point a view, the logical Church-Turing thesis (CTT)—according to which effectively computable functions are computable by Turing machines—seems to be preserved whatever the account that is considered. Arguments against the CTT can be developed if the relationship between human computers and computability is strengthened, i.e., if specific epistemic constraints—such as the one proposed by [6]—are added to computability. The formulation of the PCTT that is considered in this paper may be set out as follows: functions that are computable by physical processes are computable by Turing machines.
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