Free agency and determinism: is there a sensible definition of computational sourcehood?

TL;DR

This paper explores a refined concept of computational irreducibility called computational sourcehood, aiming to formalize how certain processes inherently contain their own source of actions, impacting free agency and determinism debates.

Contribution

It introduces a formal analysis of computational sourcehood, linking it to simulation preorders on Turing machines and identifying key structural challenges in defining it.

Findings

Analysis of the relation between sourcehood and simulation preorders

Identification of structural obstacles to formalizing sourcehood

Highlighting the importance of structure-preserving functions in simulation

Abstract

Can free agency be compatible with determinism? Compatibilists argue that the answer is yes, and it has been suggested that the computer science principle of "computational irreducibility" sheds light on this compatibility. It implies that there cannot in general be shortcuts to predict the behavior of agents, explaining why deterministic agents often appear to act freely. In this paper, we introduce a variant of computational irreducibility that intends to capture more accurately aspects of actual (as opposed to apparent) free agency: computational sourcehood, i.e. the phenomenon that the successful prediction of a process' behavior must typically involve an almost-exact representation of the relevant features of that process, regardless of the time it takes to arrive at the prediction. We argue that this can be understood as saying that the process itself is the source of its actions, and we conjecture that many computational processes have this property. The main contribution of this paper is technical: we analyze whether and how a sensible formal definition of computational sourcehood is possible. While we do not answer the question completely, we show how it is related to finding a particular simulation preorder on Turing machines, we uncover concrete stumbling blocks towards constructing such a definition, and demonstrate that structure-preserving (as opposed to merely simple or efficient) functions between levels of simulation play a crucial role.