On Two Different Kinds of Computational Indeterminacy

Abstract

It is often indeterminate what function a given computational system computes. This phenomenon has been referred to as “computational indeterminacy” or “multiplicity of computations.” In this paper, we argue that what has typically been considered and referred to as the (unique) challenge of computational indeterminacy in fact subsumes two distinct phenomena, which are typically bundled together and should be teased apart. One kind of indeterminacy concerns a functional (or formal) characterization of the system’s relevant behavior (briefly: how its physical states are grouped together and corresponded to abstract states). Another kind concerns the manner in which the abstract (or computational) states are interpreted (briefly: what function the system computes). We discuss the similarities and differences between the two kinds of computational indeterminacy, their implications for certain accounts of “computational individuation” in the literature, and their relevance to different levels of description within the computational system. We also examine the inter-relationships between our proposed accounts of the two kinds of indeterminacy and the main accounts of “computational implementation.”

Computing in the nick of time

“…For example, in isolation, the very same system may be describable as implementing both an OR and an AND gate (Shagrir, 2001, 2020). Many solutions have been proposed to this problem, including ones that emphasize the importance of the context in which computing devices are embedded (for overview of the available views, see Curtis‐Trudel, 2022; Papayannopoulos et al, 2022). From our vantage point, however, the problem is an artefact of starting‐off with a conception of computing tasks that eschews matters of timing, which is inherently determined by the context in which a device is embedded.…”

“….5 Such a mechanistic view, or other some contextually-sensitive view of computational explanation, would have to be modified, however, if computation is not medium-independent (as discussed below). In the case of the mechanistic view, this would be simple to accommodate since computing mechanisms are a special case of functional mechanisms more broadly and instances of real-time computing will straightforwardly already qualify as mechanistic in this broader sense.6 Strictly speaking there are may be two sense of computational indeterminacy(Papayannopoulos et al, 2022): (i) how physical states of a device are grouped together relative to abstract states; and (ii) how the abstract states are interpreted to determine what function the device carries out. We believe neither of them present special problems in the case of real-time computing.…”

Computational indeterminacy and explanations in cognitive science

“…Let us make some general observations about IC and see some more examples. In what follows, we will adopt a distinction proposed by Papayannopoulos et al (2022) between two kinds of IC; an interpretative and a functional kind. Both species of indeterminacy pertain to computational individuation to a greater or lesser extent.…”

“… See Fresco et al (2021) andPapayannopoulos et al (2022) for examples.2 The term is due to Jack Copeland.…”