The structure of analog representation

Abstract

This paper develops a theory of analog representation. We first argue that the mark of the analog is to be found in the nature of a representational system's interpretation function, rather than in its vehicles or contents alone. We then develop the rulebound structure theory of analog representation, according to which analog systems are those marked by the use of interpretive rules that map syntactic structural features onto semantic structural features. The theory involves three degree-theoretic measures that capture three independent ways in which a system can be more or less analog. We explain how our theory improves upon prior accounts of analog representation, provides plausible diagnoses for novel challenge cases, extends to hybrid systems that are partially analog and partially symbolic, and accounts for some of the advantages and disadvantages of representing analogically versus symbolically.

Contents and Vehicles in Analog Perception

“…While it is typically treated as binary (prima facie the distinction seems to mark a difference in kind), there are dissenters. For example, Lee et al (2022) maintain that analog representation is graded along multiple dimensions. In defense of this claim, they construct hypothetical cases of artificial representational systems and argue that a graded account best accommodates the intuitions that these cases engender.…”

“…On some of those precisifications, the concept will emerge as graded. Lee et al (2022) provide one account of what such a graded precisification might look like. Kulvicki (2015) provides another.…”

The Formats of Cognitive Representation: A Computational Account

“…Existing theories of representational formats can be grouped into three broad categories, depending on what conceptual component of the notion of representation they take to be central to individuating formats: contents, vehicles, or the function from the former to the latter (Lee et al 2022).…”

“…The third family of views, the function-based account, is often conflated with the former two and especially with the vehicle-based one. This account has it that representational formats are individuated by the function that maps vehicles into contents (Lee et al 2022). A view along these lines might, for example, identify a type of format in terms of vehicles structurally resembling, or mirroring, their contents (Beck 2018).…”

Organized representations forming a computationally useful processing structure

“…Two dances performed on different occasions are temporally related-they are separated by time t. But the temporal separation t is not something consumer bees are sensitive to or that otherwise enters into downstream computations. Similarly for the places at which two dances are performed (within the hive, or when the hive moves).4 Lee et al (2023) put organization-what they call 'analog mirroring'-at the centre of their account of what it is to be analogue.…”