Contents, Contexts, and Basics of Contextuality

TL;DR

This paper introduces the theory of contextuality called Contextuality-by-Default (CbD), emphasizing that a variable's identity depends on both content and context, with implications for understanding empirical systems and their noncontextuality.

Contribution

It presents a non-technical overview of CbD, clarifying how context influences variable identity and addressing misconceptions about paradoxes and holistic views.

Findings

Contextuality is defined as the difference between content-based and context-based differences.

Deterministic systems are trivially noncontextual in CbD.

Epistemic systems can be modeled as random variables, extending the theory's applicability.

Abstract

This is a non-technical introduction into theory of contextuality. More precisely, it presents the basics of a theory of contextuality called Contextuality-by-Default (CbD). One of the main tenets of CbD is that the identity of a random variable is determined not only by its content (that which is measured or responded to) but also by contexts, systematically recorded conditions under which the variable is observed; and the variables in different contexts possess no joint distributions. I explain why this principle has no paradoxical consequences, and why it does not support the holistic "everything depends on everything else" view. Contextuality is defined as the difference between two differences: (1) the difference between content-sharing random variables when taken in isolation, and (2) the difference between the same random variables when taken within their contexts. Contextuality thus defined is a special form of context-dependence rather than a synonym for the latter. The theory applies to any empirical situation describable in terms of random variables. Deterministic situations are trivially noncontextual in CbD, but some of them can be described by systems of epistemic random variables, in which random variability is replaced with epistemic uncertainty. Mathematically, such systems are treated as if they were ordinary systems of random variables.