Progressive Refinements
Understanding is a dynamic process: definitions evolve as understanding deepens. To capture this idea, we embrace principled ambiguity: an article is viewed as an ordered sequence of definitions, examples, and refutations, all aimed at elucidating a phenomenon. Individual definitions may be ambiguous, but the final set—formed by the most recent version of each definition—contains no ambiguities, even as the article preserves the path that led to that set.
Introduction
Understanding requires definitions. Below we describe an incremental approach to writing definitions through successive refinements. An article that aims to capture the essence of a phenomenon is viewed as an ordered sequence of definitions, refutations, extensions, and integrations. Each of these elements is marked by a dedicated block to facilitate scanning of the article and is assigned a unique identifier (UUID).
Objective
Guide the construction of an article that seeks to capture an idea using clear and appropriate definitions.
Context
Definition
A definition introduces a new name together with its associated meaning. To make definitions easy to locate, we present them using blocks that look as follows:
<description> NewName <description>.
Example
A definition may be followed by an example, introduced using a block as follows:
Example of what we mean by NewName.
Refutation
A refutation demonstrates that, within a given context, the current definitions lead to undesired or problematic consequences. It can therefore justify updating or replacing those definitions. While a refutation itself may be lengthy, the block highlights its key finding (and sometimes contains the refutation in full).
<content>
Extension
Definitions are introduced sequentially. If a definition D2 defines the same name as a previous definition D1, then D2 replaces D1 from that point onward.
This mechanism supports the introduction of definitions through successive refinements. Some properties of D2 may be inherited from D1, while others may contradict D1 in certain respects. In other words, D2 extends D1.
Integration
A definition DN represents the accumulation of all prior refinements from D1 onward — i.e., its integration. To avoid repeatedly reconstructing DN from earlier definitions, integrated versions are explicitly stated when necessary.
Result
Article :≡ List(Definition + Example + Refutation + Extension)
An article whose goal is to capture an evolving understanding of a subject can proceed by adding sections that introduce, extend, or refine definitions. Definition integration reduces the cognitive burden of reconstructing definitions from their history of refinements. Examples illustrate how the definitions operate in practice. Refutations motivate the addition or extension of definitions.