Explanation
A diagram is a sign that represents relations in its object through traceable relations among its own elements. Distance, direction, connection, enclosure, or position on an axis performs structural work without necessarily resembling the object's outward appearance. Diagrams may measure, explain, compare, or support inference, yet every representation involves selection, convention, and transformation. Apparent immediacy must therefore not be confused with neutrality. The conceptual movement translates a domain into spatially or formally ordered relations, tests the mapping rule, and then reads newly visible connections from the constructed form back into the domain.
Movement of thought
1. A domain is first analysed into relevant units, quantities, and relationships. 2. A representational rule maps those relations onto visual, spatial, or formal relations in the sign. 3. The viewer follows lines, positions, and differences to reconstruct the represented structure. 4. A counter-test examines scale, selection, legend, and omission rather than taking visual evidence for granted. 5. New comparisons or inferences may arise within the model and are then referred back to its object.
Scientific use case
Semiotics, scientific visualisation, and diagram studies examine what operations representations enable and what decisions they conceal. Reproducible data binding, legends, and accessible alternatives are central criteria.
Example
A network map places concepts as nodes and attested relationships as differently coded lines. Spatial proximity means semantic proximity only if that mapping has been defined explicitly.
Counterexample
A decorative image is not a diagram when arrangement of its parts carries no systematic relation to the object. An impressive graphic may also mislead if its scale or mapping rule changes unnoticed.
Distinction
Distinguish a diagram from illustration as pictorial depiction, a table as primarily cellular arrangement, and a map as spatial representation. Diagrams represent through rule-governed relations among their parts.
Effect on thought and perception
Diagrams condense complex relations and make patterns visible and manipulable. Their persuasive force may nevertheless conceal uncertainty, absent data, or normative selection.
Resonance
Relations in the object acquire a second body of lines, areas, and distances. Within this model, structures can answer that had remained silent in the material.
Cite this entry
Reich, Michael (Hrsg./ed.): „Diagram“. Atlas der Sprache, AT-119-039. ATLAS 260, data model 1.6.0. https://atlasoflanguage.com/concept/AT-119-039The address remains stable; editorial content may evolve. Editorial reading state: 2026-10-15. Include your access date for precise references.
Historical background
Peirce’s diagrammatic reasoning proceeds through constructing a representation, attending to its relations and making permitted transformations that reveal further relations. The diagram is not useful merely because it is easier to look at than a sentence. Its arrangement must preserve the structure relevant to the inference, while incidental graphic features must not be mistaken for properties of the object. The 1904 and 1906 passages therefore make a diagram an instrument of inquiry rather than an illustration added after reasoning has finished. For the Atlas, this supplies a historical basis for asking what a graphic enables a reader to discover and how that discovery can be checked. An elegant arrow or proximity on a page is not itself evidence of a semantic or causal relation. The representational convention has to be stated. These manuscript excerpts are accessed through a later compilation and have not been collated with the originals. They document Peirce’s treatment, not the much older history of diagram as an English word or the origin of geometrical diagramming.
How conceptual history changes the analysis
Diagrammatic evidence requires a tested relation between representational rule and object.
References for the historical section
- Charles S. Peirce, primary passages identified by work/date and Collected Papers paragraph or manuscript number; online compilation by Joseph Ransdell, The Role of Icons in Predication (2005) · MS 517, Eisele IV:238 (1904); MS 339.544, Logic Notebook (1906)
Named primary excerpts read in the online compilation, not collated against original manuscripts. CP numbers are paragraphs, not pages; approximate dates remain approximate. The compilation is not proof of first coinage. Changes across Peirce’s classifications must not be flattened into a single immutable system.