Symbol System

In the AI Story

Goodman's account of symbol systems rejected the copy theory of representation that had dominated aesthetics since Plato. A landscape painting, in the traditional view, succeeds by accurately reproducing the visual appearance of an actual landscape. Goodman demonstrated that this theory is incoherent: there is no single 'visual appearance' to reproduce, because what the eye sees is already organized by perceptual habits, cultural conventions, and the purposes of looking. The painting does not copy the landscape; it constructs a version of the landscape using the specific resources of pictorial representation—perspective, color mixing, compositional arrangement—and the version is no less real than the physicist's version in equations or the geographer's version in topographic maps. Each version reveals features the others miss, and each is answerable to standards of rightness internal to its symbol system rather than to a standard of correspondence with a version-independent reality.

The modes of symbolic reference Goodman identified—denotation, exemplification, and expression—operate simultaneously in most aesthetic works. A portrait denotes its subject, exemplifies certain visual properties (the density of brushwork, the palette's warmth), and expresses qualities it metaphorically possesses (dignity, melancholy, vigor). The interplay among these referential modes produces the work's cognitive contribution—the understanding it provides cannot be reduced to any single mode of reference. A viewer who attends only to denotation (what the portrait depicts) misses the exemplification and expression; a viewer who attends only to formal properties misses the denotational contribution. The cognitive engagement art demands is precisely this multi-modal attention to how symbols refer in multiple ways simultaneously.

Symbol systems differ in their formal properties—syntactic and semantic density versus differentiation—and these formal properties determine the kind of cognitive work the system can perform. Dense systems like painting provide for infinitely many discriminable marks, demanding continuous attention to minute variation; differentiated systems like musical notation provide discrete, clearly separated characters that permit reliable reproduction. The difference is not merely technical—it is epistemological. Dense systems yield the kind of understanding that comes from sustained attention to particular, unrepeatable configurations; differentiated systems yield the kind of understanding that comes from grasping general, reproducible structures. Both are genuine forms of knowledge, irreducible to each other.

The application to AI-generated outputs is structurally precise: large language models and diffusion models operate through differentiated symbol systems (tokens, pixels) to produce outputs that simulate the appearance of density. The simulation can be extraordinarily convincing—AI-generated prose reads smoothly, AI-generated images display subtle tonal gradations—but the underlying symbolic architecture remains fundamentally discrete. Between any two tokens the model might select, there is no intermediate token; the apparent continuity is an artifact of high resolution in a differentiated space, not genuine density. What this means for the cognitive value of AI outputs is the question Goodman's framework forces into view: whether the simulation of density is adequate for the cognitive functions that genuine density serves, or whether something irreducible is lost in the translation from the continuous to the discrete.

Origin

Goodman developed his symbol-system framework across the 1960s while writing Languages of Art, his most influential work. The book emerged from his attempt to apply the rigorous methods of analytic philosophy—formal logic, careful definition, systematic analysis—to questions about art that philosophers had largely abandoned to impressionistic criticism. His starting point was the observation that the same philosophical apparatus used to analyze scientific theories could illuminate how paintings, musical scores, and literary texts function as cognitive instruments. The insight was not that art is like science, but that both are worldmaking enterprises employing different symbol systems to construct understanding.

The technical vocabulary he developed—denotation, exemplification, expression, dense and differentiated systems—was designed to replace the vague, psychologistic language that dominated aesthetic theory. Terms like 'beauty,' 'emotion,' and 'expression' were, in Goodman's view, too imprecise to do philosophical work. His substitution of technical analysis for impressionistic description alienated some readers but established aesthetics as a domain where analytic philosophy could make genuine progress. The framework has proven durable precisely because it addresses formal properties of symbolic functioning that remain constant across technological changes—the same distinctions that illuminated the difference between painting and photography in 1968 now illuminate the difference between human-generated and AI-generated creative work in 2026.

Key Ideas

Symbols construct, not copy. Representations do not reproduce a pre-given reality—they construct versions of reality through structured reference, and multiple incompatible versions can all be right.

Three modes of reference. Symbols refer through denotation (labeling), exemplification (possessing and highlighting properties), and expression (metaphorical exemplification)—often simultaneously in the same work.

Formal properties determine cognitive function. Whether a symbol system is dense or differentiated, repletive or attenuated, determines what kind of understanding it can provide—aesthetic cognition characteristically requires density.

Rightness, not truth. Symbol systems are evaluated by rightness of rendering—coherence, fit, productivity, standards-compliance—rather than by correspondence to a version-independent world that does not exist.