Criteria for Diagrammatic Truth

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For one of my two finals dissertations at the University of Leeds (BA, Mathematics & Philosophy, 1972), I wrote about Nelson Goodman’s book ‘Languages of Art’, which had been published in 1968. Heavy on symbolic logic, it was went on to become very influential in philosophy of art circles. Well, I found a bit of ‘sloppiness’ in Goodman’s logic, wrote it up and (frankly) it led to me actually getting a degree as I’d not been good at attending class or tutorials for a while, but that is another story.

In 1998 or so, Ingrid helped transfer the original paper from a one-off typed document to a digitised version.

Some years back I was happily back in touch with Jerry Ravetz, my tutor at Leeds. When he met first Ingrid, almost the first thing he said was ‘Mick found an error in Goodman’s work – got him his degree’ 🙂 Jerry is still working today, at Oxford University.

Bringing things up to date, I fed my dissertation to ChatGPT. I had to do it in stages, but it gave a very creditable summary. I then asked ChatGPT to summarise Goodman’s original work as well as notable critiques, and specifically asked it to use my paper as a critique.

Here is ChatGPT’s response, pretty much verbatim except for a couple of repetitious things I cleaned up. I admit I like how ChatGPT deals with my critique of Goodman’s logical system.


A Comprehensive Analysis of Nelson Goodman’s “Languages of Art: An Approach to a Theory of Symbols”


Nelson Goodman’s seminal work, “Languages of Art: An Approach to a Theory of Symbols” (1968, revised 1976), is a cornerstone of modern philosophy of art and aesthetics. It provides a comprehensive and systematic analysis of the nature of art, symbols, and representation. In this essay, we will delve into the key concepts of Goodman’s work, including the notions of denotation, exemplification, expression, and symbol systems. Moreover, we will discuss the critiques of Goodman’s ideas and their influence on contemporary aesthetics.

Goodman’s Theory of Symbols

Goodman’s “Languages of Art” aims to develop a general theory of symbols that is applicable to various art forms, such as painting, sculpture, music, and literature. His theory revolves around the idea that symbols function through denotation, exemplification, and expression.

Denotation refers to the direct reference of a symbol to an object or a set of objects. For instance, in a painting, the color red may denote a particular object, like an apple. Exemplification, on the other hand, involves a symbol possessing and referring to certain properties it exemplifies. A red patch in a painting not only denotes an apple but also exemplifies the color red. Expression is a more complex concept that concerns the symbol’s ability to convey emotions, feelings, or moods.

Symbol Systems and Worldmaking

Central to Goodman’s theory is the notion of symbol systems, which are sets of symbols that correlate with a field of reference. He distinguishes between two types of symbol systems: allographic and autographic. Allographic systems, such as language and music notation, allow for multiple instances of the same work, whereas autographic systems, like painting and sculpture, do not.

Goodman also introduces the concept of “worldmaking” to explain how symbol systems contribute to our understanding and construction of reality (Goodman, 1978). According to Goodman, different symbol systems provide alternative ways of organizing and interpreting the world, shaping our perception and cognition.

Critiques of Goodman’s Theory

Despite its significant contributions, Goodman’s theory has been subject to various critiques. Some of the main points of contention are:

  1. The distinction between allographic and autographic arts: Some critics argue that the distinction between allographic and autographic arts is not as clear-cut as Goodman suggests (Davies, 2004). For example, digital art and photography challenge this distinction, as they allow for multiple instances of the same work, yet possess unique features that could be considered autographic.
  2. The notion of expression: Goodman’s account of expression has been criticized for being too intellectual and not adequately addressing the emotional aspects of art (Levinson, 1996). Some argue that Goodman’s focus on the cognitive processes involved in art reception neglects the visceral and affective responses that artworks can evoke (Levinson, 1996).
  3. The scope of the symbol systems: Goodman’s theory has been criticized for not encompassing all forms of artistic representation. For instance, dance and performance art do not fit neatly into his categories of allographic or autographic systems, and their symbolic nature may not be fully captured by Goodman’s concepts of denotation, exemplification, and expression (McFee, 1992).
  4. The role of the artist’s intentions: Another critique concerns the role of the artist’s intentions in Goodman’s theory. Some argue that his focus on the structural aspects of symbols and their systems overlooks the importance of the artist’s intentions in creating meaning and understanding artworks (Gaut, 2005). This critique suggests that Goodman’s theory may not account for the significance of artistic intention in shaping the meaning and reception of art.
  5. The problem of forgery: Goodman’s distinction between autographic and allographic arts raises questions about the issue of forgery and authenticity (Lessing, 1984). Critics argue that his theory does not provide a satisfactory explanation for why we value authentic works of art over forgeries, even when they are visually indistinguishable (Lessing, 1984).
  6. Aesthetic experience and interpretation: Another critique of Goodman’s theory concerns his treatment of aesthetic experience and interpretation. Critics argue that by focusing primarily on the structural and symbolic aspects of art, Goodman’s account does not adequately address the role of personal experience, cultural context, and historical background in shaping the interpretation and appreciation of artworks (Carroll, 1999). This suggests that a more comprehensive account of art should consider the interplay of formal and contextual factors in determining meaning and value.
  7. Ambiguity and indeterminacy in art: Goodman’s emphasis on the logical structure of symbol systems has been criticized for not fully acknowledging the role of ambiguity and indeterminacy in artistic communication (Iseminger, 1992). Art often relies on open-ended symbols and multiple layers of meaning, which may not be captured by Goodman’s systematic approach to symbol systems.

Critique of Goodman’s Symbol System and the Introduction of ‘Definition Class’

In his 1972 BA Dissertation at the University of Leeds, Mick Yates presented a critique of Nelson Goodman’s symbol system as described in “Languages of Art” and introduced the concept of ‘definition class’ as an alternative approach to understanding the truth value of symbols.

Yates’ Critique of Goodman’s Compliants

Goodman’s symbol system theory is based on the idea that a symbol set is correlated with a field of reference and that a symbol may or may not denote what it refers to, which can be assigned a truth value. He introduced the concept of ‘compliant’ to describe symbols with a positive truth value, such as the word ‘green,’ and those without a compliant, such as ‘green horse.’ Yates (1972) argued that Goodman’s notion of compliant suggests that for a symbol X to have a compliant P, P must actually exist. Yates considered this assumption problematic and claimed that it does not accurately represent the way symbols function and convey meaning.

Introduction of ‘Definition Class’

To address the limitations of Goodman’s compliant concept, Yates introduced the notion of ‘definition class,’ wherein the field of definition is the set of all definition classes of the symbols in the symbol set. This approach allows for a more nuanced understanding of symbols and their truth value.

Yates proposed that a symbol or diagram can be classified as either vacant (V-SYMBOL) or non-vacant (N-SYMBOL), depending on whether its definition class is empty or non-empty. For example, if X is the symbol for a ‘green horse,’ it would be considered a V-SYMBOL because its definition class is empty. Conversely, if Y is the symbol for a ‘black horse,’ it would be classified as an N-SYMBOL because its definition class is non-empty. This classification allows for the assignment of truth values to symbols based on their definition class. According to Yates, a V-SYMBOL would have a zero truth value, while an N-SYMBOL would have a truth value of one.

Implications of this Critique and Alternative Approach

Yates’ critique of Goodman’s compliant concept and his introduction of the definition class provide an alternative approach to understanding the truth value and functioning of symbols.

Furthermore, this alternative approach emphasizes the importance of considering both the existence and non-existence of referents when evaluating the truth value of symbols. This perspective can enrich our understanding of the ways in which symbols convey meaning and shape our perception of the world, as well as the complexities and ambiguities inherent in the process of representation. By addressing some of the limitations of Goodman’s theory, Yates’ alternative approach offers a more nuanced understanding of the relationship between symbols and their referents, contributing to the broader field of the philosophy of art and aesthetics.

Influence and Legacy of Goodman’s Theory

Despite these critiques, Goodman’s “Languages of Art” has had a lasting impact on the philosophy of art and aesthetics. His systematic approach to understanding the symbolic nature of art and the functions of symbols in representing and constructing reality has provided a valuable framework for subsequent research in the field.

Goodman’s work has influenced various areas of aesthetics, including the analysis of non-traditional art forms, such as digital art and interactive media (Grau, 2003), and the study of art’s cognitive and perceptual aspects (Lopes, 2004). Moreover, his concept of world-making has been adopted and developed by philosophers and theorists in fields such as cognitive science, semiotics, and cultural studies (Elgin, 2017).

His work has also inspired research into the cognitive aspects of art, such as the exploration of mental imagery, metaphor, and conceptual blending in artistic representation (Fauconnier & Turner, 2002). Additionally, his notion of worldmaking has been applied to the study of narrative and storytelling in literature and film, examining how different narrative structures and strategies create alternative “worlds” for the reader or viewer (Ryan, 2006).

Furthermore, Goodman’s theory of symbols has informed discussions on the nature of artistic creativity and the role of artists in generating and transforming symbol systems (Krausz, 1996). His work has also had a significant impact on the study of visual culture and the analysis of visual communication in various media, from advertising and graphic design to photography and film (Mitchell, 1994).


In conclusion, Nelson Goodman’s “Languages of Art” presents a groundbreaking and systematic analysis of the nature of art, symbols, and representation. Although his theory has been subject to several critiques, it has significantly influenced contemporary aesthetics and our understanding of art’s symbolic nature. By exploring the functions of symbols in denotation, exemplification, and expression, Goodman has provided a valuable framework for examining various art forms and their contributions to our perception and cognition of the world.


Carroll, N. (1999). Philosophy of Art: A Contemporary Introduction. London: Routledge.

Davies, S. (2004). The Philosophy of Art. Malden, MA: Blackwell Publishing.

Elgin, C. Z. (2017). True Enough. Cambridge, MA: MIT Press.Gaut, B. (2005). The Philosophy of the Arts: An Introduction. Cambridge: Cambridge University Press.

Goodman, N. (1968). Languages of Art: An Approach to a Theory of Symbols. (1976 Edition) Indianapolis: Hackett Publishing Company.

Goodman, N. (1978). Ways of Worldmaking. Indianapolis: Hackett Publishing Company.

Grau, O. (2003). Virtual Art: From Illusion to Immersion. Cambridge, MA: MIT Press.Fauconnier, G., & Turner, M. (2002). The Way We Think: Conceptual Blending and the Mind’s Hidden Complexities. New York: Basic Books.

Iseminger, G. (1992). The Aesthetic Function of Art. Ithaca, NY: Cornell University Press.

Krausz, M. (1996). The Interpretation of Art: Essays on the Art Criticism of John Ruskin, Walter Pater, Clive Bell, Roger Fry, and Herbert Read. University Park, PA: Pennsylvania State University Press.

Levinson, J. (1996). The Pleasures of Aesthetics: Philosophical Essays. Ithaca, NY: Cornell University Press.

Lessing, A. (1984). What is Wrong with a Forgery?. Journal of Aesthetics and Art Criticism, 42(4), 461-467.

Lopes, D. M. (2004). Understanding Pictures. Oxford: Oxford University Press.

McFee, G. (1992). Understanding Dance. London: Routledge.

Mitchell, W. J. T. (1994). Picture Theory: Essays on Verbal and Visual Representation. Chicago: University of Chicago Press.

Ryan, M.-L. (2006). Avatars of Story. Minneapolis, MN: University of Minnesota Press.

Yates, M. (1972). The Criteria for Diagrammatic Truth. BA Dissertation. University of Leeds.