Notes on Goodman's "Languages of Art"


Neil Goodman is trying to define what it means to be a precise language, such as a musical notation, and in order to do this he tackles questions of representation and reference.

Here is some starter terminology. Goodman does not explicitly define these, and takes these and default terminology used in a "common-sense" manner I assume, but I think it is useful to be as explicit as possible with our terminology.

Object: Anything that can be distinct from anything else. This includes things such as emotions, the hue the setting sun puts over a valley, as well as more concrete things such as airplanes, Marvin Minsky, and the Eiffel Tower. Often this is used most naturally in a way when referring to physical objects, such as "extensions" in philosophy.

Mark: An object that has no meaning. Such as chicken-scratch. An inscription is thought of a mark that should have meaning as a component of some symbolic scheme, even if its meaning is unknown.

Reference (denote, signify): A non-physical relationship between an inscription and another object that is taken to be significant. The relationship is dyadic and directional. The object being referred to is the denotation (also often called a referent or meaning.) and the inscription that refers to the denotation is the representation or symbol. This is the relationship between the the British flag (representation) and the nation of Britain (denotation), or a picture of the Eiffel Tower (representation) and the Eiffel Tower (denotation) itself

Exemplification: The opposite of denote. For example, the actual Eiffel Tower exemplifies a monument. An actual dog exemplifies the word "dog."

Significant: Worthy of notice by an observer. An observer of some sort must be involved for anything to have meaning.

What is a Representation?

There is a difference between a representation and resemblance. In ancient Egyption hieroglyphs, often the symbol that was being used to denote something like a man often resembled (physically looked like) a man. However, the marks that form the word "corncob pipe" do not look like a corncob pipe. There are therefore many different types of representations for any given denotation, such as picture of the pipe, the word "pipe" written, the word "pipe" spoken, and so on. The type of representation that is a picture is a representation that resembles its denotation.

Representation as Extended Metaphor

Goodman believes that essentially all language is metaphor. Labels are way of classifying representation, an abstraction over representations and objects. Groups of labels are schemata. Every act of perception involves the use of schemata. The schemata that we use by default to classify an object is its literal interpretation. A unusual schemata applied to an object is metaphorical. However, there is no clear distinction: metaphors, once used enough, become literal interpretations. Metaphors are everywhere then, and are only the function of the age of the use of the schemata and the adequacy of the schemata than a fundamental difference between literal and metaphorical interpretation. For example, even numbers are higher and lower.

Note: no good definition of expression in Goodman I can find or property, so I'll make them up...

Property: An object that belongs to another object, and cannot be conceived as existing without that object. The object the property belongs to is not necessarily unique. For example, the color of the amethyst is purple, and so a purple color is a property of amethyst. Here's one test for a property: one can imagine the abstract concept of the color purple, but one cannot imagine it as an object by itself.

An object is an expression if it both exemplefies a property and metaphorically posesses it.

True and False

Having an interest in art, Goodman is interested in how one could possibly detect a fake Mona Lisa from the real Mona Lisa. Given any two objects, how can you tell an imperfect representation from its denotation? In cases, like in fake paintings, where the representation is a picture whose denotation is another picture, it can be very difficult. Is there a way to spot a difference that makes a difference? Goodman then claims that we can always find some difference on some level, but perhaps not through viewing the object using a normal schemata or methodology. A microscope might be necessary, and yet one can imagine two objects, one the "true" object and another a "false" copy, that are microscopically alike and similar. When considering a "false" copy the issue at hand is not the physical characteristics of the copy itself, but its history of production. A fake picture is one that was not painted by Van Gogh, and would still be fake even if the copy was exactly the same except that for the fact that it was made by a copycat instead of Van Gogh. Unlike pictures, music can be copied perfectly, so there must be a crucial difference. This is because the symbols of music compose a notational system.

What is a Notational System?

A notational system can be copied and still be the same - which is very close to the notion we use as ad digital. One thing to notice about "notational systems" is that their status of copies is transitive, so that a true copy of a true copy is also a true copy.

There are the five requirements of any notational system. They are divided into syntax and semantics.

Syntax: Representations qua marks. When describing notational systems, Goodman tends to use the word "symbol" instead of representation and a mark is called a character if belongs to a symbolic scheme and is defined as an inscription whose value both as a symbol and denotation has yet to be determined as part of a notational system.

Semantics:: The denotations of the inscriptions.

Dense: If for any symbol in the system, there is another symbol between it and the next symbol. A symbolic system that is not dense is articulate.

If a symbol has more than one denotation, then it is ambiguous.

If a denotation has more than one symbol, then the system is redundant.

The potential field of reference (total denotations) of a character is its compliance class and the denotations of the compliance class the compliants of that class. Inscriptions without compliants are vacant.

A syntactic inscription is either atomic or compound. An inscription if it contains no other inscriptions, and it is compound if it does. For example, the inscriptions of the alphabet "nam" when regarded as "n", "a", and "m" are atomic. "nam" as an inscription is compound. However, both "a" and "nam" can be separate and disjoint characters.

A semantic denotation is either prime or composite The use of "composite" is similar to the use of "compound" for syntax, as a semantic denotation is composite if it contains other denotations, however, an inscription is prime if it can not be thought of as composed of parts. For example in Goodman, "green" and "horse" are prime. Even though one can have the "head of a horse" it is till thought of as semantically being part of the horse. Likewise, "green horse" is a semantically vacant term, since it has no real compliance class - unless one puts imaginary objects as valid possible compliance classes.

A character is a potential symbol in a notational system.

Troublesome note on IV,4 - a symbol may or may not denote what it refers to (II), but cannot find distinction (Harry). May need a bit more clarity on difference between representation and symbol if any, and symbol and inscription.

Note the system is notational if:

  1. Syntax

  2. Semantics

Using Art Possible Notational Systems

Here are some examples of notational systems: