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
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
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
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
If a denotation has more than one symbol, then the system is
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:
- Character indifference: For any two characters the
instances of each characters are indifferent if for "each is an
inscription and neither one belongs to any character the other does
not" and so "no mark may belong to more than one character". This
means the set of characters must be disjoint. A "small a" or
small d" must be either a "a" or a "d," and not both. Goodman notes
that this is actually a very hard requirement since the world does
not come sorted into neat character-classes, but into marks that
vary in a myriad of ways. Character indifference does not rule out
the use of context, unless a mark can belong to two
character classes at once!
- Syntactic Finitely Differentiation: For every character
there must be some test that determines whether or not a mark
belongs to a particular character. This means the syntax is not
dense throughout (such that every mark can be a member of
the notation), although it is dense and so the syntax can be
called articulate. This is not the same as a finite
number of characters - Arabic fractional notation is articulate and
dense and there are infinite members. However, Arabic fractions are
syntactically dense since between each character there can
be a third. Note that this requirement is violated if any mark can
unless a given mark can not be determined to either belong to a
particular disjoint character or not.
- Compliance Class Disjointness: For any two semantic
compliance classes, they must be disjoint, so that no member of one
compliance class may be a member of another class. This is because
of the transitive nature of semantic compliance, the two classes
would effectively become one class. However, this does mean that
physically the two classes must be disjoint. Indeed, a
"county" and a "state" in the United States (or a "the city of
Edinburgh" and the "region of Lothian" are effectively disjoint.
Note that this rules out any semantic ambiguity.
- Semantic Disjointness: Not only must the semantic
compliance classes must be disjoint, but so must the compliance
class of each character. This example rules out most ordinary
languages even if we suppose them free of ambiguity."For example,
the compliance class of "horse" cannot be included with a more
particular term such as "Shetland pony" and neither can it with a
more general term such as "animal."
- Semantic Finite Differentiation: For every two
characters that do not have an identical compliance class, and for
every object that does not comply with either character, a test to
see if the object fits one compliance class or another must be
possible. This is parallel to the syntactic finite differentiation
condition. A scheme is semantically dense if there can always be
the insertion of a new compliance class without any disturbance.
For example, a "system consisting of fully reduced Arabic
fractional numerals taking as complaints physical objects according
to their weights in factions of an ounce fulfils the syntactic
requirements, but is semantically dense, and so violates the
condition of semantic finite differentiation since no limit is set
upon significant difference in weight, there will always be many
characters that even the finest measurement can attest that an
object does not comply with them all".
Using Art Possible Notational Systems
Here are some examples of notational systems:
- Music is a precise notational system for the most
part. However, even music is not a notational system. For example,
there are multiple ways to write a full note. Is any language a notational system? Perhaps computer programming languages.
- Painting is not a notional system, and its defining
power is given by its semantically dense varieties of color and
- Written and spoken "languages" are not notational
systems. Think about the difference of "sound-English" and
"object-Engish" - for example, the compliance class of individual
letters are sounds "k" while in general the compliance class of
words are objects. The compliance class of "k" is the pronunciation
of "k" while "kettle" has a semantic compliance class. These are
both syntactically notational systems, but semantically fail due to
- Literature is syntactically a notational system, but
semantically dense. The script of a work of literature, the actual
character inscriptions, are notational and can be copied, but the
semantics of the words are usually ambiguous.
- Dance? Possible?
- Art is simply the use of emotions and cognition in an
attempt to classify representations, and art shows both emotion and
cognition to be interdependent, and Goodman believes that the same
also holds true of science.