From Dr. Jonathan Miller’s Partial Translation of

The Philosophical Dialectic on the Art of Painting.


Arguments Concerning Painting


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At the same time, s, d, I, S, M, D, and O each name a primary property of a relation. Relations also have secondary properties, examples of which are: hue (h), intensity (i: hue-to-gray ratio in a color), and gray (g: white-to-black ratio in the “gray” element).

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This is a (linear) proposition that says, “Orange is identical in hue to brown.” “O-Ih-Bn” means the same thing

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“Red is similar in hue to orange,” or “R-Sh-O.”

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“Red is moderational in hue to yellow-orange.”

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“Red is dissimilar to yellow-green.”

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“Red is the opposite of green.”

In these examples:

I: The number of DIF relations = 0 [zero].

S: The number of SAM relations > the number of DIF relations, etc.

Here is a scale of the derived relations—a more precise way of naming these relations:

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Here is an M scale:

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Relational propositions can be joined to produce complex relational propositions. The following linear proposition describes three colors.

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Another secondary kind of relation is the spatial relation (s).

Another secondary kind of relation is spatial quantity (q).

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. . .

Where “Rx” stands for some relation:

Orientation, Ro, is different from direction (Rdx).

Color is a secondary kind of visual-field derived-relation, Rc. But color as a property has component properties, which are themselves tied to secondary kinds of derived relation—the kinds that should be considered are:

1. hue (Rh)

2. gray value (Rg)

3. value (Rv)—amount of light perceived—black to amount of light associated with pure white

4. purity (Rp)—black to (pure hue or pure hue with white or pure white)

. . .

Another secondary relation is group (Rgp).

. . .

In complex cases, there are groups within groups; for example where spatially defined groups are interlaced with color-defined groups in intricate patterns.

Difference relations can hold between groups. Derived relations can hold between groups.

Combinative relations: When Rx and Ry both hold between two objects, there appears a third relation, Rx+y, which is in some sense a combination of, or at least grounded upon, the first two.

Rc is probably an average of its components.

Two complex shapes can be compared in derived-relational terms (Rsh).

What is balance? Placement of point P, which presents a variety of Sq and Dq relations between the P-to-frame distances, such that a relation approaching a Mbal relation exists.

Relevant derived relations exist among single points, naturally defined groups, derived relations themselves, and among the parts of a shape’s contour.

. . .

To say that an image is moderation-rich is to say that it presents an abundance of moderation relations (M).

The claims for this dialectic include the following.

Statement 1: The awareness of moderation richness is, as a rule, a fundamental good (informal paraphrase: awareness of moderation richness makes us happy).

Statement 2: Many objects—including art found in the caves of Pashnaku, Shalleshatoh portraits, and Mahkat abstracts—are moderation-rich (both in 2-D and represented 3-D), and this is, at least primarily, what accounts for the high esteem in which they are held. (Other values partially account for this esteem—expression, for instance. But expression fails without moderation richness.)

Why does moderation richness affect us this way? We have evolved a faculty for the immediate enjoyment of perceiving that which unifies the many: the species among the individuals, the genera among the species, the natural law, the general theorem. We have evolved such a faculty because learning via the general is on the whole more efficient than learning via the particular, and all other things being equal, a species that is fitter to learn is fitter to survive. This faculty has a simple character, as defined in Statement 1 above. Thus the search in science for some fundamental natural law could be said to be the response to a primary functioning of the faculty (since the faculty is operating toward those ends toward which it was designed to operate, so to speak), while the painting of a picture would be a response to a secondary functioning of it.

We see something similar in music. In music each note is separated by twelve notes (an octave) from a note having the same letter name. These two notes are the same (they are both k’s, for instance, and possess a certain sameness of quality) and different (they are different k’s, for instance, and possess a certain difference of quality). The fact of their sameness implies the existence of a hue-circle-like oppositional dimension of twelve notes.

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Thus, for instance, f is oppositional to l, is similar to g and to h, is dissimilar to j and to k, and is moderational to i and to c.

In general if we play a series of notes, creating a melody on a keyboard, the most satisfying resolution occurs when the first note of the scale follows the fifth note—for instance when d follows k. Keeping in mind that e is oppositional to k, it may be seen as evidence for the moderationalist thesis that k, with its two moderation notes—b (midway between k and e, up) and h (midway between k and e, down)—are precisely those notes that, with d itself, make up the set of the first seven harmonics of d:





Thus, playing d after k repeats the k while supplying k’s moderation notes, creating a satisfying cadence.

It is interesting that the only two-note progression within a scale whose second note supplies no M notes at all to the first note is the 4--, 1-- progression—and when we arrive at the fourth note, generally in the middle of a phrase, we are indeed left hanging, having to work our way back to 1-- via the 5--.