Tuesday, July 19, 2011

Outlines 2

Although it is somewhat of a blunt instrument, mathematical logic is the only tool, I feel, that is capable of giving a field which hitherto has not had adequately rigorous theoretical grounding.


The thesis of this book boils down to this:

(1) "Ordered sequences of images and text consist of a series of assertions about a conceptual world."

(1.1) "In order to make sense of the assertions given, there must be a grammar around which a visual language is formed."

(1.1.1) "The grammar of this language can be adequately described by first order logic (F.O.L.)."

Descriptive language consists of assertions of the form, "It is the case such that p is true", or:
  1. ⊢p

Wednesday, July 13, 2011

Let ">" be an asymmetrical two-place predicate such that a is the "predecessor" of b, and b>a is false for ">", if {a, b, c, ...} form a well-ordered set.

Let P1 and P2 be any arbitrary sets on L.

⊦⌜ a>b⌝ & [a∈P1 & b∈P2 ] ⊃ ⌜P1>P2

Tuesday, February 22, 2011

Part I, Chapter 1: Fundamentals, Section 1.7

§1.7) Comics as Language, Separate from Art

Is it possible for pictures to denote logical statements in language? Ordinarily, no. For example, an image of a cat on a mat can certainly be understood, insofar as it can be seen by an entity with visual apparatus compatible with our own, but without the referential concepts of "cat", "mat" and some conceptual understanding of "on", it will appear to that entity as a bundle of shapes and colours. It requires, therefore, the existence of a surrounding linguistic context, which I call "concept-space", to establish the necessary semantic apparatus for pictures to denote statements. This is why abstract art seems confusing to some people, upon first viewing, as they have not entered the concept-space necessary to provide the viewer with a ready supply of concepts to understand the ideas denoted by the visual objects.

In the example given earlier, one must already have an idea of what a cat and a mat is, and be able to draw the abstract relation from this concept space to understand what the complex of visual objects in the picture means. It is then understood that the picture contains two certain elements, let us call them "c" for "cat" and "m" for "mat". In addition, the concept-space must also contain a universe of predicate relations, if the viewer is to be able to establish syntactic relations between elements in any given picture. Therefore, the concept of "On", in the example, is a dyadic relation "R" that also exists within the concept-space of the picture.

It is only when the concept-space is understood, that we can truly say that the picture of a cat on a mat, denotes the logical statement "cRm".

This has definite applications to the theory of comics. For one, all comics, I think, draw upon the same concept-space -- that all comics are commonly understood to be attempting to convey a meaningful series of sentences, in visual form. I...t is generally understood that comics will have some distinct sequence of images, and in most cases, text. This distinguishes them from art alone, because while individual artistic pieces draw upon their own individual concept-space, all comics, by virtue of being comics in themselves, must draw from one general concept-space; all comics must in some way show some sequence of events in a world, and must do so in a certain order if the sequence is to be understood.

Hence, it is always possible to draw linguistic inferences from objects denoted in a comic layout -- they are, in a sense, always pictures of a state of affairs, a representation of a world of facts, in the Wittgensteinian[1] sense, and whose facts, being the individual elements of a comic layout, are connected by definite syntactic relations. That is to say, while a painting of a cat on a mat may not be equivalent of the sentence "the cat is on the mat", as in the concept space of the painting in question what appears on the painting may be quite different from consensual conceptions of what a cat and a mat are in reality -- that a painting may denote a cat and a mat without being a one-for-one representation of a cat and a mat -- a comic showing a cat on a mat, by virtue of it being a comic, will always have a one-for-one relation to the sentence "the cat is on the mat".

This is because, as a sentential representation of some given sequence of events, a comic must establish the semantic correspondence between its images and the desired sentence in language, if there is to be any communication at all.

What, then, is the precise difference between an individual piece of art, and a comic?

Consider a picture of a vase on a table. A vase on a table in reality is something different from the phrase "a vase on a table", is something different still from a... picture of a vase on a table. The vase on the table in reality is a pile of atoms, interacting via physical laws, with another pile of atoms. Beyond that, there is nothing we can say. Sam, my artist friend, said that "Of course the vase on the table! I see the vase, and somewhere near the table, and so it's obviously on the table. You'd have to be a very bad artist for it not to have the property of 'on' the table." Herein is a distinction. I separate the linguistic property "on" from that collection of colours on a flat 2-d sheet, which reflect light into my eyes in such a way that my brain connects these shapes to some memory of vases and tables. I also separate the linguistic property "on" from the world of atoms interacting with each other through the physical forces of nature.

There is no "on" in nature. You cannot run the Large Hadron Collider high enough to produce evidence for a particle that means the word "on". No matter how deep you dig, how high you fly into the heavens, you will never be able to reach out your hand and isolate so intangible an idea as "on". To propose otherwise is Platonism.

Here is a painting. It is a collection of shapes and textures, on canvas. The paints have colours, and are arranged in all sorts of ways. Human beings with eyes can see this painting and connect the shapes it makes in certain ways to things in their experience. But what meaning exists in the paint itself? If there were no humans to see it, would the artist's concept of whatever he painted still be inscribed in the painting, embedded into the world as if he had plucked the concept out of his brain and put it into a jar of formaldehyde? This is patently ludicrous.

Draw back from the world of just paintings, to the world of "art" in general. Consider a Ming vase, a 20,000 year old Aboriginal cliff drawing, the pattern on a Zulu shield, a Navajo blanket, "Fountain" by Marcel Duchamp, and Da Vinci's fresco of the Last Supper. What do these all have in common, if art is to be some kind of "language"? They express a thing, so far as they are made to evoke some kind of memory, feeling, or image in the minds of humans. But what is this thing? Does the structure of the "thing" evoked by any of these items bear any resemblance to the structure of the "thing" evoked by any other? Is the African mask really saying something in the same way as my saying "Hi there everyone, I'm Anh-vu and I am arguing with you!" Any individual work of art can mean something different, evoke something different, in each person who sees it. Certainly the sense-data are similar insofar as we are all "seeing" it, but how do these sense-data assemble to make sense in our minds? Regularly or irregularly? If it is regular, then it is linguistic; if it is irregular then it is not.

Why is it that we can have disputes about what a painting "means", about what an artist was trying to "express", when we do not have disputes over what I mean when I say "two plus two equals four"? One is a statement of language, the other is an argument over differing opinions. Certainly one can quibble over the semantics of what Samuel Taylor Coleridge was really "symbolizing" when he wrote Kubla-Khan, but we would not quibble over the way in which he delivered those words.

When Coleridge writes:

"In Xanadu did Kubla-Khan,
A stately pleasure-dome decree".

We can ask "What did he mean to symbolize by this?" But two people won't read this same sentence, and the one says:

Anh-vu: I read it and what he wrote was "Goobla moobla boopity boo"

While the other says:

Sam: You're mistaken. What he wrote was "Paffle faffle naffle waffle".

When we are confronted with Duchamp's "Fountain", what kind of statement comes into mind? Do all people come to the same statement, or is each statement different depending on the viewer? One man says "Duchamp was saying that all of art is now in the toilet." Another says "Duchamp needed to go to the bathroom." Another says "Everything in the world is now art." Another says "Nothing is art." Just by looking at the same painting, multiple people may conclude, if asked what the artist was trying to "say", an infinite multitude of different statements. When one is confronted with a statement of language, there is only the one statement. What it is is clear. Coleridge said: "In Xanadu..." and not anything else. What he was symbolizing by it is a question of a higher order. But it's obvious that when a sentence of language says a thing, it says only that thing, nothing else.

Consider the African mask. What does it "say"? "I am strong"? "I am wise"? "I am fearsome"? "God is dead"? What? We can read a multitude of different statements just from the same object.

Return to the vase upon the table.

One person, when asked, "What does the painting say?" Replies, "It's a memoir of the artist's grandmother". Another: "The old vase is on the dirty table". Another: "The vase on the table bore telltale signs of years of neglect". Another: "I'm bored and there's nothing else in the room to paint." Another: "My vase is old, and I should clean my table".

These are all different statements, even if they can refer to the same sorts of objects. From the same painting bursts a multitude of different phrasings, interpretations, predicates. One can read the "statement" made by the painting of the vase on the table any number of ways. The form of the statement is nebulous, not specific.
Such sentential notions are unique to language, not works of art.

Yet sentential notions do exist in comics. We perceive art pieces as making statements any number of ways, but given a certain sequence of sequential art, one will always interpret that sequence in the same way; in a sense, if one is to understand the meaning of the events portrayed in the sequence at all, one must submit to the general concept-space which defines sequential art. There can be only one statement derivable from any given sequence of sequential art, and this statement, being a statement of logical facts, must be form-independent.