Abstraction and Symbols

In philosophy, the study of the nature of knowledge is perhaps the most important branch of philosophy, though not the fundamental one. (Metaphysics is the fundamental one.) In that study there are two very important concepts: abstraction and symbols. Almost all of philosophy is mistaken about the nature of both abstraction and symbols as they relate to knowledge.

What Is Abstraction?

An abstraction is a representation of something, either in language or graphics, in which some detail is left out. The more detail that is left out, the more “abstract” the representation is.

In literature, many metaphors are abstractions. For example, the metaphor, “many hands” in the expression, “many hands make light work,” leaves out (abstracts) the rest of the human being to whom the hands belong. The abstract “hands” represents people. If that fact were not readily apparent, the abstraction would be meaningless.

There is another way to think about this abstraction. The word “hands” actually stands for “people.” In that sense “ hands” is being used as a “symbol” for people.

Abstraction, Symbols, and Language

For most of us, what comes to mind when we think of an abstraction is usually an image in which some or most detail has been left out, but which is still recognizable as in the two images below.

(missing image carla3.jpg)(missing image _carla3abs.jpg)

In this case, the abstract image was created simply by increasing the contrast until all the middle tones were eliminated. But abstract images can be much simpler, such as this line drawing of an ox:

(missing image ox.jpg) Which can be made even more abstract: (missing image ox2.gif)

This final abstraction of an ox is actually one historians believe was one of the earliest symbols used in a written language. Because the symbols in such languages were “little pictures,” they are called “pictographic” languages.

No one knows for certain, but it is guessed, and probably correctly, that originally such abstract images represented the objects they resembled—in this case an ox. In other words, in that earliest form of writing, the symbol that looked like an ox was the written word for “ox.”

A symbol, then, is anything, a little picture or a mark, that “represents” something, or more precisely, “identifies” something, and the something it represents or identifies is what it, “means.” It does not describe that identity, and it does not provide any detail at all about that identity, it simply “points out” whatever it identifies.

In fact “points out” is the best description of what it actually does. In pictographic language, “I want to sell you my (missing image ox2a.gif),” is identical to saying, “I want to sell you that,” while pointing to one’s ox. Using the symbol (missing image ox2a.gif) or pointing at an ox preforms the same function, they both identify what one “means” by the symbold or the “point.” They both mean “that,” an actual ox. The “meaning” of the symbol is “ox,” and where no specific ox is specified, it is any actual ox, with all the attributes that make it an actual ox, and all that is or is not known about any ox.

While very little is actually known about pictographic languages that used symbols like our example of the ox, it is unlikely, and probably impossible, that the meaning of words could have been established by means of definitions. The meaning of most words was most likely learned by hearing how others used them, or ostensibly, by hearing the word ox spoken while someone pointed to an ox, and hearing the word ox spoken when someone pointed at the symbol of an ox.

Meanings and Ideas

Before definitions were possible, the meaning of words, either written or spoken, could not be learned, if what they meant did not already actually exist. It would be impossible to learn what the word ox means if there were no oxen, because an actual ox is what the word ox means and there would be no way to associate the word with a non-existent ox.

Before one can associate a word with a meaning, there must already be in consciousness (by seeing it for example) the thing the word means. But a thing is in consciousness by seeing it only so long as one is looking at that thing. The moment one looks elsewhere, it is no longer in one’s consciousness (visual field, for example) because it has been replaced by whatever one is currently looking at.

Once a word is associated with something, (its meaning), it is no longer necessary to be looking at something to be conscious of it. It becomes possible to be conscious of the thing by means of the word which is the symbol for that thing. How a word is held in consciousness is a complex subject I’ve addressed elsewhere, but essentially it is either envisioned as the written version of the symbol, or tentatively “spoken” though not actually, as when we read silently to ourselves, a sophisticated act which must be learned.

When we are conscious of a thing by means of a word, what we are conscious of is called an idea, or concept. The idea is the meaning of the word. In our example, the idea we have by means of the word ox, is an actual ox. In some cases, when we think of something, we may have a mental image of the thing we are thinking, but the image is not the idea, it only accompanies the idea, and we can think “ox” without having to picture one, and its meaning is the same, “an ox,” whether we picture one or not. This distinction is very important, because it is the source of endless mistakes in philosophy, particularly epistemology, the study of knowledge.

An idea or concept then, is our consciousness (or potential consciousness) of a thing by means of a word, which is a symbol for that thing.

Symbols, Written and Spoken

There are three elements in learning of a word’s meaning ostensibly. There is what the word means (an actual ox), how the word sounds and is spoken, and what the written symbol for that word is.

It is conceivable that one might learn the word (symbol) for ox and its meaning (an actual ox) without learning the spoken word. It is also conceivable that one might learn the spoken word for ox and its meaning, without learning what the symbol for that word looks like.

It is tempting to think of the written word (symbol) is a symbol for the spoken word, but that would be a mistake. [There is a case for this, important to language and logic in alphabetic languages, however.] Both the written word and spoken word are symbols, in the sense that they both identify something else, in this case, an ox. In pictographic languages there is no direct relationship between written symbols and spoken symbols. It will take the invention of alphabets to make such a relationship possible, which is perhaps one of the greatest inventions in history, but has also led to some very bad philosophy.

Pictographs to Alphabets

If all the surmises and guesses about pictographic languages are correct, what cannot even be guessed is how any of the words in such languages were spoken or sounded. At some point, however, some genius discovered that spoken words had a limited number of sounds from which they were constructed, and that those unique sounds could also be represented with symbols. Using symbols for sounds, every spoken word could be recreated with those symbols. For example, if the sound “ aw” is represented by a small circle (o), and the sound “ks” is represented by a small cross (x), the word that sounds like “awks” can be written “ox.”

The history of the development of alphabets is an interesting one, but irrelevant to this discussion. The rest of this discussion takes that development for granted, and will concentrate on the good old English alphabet.

The letters of the alphabet are symbols for sounds. Which sounds any particular letter is the symbol for is not always straight-forward, and will vary depending on the combinations of letters and context within words, but it is important to point out, letters are not symbols with any other significance than how a word should be pronounced when spoken or look when written. The letters of the English Alphabet are totally abstract, and have frequently changed their specific design (observe the difference between cursive and printed letters) but the sounds they represent (are symbols for) are the same despite variations in the symbols themselves.

Though the letters of any alphabet are abstract, with little or no relationship to actual existents, their very simplicity is their power. But that abstractness has been a bane to philosophy which has confused the abstractness of written alphabetic languages with abstractness in the concepts the words of such languages represent.

Abstractness only pertains to the symbols, never to the ideas or concepts those symbols, whether pictographs (missing image ox2a.gif) or alphabetic symbols (ox), identify. Words are abstractions, the concepts they identify are not abstractions.

Abstraction and Concepts

Concepts are not abstractions, but there is one sense in which the process of abstraction is used in forming concepts. The word “ox” means “an ox,” which might be a particular ox, such as, “your ox,” or any ox. When it means a particular ox, it means that very ox, with all its attributes and characteristics and everything that can be known about it. When it means “an ox” but no particular one, it means “one of those animals that has all the characteristics that make it an ox,” (such is hoofed, ruminant, horned, etc.) with none of its unique attributes and characteristics (such as color, size, location, owner etc.) specified.

The idea or concept the word “ox” means in this latter sense of “any ox” is not the idea of an entity, but of a kind of entity. Such ideas or concepts are sometimes called, “universals.”

Since the word “abstract” is “a representation of something, either in language or graphics, in which some detail is left out,” and since a universal “leaves out” those unique attributes and characteristics that distinguish particular oxen from each other, that “leaving out” might be considered an abstraction. In fact, however, the unique distinguishing characteristic are not left out, but are specified as “unknown.” The meaning of “ox” is any actual ox. Every ox will have all the attributes it must have to be an ox, as well as all the unique attributes that distinguish it from all other oxen. It must have those attributes to be an actual ox. In my philosophy I call all those attributes that a thing must have to be the kind of thing it is “necessary qualities,” and I call those uniques distinguishing attributes a thing can have, but does not necessarily have, “possible qualities.”

An idea or concept then means an actual existent, such as an ox, with all its necessary qualities and at least some possible qualities that distinguish it as a particular existent from all others of that kind. As a concept for that kind of existent, though every particular one of those existents must have some possible qualities, they are included as unspecified.

The idea or concept itself does not include any attributes or qualities in its meaning. The qualities and attributes are necessary to the existent the idea or concept means (identifies), but the idea only means that existent, or kind of existent. Ox only means “an ox” whatever it’s necessary and possible qualities are, because an actual ox must have them, but the idea “ox” does mean those qualities, it only means the thing that has them.

Philosophy’s Bad Idea

Since Plato, there has been in all of philosophy, in various forms, a view of concepts or ideas that is both incorrect and very destructive to philosophy. Ideas and concepts are portrayed throughout the entire history of philosophy as something vague, incomplete, or inexact. To this day philosophers write such things as, “every concept is an abstraction, and no abstraction is ever complete or exact, and since all our knowledge consists of concepts, no complete or exact knowledge is possible.”

Hume managed to turn this piece sophistry into a science which has been swallowed whole by almost every philosopher since.

The following refers to Hume’s An Enquiry Concerning Human Understanding [1739].

In the second section, “Of the Origin of Ideas,” he writes:, “… there is a considerable difference between the perceptions of the mind, when a man feels the pain of excessive heat, or the pleasure of moderate warmth, and when he afterwards recalls to his memory this sensation, or anticipates it by his imagination. … These faculties may mimic or copy the perceptions of the senses; but they never can entirely reach the force and vivacity of the original … therefore we may divide all the perceptions of the mind into two classes or species, which are distinguished by their different degrees of force and vivacity. The less forcible and lively are commonly denominated Thoughts or Ideas.” Hume labels the original direct percepts “of the senses” “impressions. “… impressions are distinguished from ideas, which are the less lively perceptions, of which we are conscious” [By “lively,” Hume means what we mean by “vivid,”.]

For Hume, “ideas” are like fuzzy pictures or representations of what we directly experience. The idea “dog” or “table” is just an incomplete “picture” of a dog or table recalled from memory. This is the epistemology of a child or a brute, not that of a philosopher.

I wrote earlier, “In some cases, when we think of something, we may have a mental image of the thing we are thinking, but the image is not the idea, it only accompanies the idea, and we can think “ox” without having to picture one, and its meaning is the same, “an ox,” whether we picture one or not.” The idea or concept is the identification of which a word represents. Whether that word is itself a little picture, as in a pictographic language, or a word formed with letters of an alphabet, the word is only a symbol representing the idea which means the entity or existent it identifies.

What Hume failed to do, and every philosopher influenced by him has since failed to do, is to identify exactly what an idea or concept actually is, and to confuse the symbols for a concept with concepts themselves. Hume regarded thinking as the manipulation of vague pictures or impressions, and to this day the logical positivists and those they influenced describe thinking is the manipulation of symbols. It seems almost incredible that some of the best minds have never discovered that the symbols of a language are not ideas or concepts, but only the tools by which we are conscious of those ideas, and it is the ideas or concepts that are the basis of our thinking and knowledge, not the symbols which represent them.

Ideas and concepts are not abstractions. Symbols are abstractions, but they are not concepts, only representations of concepts. There is nothing vague or fuzzy about concepts, because they only identify things, such as entities, attributes, events, relationships or other ideas and concepts. They identify them exactly if properly defined, as exactly as if one pointed at the thing the concept identified.

It is certainly possible for people to have ideas or concepts that are incorrectly defined, but such concepts are not wrong because there is anything vague or fuzzy about them, but because what they are supposed to identify does not exist or is something different from the supposed identity or involves some contradiction in that identification.

Why This Is Important

One of the weapons in the arsenal of those at war with objective knowledge and reason, like the postmodernists and critical theorists, is the assertion that all concepts are in some way incomplete, imperfect, vague, or fuzzy representations of reality, which means that all or knowledge and reasoning is ultimately incomplete, imperfect, vague and fuzzy as well.

It is certain that almost anything you read today that deals with principles or values will contain this sophistry as an established unquestioned fact. It is, as we’ve seen, nothing but ignorance of what ideas and concepts truly are. Whenever you run across it, in text books, college classes, journals, discussions, or the media, you do not need to contradict it or argue against it (those who have swallowed it are usually incapable of understanding such arguments), but to clearly identify and note it for yourself. Armed with this identification and your knowledge that concepts are not abstractions, but identifications of facts and principles, complete, precise, and exact, you will be immune from all of the leftist, socialist, collectivist, pseudoscientific anti-intellectualism that infects all of academia, culture, and society today.

—(03/12/10)