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Concept Formation

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I've been trying to write my own version of the basics of concept formation for my website, but I'm having a hard time finding the right words. Looking for some help with it.

So far this is what I've got.

Concepts & Integration:

Human beings have the ability to think conceptually rather than just in terms of percepts. Without this ability one would have to treat every entity as entirely unique and different, allowing for no significant progression or development of knowledge. Concept-formation is a means to achieving a unit-economy, i.e. to economize an unlimited amount of information into a finite number of easily processed, abstract units. A concept then, is the integration of two or more particulars (units - i.e. a separate member of a group with two or more similar members) into a single mental classification, isolated and unified by specific characteristics. For example when you think of the concept "cow", you don't think of one cow in particular, you think of every cow that has ever been and that will be as a single generalized whole. Concepts aren't bound to the particulars that they derive from, so if all cows were destroyed, the concept would still exist.

Concepts can be also be used as units themselves and integrated to form higher-level concepts, for example the concept of art requires the concepts of sculpture, painting etc., which themselves depend upon other concepts. Concepts are contextual, in that they can be expanded and / or made more specific or complex as one's knowledge grows and as certain concepts become obsolete in light of new knowledge and must either be revised or become useless.

A concept is formed by a mathematical process, taking similarities between multiple entities, whilst discarding the differences and the particular measurements of the similarities ("measurement omission"). An attribute is a characteristic of a thing which is reducible to a unit of measurement, such as shape, size, velocity, weight, colour etc. A commensurable (commonly measurable) attribute is taken as the CCD (Conceptual Common Denominator) which allows differentiation and integration. The concept of table, therefore, is formed by isolating the attributes (CCDs) that constitute "tableness", i.e. support(s) and a flat surface upon which items may be placed, and omitting the specific measurements involved, such as height, weight, color, number of supports, diameter of surface, etc. The process of concept formation is comparable to algebra: Specific measurements of perceptual concretes (such as the overall height of a given table) are replaced by variables (x, y, z etc.) which denote some quantity. It is in what relation the quantities are to each other, and whether the quantities fall within the range of the concept, which is of importance. For example a helmet would no longer be a helmet were it made from cotton (it would be a hat instead).

Definition:

The definition of a concept is the final stage of conceptualization. The basic function of a definition is to distinguish a concept from all other concepts and thus to keep its units differentiated from all other existents. A definition identifies a concept's essential characteristics, which are the genus (CCD) and the differentia (differences from other existents that share the same genus). These characteristics must be fundamental, i.e. they must be responsible for all or most of the units' remaining distinctive characteristics. An excellent metaphor for the term "definition" is that of a file folder with a label. The file folder represents the concept, while the label represents the definition. The contents of the folder can increase as more sensory knowledge of the concept is obtained, but the definition remains the same.

Would a twenty foot tall helmet actually be a helmet at all? Can the measurements of a concept be potentially infinite, as long as the relationships between the measurements of the attributes chosen as similar in the first place remain the same?

Edited by DarkReaver13
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A helmet has to be worn on the head. So, no (unless you can find a 19ft head). It might be a piece of artwork or a building, and you could certainly refer to it as the giant helmet (because everyone would know what you are talking about). But, conceptually, it wouldn't be a helmet.

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A helmet has to be worn on the head.
This is an example of a very general difference between words and concepts. The word "helmet" stands not just for the concept of the concrete headgear, but also for any representation. The same goes for other words -- "dog" refers not just to actual canines, but also statues and cartoons, and "car" refers to pictures of cars, toy cars, and real cars.
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Here are some nits for me to pick.

'For example when you think of the concept "cow", you don't think of one cow in particular, you think of every cow that has ever been and that will be as a single generalized whole.'

I don't know what it means to think of a concept, so I don't know if this is true. I do know that the concept cow subsumes all specific cows, and that concepts are mental. I would suggest explaining what you mean by "think about a concept". Thinking is an active mental process, and when I think about cows, I do not actively think specifically about cows which are yet to be born. I am implictly mentally involving future and unknown cows, but I am not actively doing so. Maybe sharpening up the statement about "thinking" would be in order.

The issue I see with the helmet is that you don't identify the CCD of a helmet. The material per se is not relevant, nor is the size: what is important is the function. So it is by combining the size of a normal human head that you can conclude that helmets can't be 20 ft. tall (though a representation of a helmet can be). However, Mimir might have worn a 20 ft tall helmet, had he (it?) existed. With current technology, cotton makes a lousy helmet, but I can imagine developments in materials science whereby a cotton helmet is possible. It is by clearly identifying a CCD that it makes most sense to talk about why a particular concept excludes certain entities -- that is, it's not just that a cotton helmet would be peculiar, it's that it would be totally disfunctional, right now.

"The contents of the folder can increase as more sensory knowledge of the concept is obtained, but the definition remains the same". Let me point you to ITOE p. 46: "When he moves into a wider field of action and thought, when new evidence confronts him, he has to expand his definitions according to the evidence, if they are to be objectively valid". Definitions cannot remain static (otherwise, we would be stuck with the problem that we face from infancy, that man and dog are identical).

One other point which I think would be worth making explcitly is that expansion of knowledge will lead to the creation of new concepts. For example, hypothetical rational arachnids would be subsumed under the standard "rational animal" definition, which suits us fine, but were a race of rational outer space spiders to be discovered, a new concept would have to be created to handle this fact.

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