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The nature of concepts.

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An algebraic equation represents a quantitative a relationship between variables. A concept represents entities of a certain kind. Where's the grandiose connection here?

In algebra, a symbol is used to represent a variable. Similarly, a word is used to represent a concept. Any specific number can potentially be used in place of that symbol - and the use of that symbol represents this fact.

Likewise, in a recipe that calls for "1 pound of ground beef" and "5 strips of bacon" - any specific pound of ground beef, or piece of bacon, can potentially be used in the creation of the meal. The recipe does not state "1 pound of ground beef directly from the rump of my favorite cow". The concept "ground beef" (like the variable "x"), allows you to potentially substitute any actual example of ground beef (or number).

Edited by brian0918
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My answer is logically equivalent to the next previous one, but I'm going to write it out anyway, in hopes that it might be easier to understand.

The same symbol, x, is used in many different equations. In one sense, it means the exact thing in all of them--it means a quantity. But exactly which quantity it indicates varies with the formulations of the different equations. So in "x + 4 = 21," x means a quantity, and in "x - 4 = 25," x also means a quantity (I do realize you know this, just bringing it to mind.) Still, in the first equation, x = 17, while in the second one x = 29. Statements with an unknown all refer to some specific quantity, and that's what x means in every one of them. Which specific quantity satisfies the equation varies with the equation, of course, and that gives the generality, the categorical members of "x."

The things that are meant by a given concept are exactly alike in being what that concept conveys, yet they are different in other ways, the non-essential ones and the variable (like now sitting, now standing) ones. Generality means the exact same thing is true of multiple particulars, but multiple particulars cannot be identical. Generality, thus, obtains only to abstractions, that is, to aspects of things. Meaning is thus ALWAYS abstract. (This is true of proper nouns, in that they mean an individual (person or thing, etc.) throughout its changing history. Even an "unchangeable" thing has changing relations, since other things, which define some of its relations, change. One way to think about conceptual meaning, that is, essence, is that it represents some invariance ("invariance" just means staying-the-same,) of any characteristic across multiple particulars, or across time for the same particular.

So, being replaceable by a specific quantity is the essence of "x," because it is the invariable property of all Xs. That x is 17 is not essential, is not invariant over all instances of x.

In the case in which there are constant features or characteristics of a class of things, we choose the invariances which entail the greatest number of other invariances. (Here I'm writing theory.) Defining man, in the much-used example, as the featherless biped is a poor definition because it tells so little about him beyond his being an organism. It tells us nothing about, among other things, his intelligence. Man's intelligence is fundamental to how he survives, and is part of the explanation of most of his behavior, so it entails volumes of facts about men.

This is a slightly different statement of Rand's account of essence and fundamentality. She emphasizes that essential features have the greatest "explanatory value" regarding the full range of information pertinent to man. (The full range of information includes all facts about men: The range of sizes of men, their nutritional needs, their sexual behavior, their gestational period, their preferred postures, vulnerability to extremes of temperature, social and political and artistic, lingustic, etc. etc. behavior... and all other facts about specific idividuals, throughout time! That's where economy is so important.)

One reason the concept of invariance is so useful (I find it so) is that it applies at all levels of cognition. As the basis of Gibson's theory of perception, it defines the relation between sensory energy in the environment and perceptual contents, and this relation is subject to experimental proof. It can be gauged of whatever is ostensible, of any manifestation or exhibition, that is, any quality, feature, aspect, object or part of an object, sensory content--any qualia whatsoever, and is thus a common denominator of great compass. It means the same thing when used to refer to objects and their characteristics as it means when referring to conceptual meaning or perceptual content, etc.

The concept is simple in itself, and not subject to ontological puzzles. The most interesting part of all this is that it is known that nerve nets do, and how they can, extract invariances from sensory energies.

Having gotten a bit off the track, I trust this is nonetheless of sufficient interest...

-- Mindy

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