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Conceptual Common Denominator (CCD)

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Selkc
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To take one of Rand's examples from the place you're referencing, when you're conceptualizing colors, you use hue as the CCD, and you conceptualize by thinking of various ranges of hues. So, blue is anything from *this* hue to that *hue*. Such a range would be the "distinguishing characteristic" within hue. 

The CCD is like an axis or dimension within the observational space, and the distinguishing characteristic is the set of values within that dimension/axis that you conceptualize as being "similar" for your purpose. (Of course, you may not identify it as such, may not understand the unit of measure, and perhaps do not even think you're measuring anything. ) 

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Selkc, lets concretize the following passage:

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the distinguishing characteristic of the new concept is determined by the nature of the objects from which its constituent units are being differentiated, i.e., by their "Conceptual Common Denominator,"

Every concept has what I call its generative context of differentiation. That is, every valid concept has its origin in a set of experiences that require the observer to separate a certain category of existents from another group by means of something both groups share in common, while also integrating the new group (or particular, to itself) to each other by an essential difference the new group doesn't share with the "from" group.

   An example:

Imagine you have a box with two holes in the top of different diameter. You are instructed to put all the balls from a set of balls you are given, into the box via the holes on top. You then find that, like the holes in the box, not all the balls are of the same diameter either. In order to perform this task you must separate the balls that are equal to or less than the diameter of the hole on the left from the ones that will fit the hole on the right. Both groups of balls have the necessary shape roundness required to fit in the holes but one set of balls is too large to fit one of the holes. The category of measurement that differentiates one group of balls from the other and to itself, is "size".

The CCD is "shape" and the differentia is "size". All the balls are the right shape (similarity) but not all are the right size (difference). The task involved and the nature of the entities involved set the context for the conceptualization done.

From's and to's. Differentiation and integration.

This process will guide the creation of the definition used to cognitively economize the mental process described above.

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The rules of correct definition are derived from the process of concept-formation. The units of a concept were differentiated—by means of a distinguishing characteristic(s)—from other existents possessing a commensurable characteristic, a "Conceptual Common Denominator." A definition follows the same principle: it specifies the distinguishing characteristic(s) of the units, and indicates the category of existents from which they were differentiated. The distinguishing characteristic(s) of the units becomes the differentia of the concept's definition; the existents possessing a "Conceptual Common Denominator" become the genus. Thus a definition complies with the two essential functions of consciousness: differentiation and integration. The differentia isolates the units of a concept from all other existents; the genus indicates their connection to a wider group of existents.

The balls that will fit the hole on the right could be called "group A" and the balls that fit the hole on the right "group B".

A definition would be something like : Group A is defined as all the balls having a diameter that corresponds to hole A such that it will alow it to pass through..

 Notice my error above? I said "right" instead of "left". I mixed up my "to's and "from's". That is what it means to "drop context".....

Edited by Plasmatic
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  • 1 month later...

Realize the necessary dual level of noticing similarities from differences.  

When you validate (not necessarily form) the concept automobile within the full context of all the available knowledge known for an adult.  You are looking at or comparing your knowledge of motor vehicles (cars, trucks, airplanes, boats, etc), and you are looking at all of their measurements.  You are then comparing your knowledge of gliders, horse drawn carriages, bicycles, etc (non-motorized vehicles) and all of their measurements and other items (non-vehicles motorized and not motorized) such as rocking chair, merry go round, and all of their measurements, etc.  You now have enough information to hold the concept motorized vehicles due to the same differences it has with these other items that you have differentiated them from (non motorized vehicles and other man made objects, especially those that create motion but don’t take you anywhere).  Motorized vehicles: A man made object that carries people from place to place via a powered man made engine.

 

The next step is to differentiate automobiles from other motorized vehicles so you go through the same process, you look at all the characteristics (to a degree – don’t take all literally, but more than is used in the distinguishing characteristic) of the different items, trucks, cars, airplanes, boats, etc (not an easy or quick process), and you start to focus in on the same essential differences that trucks and cars have to the others, that they travel on land.  An automobile is a motor vehicle that travels on land.  Then you discover a train and a motorcycle and you have to revise your definition.  An automobile is a motor vehicle with an enclosed compartment and rubber tire surface for transporting people and items on land.   

 

Remember the purpose for concept formation and their definitions.  Unit economy and clarity.  For your purpose.  If someone creates a hybrid, motorcycle with an enclosed compartment, not really a big issue or seen as crumbling the entire concept formation theory.  You either treat it as a one off item, create a subcategory for it, or a separate concept or disregard it since you don’t use it, study it, work on them, etc.  If it is not important for YOU – you don’t have to conceptualize it!  That’s true for a one off item, not true for your entire knowledge base and items, as everything is related and integrated and not subjective.

 

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Similarity and Differences:  Please clarify your statement if you ever use these in the same sentence.

Anytime the term similarity is used, it is a result of common differences from another group.  If you only look at a apple and an orange - they are not similar.  They are only similar for example if you compare them to a vegetable.  When people speak of noticing similarities and differences - that is just too vague because it doesn't elaborate the frame of reference - what is similar to what?  What is different than what?  Plus, the context of whether we are in the frame of reference of 1st person perspective or 3rd person perspective, changes the answer.

For example, as the apple/orange example points out, you don't notice similarities among/between just two items that you perceive.  Although that is the way it can be experienced from a 1st person perspective.  You don't notice similarities and differences among the same units in a concept.  What you notice is similarities of the automobile, train, plane, etc. from a wider group of existents, via the differences that these motorized vehicles have with a wider category.  Then you notice the ways in which these automobiles are different than the other motorized vehicles.  First you have to form the genus, then the distinguishing characteristic that forms the concept at hand.  Step one is you notice common differences with a higher group to create the genus, then step two you notice common differences between the concept (distinguishing characteristic) and the genus.  

From a first person perspective you can say I notice similarities.

From a third person perspective/ analysis of the process, you can say I notice common differences.  

To say you you notice similarities and differences in the same sentence implies you are using the same frame of reference!  To not elaborate on the frame of reference for the concept and topic at hand is a crime.

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Good point - I'm just randomly posting thoughts B), expecting agreement or disagreements.  I'll control it a little better going forward.  A lot of this has been a process for me recently as research for the 2nd half of a chapter to my book.  I'll be moving on soon.

Thanks,

Mike

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