Concepts as two or more units

[A is A]

They fit quite nicely as celestial objects referred to by proper names distinct from celestial objects such as stars, moons, comets, asteroids, galaxies and solar systems.

There are thousands of stars, comets, galaxies, etc, with names.  I fail to see an epistemological difference between such a division of celestial objects.  They all fall under the same concept, and the names are not concepts.

[dream_weaver]

The epistemological difference is one of listing all the celestial objects by name, and listing them by conceptual classification. Prior to identifying the moons of Jupiter, or the Sun as a star, the designation "moon" was a proper name, and now has the additional sense of being the concept that identifies a satellite of a planet. There are probably other concepts that started out as a proper name and discovering other instances of the same phenomena, took the extended sense of the designation of the later discovered concept. "Singleton" rings of trying to create a concept to cover blonde-haired, blue-eyed, 5'4", 25 year old women. It defeats the purpose of epistemological economy.

[A is A]

The epistemological difference is one of listing all the celestial objects by name, and listing them by conceptual classification. Prior to identifying the moons of Jupiter, or the Sun as a star, the designation "moon" was a proper name, and now has the additional sense of being the concept that identifies a satellite of a planet. There are probably other concepts that started out as a proper name and discovering other instances of the same phenomena, took the extended sense of the designation of the later discovered concept. "Singleton" rings of trying to create a concept to cover blonde-haired, blue-eyed, 5'4", 25 year old women. It defeats the purpose of epistemological economy.

i agree with you.

[aleph_1]

A is A, I'm sorry, I did not mean to impune, or even to impute, anything into what you said.

Nicky, I was referring to the set of real numbers. The set of real numbers is a single thing-a higher order concept, just like the set of complex numbers or rhe set of rational numbers. These are all units of the concept "field" in mathematics.

"Things named Jupiter", just like "encirclist", is a concept, A is A. OPAR does not imply that encirclist is not a concept. It just says that "encirclist" is a cognitive disaster.

"Complete field" has units of fields sharing a similarity. It is a concept.

By a process that I call "double distinction", singletons may be easily formed. When the units of two concepts overlap, a new concept formed by taking the differentia of the two and applying it to the new concept results in a more narrow concept. Sometimes, the narrow concept has only one element, as in complete ordered fields. It is easy to construct model examples of the process.

I thank all of you for helping me to clarify my understanding of "concept" and "name", etc. This is a real moment of clarity for me. You have been most helpful.

[A is A]

A is A, I'm sorry, I did not mean to impune, or even to impute, anything into what you said.

Nicky, I was referring to the set of real numbers. The set of real numbers is a single thing-a higher order concept, just like the set of complex numbers or rhe set of rational numbers. These are all units of the concept "field" in mathematics.

"Things named Jupiter", just like "encirclist", is a concept, A is A. OPAR does not imply that encirclist is not a concept. It just says that "encirclist" is a cognitive disaster.

"Complete field" has units of fields sharing a similarity. It is a concept.

By a process that I call "double distinction", singletons may be easily formed. When the units of two concepts overlap, a new concept formed by taking the differentia of the two and applying it to the new concept results in a more narrow concept. Sometimes, the narrow concept has only one element, as in complete ordered fields. It is easy to construct model examples of the process.

I thank all of you for helping me to clarify my understanding of "concept" and "name", etc. This is a real moment of clarity for me. You have been most helpful.

I think your understanding is in error in the issues we've discussed.  "Things named Jupiter" is not a concept.  It is 2 concepts and a name.  A concept is ONE word formed by the process described in ITOE.  

[aleph_1]

I think your understanding is in error in the issues we've discussed. "Things named Jupiter" is not a concept. It is 2 concepts and a name. A concept is ONE word formed by the process described in ITOE.

Okay, let a comfield be a complete field and let an ofield be an ordered field. Now, let an ocomfield be a complete ordered field. Done.

Edited August 3, 2013 by aleph_1

[A is A]

HA.  And your entire sentence is a concept: lacbacfalao

[aleph_1]

HA. And your entire sentence is a concept: lacbacfalao

My definitions differentiated between units based on similarities. I even assigned names to those concepts. Your lacbacfalao does that how?

[Harrison Danneskjold]

Each number is an abstraction from its counting-measurement (of things in reality) and really is sort of the essence of 'unit' as such.

 

The number 1 is composed of the idea of one unit- as against 2 or 3, et cetera.  It could be considered a singleton except for the fact that it only applies where other numbers could also apply.

For instance- it makes perfect sense for me to speak of one dollar or one apple.  But if I was rattling off a guest list of names, how would you react if I did so as:  "One Harrison Jodeit" etc.?  It would be nonsensical.

 

Now, I'm not a mathematician at all, but you seem to be referring to the fact that there is only one set of real numbers; i.e. "One, two, three" as opposed to "One, three, seven" etc.  That's certainly true.

But the concept of a "set of real numbers" is obviously a composite abstraction- from real numbers, themselves.  So to call that a singleton is equally nonsensical.

 

What you described in the OP applies perfectly well to names for the perceptually-given.  It doesn't apply to abstractions.  There is no higher-order concept formed from itself; that's a logical impossibility.

[Harrison Danneskjold]

And as far as numbers go, honestly, the only thing that could possibly be considered a borderline case would be the concept of "one" in and of itself.  That might be a singleton; it's debatable.

Everything greater than one or less than one is an abstraction from multiple units, where each unit IS "one"!

[dream_weaver]

Corvini discussed "one" on her "Two, Three, Four, and all that" talk. She stated something like 2, 3, 4 are perceptually discernable and where we derived our first notions of number. She didn't think 1 was abstracted until later on. Starting the sequence with 1 made possible a "portable set of mental pebbles" which could then be used for the pairing process.

[Plasmatic]

Weaver, that, to me, makes perfect sense. Since we actually observe a multiplicity and have to isolate particulars from their background. "Out of many, one"..... This relates to something Ive been considering on this topic. Their is a sense one could construe the cognitive isolation involved in differentiating entities as "abstraction".... Just a passing thought currently.

Edit: also consider "entity", as the basis of "one", is only implicit till much later in conceptual development.

Edited August 3, 2013 by Plasmatic

[aleph_1]

And as far as numbers go, honestly, the only thing that could possibly be considered a borderline case would be the concept of "one" in and of itself. That might be a singleton; it's debatable.

Everything greater than one or less than one is an abstraction from multiple units, where each unit IS "one"!

Harrison, I suggest that you read OPAR p. 116 on "culture" as an abstraction from abstractions. Peikoff speaks of "units" such as "art", etc.

Once you understand the process of integration, you will understand how the set of real numbers can be considered a unit of the set of fields. Examples of other such units are the complex numbers and the rational numbers. I am simply using the process of integration and differentiation that I thought most here were familiar with. Perhaps I should have been more pedantic in approach.

[dream_weaver]

Another example that occurs on occasion: A rainbow.

 

Seen most oft when rain is falling whilst the sun is shining. As a perceptual concrete, it requires no other concepts to isolate it within the visual field. A child can point to it ostensibly and ask what it is. Similar to the moon, it is observed periodically although not produced by the same cycle.

 

They most often are observed as a single arc, less frequently as a double arc, and reports of a triple arc are not unheard of.

 

Unlike an object such as the moon, an entity in and of itself, a rainbow is an effect produced by atmospheric conditions. Unlike many perceptual concretes, a rainbow is not an enduring entity as the moon or a person or any other existential object such as a specific tree, rock or building that appears to you when they return or you return to where the object persists - a rainbow appears when circumstances are "ripe" for its appearance.

 

Unlike the moon where one object serves as a unit, a rainbow has arguably many units which can be integrated. Like the moon, a rainbow, thanks to Newton, has an description that serves as the same cause, same effect or same unitary explaination, if you will.

 

Secondarily, the choice between this thread and the one entitled: Conceptual lineage, seem closely related in some respects.