Concepts as two or more units

[Nicky]

"A concept is a mental integration of two or more units..."

I say this is not so. A concept may be constructed from one. For example, for most of human history, there was one and only one moon. Was "moon" an invalid concept until the discovery of Jovian moons by Galileo? Certainly not. What have I misunderstood?

"concept" is a concept. It is important to understand what it means, and why it exists. It's not used for naming things. It's used as a tool in the process of abstraction. Abstraction, (very) roughly, means "categorizing different things into one category, based on essential common elements, while ignoring non-essential differences". 

 

When you look at the Moon, and decide to call it the Moon, you're not abstracting. That's not a concept, it's just a name. Only when you decide to call two different existents by the same name are you "abstracting away some differences". Once you have two separate, in many ways different, large objects circling planets, do you have an opportunity to identify what essential traits they have in common, and only then do you have the opportunity to bunch them into a category.

 

Another example you brought up is "I": again, "I" is just what you call yourself. The concept that refers to one's self is "self", not "I". If you were the only conscious existent in the Universe, the concept "self" wouldn't exist, because there would be no use for it. There would be only "I". Saying that "I" is your "self" would mean nothing. Your "self" as opposed to who else's?

[aleph_1]

Okay, I will give you a compelling example. Consider the equivalence class, up to isomorphism, of complete ordered fields. This is clealy a concept, but it is a theorem of mathematics that there is only one, which we commonly call the real numbers. The proof that there is only one such thing is a banner achievement of mathematics. By your logic, this is only a name and not a concept-an absurdity.

Your argument concerning "I" also falls short since all entities are distinguished from other entities but that does not rise to the level of a discussion of concepts.

[aleph_1]

I should mention that Dedekind and Cantor came up with different constructions of the real numbers as complete ordered fields. These are isomorphic. It turns out that all complete ordered fields are isomorphic. The set of equivalence classes under isomorphism of complete ordered fields has only one element. This means that up to isomorphism, there is only one complete ordered field-the real numbers.

This is a singular CONCEPT. It is surely an abstraction. There are NOT two of such things as a matter of mere proof. Game, set, match.

Edited July 31, 2013 by aleph_1

[Nicky]

Okay, I will give you a compelling example. Consider the equivalence class, up to isomorphism, of complete ordered fields. This is clealy a concept, but it is a theorem of mathematics that there is only one, which we commonly call the real numbers. The proof that there is only one such thing is a banner achievement of mathematics. By your logic, this is only a name and not a concept-an absurdity.

So what is the concept that you contend there is only one of? Just name the concept. If there is only one of it, then the name alone should be enough to identify exactly what you mean. 

Edited July 31, 2013 by Nicky

[aleph_1]

So what is the concept that you contend there is only one of? Just name the concept. If there is only one of it, then the name alone should be enough to identify exactly what you mean.

I did. The real numbers. In particular, the equivalence classes of complete ordered fields has a unique element. The real numbers.

[A is A]

Your error is within your own paragraph. The concept car model has units such as Accord. The concept Accord has units like my wife 's car. This makes car model a second-order concept. It does not reduce Accord to a name disassociated from units or concepts. The same is true for countries and McD's. Your McD example is good because it illustrates my point. McD was once a singleton.

It is obvious that you don't grasp what a name is if you regard 'Accord' as a concept.  So, I will leave this discussion at this point.

[dream_weaver]

Each counting number is a concept that allows us to hold the relationship of a group of similars based on one of its members taken as a unit.

The relationship bore by all groups that consist of any particular number is exactly the same.

 

The real numbers are an extension of that idea allowing us to apply number to measurement along a continuum.

 

The moon is the name we gave to the celestial object that went through its cycle every 29.5305882 days. When Galileo discovered the satellites or moons of Jupiter, we expanded our understanding to encompass that our moon was a moon we call the moon.

[aleph_1]

It is obvious that you don't grasp what a name is if you regard 'Accord' as a concept. So, I will leave this discussion at this point.

I encourage you to apply the law of identity to "concept". Read the definition again and then tell me why "Accord" is not a concept. A is A.

[aleph_1]

The real numbers are a unit of the concept "field". Other fields include the rational numbers, the complex numbers, finite fields, field extensions to various fields, etc. There are many fields, not just the real numbers. We may also talk about complete fields, such as the complex numbers and the real nimbers, but not the rational numbers. Then there are ordered fields, such as tge real numbers and the rational numbers, but not the complex numbers. The real numbers are, up to isomorphism, the unique complete ordered field.

A priori, there didn't have to be just one. However, it is a matter of proof that there is exactly one. Would you have me believe that complete field is a concept and ordered field is a concept, but complete ordered field is not?

You could correctly argue that real numbers are an abstraction resulting from an analytic-synthetic dichotomy and is hence not a valid Oist conccept. Then again, you may not.

Singletons rule the field.

[A is A]

I encourage you to apply the law of identity to "concept". Read the definition again and then tell me why "Accord" is not a concept. A is A.

Because it is not a mental integration of two or more units.  It is a name given to a style of car designed by an engineering firm.

[aleph_1]

Because it is not a mental integration of two or more units. It is a name given to a style of car designed by an engineering firm.

The individual cars are units. The style is exactly what differentiates these units from others. The collection of cars having that specific style forms a concept. "Accord" is the mental integration of two or more cars (units) that possess a particular style. This is a concept.

Even if you can't bring yourself to accept the above truth, you must surely accept that "ordered field" is a concept, as is "complete field" and also "complete ordered field". Singletons exist as a matter of mere proof. This you cannot reasonably deny. Any refusal removes you from the realm of reason.

[Plasmatic]

Isnt the difference between a PROPER name and non proper name being ignored here? Their are collective nouns like "universe" and proper nouns like Greg....

[A is A]

The individual cars are units. The style is exactly what differentiates these units from others. The collection of cars having that specific style forms a concept. "Accord" is the mental integration of two or more cars (units) that possess a particular style. This is a concept.

Wrong. The concept you're talking about is "model" that is formed by these cars. Accord is the name of the model.

Even if you can't bring yourself to accept the above truth, you must surely accept that "ordered field" is a concept, as is "complete field" and also "complete ordered field". Singletons exist as a matter of mere proof. This you cannot reasonably deny. Any refusal removes you from the realm of reason.

Don't impune motive to me. You're not my psychologist. "Ordered field" is two concepts. As I said before, I don't accept your concept of singleton, so I do deny it. I have no idea what "mere proof" means. You are free to judge whether I use reason or not, just as I judge you. But, as I said before, we'd better stop discussing the issue, otherwise others might think we are using reason.

[A is A]

Isnt the difference between a PROPER name and non proper name being ignored here? Their are collective nouns like "universe" and proper nouns like Greg....

It is not I who is ignoring it. Names are not concepts.

[Plasmatic]

Consider:

"AR:.....Well now, as a process yes, you

first have to separate them as you described. And in the

process of deciding that these three have something in

common and are different from others, you are treating

them as a unit. You are now looking at them not only as

three blue objects, but three units of one group that

have something in common as against everything else.

Prof. D: I've described the process, but I have

arrived also at a product which is: these regarded as

units. Now at that point do I have the concept of "pad,"

or do I still have something further to do, a further

integration to make, before the product would be a

concept?

AR: Yes. You have to give it a name."

ITOE

Clearly Ms. Rand calls the word given to a unit a "name".....

[A is A]

Consider:

"AR:.....Well now, as a process yes, you

first have to separate them as you described. And in the

process of deciding that these three have something in

common and are different from others, you are treating

them as a unit. You are now looking at them not only as

three blue objects, but three units of one group that

have something in common as against everything else.

Prof. D: I've described the process, but I have

arrived also at a product which is: these regarded as

units. Now at that point do I have the concept of "pad,"

or do I still have something further to do, a further

integration to make, before the product would be a

concept?

AR: Yes. You have to give it a name."

ITOE

Clearly Ms. Rand calls the word given to a unit a "name".....

Pad is not a proper name; it is a word for the concept. Clearly, that is what she is here calling a name, as she often says in many other places. And it is a word formed by the mental processes used to form the concept 'pad'. That is not how proper names are arrived at.  No integration is occurring when a model is called "Accord."

[Plasmatic]

AisA said:

"Pad is not a proper name; it is a word for the concept. Clearly, that is what she is here calling a name, as she often says in many other places. And it is a word formed by the mental processes used to form the concept 'pad'. That is not how proper names are arrived at. "

You do realize this is what Im saying, right?

Edited August 2, 2013 by Plasmatic

[A is A]

AisA said:

"Pad is not a proper name; it is a word for the concept. Clearly, that is what she is here calling a name, as she often says in many other places. And it is a word formed by the mental processes used to form the concept 'pad'. That is not how proper names are arrived at. "

You do realize this is what Im saying, right?

I thought you were supporting Aleph's position by implying that 'pad' was a name.  Perhaps you need to amplify your meaning.

[Plasmatic]

Pad is a non PROPER name.

[A is A]

Pad is a non PROPER name.

In other words, a word.

[A is A]

If Aleph really wants to claim that proper names are concepts, then the following example would serve this purpose.

 

Integrate the following entities:

 

The fifth planet from the sun;

A summer resort on the Black Sea;

A tugboat preserved in Philadelphia, Pennsylvania;

Mozart's 41st Symphony;

A large, round, slightly conic apple;

The Roman king of the gods and the god of the sky and thunder.

 

I challenge Aleph to perform a mental integration of these units, isolated by abstraction and united by a specific definition, yielding the concept 'Jupiter.'

 

 

[dream_weaver]

Then try integrating: categorizing the following:

 

Sun

Moon

Venus

Mars

Jupiter

Europa

Io

Big Dipper

North Star

Alpha Centauri

Messier 15

Edited August 2, 2013 by dream_weaver

[A is A]

Then try integrating: categorizing the following:

 

Sun

Moon

Venus

Mars

Jupiter

Europa

Io

Big Dipper

North Star

Alpha Centauri

Messier 15

Why?  Why those?  Aren't there already several concepts for which such objects are referents? 

[Nicky]

I did. The real numbers. In particular, the equivalence classes of complete ordered fields has a unique element. The real numbers.

So your answer is "the real numbers"? You're answering the question "what's a concept that refers to only one existent?" with a plural?

Real numbers is the plural of "real number", a concept that refers to numbers like Pi and the number 1. I count two right there.

Edited August 2, 2013 by Nicky

[dream_weaver]

Why?  Why those?  Aren't there already several concepts for which such objects are referents? 

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.