Units

[Matthew]

Greetings;

I am having trouble understanding units. I have read Rand’s description several times in “Introduction to Objectivist Epistemology” and would greatly appreciate any comments or corrections to my concept of unit:

A unit is a (partial?) capture of the identity of an existent in man’s consciousness. Units must refer to a perceived concrete. Units can refer to existents other than physical concretes such as length. The relationship between a unit and attributes is composition: units are composed of attributes in various measurable quantities. The relationship between antecedent units and a concept is aggregation.

Questions

1. Does a unit always refer to an instance of a concrete or can it be a generalization too? For example: a book vs. a particular book, Color vs. a particular shade of blue, weight vs. 100 pounds (or is 100 an attribute of a unit “collection of pounds”).
   
2. Does measurement omission apply to units as well as concepts?
   
3. Is a unit a concept as well?
   

[DavidOdden]

A unit is a (partial?) capture of the identity of an existent in man’s consciousness.

This may help (p. 6,7): 'A unit is an existent regarded as a separate member of a group of two or more similar members....Thus the concept "unit" is a bridge between metaphysics and epistemology: units do not exist qua units, what exists are things, but units are things viewed by a consciousness in certain existing relationships'. The important thing to keep in mind is that a unit is an existent. Thus units don't refer to perceived concretes. My left foot is a unit, so is this keyboard I'm using.

Higher order abstractions exist as well, and they are existents. A concept is a unit (p. 9: 'The uniting involved is not a mere sum, but an integration, i.e., a blending of the units into a single, new mental entity which is used thereafter as a single unit of thought (but which can be broken into its component units whenever required).'). So, the concept "blue" refers to very many particular shades, and each of them is a unit (even though they won't all be concepts, lacking the "symbolic differentiation" that makes concepts).

One unit cannot be a concept, since 'A concept is a mental integration of two or more units which are isolated according to a specific characteristic(s) and united by a specific definition'. For that matter, two units do not automatically form a concept, but they are the foundation of a concept, when you mentally integrate them into one higher unit.

[Thomas M. Miovas Jr.]

The important thing to keep in mind is that a unit is an existent. Thus units don't refer to perceived concretes. My left foot is a unit, so is this keyboard I'm using.

That's not quite the way to put it. Your foot is only a unit when considered in mental relationship to other feet under the concept "foot". Likewise, a particular keyboard is only a unit in mental relationship to other keyboards under the concept "keyboard."

One can think of the term "unit" to mean "one of the items being integrated to form the concept." The unit that serves as the standard is the one that most closely identifies those units conceptualized; say the standard keyboard versus one that is multi-colored or one of those newer ergonomic keyboards where the buttons are spread out in a fan-like manner.

As one goes higher up the hierarchy, non-entity existents can be units; such as capitalism, socialism, communism, fascism, and Nazism each being a unit of the concept "political system". Or an easier one, horse, cow, pig, rhino; where each abstraction of those animals are units for the concept "animal."

An existent is wider than the concept "entity" -- it basically means something that exists. For example, red, blue, yellow, and green are each units of the concept "color" though each of these colors exist, none of them is an entity.

This essay is a unit for the concept "posting" or "essay," in mental relationship to other postings or essays.

[Matthew]

Thank you all for this information.

In summary:

• Entities are specific types of existents.
  
• Concepts are units - the antecedent components are units themselves (this is an abstraction). Units are not necessarily concepts if the antecedent components are precepts.
  
• Is there ever a case where a concept is made up of units and precepts? Or must perceptions always be “boxed” into a unit before the percept can be used as a conceptual component?
  
• Is it proper to say that the identity of an existent exist in man’s consciousness as a unit?
  

Many thanks,

Matthew

[DavidOdden]

Concepts are units - the antecedent components are units themselves (this is an abstraction).

When a concept itself is regarded as one member of a group, then the (lower) concept is a unit. I can't think of a way to consider the concept "existence" as one member of a larger group.

Units are not necessarily concepts if the antecedent components are precepts.

Percepts ("precept" means, roughly, "rule"). A concept is a mental integration of two or more units, and units are existents. Take the case of "pebble", and a dozen units (actual pebbles) before. Each is a unit when considered with respect to all pebbles. No individual pebble is a concept. I think that is what you meant.

Is there ever a case where a concept is made up of units and precepts?

I don't know what you mean by "made up of". For instance, carbon is made up or electrons, protons and neutrons; but the concept "dog" not made up of actual dogs in the same way (concepts are mental, dogs are quadupedal pedal and bigger than the average skull). I think the answer hinges on what exactly you mean by "made up of".

Is it proper to say that the identity of an existent exist in man’s consciousness as a unit?

The identity of a pebble is (in) the pebble, that is, you cannot have a pure existential state of "being" without identity, not can you have identity abstracted out of existence. So unless a man has rocks in his head, the identity of a pebble is not in his consciousness. A man can have knowledge of that identity.

[EC]

This is a more general reply rather than specifically aimed at any of the questions in bullet points, but I think a lot of anwers on this subject can be directly deduced by keeping in mind that there is correlation to algebra here. For instance, x can stand for any number (concept), but a number--say 5-- is the actual unit. This would be comparable to the perceptual level. But you can also take a whole equation say f(x) = x + 1 and make that comparable to an abstract concept with a specific number plugged in 6 = 5 + 1 , and this then becomes your "concepts" new "unit".

Keeping the above in mind helps me answer similar questions to those asked in this thread.

[Matthew]

Greetings;

OK thanks all - I am beginning to understand the relationship of units to concept formation. Thinking in terms of numbers and variables is indeed easier. An example concept formation:

I perceive three existents: the number 5, the number 4, and a cat. Isolation would be to separate the units "4" and "5" from "cat". Integration would be to unite "4" and "5" under a definition, say "arithmetical value" and then assign a word to the definition: "number". For any future existent I perceive, I can again isolate it by observing it's attributes (this new existent happens to be a "6") and then integrate it under my already formed concept "number". If I encounter yet another existent, say a "dog" and isolate it incorrectly so that it leads me to integrate it under the concept of "number" - this would be a contradiction.

What is still confusing me about units is the following statement:

"The concept of unit is a bridge between metaphysics and epistemology: units do not exist qua units, what exists are things, but units are things viewed by a consciousness in certain existing relationships" -- Introduction to Objectivist Epistemology, p.7

This is what has given me the idea that units exist only in consciousness.

Sincerely,

Matthew

[DavidOdden]

I perceive three existents: the number 5, the number 4, and a cat.

It's not hard to perceive a cat, or the letters "5" and "4". I question whether it's correct to ever say that you "perceive 5", especially separate from the 5 whats that you can actually perceive. You can perceive 5 cats and focus on the fact that there are 5 of then. Or, or course, you can perceive the symbol "4" and the Roman symbol "V".

Isolation would be to separate the units "4" and "5" from "cat".

Right, differentiation (lemme just slip in the relevant term) separates "4" and "5" from the cat. I'm not sure how these things got together in the first place, but let's say that these are the things on a page. But to be at this stage, you need to already have a good grasp on the concept of "number". Otherwise, the shape "4" and "V" have nothing significant in common, so you would not form a concept "number" just base on letter shapes.

Here's a model. You perceive dog, dog, dog, dog dog, dog, DOG and now form the concept "dog". Now you perceive cat, cat, cat, cat, cat CAT cat, cat, cat, hence the concept "cat". Soon, you can perceive dog, dog dog, dog dog dog as well as cat, cat cat, cat cat cat. This allows you to form the concepts "1", "2", "3". Especially when you get a handle on pig, pig pig, pig pig pig, you can apply "1", "2", "3" generally and now grasp the concept "number". You can't have a higher level concept "number" until you have some specific numbers like "1", "2", "3". That's why I objected to the idea of "perceiving 4", since you never perceive floating 4.

What is still confusing me about units is the following statement:

"The concept of unit is a bridge between metaphysics and epistemology: units do not exist qua units, what exists are things, but units are things viewed by a consciousness in certain existing relationships" -- Introduction to Objectivist Epistemology, p.7

This is what has given me the idea that units exist only in consciousness.

This is about what's often known as the problem of transduction, which in my opinion is the hardest part of epistemology and cognitive science. As you can see, it combines aspects of the external world -- actual dogs -- and consciousness. Groupings such as "dog" or "salmon" are not rigorously pre-determined by nature, rather they are man-made. But they are not made by man willy-nilly, they are made by our choice to focus on one aspect of the existents, versus another. I see Rand's introduction of "unit" as being an important clarificatory step, in combining the hardness of reality with the volitionality of focus. Duckbilled platypi end up being mammals because in forming these concepts, we focus on certain aspects of animals, not because the category "mammal" is automatically predetermined.

[Thomas M. Miovas Jr.]

I agree with the general gist of David Odden's reply, but one actually starts off with the perceptually self-evident similarities. One man looks very similar to another man, if they are differentiated from, say, the family pet. So, one might perceive mom, dad, uncle Billy and a guest, which are perceptually different from the family pet (a dog or a cat) because the dog or cat walks on four legs, while all those other walking creatures walk on only two legs. There are many other perceptual similarities between mom, dad, uncle Billy, and the guest -- I mean it becomes obvious on the perceptual level that these are similar. So, one mentally isolates those perceived entities, which is the beginning of unit formation, and then mentally integrate them together to form the concept "man." Unitization begins when one observes that the entities are similar (within a context), and just before one integrates them mentally: Each of these observed entities (mom, dad, uncle Billy, and the guest) is similar (can be mentally interchanged), but only if one differentiates them properly and then integrates them properly.

The reference to mathematics might be useful, in that for the equation x+y=z all of the following are interchangeable conceptually:

1+1=2

2+4=6

5+3=8

10+15=25

Etc.

In other words, x can be any number, and y can be any number, but it has to be a number and not something else. So, for a given concept, "dog" for example, any dog can fit under the definition, but it has to be a dog -- and not a cat or a car. For each of these dogs, they are interchangeable mentally, since each one is a unit of the concept.

Units exist in man's mind in the sense that they have to be grasped mentally, but it is a mental grasp of something one actually observes; which is why Miss Rand says that it is a bridge between metaphysics (what exists in reality) and epistemology (consciousness, or that which one is aware of). It is a relationship between man's mind and existence.

Without man's mind or without the conceptual grasp, a dog is just a dog, and has no special relationship to a human mind. That special relationship is considering it as a a unit; as one of many things that can be considered similar within a context such that one can form a concept of those items into one mental grasp.