Understanding orders of abstraction and reduction.

[fatdogs12]

Wow I am glad to see there is a forumn here to discuss this all. I have been reading Ayn Rand's non fiction as well as Peikoffs for about 2 years now. I have a huge issue though that doesn't seem to make any sense to me.

What I want to be able to do is reduce concepts and ideas to thier perceptual roots in order to know if what I "know" is accurate. So I started looking at the definitions that I had for a concept and tried to reduce it. That brought up a problem. First of all it seems that the Genus of a concept is (maybe by it's nature) more abstract than the concept it self.

Take the concept running for example. Using a basic defintition I would say it would look like this:

Genus: an activity

Differentia: where a creature moves quickly through use of it's legs.

Okay so lets say we were trying to reduce running to it's perceptual roots. I would think we would need to look at the terms of the defiinition and reduce those (though I have been since told that is called rationalism). The issue though is that "activity" subsumes running, walking and everything else.

But wait... Don't we need the concepts running, walking, etc to form the concept activity? isn't activity dependant on these concepts? If that is the case does that mean we ignore the the genus? How would reduction work?

This is the issue that i have with the hierarchy of concepts. I have been trying to digest this issue for over a year but it just won't go down... Doesn't make sense.

What do you guys think?

[Hal]

What do you mean by 'reduce running to its perceptual roots'? The perceptual roots of running would surely just be people running - you dont need the concept 'activity' here. I dont think that Ayn Rand viewed forming definitions as involving reducing concepts to percepts - rather it involves identifying what role a concept has in our framework. Rand held that our definitions could change over time as our knowledge increased, but we wouldnt say our perceptual roots changed in this way.

Is there any reason why a concept shouldnt be defined in terms of something more abstract? The purpose of definitions isnt to break down our concepts into their 'simple parts' like it would be in Russell style "linguistic analysis".

Edited April 4, 2005 by Hal

[fatdogs12]

I guess I don't get it then. It's true that we can see people running but if concepts are hierarchial in nature how can we reduce our concepts to thier percentual roots in order to validate those concepts or ideas? Take a much more abstract concept like computer. We obviously can see a computer but we defintely need other concepts to understand what a computer is.

Edited April 4, 2005 by fatdogs12

[Hal]

Can you clarify what you mean by 'reduce a concept to its perceptual roots'? Do you mean identifying the existents involved in its formation, or something else?

Edited April 4, 2005 by Hal

[JMeganSnow]

You can't reduce concepts for simple concretes like "table" or simple actions like "running". They aren't abstract concepts, they are concepts for perceptual concretes.

You CAN reduce the concepts for abstractions like "furniture" and "activity" though.

The genus is not necessarily more abstract than the concept, either. Take, for example, the concepts "table" and "dining table". "Dining table" requires an extra abstraction . . . another measurement than the simple one defining "table" which is "shape" . . . you also have to understand the "purpose" of the table. Yet "table" is the genus of "dining table" and also "coffee table" etc.

[Hal]

You can't reduce concepts for simple concretes like "table" or simple actions like "running".  They aren't abstract concepts, they are concepts for perceptual concretes.

...

Yet "table" is the genus of "dining table" and also "coffee table" etc.

I dont think I like this formulation. If table is a simple concrete, then what is a dining table? Arent dining tables types of tables in the same way tables are types of furniture?

[fatdogs12]

Good point. I guess what I mean is that concepts have a hierarchial dependancy on other concepts all the way to the perceptual root right? How do I work my way down that ladder all the way back to the perceptual level? How do I perform that? Do I use the definition in some way?

Ultimately I want to be able to retrace a concepts nessasary development and figure out how it is formed as well as be able to work backwards

[Hal]

Ultimately I want to be able to retrace a concepts nessasary development and figure out how it is formed as well as be able to work backwards

Well, I dont think it's always going to be the case that concepts are formed in the same order you would reduce them. For instance, I formed the concept of 'animal' before I formed the concept of 'komodo dragon', even though komodo dragons would be lower in any logical hierarchy. I think you could either do a 'logical' reduction of a concept, or an analysis that is based upon the order in which most people would actually form it. I would personally say the second is most useful, and I dont think the first would even be possible in a lot of cases.

I would personally say the best way to do it would be to consider a human child and try to work out what he would actually be likely to do, rather than meditating on the concepts themselvse.

Edited April 4, 2005 by Hal

[fatdogs12]

That statement you just made HAL is pretty much incredible. Ayn Rand talks about how it's important to understand EVERY concepts interelations hierarchially to understand which concepts depend on which, which come from which, etc. Maybe I am misunderstanding

[Hal]

That statement you just made HAL is pretty much incredible. Ayn Rand talks about how it's important to understand EVERY concepts interelations hierarchially to understand which concepts depend on which, which come from which, etc. Maybe I am misunderstanding

But this is surely different from investigating the order in which they were actually formed? I mean 'morality' depends on 'philosophy', but wont some people have the concept of morality before they have the concept of philosophy? And almost everyone will know 'table' before they know 'dining table' (it's hard to imagine how someone could have the concept of dining table before they had the concept of 'table' - as JMeganSnow said, it involves further abstractions).

Edited April 4, 2005 by Hal

[fatdogs12]

That is what I am saying, what matters is not what order you formed it but whta concepts are dependant on which others.

[Gabriel_S]

What I want to be able to do is reduce concepts and ideas to thier perceptual roots in order to know if what I "know" is accurate. So I started looking at the definitions that I had for a concept and tried to reduce it. That brought up a problem. First of all it seems that the Genus of a concept is (maybe by it's nature) more abstract than the concept it self.

Take the concept running for example. Using a basic defintition I would say it would look like this:

I think part of your confusion stems from a certain misapprehension regarding the purpose of conceptual reduction in a normal person's life. I don't think the sort of concepts you should be aiming to reduce to the perceptual level, are lower level items, such as running or furniture. That won't be very rewarding. Are you going to reduce thousands of near-perceptual level concepts?

Reducing these low level concepts are what you should have already done, assuming you are a speaking adult, as a child. If you can use the concept running in the following sentence and understand it, you've already done your reduction (years ago): Bob is running across the street. I'll assume you can clearly understand that sentence. If so, skip trying to reduce running because your running down a dead-end street.

What the average person (i.e., one who is not validating knowledge in some specialized field of study) needs to reduce is, basically a handful of concepts. I'm referring, here, to abstract, philosophic concepts, such as freedom, justice, egoism, art, and so on. Try to reduce these kind of concepts, and I think you'll find it much more fruitful.

[Gabriel_S]

I would personally say the best way to do it would be to consider a human child and try to work out what he would actually be likely to do, rather than meditating on the concepts themselvse.

I.e., what facts of reality give rise to the need for such a concept as X?

Edited April 4, 2005 by Gabriel_S

[Nate T.]

That is what I am saying, what matters is not what order you formed it but whta concepts are dependant on which others.

This is the distinction between the logical order of concepts and the chronological order of concepts. One can both specialize concepts by subdividing them into narrower categories, and integrate concepts under a new concept.

For example, one can form the concept "apple" first, and then later subdivide to "Macintosh" and after that form the wider concept "fruit." However, the logical order (Macintosh is an apple is a fruit) does not necessarily have anything to do with the order in which you formed these concepts-- it depends on the amount of knowledge you have avaliable to you and the objective need of forming the concept.

[Gabriel_S]

That is what I am saying, what matters is not what order you formed it but whta concepts are dependant on which others.

Yes, but what it comes down to is that conceptual dependency itself means what must be learned before what. Conceptual hierarchy is a product of the order by which we learn concepts. There are sometimes options in the order of learning, but where there aren't any, there is a necessary logical dependence of one concept upon another. In those cases, using a concept while denying or ignoring the more basic concept upon which it depends, is what Objectivism refers to as the fallacy of the stolen concept.

[Gabriel_S]

That statement you just made HAL is pretty much incredible. Ayn Rand talks about how it's important to understand EVERY concepts interelations hierarchially to understand which concepts depend on which, which come from which, etc. Maybe I am misunderstanding

Surely you can't be saying that you must reduce every concept? That doesn't seem possible (nor is it actually necessary).

[fatdogs12]

Gabriel what I am saying is that I want to reduce higher level concepts. I didn't even realize that "running" was a lower level concept until i was told. That is the point though. Lets say I want to reduce computer to understand it's hierarchial depenedance how would I do it?

The things you say about the order in which you learn things is the dependance is not true however (from what I have read) and Peikoff and Rand both state that there is a difference and what does NOT matter is the order in which is what learned. What matters is what things actually depend upon for creation.

[Gabriel_S]

Gabriel what I am saying is that I want to reduce higher level concepts. I didn't even realize that "running" was a lower level concept until i was told. That is the point though. Lets say I want to reduce computer to understand it's hierarchial depenedance how would I do it?

Why would you want to reduce "computer," if may ask? Why not, for instance, ethical or political concepts, the sort of concepts that a normal person is going to be quite confused about (and which will really make a difference in their life)?

The things you say about the order in which you learn things is the dependance is not true however (from what I have read) and Peikoff and Rand both state that there is a difference and what does NOT matter is the order in which is what learned. What matters is what things actually depend upon for creation.

I'm sorry, but I don't really understand what you are saying here. The best I can gather is that you are really mixed up on this subject and it's a little more than I can tackle at this point in the day. I think your last sentence is a good clue as to why you are having such a difficult time reducing even very simple concepts. Perhaps this question will help get you to see where you are mixed up: what do you think it means for a concept to depend upon another concept? Give me an answer from your own understanding, in your own words, with a few clear examples.

[dougclayton]

If you can use the concept running in the following sentence and understand it, you've already done your reduction (years ago): Bob is running across the street. I'll assume you can clearly understand that sentence.

Excellent example, Gabriel. This shows how running is very close to a first-level concept. In reality, no one has any difficulty understanding the referents of "running," which is why people understand the meaning of that sentence.

What the average person (i.e., one who is not validating knowledge in some specialized field of study) needs to reduce is, basically a handful of concepts. I'm referring, here, to abstract, philosophic concepts, such as freedom, justice, egoism, art, and so on. Try to reduce these kind of concepts, and I think you'll find it much more fruitful.

Agreed again. I think your examples might be a little tough for first exercises, though. A better model would be Peikoff's example of reducing "friend." Friend is abstract enough for the reduction to be worthwhile, yet concrete enough that you can do it without going too far astray.

[JMeganSnow]

I dont think I like this formulation. If table is a simple concrete, then what is a dining table? Arent dining tables types of tables in the same way tables are types of furniture?

A table is an obvious, physical, perceptual concrete. The attribute differentiating it from all other objects is a simple, single, perceptual one; shape.

The concept "dining table" (which is actually a qualified concept, but close enough) requires an extra abstraction, as I said, the identification of the purpose to which the table is put. You cannot form the idea "dining table" without first having the idea "table" . . . you cannot differentiate tables by purpose without first differentiating tables from all other physical objects.

Dining tables ARE types of tables just as tables are types of furniture, but what I am saying is that you START with the idea "table" and go both up and down from there, differentiating the concept further into qualified examples ("dining table") and integrating it into more abstract concepts ("furniture").

[dougclayton]

The things you say about the order in which you learn things is the dependance is not true however (from what I have read) and Peikoff and Rand both state that there is a difference and what does NOT matter is the order in which is what learned. What matters is what things actually depend upon for creation.

I believe the point Gabriel is making is that you can't learn concepts in just any order. If concept A logicaly depends on B and C, you can't learn A before B and C. You can memorize the definition of A but you can't really understand it. Furthermore, using it will almost certainly result in the fallacy of the stolen concept, because you will use A while denying B or C without realizing it.

Of course there is plenty of variation in the order you learn things, but there is a broad order as well. Mathematics gives a very good example, in that you must learn how to count before learning multiplication or (god forbid) set theory.

[JMeganSnow]

Reducing a concept is basically a process of saying, "What are the referents?" (as Gabriel said--the referents in reality).

You may find it useful to identify what basic category the concept belongs in before you try to reduce it: is it an entity (a table), an attribute (blue), an action (running), or a relationship (next to)?

For example: the concept "friend" is used to denote a certain relationship between two human beings.

Reducing a concept is not necessarily the same as defining it; it means that you have placed it relative to all of your OTHER concepts.

A more difficult example; justice is actually an attribute of a relationship; certain relationships can be described as "just" or "injust". Without that relationship, there can be neither justice nor injustice. So, that places the concept of justice within a hierarchy; it requires relationships between human beings, most specifically, relationships of EXCHANGE. (Physical proximity etc. are relationships, but they don't have anything to do with justice. The bizarre laws in some cultures such as "no one's head may be higher than the king's head" are a failure to understand that justice applies only to relationships of exchange, not HEIGHT."

[FluxCapacitor]

Hi, I recently began reading through Leonard Peikoff's book Objectivism: The Philosophy of Ayn Rand, and I have encountered something which I do not quite understand. It is perhaps a minor point, but it is annoying me greatly, so I would appreciate any clarification anyone could provide on the matter.

The issue I speak of is that of "higher-level" concepts, or "abstractions from abstractions." Dr. Peikoff discusses this on page 91 under the heading "Concepts of Consciousness as Involving Measurement-Omission." The only online source I have found dealing with this topic is in William Thomas's explanation of Rand's theory of concepts.

In both cases, there are described certain "higher-level" concepts which, it is claimed, cannot be formed directly from perceptual data. Peikoff uses the example of the concept of "animal", which he says requires concepts such as "cat", "dog", and "horse" to already be in place. In other words, I if am understanding him correctly, one cannot, by looking at a specific cat, dog, and horse, form a concept encompassing all three of these objects. I think I must be missing something here, because it seems pretty obvious that we can do just that. A rudimentary definition of "animal" from looking at these objects might be, to follow the definition presented for a child's conception of man, "a furry entity with four legs which moves and makes sounds." Then, if we saw a fish, and wanted to classify with the rest of our animals to differentiate it from, say, a toaster, we might revise our definition to say "an entity which moves of its own accord."

My question is, why can't we form concepts such as "animal" and "food" without first conceptualizing "cat" and "dog or "hot dog" and "hamburger"?

I would greatly appreciate any clarification, or correction of anything I am not comprehending correctly. Thanks!

[JMeganSnow]

Conceptualization is much more thoroughly addressed in Introduction to Objectivist Epistemology.

In the appendix, a question very similar to your question is raised, however, the reason is really very simple.

A very small child, when first forming concepts from perceptual data, doesn't think in terms of verbal definitions (having a definition like that would require a large range of concepts.) Instead, their first concepts are defined ostensively with the aid of their parents and anyone else around that happens to have some concepts("where's the horsie!?").

You cannot form a definition for a higher-level concept easily from simple ostensive evidence. Ayn Rand uses the concept "furniture", she mentions that a child would not have the perceptual DATA to form the concept "furniture" before that of, say, "table" unless he happened to live in a furniture store.

There are a great many options as to the order in which children form concepts. Higher-level concepts are also called "higher-level" because they subsume under their definition many lower level concepts; furniture subsumes tables, chairs, etc. Higher-level concepts can also be LESS specific (particular breeds of horses, for example) but require further abstraction because you have to recognize a new idea in order to form them; the idea of what a "breed" entails.

Really, I recommend reading ITOE, it's more helpful than I'm going to be.

[dougclayton]

My question is, why can't we form concepts such as "animal" and "food" without first conceptualizing "cat" and "dog or "hot dog" and "hamburger"?

I think you could conceivably form "animal" first, but it would require unusual circumstances (similar to the furniture-store thought experiment). If you lived in a zoo with exactly one of each type of mammal, you might form the concept of, say, "moving, breathing thing." But this requires that you not see several cats at once, because the similarities between cats are far greater than the similarity between mammals. In other words, if you lived around 20 cats, 20 dogs, 20 horses, 20 cows and 20 mice, you could not possibly see the similarities between all of them before you saw the differences. The human mind just doesn't work that way.

In support of this point, I remember when my little sister was having difficulties with the way "person" is related to "boy" and "girl" when she was three years old. She kept telling me I could not be a person because I was a boy.