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The Conceptual Hierarchy

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I don't mean reduction. A concept's genus (it's "parent" concept in the hierarchy) is more abstract than the concept. So

table -> furniture -> man-made object -> entity -> existent -> existence

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The correct order is: existent > entity > table > furniture > man-made object > metaphysically given > existence

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Oops. The concept "unit" should be between entity and table.

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That last would be better as "If you mean that there's no single, root concept at the base or 'point,' then could you elaborate?"

That's what I meant--that there is no single concept at the top of the hierarchy. In particular, the axioms such as existence do not belong at the "top."

Since axiomatic concepts are not formed by differentiating one group of existents from others, but represent an integration of all existents, they have no Conceptual Common Denominator with anything else. They have no contraries, no alternatives.

[...]

The concept "existence" does not indicate what existents it subsumes: it merely underscores the primary fact that they exist. The concept "identity" does not indicate the particular natures of the existents it subsumes: it merely underscores the primary fact that they are what they are. The concept "consciousness" does not indicate what existents one is conscious of: it merely underscores the primary fact that one is conscious.

The axiomatic concept "existence" doesn't depend on lower concepts (like table, chair, etc.). It is grasped before them--at the first sensation. The axioms are the province of metaphysics. The conceptual hierarchy doesn't arrive until we get to epistemology.

Epistemologically, the formation of axiomatic concepts is an act of abstraction, a selective focusing on and mental isolation of metaphysical fundamentals; but metaphysically, it is an act of integration—the widest integration possible to man: it unites and embraces the total of his experience.

[...]

although they designate a fundamental metaphysical fact, axiomatic concepts are the products of an epistemological need—the need of a volitional, conceptual consciousness which is capable of error and doubt. ... It is only man's consciousness, a consciousness capable of conceptual errors, that needs a special identification of the directly given, to embrace and delimit the entire field of its awareness—to delimit it from the void of unreality to which conceptual errors can lead.

Keep in mind that we form concepts for a reason. They help us (successfully) deal with the virtually unlimited number of concretes we encounter. Even though they are implicit in any thought, the axiomatic concepts are consciously grasped and identified much later for a specific purpose: to "delimit [man's consciousness's awareness] from the void of unreality to which conceptual errors can lead."

So there are two basic facts I've highlighted at this point:

(1) That "existence" doesn't depend on any particular existents or refer to those which it subsumes

(2) We form the axiomatic concepts to help prevent errors in concept-formation

The axiomatic concepts, then, are very abstract. They are in a particular strand of abstraction pretty far from the perceptual level--up in the realm of philosophy. This does not imply that the axioms (in a metaphysical sense) depend on everything below them in the conceptual hierarchy--in fact any concept-formation whatsoever implicitly accepts the axioms. Rather, the proper epistemological identification of them depends on all that which is below them in the hierarchy.

Existence, then, is not at the "top" of the hierarchy with the purpose of bringing everything together into some grand concept at the apex of all human knowledge. Rather, it is a concept used to guide man's concept-formation in helping to prevent errors.

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I think your diagram goes in the wrong direction.  One does not trace a concept back to the axiomatic concepts; one traces a concept back to the perceptually given - the directly perceivable.

The direction in which one traverses the hierarchy depends on one's purpose.
The process of observing the facts of reality and of integrating them into concpets is, in essence, a process of induction.
That's not what I'm doing here.
The process of subsuming new instances under a known concept is, in essence, a process of deduction.
That's also not what I'm doing here.

I dont' have an AR quote for this, but what you stated above is covered by this: the process of tracing a concept back to the perceptually given is, in essence, a process of reduction. That's not what I'm doing here.

I'm not forming or validating concepts (induction and reduction, respectively), and I'm not placing new instances into existing concepts (deduction); for purposes of what I'm trying to accomplish here, we can assume that all that is already done. I'm examining the conceptual hierarchy itself.

The axiomatic concept is "on the other side" - it is the most abstract of all concepts.  As mentioned in ITOE, the concept existence is an abstraction "of a basic fact from all facts."

Right. And what I want to know is this: is there only one "most abstract of all concepts?" If so, what is it? If not, why not and how many are there?

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And what I want to know is this: is there only one "most abstract of all concepts?" If so, what is it? If not, why not and how many are there?

Didn't the initial posts in this thread answer that question, along with providing quotes explaining why "existence" is the widest of all concepts? Do you disagree with that answer? If so, why?

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The correct order is: existent > entity > table > furniture > man-made object > metaphysically given > existence

This is incorrect. To see why, read it this way: a table is a kind of furniture (true); an entity is a kind of table (false); an existent is a kind of entity (false, though less obviously so).

Not all existents are entities. For example, Peikoff states in OPAR that air is not an entity, though it is clearly an existent. And certainly not all entities are tables. "Existent" and "entity" are more abstract than "table," therefore they're not closer to the perceptual level, which is to the left in your diagram.

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The direction in which one traverses the hierarchy depends on one's purpose.

But one's purpose does not change the order of the hierarchy. You said "traces back." [my emphasis] To trace back is to go back to the perceptual level. The other direction would be "traces forward or up."

That's not what I'm doing here.That's also not what I'm doing here.  I dont' have an AR quote for this, but what you stated above is covered by this: the process of tracing a concept back to the perceptually given is, in essence,  a process of reduction. That's not what I'm doing here.

I'm not forming or validating concepts (induction and reduction, respectively), and I'm not placing new instances into existing concepts (deduction); for purposes of what I'm trying to accomplish here, we can assume that all that is already done. I'm examining the conceptual hierarchy itself.

Right. And what I want to know is this: is there only one "most abstract of all concepts?" If so, what is it? If not, why not and how many are there?

So, let me understand. You're not deducing, inducing or reducing??? Well, I'm not familiar with other methods of reasoning. How would you grasp "the most abstract of all concepts" without those 3 methods? Did I not answer your question in Post #2?

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Didn't the initial posts in this thread answer that question, along with providing quotes explaining why "existence" is the widest of all concepts? Do you disagree with that answer? If so, why?

It did, and I agree. I'm remaining open to contrary arguments for the time being to be sure I haven't missed something - there are enough people here who might have a better understanding than I do that I want to hear from them if those contrary arguments are there to be made. I don't think they are, and I think I have a strong grasp of Objectivist epistemology, but I've also been wrong before when I was sure I was right.

Everything else has been the attempt on my part to clear up what appear to me to be wholesale misunderstandings of what I'm after here.

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This is incorrect. To see why, read it this way: a table is a kind of furniture (true); an entity is a kind of table (false); an existent is a kind of entity (false, though less obviously so).

I'd urge you to read or re-read ITOE and then think about that. I think you are confusing the concept with the specific referent, i.e., you are not grasping that unit is a thing regarded as a member of a class of things. When you classify something as a "table" you've already observed and conceptualized that it is a member of a group of units (entities) that have similar characteristics. To give you some of what Rand said on the subject:

The building-block of man's knowledge is the concept of an "existent"—of something that exists, be it a thing, an attribute or an action.

The (implicit) concept "existent" undergoes three stages of development in man's mind. The first stage is a child's awareness of objects, of things—which represents the (implicit) concept "entity."

The third stage consists of grasping relationships among these entities by grasping the similarities and differences of their identities. This requires the transformation of the (implicit) concept "entity" into the (implicit) concept "unit."

Not all existents are entities. For example, Peikoff states in OPAR that air is not an entity, though it is clearly an existent. And certainly not all entities are tables. "Existent" and "entity" are more abstract than "table," therefore they're not closer to the perceptual level, which is to the left in your diagram.

The identification of air as an existent is a scientific issue not a philosophic issue. Human consciousness does not perceive air (as well as many existents) as a solid object. The fact that air is not an entity does not invalidate the means by which man forms concepts. The concept of air was most likely conceptualized by observing the effects it had on objects, such as the wind.

As Rand mentions above and in ITOE, "existent" and "entity" are closer to the perceptual level than table. The fact that "existent" is more abstract than "table" does not mean it is further from the perceptual level. One must distinguish between the metaphysical and the epistemological here. Epistemologically, the first stage of awareness is awareness of something, i.e., existent. The fact that you are aware of tables before you grasp the concept of "existent" is not the issue.

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But one's purpose does not change the order of the hierarchy.  You said "traces back." [my emphasis]  To trace back is to go back to the perceptual level.  The other direction would be "traces forward or up."

Yes, and that was careless on my part (not the first time). "Trace up," i.e. toward the more abstract, would have been better.
So, let me understand.  You're not deducing, inducing or reducing???  Well, I'm not familiar with other methods of reasoning. How would you grasp "the most abstract of all concepts" without those 3 methods?  Did I not answer your question in Post #2?

Yes, you answered the question, and with the answer I had come to on my own before asking the question (see my reply to Stephen just above for why I continued despite having an answer I agreed with).

This (all of this, not just your post) is maddening! It's so very clear to me, but for some reason I am unable to get my meaning across, and I can't figure out why.

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--------------

This (all of this, not just your post) is maddening! It's so very clear to me, but for some reason I am unable to get my meaning across, and I can't figure out why.

This tells me maybe you should take a break and think more about the subject in light of what has been said on this thread and come back to try to reformulate your question. I think you're misunderstanding some issues.

An alternative track is to try to explain to me or others what you think is wrong with our reasoning. You haven't demonstrated that you've fully understood what we're saying to you.

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Yes, and that was careless on my part (not the first time). "Trace up," i.e. toward the more abstract, would have been better.

Yes, you answered the question, and with the answer I had come to on my own before asking the question (see my reply to Stephen just above for why I continued despite having an answer I agreed with).

This (all of this, not just your post) is maddening! It's so very clear to me, but for some reason I am unable to get my meaning across, and I can't figure out why.

The fact that we gave an answer that you agreed with does not mean that we agree with your reasons for holding that answer. When it comes to epistemology, one should be careful about how one holds certainty in one's mind. If someone offers an argument or example that doesn't fit into your understanding, then you need to consider it carefully and not keep repeating what you've already stated.

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An alternative track is to try to explain to me or others what you think is wrong with our reasoning.

Here's an attempt at that:
I'd urge you to read or re-read ITOE and then think about that.  I think you are confusing the concept with the specific referent, i.e., you are not grasping that unit is a thing regarded as a member of a class of things.  When you classify something as a "table" you've already observed and conceptualized that it is a member of a group of units (entities) that have similar characteristics.

A table is an existent, an existent is not necessarily a table. The concept "existent" integrates many more concretes than just "table," therefore it is more abstract than "table." (Substitute "unit" for "existent" and the argument is the same.) More abstract concepts are further from the perceptual level than less abstract concepts. Your original diagram:
existent > entity > table > furniture > man-made object > metaphysically given > existence

states the following: an existent is an entity, an entity is a table, a table is furniture, furniture are man-made objects, man-made objects are metaphysically given, and the metaphysically given is part of existence. When one states, in the context of the conceptual hierarchy, that A is a type of B, it means that every A is a type of B, because B, being the genus, subsumes all As. And, to pick the most obvious example from your diagram, it's simply a fact that not all entities are tables. A platypus is an entity, but it's not a table.
As Rand mentions above and in ITOE, "existent" and "entity" are closer to the perceptual level than table.

No. What is perceptually given are tables. I can point at a table, I cannot point at an existent qua existent.
The fact that "existent" is more abstract than "table" does not mean it is further from the perceptual level.

Yes it does. "Further from the perceptual level" is a necessary result, if not just about the definition, of "more abstract."
One must distinguish between the metaphysical and the epistemological here.  Epistemologically, the first stage of awareness is awareness of something, i.e., existent.  The fact that you are aware of tables before you grasp the concept of "existent" is not the issue.

It doesn't matter to their proper place in the hierarchy in what order the concepts are formed. Yes, a child first experiences percepts as undifferentiated "things" (i.e. existents), but that doesn't lock "existent" at the perceptual level in the hierarchy any more than the fact that the child forms "dog" before he forms "poodle" makes "poodle" more abstract than "dog." "Existent" is not a first-level (i.e. immediately derived from the perceptual) concept, "table" is.

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I don't mean reduction. A concept's genus (it's "parent" concept in the hierarchy) is more abstract than the concept. So

table -> furniture -> man-made object -> entity -> existent -> existence

So I'm not talking about reduction, which goes from abstract to concrete (e.g. from the concept "table" to "actual existing tables"). I'm talking about going the other direction in the hierarchy, and determining whether it's true that for all concepts the end of that path is the same, identical concept.

Do you really mean going from the concrete to the more abstract? Subdivisions of concepts into narrower concepts are just as abstract -- just as removed from the perceptual level -- as integrations of concepts into wider concepts:

table --> dining table --> trestle table

Maybe you mean going from narrower concepts to wider concepts. If so, the widest concept is existence.

Now, in forming concepts, moving from the relatively more concrete to the more abstract would be induction. But that's not what I mean, either, because in this case we're not forming the concepts, we're examining a hierarchy that's already formed (actually a theoretically "complete" conceptual hierarchy).

"Hierarchy," as I understand it, refers to the logical order in which concepts are grasped. While some concepts are necessarily dependent on others, there are still many options as to the order in which a person grasps concepts. The particular narrower-to-wider classification may vary, even for the same person, depending on his context and his purpose in integrating and classifying. An example could be:

table --> wooden entities --> buoyant things

A "hierarchy" is always somebody's hierarchy and those of rational people will differ because individuals vary in their purposes and in their contexts of knowledge.

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This tells me maybe you should take a break and think more about the subject in light of what has been said on this thread and come back to try to reformulate your question.  I think you're misunderstanding some issues.

Not just "some issues:" if what you're saying on this topic is correct, then I have completely misunderstood all of Objectivist epistemology. Yet what you wrote appears to be inconsistent not just with my understanding but also with everything relevant I can recall reading from those whose expertise in this area I believe to be genuine.

At this point I'll just say that I continue to disagree and let it go at that.

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----------

And, to pick the most obvious example from your diagram, it's simply a fact that not all entities are tables. A platypus is an entity, but it's not a table.

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But you do not perceive a "platypus." You observe an entity, an object. You conceptually classify it as a platypus because you regard the entity as a unit, a specific type of entity in relation to other classes of entities (units), and by abstracting similarities and differences among all enities, then you classify it as a platypus. You abstract away the differences from all other entities and integrated the similiaries to form the concept "platypus."

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Do you really mean going from the concrete to the more abstract?  Subdivisions of concepts into narrower concepts are just as abstract -- just as removed from the perceptual level -- as integrations of concepts into wider concepts:

table --> dining table --> trestle table

Maybe you mean going from narrower concepts to wider concepts.

That could be at least part of my problem here. Let me give it some thought.
If so, the widest concept is existence.

I agree. Now, when you say "subdivisions of concepts into narrower concepts are just as abstract...as integrations of concepts into wider concepts," are you saying that "existence," while wider, is no more or less abstract than "trestle table?"
"Hierarchy," as I understand it, refers to the logical order in which concepts are grasped.  While some concepts are necessarily dependent on others, there are still many options as to the order in which a person grasps concepts.  The particular narrower-to-wider classification may vary, even for the same person, depending on his context and his purpose in integrating and classifying.  An example could be:

table --> wooden entities --> buoyant things

I've given a lot of thought recently to corollary concepts. For example, "identity" is a corollary of "existence:"
Prof. B: I'm interested in the fact that "existence" and "identity" have the same units, yet they are different concepts. In general, would it be true that if two different concepts have the same units, then what makes them two concepts rather than one is that in each case the units are differentiated from something else? For instance, in the case of "concrete" versus "entity," the units are the same, but the concept "entity" distinguishes entities from attributes, while the concept "concrete" distinguishes entities from abstractions.

AR: That's correct.

Prof. B: Then is it the case that what distinguishes the concepts "existence" and "identity" is that the concept "existence" differentiates this object from nothing, while "identity" distinguishes this from that?

AR: You could put it that way. The distinction between these two is really an issue of perspective. "Existence" is the wider concept, because even at an infant's stage of sensory chaos, he can grasp that something exists. When he gets the concept "identity," it is a further step—a clearer, more specific perspective on the concept "existence." He grasps that if it exists, it is something. Therefore, the referents of the concept "identity" are specific concretes or specific existents.

My thought here is that a variance in classification could really be a use of, or at least a use similar to, corollaries, i.e. different perspectives on the same referents.

This just occurred to me: "existence" and "identity" are corollary concepts and have two different words to denote them. In your example, "table" is an instance of "wooden entity," and in the classic Objectivist example "table" is an instance of "furniture." Perhaps the first "table" and the second "table" are also corollaries, and it just happens that they use the same word (in a manner similar to the way the word "like" has many different definitions each representing a different concept).

I had been concerned that, given different classifcations, there could contradictions between two individually valid hierarchies. Now I see that that's not the case, that "table," to continue with that example, can have two classifications and not be two different things at the same time (and thereby violating the law of identity).

A "hierarchy" is always somebody's hierarchy and those of rational people will differ because individuals vary in their purposes and in their contexts of knowledge.

True. Now, consider an attempt to create a more comprehensive hierarchy by combining the hierarchies of two or more individuals (to some extent this is what learning is, although I have something else in mind in mentioning this). Even though two particular individuals might have, let's say, the one of the two variant classifications for "table," if it's valid to treat them as corollaries then there need be no contradiction in combining the two hierarchies ("table" can be an instance of "furniture" and of "wooden entity" - that is, neither classification is incorrect, and the difference is the kind of perspective AR mentions above). In fact there should be no contradictions in integrating any number of hierarchies into one (so long as all the concepts in each hierarchy is valid, but let's assume that's true).

So, it ought to be possible to create a conceptual hierarchy containing all concepts, a kind of "unabridged dictionary" of conceptual integration. Or, at least, it ought to be possible to represent in some human-accessible form (a database, for example), that all-encompassing hierarchy.

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But you do not perceive a "platypus."

I didn't say that one perceives a "platypus," I said that one perceives a platypus.* :) That is, one does not perceive the concept "platypus," which would be a Platonic reification, but an actual entity. But that is not to say that one is perceiving an entity qua entity. That which one perceives has identity, it is what it is, and in this case it's a platypus, whether or not one has formed the concept "platypus" yet. It's identity is at all times more specific than just "an entity."
You observe an entity, an object.  You conceptually classify it as a platypus because you regard the entity as a unit, a specific type of entity in relation to other classes of entities (units), and by abstracting similarities and differences among all enities, then you classify it as a platypus.  You abstract away the differences from all other entities and integrated the similiaries to form the concept "platypus."

This sounds to me like you're saying that it doesn't gain its identity as a platypus until you've formed the concept "platypus," and before that it's just a thing. But identity is prior to conceptualization - it is what it is whether or not anyone ever forms the concept "platypus," just as some creature living right now on some extrasolar planet is what it is even though no one has formed a concept for it yet.

*Note to someone who knows who I mean here ;): this is where a more formal typographical convention for distinguishing concepts from their referents would be very useful and clarifying.

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This sounds to me like you're saying that it doesn't gain its identity as a platypus until you've formed the concept "platypus," and before that it's just a thing. But identity is prior to conceptualization - it is what it is whether or not anyone ever forms the concept "platypus," just as some creature living right now on some extrasolar planet is what it is even though no one has formed a concept for it yet.

To quote something fundamental from Galt's speech: "Existence is Identity, Consciousness is Identification." What a thing is, *is* its identity, but it is the task of consciousness to *identify* that thing. From a mechanistic standpoint, identification is a sort of pattern recognition: given such-and-such information about the characteristics of something, then map those characteristics into a condensed mental unit. At the pre-conceptual level of consciousness, animals can clearly identify specific kinds of prey, trees to nest in, and so forth, in a very crude, non-hierarchical form of pattern recognition, but still a kind of identification in their consciousness. (In other words, they can correctly identify, say, any particular instance of a fish that they want to eat even though in literal sensory/perceptual details, every fish they observe will be different and distinct.)

At the conceptual level, our ability to abstract means that the process of pattern recognition, involving measurement omission (only matching essential characteristics and omitting inessentials, which is fundamental to what it means to perform the mental unit compression of pattern recognition), can occur hierarchically (abstractions from abstractions), which is a fundamental difference. Then the pattern recognition occurs at multiple levels, and if we have an existing well formed hierarchy of concepts, we can match the thing we're focusing on using that framework. (This isn't necessarily a flawless process but it can be corrected by contradiction-checking and integration, i.e. logic.)

In this hierarchy, a particular identification can occur simultaneously at multiple levels, or is logically implied by the hierarchy. For instance, to take the typical table example, to identify a table means to logically identify it as a piece of furniture - as a man-made object - as an entity - and as an existent. All at once. And you get the most information, the deeper down the tree you can form the identification (i.e. to specialized concepts such as "doll table"), because you automatically have the benefit of knowing that you've identified it all the way up the hierarchical tree to "existent". At each level of the hierarchy, there's a definition of the concept involved, and a proper identification will fit *every one* of those definitions at every level up the tree, but encompassing more and more things in the world (e.g. a Doll table "is-a" table "is-a" man-made-item "is-an" entity "is-an" existent.) Proper definitions actually serve to create the hierarchy, by splitting the widest concept "existent" into finer and finer sets of things based on differentiating characteristics.

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Now, when you say "subdivisions of concepts into narrower concepts are just as abstract...as integrations of concepts into wider concepts," are you saying that "existence," while wider, is no more or less abstract than "trestle table?"

Correct. You can ostensively define "existence" as a first-level concept and a five year-old can grasp it. You sweep your hand around everything in view saying "'Existence' means ALL of this."

I've given a lot of thought recently to corollary concepts. For example, "identity" is a corollary of "existence:"My thought here is that a variance in classification could really be a use of, or at least a use similar to, corollaries, i.e. different perspectives on the same referents.

By "referents" do you mean individual entities that are units of a concept? If so, there are many, many ways you can classify a particular entity using concepts depending on what characteristics you wish to focus on, what similar things you want to integrate it with, and what you intend to differentiate it from. I can classify an ear of corn with the concepts "yellow," "solid," "food," "crop," etc.

In your example, "table" is an instance of "wooden entity," and in the classic Objectivist example "table" is an instance of "furniture." Perhaps the first "table" and the second "table" are also corollaries, and it just happens that they use the same word (in a manner similar to the way the word "like" has many different definitions each representing a different concept).

No, the two "tables" are the same unique table classified as units of different concepts ("wooden" and "furniture").

I had been concerned that, given different classifications, there could contradictions between two individually valid hierarchies. Now I see that that's not the case, that "table," to continue with that example, can have two classifications and not be two different things at the same time (and thereby violating the law of identity).

Certainly.

True. Now, consider an attempt to create a more comprehensive hierarchy by combining the hierarchies of two or more individuals (to some extent this is what learning is, although I have something else in mind in mentioning this). Even though two particular individuals might have, let's say, the one of the two variant classifications for "table," if it's valid to treat them as corollaries then there need be no contradiction in combining the two hierarchies ("table" can be an instance of "furniture" and of "wooden entity" - that is, neither classification is incorrect, and the difference is the kind of perspective AR mentions above). In fact there should be no contradictions in integrating any number of hierarchies into one (so long as all the concepts in each hierarchy is valid, but let's assume that's true).

So, it ought to be possible to create a conceptual hierarchy containing all concepts, a kind of "unabridged dictionary" of conceptual integration. Or, at least, it ought to be possible to represent in some human-accessible form (a database, for example), that all-encompassing hierarchy.

I still don't understand "What for?" Isn't it sufficient for a person to grasp and integrate the concepts necessary for him to understand and deal with the facts that confront him and the values he seeks?

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To quote something fundamental from Galt's speech: "Existence is Identity, Consciousness is Identification." [...] At the pre-conceptual level of consciousness, animals can clearly identify specific kinds of prey, trees to nest in, and so forth, in a very crude, non-hierarchical form of pattern recognition, but still a kind of identification in their consciousness. (In other words, they can correctly identify, say, any particular instance of a fish that they want to eat even though in literal sensory/perceptual details, every fish they observe will be different and distinct.)

27745

Thanks for that analysis; I thought it was very insightful and it expanded my own understanding of the issue.

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I didn't say that one perceives a "platypus," I said that one perceives a platypus.* :) That is, one does not perceive the concept "platypus," which would be a Platonic reification, but an actual entity. But that is not to say that one is perceiving an entity qua entity. That which one perceives has identity, it is what it is, and in this case it's a platypus, whether or not one has formed the concept "platypus" yet. It's identity is at all times more specific than just "an entity."

This sounds to me like you're saying that it doesn't gain its identity as a platypus until you've formed the concept "platypus," and before that it's just a thing. But identity is prior to conceptualization - it is what it is whether or not anyone ever forms the concept "platypus," just as some creature living right now on some extrasolar planet is what it is even though no one has formed a concept for it yet.

*Note to someone who knows who I mean here ;): this is where a more formal typographical convention for distinguishing concepts from their referents would be very useful and clarifying.

I'm sorry, but I don't follow your reasoning here. You seem to be arguing about something that I did not state. I cannot figure out how to untangle this. So unless you can get to one point or simplify what you mean, I'll leave my arguments where they stand at this point.

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To quote something fundamental from Galt's speech...Proper definitions actually serve to create the hierarchy, by splitting the widest concept "existent" into finer and finer sets of things based on differentiating characteristics.

27745

I agree with all of this, but I still think the hierarchy you presented in your diagram is incorrect.

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Correct.  You can ostensively define "existence" as a first-level concept and a five year-old can grasp it.    You sweep your hand around everything in view saying "'Existence' means ALL of this."

There are not degrees of abstraction, only differences in how much is integrated by different concepts. So when AR says in ITOE
Observe that the concept "furniture" is an abstraction one step further removed from perceptual reality than any of its constituent concepts. "Table" is an abstraction, since it designates any table, but its meaning can be conveyed simply by pointing to one or two perceptual objects. There is no such perceptual object as "furniture"; there are only tables, chairs, beds, etc. The meaning of "furniture" cannot be grasped unless one has first grasped the meaning of its constituent concepts; these are its link to reality.
she is not saying that being "one step further removed from perceptual reality" is more abstract.

Is that a correct understanding of what you're saying?

By "referents" do you mean individual entities that are units of a concept?

Yes.
If so, there are many, many ways you can classify a particular entity using concepts depending on what characteristics you wish to focus on, what similar things you want to integrate it with, and what you intend to differentiate it from.  I can classify an ear of corn with the concepts "yellow," "solid," "food," "crop," etc.

Agreed.
No, the two "tables" are the same unique table classified as units of different concepts ("wooden" and "furniture").

That's not what I meant. I meant that the concept "table" (not the unique existent) that is below "furniture" in the hierarchy is a different concept than the one that's below "wooden object," in the same way that "existence" is a different concept than "identity" even though they have exactly the same referents. The difference is one of perspective, as AR said in that passage from ITOE that I quoted previously - each one emphasizes something different about the referents. It just happens that here with "table" both those concepts are represented by the same word. Note that if the word for, say, the "wooden object" version was something else then the correlation with "existence" and "identity" would be exact.

The alternative is that there can be only one "table" concept but it can have more than one genus. I find that problematic - what then would be the definition of the concept "table?" If it's a single concept then it has a single definition. If there are two definitions then there are two concepts, even if they're denoted by the same word. It's common that the multiple concepts denoted by a single word are unrelated to one another (i.e. have completely different referents). Here it happens that the two concepts represented by the word "table" are corollaries (they have the same referents).

Corollary concepts aren't just two words denoting exactly the same concept, despite the fact that their referents are identical. If that were the case we could do away with one of the words and lose nothing. But consider what we would lose if we dispensed with, say, "identity" merely because it has the same referents as "existence." Regarding "table" here, whether separate words denote the corollaries or just one word makes no difference to the fact that they're distinct concepts.

I still don't understand "What for?"

For the same reason we create dictionaries. I think there would be great value in creating a "dictionary" that presents knowledge in the form of the conceptual hierarchy, formally classifying concepts by genus and differentia, showing explicitly how they relate to one another, identifying corollaries as such, permitting the user to traverse the hierarchy, and so on. It would be a reference tool that I think would offer a perspective importantly different than dictionary, thesaurus, lexicon, concordance, or any other traditional presentation of the knowledge represented by words.
Isn't it sufficient for a person to grasp and integrate the concepts necessary for him to understand and deal with the facts that confront him and the values he seeks?

Sure, just as a person could go through life never using a dictionary and function perfectly well. That doesn't affect the value of a dictionary to those who use it, though.

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I think there would be great value in creating a "dictionary" that presents knowledge in the form of the conceptual hierarchy, formally classifying concepts by genus and differentia, showing explicitly how they relate to one another, identifying corollaries as such, permitting the user to traverse the hierarchy, and so on.

[bold added for emphasis.]

What do you mean by "the" hierarchy? Are you assuming that there is one hierarchy for all individuals at all times? Is there a right hierarchy forever frozen in time?

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