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So where's the solution to the 'Problem of Universals'?

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So even according to Rand the class property of straightness exists, or to use your language, a 'floating abstraction' exists, despite the fact that it doesn't exist physically as there is nothing to match the paradigm of what straightness is. The paradigm, of course, must have the line never deviating or else it is no longer a straight line, whereas in reality all "straight" lines deviate. The problem of universals is to determine its relationship to reality so that the property of straightness is no longer 'floating.'

Any definition of straightness must be measured against the standard of "the most direct path between two points." Assuming that two points exist in reality, there also exists in reality the most direct path between them.

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The "property" you refer to is still an attribute; it is our ability to regard the attribute as a unit that seems to be at the root of (at least one) complaint.

Properties only hold for classes of entities, a distinction Rand failed to make in ITOE in which the developmental hierarchy never rose above the level of the "unit." If she had upleveled the discussion just one more time, from 'entity' to 'identity' to 'unit' to 'class', she would have found herself on our turf and would have at last had grounds for discussing a problem she herself mentioned. Her question about finding the man-ness in men never got around to asking about man's knowledge of universals. The question is not "what does the concept 'man' refer to in reality." The answer to that is obvious, it refers to particular men. The problem of universals asks: "Is the property of man-ness in one man the same property of man-ness found in all other men, and how do you know it?" Now you have a question proper to epistemology. Now you have the problem of universals.

A particular apple may not be bruised; yet, as you correctly point out, the property of being easily bruised belongs to all apples. What allows for this shared "property"? The apples are easily bruised because of their chemical makeup--they share the same chemical composition that allows for being bruised. We may properly regard the apples' chemical composition as an attribute and all apples (all apples that ever existed, exist now or may exist in the future) share the attribute.Dan

I'm asking if the property is identical for all apples, not if the property is shared by all apples. The question is to determine the nature of this universal, we already know of its universality, so when you say it is shared that adds nothing new to what we already think about apples.

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Yes; there is just one purpleness. If something is purple then it's "purpleness" is the same as that of any other purple thing.

The question then has to be, how do you know it? Because in reality there are as many purples as you can muster up examples of the color purple. Why can't each one exemplify its own unique variety of purpleness?

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The question then has to be, how do you know it?
Because I speak English and am aware of the meaning of "purple".
Because in reality there are as many purples as you can muster up examples of the color purple.
No, there is just one purple. The objects may be physically different in terms of characteristic light wavelength, but they are still one and the same concept. Surely you at least understand that much of Objectivist epistemology. For example, what is the definition of "concept"?
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Because I speak English and am aware of the meaning of "purple".No, there is just one purple. The objects may be physically different in terms of characteristic light wavelength, but they are still one and the same concept. Surely you at least understand that much of Objectivist epistemology. For example, what is the definition of "concept"?

I know enough about it to say with certainty that Rand did not ask about any problem of universals, because it has nothing to do with finding the manness in men. Who knows where she even got that idea? I also know that finding the manness in men is not equivalent to asking what does the concept 'man' correspond to reality. 'Where is the "manness" in men? What, in reality, corresponds to the concept "man" in our mind?' [iTOE2, p. 2] The answer to the second question is easy: the concept 'man' corresponds with particular men. But where is the manness in men? Since 'manness' is a universal, a property shared in common by all men, is the property of manness psychological, physical, conceptual, subjective, objective, or none of the above? And where is the purpleness in purple? You say that there is just one purple. But I was not asking about the concept 'purple,' I was asking about the property concept 'purpleness,' and whether or not it is identical for all purple entities.

Any definition of straightness must be measured against the standard of "the most direct path between two points." Assuming that two points exist in reality, there also exists in reality the most direct path between them.

"In reality" would include "in consciousness." Are you saying that the answer is subjective?

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Since 'manness' is a universal, a property shared in common by all men, is the property of manness psychological, physical, conceptual, subjective, objective, or none of the above?
It is objective and psychological. It is an objective recognition of mind-independent fact of reality.
But I was not asking about the concept 'purple,' I was asking about the property concept 'purpleness,' and whether or not it is identical for all purple entities.
A trivial distinction. "Purpleness" is just a linguistic form meaning "the concept 'purple', conveyed as an abstract noun. It's a pretty productive formation process. Looking for nouns "in" other nouns is probably not worth your time.
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I don't have the relevant quote, but the concept "existence" is formed by observing things, and abstracting the fact that they "exist." Like "7," there's no thing which is just "existence." "Existence" is not a first-level concept, it is the highest-level abstraction, with its units being all entities, all events, all attributes, all actions, and all relationships. The same goes for the concept "identity" it has the exact same units as "existence"; namely, all things which exist.

"Existence" is irreducible; to form the concept "existence" one notes the similarity that objects/actions/etc. exist, with the difference being the comparison of these things not existing. The only way to discuss existence is to merely restate what it is, as is true of all axioms. Unless you disagree about Rand validated why "existence" etc. are axiomatic concepts, I don't think your conclusion that existence is not a concept holds (actually, I don't think it holds either way).

My reading of ITOE has it that "existence" is a collective noun encompassing everything that exists.

'AR:[T]he concept "existence," at least the way I use it, is in a certain way close to the concept "universe"—all that which exists.

Prof. B: "Existence" is a collective noun almost.

AR: That's right.'

I don't see how 'existence' is almost a collective noun. Either it is or it isn't. "Universe" is a collective noun, as in "there was a universe of stars in the sky." But there is a category known as the "mass noun" under which "existence" could be subsumed.

'The rules of correct definition are derived from the process of concept-formation. The units of a concept were differentiated—by means of a distinguishing characteristic(s)—from other existents possessing a commensurable characteristic, a "Conceptual Common Denominator." A definition follows the same principle: it specifies the distinguishing characteristic(s) of the units, and indicates the category of existents from which they were differentiated.' (41) How does this principle work for conceptualizing "existence"?

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I am only showing the fact that, given Rand's own method of concept-formation which requires the formation of a unit from two or more similar existents, "existence" is not a concept.

If two entities have the property of existence, then existence is a property, and therefore a concept. To say that "existence" is not a concept, is to say that no two entities have the property of existence, and therefore, that nothing exists, or at most one thing. Since your own consciousness is the thing that you can say with greatest certainty exists, then, at most your consciousness, but no more, "exists."

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'The rules of correct definition are derived from the process of concept-formation. The units of a concept were differentiated—by means of a distinguishing characteristic(s)—from other existents possessing a commensurable characteristic, a "Conceptual Common Denominator." A definition follows the same principle: it specifies the distinguishing characteristic(s) of the units, and indicates the category of existents from which they were differentiated.' (41) How does this principle work for conceptualizing "existence"?

Again, I don't have ItOE, but Rand states somewhere, perhaps the chapter on Axiomatic Concepts, that "existence" has no Conceptual Common Denominator.

Notice that your problem here relates to definitions: "existence" is an axiomatic concept; it has no formal definition, only an ostensive one. In other words, this problem you have has no bearing on the concept "existence," if my understanding of the objective theory of concepts is correct.

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I don't see how 'existence' is almost a collective noun.

Well, think about it. A noun to my recollection denotes a person, place, thing or idea. All those things exist, and are subsumed under the concept "existence," but more things exist. Verbs--actions and states of being--are also existents, but are not nouns. And I could go on, but I think you see the point by now. So it includes everything that a collective noun would, but is not restricted to only being a collective noun. Or at least that's my off-hand thinking on this little topic.

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It is objective and psychological. It is an objective recognition of mind-independent fact of reality.A trivial distinction. "Purpleness" is just a linguistic form meaning "the concept 'purple', conveyed as an abstract noun. It's a pretty productive formation process. Looking for nouns "in" other nouns is probably not worth your time.

Making such a big deal over a collective noun "existence" is probably not worth your time.

The worthiness of the situation is not merely grammatical. It involves a process of identification,

that is, identifying exactly what the problem of universals consists of, and exactly where Ayn Rand dropped the ball. It has exactly nothing to do with relating concepts to reality. Her question about finding the manness in men is closer, since at least 'manness' is a universal. You say it is mind-independent, but you don't say exactly where it is independent of the mind.

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Well, think about it. A noun to my recollection denotes a person, place, thing or idea. All those things exist, and are subsumed under the concept "existence," but more things exist. Verbs--actions and states of being--are also existents, but are not nouns. And I could go on, but I think you see the point by now. So it includes everything that a collective noun would, but is not restricted to only being a collective noun. Or at least that's my off-hand thinking on this little topic.

Rand simply didn't have the terminology on hand to describe it grammatically. 'Existence' describes a collection of entities, but it is not a collective noun like "group" or "herd." It is a mass noun, like "furniture." You can identify a mass noun by the fact that it cannot take the plural form ("furnitures").

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It involves a process of identification,

that is, identifying exactly what the problem of universals consists of, and exactly where Ayn Rand dropped the ball.

Is it your claim that the "problem of universals" is that people cannot figure out what "X-ness" is, for various properties such as "purple, 5, man"? If so, Rand has solved the problem, and the answer is "X-ness" is the concept X, expressed as an abstract noun meaning "the property of being X". Once you understand the concept "purple", "man", "5" and so on, it's really simple to understand "the property of being 'purple'", "the property of being 'a man'", "the property of 'being (of cardinality) 5'". If you think the "problem of universals is something else, you need to say what you think the "problem" is.
You say it is mind-independent, but you don't say exactly where it is independent of the mind.
The mind-independent part is that concepts are formed (directly or indirectly) by perception of entities outside the mind, such as men.
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QUOTE (Ogg_Vorbis @ Feb 19 2008, 09:37 AM)

It involves a process of identification, that is, identifying exactly what the problem of universals consists of, and exactly where Ayn Rand dropped the ball.

Is it your claim that the "problem of universals" is that people cannot figure out what "X-ness" is, for various properties such as "purple, 5, man"? If so, Rand has solved the problem, and the answer is "X-ness" is the concept X, expressed as an abstract noun meaning "the property of being X". Once you understand the concept "purple", "man", "5" and so on, it's really simple to understand "the property of being 'purple'", "the property of being 'a man'", "the property of 'being (of cardinality) 5'". If you think the "problem of universals is something else, you need to say what you think the "problem" is.

This is why I asked Ogg V (and have not yet received an answer) if he read Rand's account of measurement omission and whether he agreed with it, and if not, why not.

It is Rand's discovery of the connection between measurement and conceptualization that is revolutionary. OV, if you will not address the role measurement omission plays in this process, then we are talking past each other.

Dan

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(quote name='Ogg_Vorbis' date='Feb 18 2008, 10:48 PM') post_snapback.gif'The rules of correct definition are derived from the process of concept-formation. The units of a concept were differentiated—by means of a distinguishing characteristic(s)—from other existents possessing a commensurable characteristic, a "Conceptual Common Denominator." A definition follows the same principle: it specifies the distinguishing characteristic(s) of the units, and indicates the category of existents from which they were differentiated.' (41) How does this principle work for conceptualizing "existence"?

Again, I don't have ItOE, but Rand states somewhere, perhaps the chapter on Axiomatic Concepts, that "existence" has no Conceptual Common Denominator.

Notice that your problem here relates to definitions: "existence" is an axiomatic concept; it has no formal definition, only an ostensive one. In other words, this problem you have has no bearing on the concept "existence," if my understanding of the objective theory of concepts is correct.

You mean you don't have Objectivism on CD?

I understand why you would think that way about axiomatic concepts. Obviously 'no definition,' ignoring ostensive ones, does not imply 'no concept.' But I am relying on the first sentence of that quote, 'The rules of correct definition are derived from the process of concept-formation.' But I don't believe that proper concept-formation ever consists in swinging one's arm in a wide circle and declaring, "I mean this." '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 contrary of the concept "table"—a non-table—is every other kind of existent. The contrary of the concept "man"—a non-man—is every other kind of existent. "Existence," "identity" and "consciousness" have no contraries—only a void.' (p. 58)

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I understand why you would think that way about axiomatic concepts. Obviously 'no definition,' ignoring ostensive ones, does not imply 'no concept.' But I am relying on the first sentence of that quote, 'The rules of correct definition are derived from the process of concept-formation.' But I don't believe that proper concept-formation ever consists in swinging one's arm in a wide circle and declaring, "I mean this." '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 contrary of the concept "table"—a non-table—is every other kind of existent. The contrary of the concept "man"—a non-man—is every other kind of existent. "Existence," "identity" and "consciousness" have no contraries—only a void.' (p. 58)

Funny, you started this thread with an example of something that you claim does not exist in reality, in order to show that concepts are not based on reality, and now are claiming that there is nothing that does not exist in reality, in order to show that reality is not based on concepts.

But the example of that which you claim does not exist in reality, actually does exist (is discoverable) in reality; and the conclusion you draw from your current claim of the non-existence of non-existents is that that which you seek (a solution to the problem of universals) does not exist.

If you want to differentiate an existent from a non-existent in order to reach an ostensive concept of "existence," it's as plain as the nose on your face and the face on your nose.

Edited by agrippa1
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Is it your claim that the "problem of universals" is that people cannot figure out what "X-ness" is, for various properties such as "purple, 5, man"? If so, Rand has solved the problem, and the answer is "X-ness" is the concept X, expressed as an abstract noun meaning "the property of being X". Once you understand the concept "purple", "man", "5" and so on, it's really simple to understand "the property of being 'purple'", "the property of being 'a man'", "the property of 'being (of cardinality) 5'". If you think the "problem of universals is something else, you need to say what you think the "problem" is.
This is why I asked Ogg V (and have not yet received an answer) if he read Rand's account of measurement omission and whether he agreed with it, and if not, why not.

It is Rand's discovery of the connection between measurement and conceptualization that is revolutionary. OV, if you will not address the role measurement omission plays in this process, then we are talking past each other.

Dan

I'm pretty sure I answered all your posts, although this browser format makes replying very difficult. I have already stated the problem of universals many, many times. Every time someone tries to bring up a side issue, claiming it to be somehow relevant, I simply reiterate the problem. If someone is still confused on the matter then perhaps it has to do with the difficulties of this posting format. But I can go over it again, and again, and again, as need requires it.

But now you've thrown a new challenge into the mix. You want to know what role measurement omission plays in some process. I have already broached the subject of similarity here. I have stated that it is nothing more than to say we know that two squares are similar, although of different sizes, by omitting the particular measurements of the figure's sides and retaining the essential fact that all 4 sides must be of equal length with internal angles adding up to 360 degrees. I have stated that mathematicians have known this for many centuries, and I don't see anything revolutionary about it. It is not only the easiest part of ITOE to understand, but Rand also showed a good comprehension of the mathematical part. Perhaps it only seems like her own discovery because she cited exactly zero sources.

I see that the person I requoted at the top did not spell out the problem of universals, so I'll spell it out for you again. It has nothing to do with what x-ness is. The problem of universals is this: Is a class property identical between all objects of a class? In the class of all purple books, is the purpleness of one book the same purpleness of another book? In the class consisting of all men, is the manness in one man the same, that is, identical to the manness in all other men?

Rand never broached the subject of class, but she should have because it fits the pattern of development she delineated in chapter one, from entity, to identity, to unit -- to class. Rand never answered the problem of universals because she never asked it, she didn't uplevel the discussion far enough. Apparently she had not developed her own ideas sufficiently, so she was personally stuck on the level of the unit. Thus she could talk about some problem of universals or other, but she would never be able to understand it having failed to develop the concepts appropriate for dealing with it. And she wouldn't have to sacrifice the mathematical analogy, for example:

http://en.wikipedia.org/wiki/Class_%28set_theory%29

"In set theory and its applications throughout mathematics, a class is a collection of sets (or sometimes other mathematical objects) that can be unambiguously defined by a property that all its members share."

That is basically the definition I have been using all along to spell out the problem of universals. The idea of a "property" is a class-theory notion, and since the problem of universals deals with properties, and not merely attributes of entities, Rand never actually broached the problem of universals in ITOE, or even broached any epistemological issues for that matter. A theory of concept-formation, revolutionary or not, cannot be used to address the problem.

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Funny, you started this thread with an example of something that you claim does not exist in reality, in order to show that concepts are not based on reality,

False, although I see you are now reduced to leveling accusations at me instead of addressing arguments. If a straight line exists in reality, it exists, as I said, only in the mind -- and according to Rand the mind is utterly chockful of existents. The question is: what is the connection between the existent in my mind of a straight line, and an existent in external reality which appears to be straight but never will be?

I'll let you chew over that one for a while.

and now are claiming that there is nothing that does not exist in reality, in order to show that reality is not based on concepts.

But the example of that which you claim does not exist in reality, actually does exist (is discoverable) in reality; and the conclusion you draw from your current claim of the non-existence of non-existents is that that which you seek (a solution to the problem of universals) does not exist.

If you want to differentiate an existent from a non-existent in order to reach an ostensive concept of "existence," it's as plain as the nose on your face and the face on your nose.

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identifying exactly what the problem of universals consists of, and exactly where Ayn Rand dropped the ball. It has exactly nothing to do with relating concepts to reality.

Ayn Rand did identify "the problem of universals" on page one of the forward to the first edition ITOE. It is the "problem" of discovering how abstractions (concepts) or "universals" can be objectively formed. She uses the rest of the book to explain how.

You haven't shown that she "dropped the ball" so please don't be insulting.

If you don't think it is important to relate concepts to reality, that is: be objective, then this discussion belongs in the debate forum.

David has already answered the color problem and as an example I would ask: have you ever been to Lowes? I've been doing some painting recently so I have spent some time looking at their color section. How do you think it is that the employees would be able to organize those colors in such a fashion (like a color wheel)?

On the basis of their similarity, as David said.

The line problem is solved in the same way.

And both "problems" are "problems of universals", which as Ayn Rand showed is not a problem at all -- concepts can be formed objectively.

How do we, as rational animals, know what we know?: conceptually. This is how we hold our knowledge and this is how we are able to apply it to the universe: in the form of concepts. This is one of the two central questions answered by epistemology. And this is why Ayn Rand wrote "Introduction to Objectivist Epistemology". The answer to: "what do we know?", would probably take encyclopedias to cover.

So in the universe of lines I bet you and I could come up with tons of real world examples that are all similar: my computer seems to have many straight lines, my book cases -- lines, hardwood floors -- lines, clapboard on the house next door -- lines, jet contrail, laser level, curtain fabric pattern. They are all similar, in the context of looking at them right now. If the context for you asking: "is that line straight?" is that you want to fly to the moon, then I suggest you use a better standard than my wood floors.

All knowledge is contextual.

and according to Rand the mind is utterly chockful of existents.

Here's your problem, she doesn't say that at all. This is what a perceptual consciousness does.

Man, is a conceptual consciousness, he stores his knowledge in the form of concepts. This is how I am able to identify a particular man from Tibet as a man even though I have never seen him before.

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The problem of universals is this: Is a class property identical between all objects of a class? In the class of all purple books, is the purpleness of one book the same purpleness of another book? In the class consisting of all men, is the manness in one man the same, that is, identical to the manness in all other men?
The person who said this completely misses the point, repeatedly. There is no such thing as "manness" or "purpleness". That person can't really be so dense that he doesn't understand this -- it's a purely academic game-term invented by some philosophers, signifying nothing. The so-called "class property" of things "in a class" is identical between all existents described by the property. I can't count how many time I've explained this.

Now:<mod>As a reminder, from the forum rules "This site supports discussion of, first, the principles of Objectivism, as defined by the works of Ayn Rand and supported by the Ayn Rand Institute; and, second, their application to various fields. Therefore participants must not use the website to spread ideas contrary to or unrelated to Objectivism." That means, inter alios, the intellectually dishonest practice of pretending to be discussing a point of Objectivist philosophy while actually using the forum to promulgate all sorts of irrelevant ideas of the "primacy of consciousness" variety. Honest questions are always welcome, but we expect some signs that you've actually integrated what you've been told, rather than just ignoring the answers.</mod>

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The person who said this completely misses the point, repeatedly. There is no such thing as "manness" or "purpleness". That person can't really be so dense that he doesn't understand this -- it's a purely academic game-term invented by some philosophers, signifying nothing. The so-called "class property" of things "in a class" is identical between all existents described by the property. I can't count how many time I've explained this.

'The issue of concepts (known as "the problem of universals") is philosophy's central issue.' Ayn Rand, Introduction to Objectivist Epistemology, page 1. 'It's a purely academic game-term invented by some philosophers, signifying nothing.' Dave Odden

'If, in the light of such "solutions," the problem might appear to be esoteric, let me remind you that the fate of human societies, of knowledge, of science, of progress and of every human life, depends on it. What is at stake here is the cognitive efficacy of man's mind.' Ayn Rand, Introduction to Objectivist Epistemology, page 3.

And I responded appropriately, and while I do not have a mod-hat to don like you do, I would find no rational reason to pull out the guns and force the issue. Since Ayn Rand brought up the issue of universals, and since it is philosophy's central issue and, moreover, the fate of human societies rest upon its solution, that makes it an Objectivist topic.

I have not determined if primacy of existence or of consciousness is the answer, I don't have any answer to discuss with you, only questions. And my question for you is still this:

How do you know that the class property is identical for all members of the class?

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I see that the person I requoted at the top did not spell out the problem of universals, so I'll spell it out for you again. It has nothing to do with what x-ness is. The problem of universals is this: Is a class property identical between all objects of a class? In the class of all purple books, is the purpleness of one book the same purpleness of another book? In the class consisting of all men, is the manness in one man the same, that is, identical to the manness in all other men?

The answer to your question is: No, there is no identical manness in man or purpleness in purple, because there is no manness or purpleness; there are only particular things in reality, and no two things in reality are identically identical. That was the problem of universals -- they don't exist. There is no straightlineness, there is no squareness. What exists are men, purple things, straight lines, and squares. This problem first arose with Plato, who claimed, in essence, that manness exists in some other dimension not directly accessible to man, but maybe to his mind's eye, so to speak. But that realm does not exist. There is no realm in which the purpleness of purple resides. So, one purple thing compared to another purple thing contrasted to a green thing is similar. Or if you want to put it another way, they are identical within a range, just like the wavelengths of light you referred to earlier; any light within the range you gave for red is observed as being red, any light within the range you gave for orange is observed as orange.

By the nature of existence, all things that exist are what they are; and they are particular, and no two are exactly, down to the infinitesimal, identical. So, one way Miss Rand dealt with the problem of the universal is to show that it doesn't exist in reality apart from man's conceptualizations; and to show that one can conceptualize because via conceptualization, one can consider something to be identical to something else within a range. For example, "A" is identical to "P" within the range of the set called the alphabet; and qua letter, they are exchangeable, one for the other, if all we are talking about is: Is it a letter?

Within the range of shades of red, each specific color is unique metaphysically, but it can be considered to be "identical" within that range that is specified with the standard that serves as a unit. Likewise, even though each man is unique, conceptually they can be considered identical within a range.

Somewhere in ITOE, perhaps in the latter areas where she has questions from professors, she goes into the issue of measurement within a range leading to "identical", since in reality, no two things are ever specifically down to the iota of measurement identical.

If you want to think about it mathematically, then for an equation like x+y=z, for that operation, all numbers for x are identical (i.e. a number) and all numbers for y are identical (i.e. a number), meaning that they work in the equation -- i.e. they all give a solution to the mathematical equation. That is what measurement omission gives you the power to do -- you can consider Bob to be identical to Mary, insofar as the concept "man" is concerned. That is, Bob and Mary are in the set because they can be considered identical within the range covered by the concept "man."

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How do you know that the class property is identical for all members of the class?

The "class property" you refer to is a particular way of regarding an attribute shared by the entities in question. The attribute exists "out there"; regarding it as a "universal" reflects the human method of knowing. Rand spells this out in the first chapter of ITOE.

For Objectivists, there is no "class property" separate or apart from the attribute(s) under consideration. I recognize your statement that you regard this, Rand's treatment of attributes, as deficient--at least as it relates to the problem of universals. Be that as it may, that is the answer to your question:

Is a class property identical between all objects of a class? In the class of all purple books, is the purpleness of one book the same purpleness of another book? In the class consisting of all men, is the manness in one man the same, that is, identical to the manness in all other men?

The answer you find unsatisfying has already been provided numerous times: The "manness" is identical in each man because the only thing under consideration is the relevant attribute(s)--with their particular measurements omitted.

Dan

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