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SpookyKitty

My Criticism of Concept Formation

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18 hours ago, SpookyKitty said:

This is a criticism of the Objectivist theory of concept-formation. Tell me what you think.

objCrit.pdf

What I see missing from your paper is an adequate discussion of Perception, which Rand spends a good deal of time doing in ITOE.

That is, the ability to differentiate and integrate objects in one's field of perception is the metaphysically given and forms the necessary precondition from which concept formation then proceeds.  Infants, long before they form words can distinguish between similar and dissimilar objects.

From ITOE, p. 5:

"A percept is a group of sensations automatically retained and integrated by the brain of a living organism."  - Note, this is not unique to humans, but is applicable to animals in general.

p. 16:

(As far as can be ascertained, the perceptual level of a child's mind is similar to the awareness of the higher animal: the higher animals are able to perceive entities, motions, attributes, and certain numbers of entities.  But what an animal cannot perform is the process of abstraction - of mentally separation attributes, motions or numbers from entities.  It was been said that an animal can perceive two oranges or two potatoes, but cannot grasp the concept "two".)

p. 164:

Suppose a child is forming a concept "table."  First he has to isolate a table from the rest of his perceptual concretes, then integrate it with other tables.  Now, in this process words are not present yet, because he is merely observing, and performing a certain mental process.  It is after he has fully grasped that these particular objects (tables) are special and different in some way from all other objects he perceives - it is then that he has to firm up, in effect, his mental activity in his own mind by designating that special status of these particular objects in some sensory form [i.e., by means of a word].

Edit:  The capacity to engage in basic Arithmetic is a given, and follows from such observed perceptual mechanisms as subitizing and chunking.  Without these basic perceptual mechanisms we could not perform arithmetic, geometry, algebra, analytic geometry, trigonometry, calculus, mechanics, etc.

 

Edited by New Buddha

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1 hour ago, SpookyKitty said:

@New Buddha, I'm not sure what your point is.

Concepts such as Primes are abstractions from abstractions - not abstractions from concretes.  Thus, in your paper where you state the following....

Consider the following question. Given the Objectivist theory of concept formation, how could we form the concept of prime number? Well, first off, by condition 1, we need at least two numbers that are referents of the concept, say 3 and 5 (but pretend we don’t know that 3 and 5 are prime yet). Still the question remains just how many examples of a prime number we would need in order to form the concept.

....you are reducing the conceptualization of Primes to an ostensive, first-level percept/concept relationship -- without taking into account the many antecedent steps necessary to arrive at the concept.  This is true for most mathematical ideas such as irrational numbers, limits in calculus, etc.  It's also true for such abstractions as "property" or "marriage".

Edited by New Buddha

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Just now, New Buddha said:

....you are reducing the conceptualization of Primes to an ostensive, percept/concept relationship --

No. Higher order concepts such as primes are formed by treating lower-order concepts as though they were percepts.

This is abundantly clear from the Objectivist concept of conceptual hierarchy.

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4 minutes ago, SpookyKitty said:

No. Higher order concepts such as primes are formed by treating lower-order concepts as though they were percepts.

All concepts are give perceptible form.  This is the purpose of numbers and words.

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Consider the concepts of “natural number greater than 0” and “natural number which dividides at least one natural number”. These two concepts have the same referents since 0 is the only number which divides no number whatsoever, and every other number is greater than 0. But they are different, hence theorem 6 is false. Therefore, by modust tollens, there exist some concepts which cannot be formed
by the Objectivist process of concept formation.

You have not invented two concepts, but two descriptions for various particular things. "Natural number greater than 0" merely describes individual numbers like 5 or 50,000. You have essentially created a complex proper name for certain, unidentified numbers. Are we playing Jeopardy? "Alex, what is 523?"

I could say, "Human being who is not dead."

"Alex, who is SpookyKitty?"

This wouldn't be a concept. It would be a proper name for every living human entity. Instead of saying, "Hi, Bob!" I could say, "Hi, human being who is not dead!"

To create your concept, you'd have to define it as "the set of natural numbers greater than zero," which is how real mathematical concepts work. This idea would include all the various numbers, or referents, in the set.

In fact, if you had only used the plural numbers instead of the singular number in your own description, you may have solved the problem yourself. Because the set part would have been implied.

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Just now, MisterSwig said:

You have not invented two concepts, but two descriptions for various particular things. "Natural number greater than 0" merely describes individual numbers like 5 or 50,000. You have essentially created a complex proper name for certain, unidentified numbers. Are we playing Jeopardy? "Alex, what is 523?"

The difference between a "mere" proper name and a descrption of a concept is that the description of the concept contains conceptual content.

"Natural number greater than 0" is only superficially the same as a complex proper name such as "migwit swamy blubber" (which we can define as "a natural number greater than 0").

The key difference is that "natural number greater than 0" allows you to determine all by yourself which numbers it does and does not refer to, for an unlimited number of numbers, whereas "migwit swamy blubber" does not. One can understand the concept of "natural number greater than 0" provided that one understands the concepts of "natural number", "greater than", and "0".

None of this holds true for a mere complex proper name like "migwit swamy blubber". In fact, one can define "migwity swamy blubber" as "a natural number greater than 0" but you can't define "a natural number greater than 0" as "migwity swamy blubber".

Now, you might claim that "natural number greater than 0" and "natural number which divides a natural number" are still the same concept. But they are not. The first depends on the concept of "greater than" while the second depends on the concept of divisibility. Someone who understands one might not understand the other. The difference in understanding can only be caused by a difference in the concepts that each has available to him.

Thus, if one person utters "natural number greater than 0" but does not understand divisibility, and another person, who does not understand "greater than" utters "natural number which divides a natural number", although they would be referring to precisely the same numbers, they would not be mutually intelligible.

Edited by SpookyKitty

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29 minutes ago, SpookyKitty said:

The key difference is that "natural number greater than 0" allows you to determine all by yourself which numbers it does and does not refer to, for an unlimited number of numbers, whereas "migwit swamy blubber" does not.

No, it doesn't. It doesn't refer to "numbers" (plural). It refers to one "number" (singular). And that number is unidentified, so no matter how many times you insist otherwise, your phrase will never allow anybody to determine to which specific number it refers.

Play word games all you like. A is still A.

Edited by MisterSwig

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Just now, MisterSwig said:

No, it doesn't. It doesn't refer to "numbers" (plural). It refers to one "number" (singular). And that number is unidentified, so no matter how many times you insist otherwise, your phrase will never allow anybody to determine to which specific number it refers.

Play word games all you like. A is still A.

Quote

The basic principle of concept-formation (which states that the omitted measurements must exist in some quantity, but may exist in any quantity) is the equivalent of the basic principle of algebra, which states that algebraic symbols must be given some numerical value, but may be given any value. In this sense and respect, perceptual awareness is the arithmetic, but conceptual awareness is the algebra of cognition.

--Ayn Rand

"natural number greater than 0" cannot possibly refer to a singular number precisely because it denotes the concept and not some specific number.

EDIT: Furthermore, if you insist that "natural number greater than 0" must refer to a single specific number, then you run into the following contradiction:

P1: 4 is a natural number greater than 0

P2: 5 is a natural number greater than 0

P3: Two things the same as a third are the same as each other

Conclusion: 4 is 5.

Edited by SpookyKitty

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8 minutes ago, SpookyKitty said:

P1: 4 is a natural number greater than 0

P2: 5 is a natural number greater than 0

P3: Two things the same as a third are the same as each other

Conclusion: 4 is 5.

It's not my contradiction. It's yours. I just helped you see it. Have fun with your new "concept." I have nothing more to say here.

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Just now, MisterSwig said:

It's not my contradiction. It's yours. I just helped you see it. Have fun with your new "concept." I have nothing more to say here.

There's no shame in admitting you were wrong about something, MisterSwig.

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13 minutes ago, SpookyKitty said:

There's no shame in admitting you were wrong about something, MisterSwig.

You crack me up, Kitty. I fear what would happen if we ever met in person.

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Theorem 5: If you are distinguishing redness, it would only need to be at least two colors, e.g. red and non-red. You'd want a similar entity, too, which could have the same exact hue. Rather than what you wrote, there must be a conceptual common denominator such that multiple values are possible.

Theorem 6: Do you mean no two distinct concepts share all of the same referents in a 1:1 relation? I don't see why. If it were something directly perceivable, couldn' t factors besides those of the referent establish the need for multiple concepts?

Theorem 7: Even if you're right about 6, your example here shows reasons to reject, alter, or reorganize concepts you hold. Or, simply, they -aren't- different concepts. You didn't establish that only one definition per concept is valid. If you insist on them being different, it is a reason to say that concepts improve over time, or that some definitions are found to be wrong.

Theorem 11: What makes that even a concept? Or why not say lacking a referent makes a concept impossible to form, thus contradicting that it is a (valid) concept?

Corollary 12: Proper nouns aren't considered to be concepts for this very reason.

You seemed to overlook aspects of fallibility here, reasoning as if you were an omniscient viewer.

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    @Eiuol said,

Quote

Theorem 5: If you are distinguishing redness, it would only need to be at least two colors, e.g. red and non-red. You'd want a similar entity, too, which could have the same exact hue. Rather than what you wrote, there must be a conceptual common denominator such that multiple values are possible.

That would make sense, but not within Rand's theory. It's clear that what Rand is going for is something like this "this match has some length", "this other match has another length", then we form the concept "length" by observing that things have length regardless of what that length actually is. And this is true for all of the examples of concept formation that Rand provides.

An artificial, but totally clear example is, take the 'percepts' "1001101" and "1011101". We can think of each position in the sequence as a characteristic. The sequence of characteristic values determines the percepts. One observers that the two percepts differ in the third characteristic, and forms the unique concept corresponding to that characteristic "10x1101". The referents of this concept are then obtained by substituting one of the possible values of a characteristic for "x" in the 'definition' of the concept, i.e., "10x1101".

Rand is right in requiring that her theory of concept formation requires the isolation of 'commensurable characteristics'. If the given percepts were "1001101" and "01101", then we wouldn't be able to form a concept from them because it isn't possible to find a natural matching 'commensurable characteristics'. This is because one could match the first characteristic in the second string with with the either the first characteristic in the first string, and get a matching like:

1 0 0 1 1 0 1

0 1 1 0 1 -  -  (the hyphens stand for blanks)

And then you might be able to (assuming that integration over multiple characteristics is possible) get the concept

1xxx101

Or the second characteristic in the second string with the first characteristic in the first string, and get

1 0 0 1 1 0 1

-  0 1 1 0 1 -

10x1xx1

Or some other strange matching such as

1 0 0 1 1 0 1

0 -  1 -  1 0 1

Regardless, the uniqueness of concept formation fails because in each of the above cases we are attempting integration by using incommensurable characteristics.

Another way to look at this is, by forming the concept of redness by abstracting from things that are different shades of red, one can then say "this entity is red regardless of the shade of red". One cannot do concept formation by comparing red things to things of different colors. That is, you can't say that "this entity is red regardless of its color". Because the first sentence makes sense and the second one doesn't, that means that shades of red are a commensurable characteristic pertaining to the concept of redness, while different colors are not. Objects of different colors are commensurable, but then one is led to the concept of color, and not redness.

I realize this is kind of confusing, but essentially, the concept of red is supposed to refer to all red things regardless of the specific measurement of the shade of red. It cannot refer to blue things because no shade of blue is a shade of red.

 

Quote

Theorem 6: Do you mean no two distinct concepts share all of the same referents in a 1:1 relation? I don't see why. If it were something directly perceivable, couldn' t factors besides those of the referent establish the need for multiple concepts?

Yes.

Can you expand on the second sentence? I don't understand what you're trying to say there.

Quote

Theorem 7: Even if you're right about 6, your example here shows reasons to reject, alter, or reorganize concepts you hold. Or, simply, they -aren't- different concepts. You didn't establish that only one definition per concept is valid. If you insist on them being different, it is a reason to say that concepts improve over time, or that some definitions are found to be wrong.

Given the two concepts "a natural number greater than 0" and "a natural number which divides at least one other natural number", which one should I reject or alter? Neither is better than the other, they are simply different concepts (although with the same referents).

I did not establish that only one definition per concept is valid because the same concept can have multiple definitions. For example "a natural number which is a multiple of 7 or divisible by 5" is the same concept as "a natural number which is divisible by 5 whenever it is not a multiple of 7".

Quote

Theorem 11: What makes that even a concept? Or why not say lacking a referent makes a concept impossible to form, thus contradicting that it is a (valid) concept?

According to Rand's theory, the concept "a number greater than 1 but which divides both 17 and 6" is invalid because it has no referents. But the concept is perfectly intelligible and can be meaningfully used in a true sentence as in,

"'8 is a number greater than 1 which divides both 17 and 6' is false".

The above statement is true and can be understood by anyone precisely because the statement '8 is a number greater than 1 which divides both 17 and 6' is intelligible but false. Every such statement is intelligible regardless of what number is placed at the beginning. Therefore, the definition 'a number greater than 1 which divides both 17 and 6' denotes a concept (with no referents).

Quote

You seemed to overlook aspects of fallibility here, reasoning as if you were an omniscient viewer.

Can you expand on this?

Quote

Corollary 12: Proper nouns aren't considered to be concepts for this very reason.

But "one" is a proper noun. Is "one", then, not a concept?

Quote

You seemed to overlook aspects of fallibility here, reasoning as if you were an omniscient viewer.

Can you explain what you mean by this?

Edited by SpookyKitty

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16 hours ago, SpookyKitty said:

That would make sense, but not within Rand's theory. It's clear that what Rand is going for is something like this "this match has some length", "this other match has another length", then we form the concept "length" by observing that things have length regardless of what that length actually is. And this is true for all of the examples of concept formation that Rand provides.

I don't see how within Rand's theory that all measurements must be different, only that at least one must be different. Even more, there needs to be at least 3 entities: the entity used for comparison, an entity with a different measurement, and an entity with a similar measurement. There can be red, i.e. what looks red within a range on the color spectrum, and non-red, i.e. anything outside that part of the spectrum. So  when Rand says "another length", I take her to mean simply "some length", not that she's excluding identical lengths.

I think you're totally missing Rand's idea of a conceptual common denominator. You seem to suggest that by Rand's theory, different colors are incommunsurable. No, this isn't true. Blue and red are commensurable, because they are the same type of characteristic; they are measured in the same way on the same scale. If you were then to form a concept out of this commonality, you get the concept "color" - the CCD. The concept "red" just points out a difference from entities on the same scale of measurement.

Rand doesn't go into detail about commensurability really past things like shape being incommensurable with color. I'd say as long as the same mode of perception or cognition is used, then the characteristic is commensurable. Clearly, "what shape is red?" makes no sense.

16 hours ago, SpookyKitty said:

Can you expand on the second sentence? I don't understand what you're trying to say there.

Consider that color is more than just a hue. What you see also depends on the lighting. That lighting isn't produced by the referent, the entity that is that color. This isn't a problem for Rand's theory, since the referent is still measurable, and the measurement is still of something objectively valid.

16 hours ago, SpookyKitty said:

Given the two concepts "a natural number greater than 0" and "a natural number which divides at least one other natural number", which one should I reject or alter? Neither is better than the other, they are simply different concepts (although with the same referents).

You could keep both of the definitions in that case. They aren't -concepts- though. See the next bit.

16 hours ago, SpookyKitty said:

The above statement is true and can be understood by anyone precisely because the statement '8 is a number greater than 1 which divides both 17 and 6' is intelligible but false. Every such statement is intelligible regardless of what number is placed at the beginning. Therefore, the definition 'a number greater than 1 which divides both 17 and 6' denotes a concept (with no referents).

According to Rand's theory, it's not even a concept anyway. "A number greater than 1 but which divides both 9 and 30" isn't a concept either, even though it has some referent. They are statements. Intelligibility is not sufficient to makes something a concept. Somewhere in ITOE Rand talks about how merely seeing an assortment of characteristics (e.g. blonde woman with a blue dress and curly hair) is not a good enough reason to form a concept.

16 hours ago, SpookyKitty said:

But "one" is a proper noun. Is "one", then, not a concept?

How is "one" a proper noun? There's only one Eiffel Tower; there are many "one"s.

16 hours ago, SpookyKitty said:

Can you explain what you mean by this?

I meant it seemed like a valid epistemology to you is one based on what an omniscient viewer would imagine.

Edited by Eiuol

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Just now, Eiuol said:

I don't see how within Rand's theory that all measurements must be different, only that at least one must be different. Even more, there needs to be at least 3 entities: the entity used for comparison, an entity with a different measurement, and an entity with a similar measurement. There can be red, i.e. what looks red within a range on the color spectrum, and non-red, i.e. anything outside that part of the spectrum. So  when Rand says "another length", I take her to mean simply "some length", not that she's excluding identical lengths.

 

Rand says in ITOE:

 

Quote

A concept is a mental integration of two or more units which are isolated according to a specificcharacteristic(s) and united by a specific definition.

 

Therefore, there need not be at least three entities, but at least two.

Later on, she also says:

 

Quote

Let us now examine the process of forming the simplest concept, the concept of a single attribute
(chronologically, this is not the first concept that a child would grasp; but it is the simplest one
epistemologically)—for instance, the concept “length.” If a child considers a match, a pencil and a stick, he observes that length is the attribute they have in common, but their specific lengths differ. The difference is one of measurement. In order to form the concept “length,” the child’s mind retains the attribute and omits its particular measurements. Or, more precisely, if the process were identified in words, it would consist of the following: “Length must exist in some quantity, but may exist in any quantity. I shall identify as ‘length’ that attribute of any existent possessing it which can be quantitatively related to a unit of length, without specifying the quantity.”

 

It's not as if one of the things has no length at all, nor is it that one of the object's areas or volumes is being compared to the lengths of some others.


 

Quote

 

The same principle directs the process of forming concepts of entities—for instance, the concept “table.”
The child’s mind isolates two or more tables from other objects, by focusing on their distinctive
characteristic: their shape. He observes that their shapes vary, but have one characteristic in common: a
flat, level surface and support(s). He forms the concept “table” by retaining that characteristic and
omitting all particular measurements, not only the measurements of the shape, but of all the other
characteristics of tables (many of which he is not aware of at the time).

 

 

Which again means that at least two tables are necessary, and not at least three.

 

Quote

I think you're totally missing Rand's idea of a conceptual common denominator. You seem to suggest that by Rand's theory, different colors are incommunsurable. No, this isn't true. Blue and red are commensurable, because they are the same type of characteristic; they are measured in the same way on the same scale. If you were then to form a concept out of this commonality, you get the concept "color" - the CCD. The concept "red" just points out a difference from entities on the same scale of measurement.

 

No, I'm not saying that at all. What I think Rand is saying is that one cannot form the concept of color before one has formed a concept of each individual color. As in here:

 

 

Quote

The first stages of integrating concepts into wider concepts are fairly simple, because they still refer to
perceptual concretes. For instance, man observes that the objects which he has identified by the concepts
“table,” “chair,” “bed,” “cabinet,” etc. have certain similarities, but are different from the objects he has
identified as “door,” “window,” “picture,” “drapes”—and he integrates the former into the wider concept
“furniture.” In this process, concepts serve as units and are treated epistemologically as if each were a
single (mental) concrete—always remembering that metaphysically (i.e., in reality) each unit stands for an
unlimited number of actual concretes of a certain kind.

 

EDIT: Point of all this is, although it may be the case that for some concepts one needs three or more entities, at least one of them has to have a different measurement from the others. But prime numbers all have the same amount of primeness.

 

Quote

Rand doesn't go into detail about commensurability really past things like shape being incommensurable with color. I'd say as long as the same mode of perception or cognition is used, then the characteristic is commensurable. Clearly, "what shape is red?" makes no sense.

 

To reiterate, "what shade of red is blue?" also makes no sense.
 

Quote

Consider that color is more than just a hue. What you see also depends on the lighting. That lighting isn't produced by the referent, the entity that is that color. This isn't a problem for Rand's theory, since the referent is still measurable, and the measurement is still of something objectively valid.

 

 

How does that lead to multiple concepts? I mean you are claiming that Rand's theory allows multiple concepts with all of the same referents, right?

 

Quote

According to Rand's theory, it's not even a concept anyway. "A number greater than 1 but which divides both 9 and 30" isn't a concept either, even though it has some referent. 1. They are statements. 2. Intelligibility is not sufficient to makes something a concept. Somewhere in ITOE Rand talks about how merely seeing an assortment of characteristics (e.g. blonde woman with a blue dress and curly hair) is not a good enough reason to form a concept.

 

1. "a number greater than 1 but which divides both 9 and 30" is not a statement. It cannot be true or false. It's not even a sentence in English.

2. But it is necessary. Are you claiming that there are intelligible abstractions which are not concepts? What are the other conditions needed to make an intelligible abstraction a concept?

 

Quote

How is "one" a proper noun? There's only one Eiffel Tower; there are many "one"s.

 

I have one apple. And I have one orange. Is the number of oranges the same as the number of apples? If so, then there is only one number of both, i.e., 'one'.

 

Quote

I meant it seemed like a valid epistemology to you is one based on what an omniscient viewer would imagine.

 

Well I imagined it, but I'm not omniscient.

Edited by SpookyKitty

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1 hour ago, SpookyKitty said:

It's not as if one of the things has no length at all, nor is it that one of the object's areas or volumes is being compared to the lengths of some others.

Right. I don't know what you're criticizing here.

1 hour ago, SpookyKitty said:

What I think Rand is saying is that one cannot form the concept of color before one has formed a concept of each individual color.

As far as I see, Rand is only claiming that two entities are sufficient. Having more than two is no problem. I disagree that only two are ever sufficient, even if Rand means "usually more than two" and was only saying two are the bare minimum. That seems besides the point, because the larger claim is that concept formation revolves around measurement and comparison between entities.

1 hour ago, SpookyKitty said:

But prime numbers all have the same amount of primeness.

Forming the concept of a prime would involve comparing primes to non-primes. Now, since primeness is boolean, i.e. it is prime or it isn't, you might have a case here because strictly speaking, that's not a measurement. It isn't not a region or set of regions, as no one even has a way to determine ALL prime numbers by a method besides brute calculation. I sort of agree with you on this point - measurement omission might not work for all concepts.

1 hour ago, SpookyKitty said:

To reiterate, "what shade of red is blue?" also makes no sense.

Yes, but they are commensurable by virtue of both being colors. A child doesn't need to have a concept "color" to see colors, as in the measurement domain is hue, or a hue x luminosity axis, or something like that. You'd only talk about red shades when forming narrower concepts of red, like cinnabar or crimson. Colors in the blue range would not be considered anyway, assuming that narrower concepts are only formed from referents of the wider concept.

1 hour ago, SpookyKitty said:

I mean you are claiming that Rand's theory allows multiple concepts with all of the same referents, right?

Yes, if by referent you meant entity possessing the trait in question. Rand speaks about cognitive need to form concepts, so it depends on the context as well. That context may include perspective like looking at a stick underwater, and some scenario where refracted light is a regular issue.

1 hour ago, SpookyKitty said:

1. "a number greater than 1 but which divides both 9 and 30" is not a statement. It cannot be true or false. It's not even a sentence in English.

Fair enough, but it's still not a concept. I meant it is a definition, so I considered that a statement with no truth value.

1 hour ago, SpookyKitty said:

What are the other conditions needed to make an intelligible abstraction a concept?

For Rand:

1) integration into a single word

2) cognitive need to access the idea economically (unit-economy is important for Rand's theory)

3) quantifiable similarity to some earlier abstraction

4) quantifiable difference from some earlier abstraction

To me, 3 and 4 are likely too narrow. Qualitative is probably fine.

1 hour ago, SpookyKitty said:

Is the number of oranges the same as the number of apples? If so, then there is only one number of both, i.e., 'one'.

If another "one" exists, it's not a proper noun. There are plenty of singular items all over... The CCD here is numeracy, or perhaps cardinality. In fact, plenty of research in child conceptual development are able to comprehend numeracy and cardinality. It is treated like a measurement of sets with 3-4 items. Nothing like a proper noun matters. The point is, a "Unique One" is a proper noun, while "one" works the same way as "length". No special reasoning required.

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Just now, Eiuol said:

Right. I don't know what you're criticizing here.

 

It seemed as if you were saying that primeness is obtained by comparison with non-primeness. So I pointed out that in Rand's examples, length is never compared to something which is not also a length.

 

Quote

As far as I see, Rand is only claiming that two entities are sufficient. Having more than two is no problem. I disagree that only two are ever sufficient, even if Rand means "usually more than two" and was only saying two are the bare minimum. That seems besides the point, because the larger claim is that concept formation revolves around measurement and comparison between entities.

 

My only point is that of the measurements of the entities involved in concept formation, at least one must be different from all the others.

(I also argue elsewhere that there are concepts with one or less referents, but that's a separate issue)

 

Quote

Forming the concept of a prime would involve comparing primes to non-primes. Now, since primeness is boolean, i.e. it is prime or it isn't, you might have a case here because strictly speaking, that's not a measurement. It isn't not a region or set of regions, as no one even has a way to determine ALL prime numbers by a method besides brute calculation. I sort of agree with you on this point - measurement omission might not work for all concepts.

Quote

Yes, but they are commensurable by virtue of both being colors. A child doesn't need to have a concept "color" to see colors, as in the measurement domain is hue, or a hue x luminosity axis, or something like that. You'd only talk about red shades when forming narrower concepts of red, like cinnabar or crimson. Colors in the blue range would not be considered anyway, assuming that narrower concepts are only formed from referents of the wider concept.

 

Exactly. That's why according to Rand's theory, such a concept should be impossible. You can't compare shades of red to blue and get a coherent concept (though you can compare the color red to the color blue (as colors) after you've formed the concept of red and blue and so on, though that should not be taken to mean that one can't observe colors unless one has a concept of them)

If you agree with me that measurement omission might not work for all concepts, that's fine for you and me, but not for Rand.

 

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Yes, if by referent you meant entity possessing the trait in question. Rand speaks about cognitive need to form concepts, so it depends on the context as well. That context may include perspective like looking at a stick underwater, and some scenario where refracted light is a regular issue.

 

She only says that man must form concepts within the context of his own knowledge (as opposed to someone else's, or some ideal sort of knowledge, or whatever). Not that the same concept would mean one thing here and another thing there.

Here's the most pertinent quote about contexts in ITOE:

 

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Concepts are not and cannot be formed in a vacuum; they are formed in a context; the process of
conceptualization consists of observing the differences and similarities of the existents within the field of
one’s awareness (and organizing them into concepts accordingly). From a child’s grasp of the simplest
concept integrating a group of perceptually given concretes, to a scientist’s grasp of the most complex
abstractions integrating long conceptual chains—all conceptualization is a contextual process; the context
is the entire field of a mind’s awareness or knowledge at any level of its cognitive development.

 

So "context" means "the entire field of a mind's awareness or knowledge at any level of its cognitive development" and not something like "situation".  Presumably, then, the fact that sticks appear to bend in water may or may not be accounted for in the concept formation of a stick, but it would not lead to two different concepts of "stick" or anything else.

 

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Fair enough, but it's still not a concept. I meant it is a definition, so I considered that a statement with no truth value.

 

It's not a statement at all (with or without truth value) because it lacks a verb.

 

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For Rand:

1) integration into a single word

2) cognitive need to access the idea economically (unit-economy is important for Rand's theory)

3) quantifiable similarity to some earlier abstraction

4) quantifiable difference from some earlier abstraction

To me, 3 and 4 are likely too narrow. Qualitative is probably fine.

 

Ok. I'll have to address those in the future.

 

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If another "one" exists, it's not a proper noun. There are plenty of singular items all over... The CCD here is numeracy, or perhaps cardinality. In fact, plenty of research in child conceptual development are able to comprehend numeracy and cardinality. It is treated like a measurement of sets with 3-4 items. Nothing like a proper noun matters. The point is, a "Unique One" is a proper noun, while "one" works the same way as "length". No special reasoning required.

 

Obviously, but another "one" doesn't exist. If it did, then the one in "one apple" and the one in "one orange" could fail to be equal.

 

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I've always thought ITOE is one of the simplest books Rand wrote, and is written for a layman. Other have countered that it is one of the most abstract and complex.  I think one has to hold the latter view to think ITOE can be addressed by this type of critique, but to me it's a straw-man in attempting to read too much detail into a introductory text.

Edited by softwareNerd

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6 hours ago, SpookyKitty said:

Obviously, but another "one" doesn't exist. If it did, then the one in "one apple" and the one in "one orange" could fail to be equal.

Another of THAT one doesn't exist, but uniqueness of that -particular- is irrelevant. One would refer to being singular. How could multiple "one"s mean any two "one"s could fail to be equal? The measurement involved is cardinality, and there are multiple instances of cardinality 1. This is nothing like there being exactly one Eiffel Tower in existence.

I'll get to the rest in a few days.

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Just now, softwareNerd said:

I've always thought ITOE is one of the simplest books Rand wrote, and is written for a layman. Other have countered that it is one of the most abstract and complex.  I think one has to hold the latter view to think ITOE can be addressed by this type of critique, but to me it's a straw-man in attempting to read too much detail into a introductory text.

Is there any way to perform a non-strawman critique of Objectivist epistemology at all, seeing as how Rand never wrote anything more advanced than an introductory text about the subject?

Edited by SpookyKitty

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