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Questions About Concepts

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47 minutes ago, Grames said:

I hope you may someday come realize that "merely classifying things" is precisely what concepts do and are for.

I agree, but that's not all that they are for. To be fair, I misspoke here. The central component of Rand's theory is that you can extrapolate values of characteristics from the range of the "crow epistemology" (measurements whose values you can directly perceive) to the conceptual level (measurements you can't directly perceive, such as distances in the light years and such). Rand's theory allows you to do this. My problem with it is that, since it only allows for the total abstraction of one characteristic at a time, the resulting concepts cannot encode complicated interdependencies among characteristics. Rand did try to mitigate this issue to some extent by allowing for some unspecified functional relationship between a single characteristic (an independent variable) and all the rest (dependent variables) by using the notion of an "essential" characteristic. But this still wouldn't be enough, since actual phenomena may not have any essential characteristic in the Randian sense. This happens all the time when you have feedback loops. When this occurs, engineers and scientists are forced to describe the behavior of such systems by using differential equations and characterizing those systems by their solution sets. And these solution sets are abstract spaces! These spaces are then understood to be the essential defining features by which systems are classified. Note that in these cases, the systems are not classified by any one nor any combination of their measurements. Indeed, they cannot be.

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That a string of numbers in one format seems meaningless but in another is easily recognizable has little to do with Rand's theory of concepts but is rather about the human body's means of perceiving.  The implicit measurements of perception are actually easier to work with conceptually than the explicit measurements of an abstract set of numbers.

No, it has everything to do with Rand's theory of concepts, because it is precisely the concepts we have that make some data-sets easily recognizable. A layman and a physicist may have the exact same perceptual apparatus, but data that is meaningful to the physicist might seem completely random to the layman. The difference is in the physicist's far superior integration of lots and lots of physics and math concepts.

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You need to become more familiar with the capabilities of networks of neurons.  They can recognize complex patterns not merely rectangular ranges.  There is thread here that brought his theory of Hierarchical Temporal Memory to my attention. 

Exactly. Which is precisely why Rand's theory of measurement omission cannot possibly be complete.

Edited by SpookyKitty
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3 hours ago, Grames said:

1. 

I'm responding to your response to Merjet because his first response to you I agree with.

1. Perhaps we can still view the different types of books as commensurable (they are comparable in terms of content), but it still illustrates what is meant by qualitative. You brought up color to point out quantitative measurement omission resulting in a qualitative measurement, which is fine. But that doesn't address differentiating in terms of anything else. The difference between a shadow and a black piece of paper is not something measured quantitatively. It would be something to do with lack of physical extension; to comprehend physical extension as a measurement requires very complex thinking way after you already form the concept 'shadow'. In this way, quality is not necessarily less concrete than measurement. 

Spatial thinking is not space; you don't literally measure the space between perceptions that you remember. It might be better to call it relational thinking, yet I don't even experience it as quantitative. Even if you are right about how to describe spatial relationships represented within the mind, these spatial relationships aren't used for differentiation. They are used after you have already differentiated. I wouldn't describe placing "poodle" within "dog" as an act of measurement omission. With quantitative measurement omission, measurement is what you use to differentiate. Measurements like that can help differentiate concepts when you retrieve them in memory and they are organized in a spatial fashion, though. Besides, I think is really stretching it when you consider directions to be quantitative measurements.

2. Sure, there are many ways to initially form a concept. But many people can and do differentiate boats in terms of quality of locomotive power. It doesn't cause problems either. Whether a characteristic really is primary isn't important when forming a concept. If anything, what we initially think is primary is often not. 

3. Yeah, entities are their attributes. All entities can be measured quantitatively, and attributes can't be removed from an entity. I don't see how this means that all attributes are quantitatively measurable. You could argue for intensity as an omitted quantitative measurement for colors, but that really breaks down if you differentiate a dog from a cat, or a hamburger from a meatloaf sandwich, or sweet from sour.

3 hours ago, Grames said:

Redness and similarity of redness means the neurons connected to the red-responding rods and cones being excited and then the same ones being excited again.

This is why I think it's fair to say that color can be differentiated with measurement omission. But there are also different cells in your that eyes are sensitive to orientation, so it's not like everything your eyes do involves implicit quantitative measurement. 

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27 minutes ago, SpookyKitty said:

Note that in these cases, the systems are not classified by any one nor any combination of their measurements. Indeed, they cannot be.

Given that Rand allowed for abstraction from abstractions and concepts of concepts,  an abstract description and categorization based on common solution sets of an underlying set of differential equations is actually still a kind of measurement if that premise that there is 'describing' going on is true.  Not only concretes are measurable.

 

32 minutes ago, SpookyKitty said:

No, it has everything to do with Rand's theory of concepts, because it is precisely the concepts we have that make some data-sets easily recognizable. A layman and a physicist may have the exact same perceptual apparatus, but data that is meaningful to the physicist might seem completely random to the layman. The difference is in the physicist's far superior integration of lots and lots of physics and math concepts.

Now it appears you conflate what is not possible to the theory with what is not possible to a man without a particular set of concepts. Nothing about the physicist's integration of multiple and highly abstract concepts is uniquely impossible to Rand's theory.  It will stretch that far, so I see no problem where you claim to find one.

3 hours ago, SpookyKitty said:

Exactly. Which is precisely why Rand's theory of measurement omission cannot possibly be complete.

What I find most interesting about the Hierarchical Temporal Memory theory is the possible discovery of the mathematical mechanics of measurement omission buried in the sparse representation matrices.

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55 minutes ago, Eiuol said:

3. Yeah, entities are their attributes. All entities can be measured quantitatively, and attributes can't be removed from an entity. I don't see how this means that all attributes are quantitatively measurable.

If it isn't quantitatively measurable then it does not exist.  In non-trivial way what it means to exist is to be measurable.  Qualities are epistemological artifacts, abstractions just as are universals and essentials.

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39 minutes ago, Grames said:

Given that Rand allowed for abstraction from abstractions and concepts of concepts,  an abstract description and categorization based on common solution sets of an underlying set of differential equations is actually still a kind of measurement if that premise that there is 'describing' going on is true.  Not only concretes are measurable.

Abstraction from abstraction isn't relevant here because what I described is an abstraction from concretes.

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Now it appears you conflate what is not possible to the theory with what is not possible to a man without a particular set of concepts. Nothing about the physicist's integration of multiple and highly abstract concepts is uniquely impossible to Rand's theory.  It will stretch that far, so I see no problem where you claim to find one.

Not at all. My point was that what patterns someone can recognize in data is a function of the concepts they have and not simply perception.

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30 minutes ago, Grames said:

If it isn't quantitatively measurable then it does not exist.  In non-trivial way what it means to exist is to be measurable.  Qualities are epistemological artifacts, abstractions just as are universals and essentials.

Yes, for an entity to exist, it must be measurable. In other words, it must have physical extension. If something has physical extension, there is something quantitatively measurable. But how does that mean that there can't also be qualitative aspects that are not quantitative? As I pointed out, orientation is qualitative. And it isn't anymore abstract than the length of an entity. Orientation is perceived just as directly as color, and perhaps even more so. Of course, anything with an orientation has physical extension, yet orientation is an example of a qualitative distinction. I suppose you could say that orientation is a measurement of angle, except when you use an orientation to distinguish things, all you need is that up is not the same as down (and requires no angular measurement). Simply based upon having a different appearance or experience.

I'm just not seeing why all qualities must be epistemological artifacts.

44 minutes ago, SpookyKitty said:

My point was that what patterns someone can recognize in data is a function of the concepts they have and not simply perception.

Wouldn't this be more of an issue about induction, rather than concept formation? 

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20 minutes ago, SpookyKitty said:

Abstraction from abstraction isn't relevant here because what I described is an abstraction from concretes.

Not at all. My point was that what patterns someone can recognize in data is a function of the concepts they have and not simply perception.

"Common solution sets of differential equations" is an abstraction, and using that commonality among abstractions as a basis to perform a mental integration into a concept is abstraction from an abstraction.  Its all well and good that there is some chain of validation for the differential equations reaching back to the concretes involved but the path to finally discriminate the commonality (Rand's CCD) was quite abstract.

Your second point relates to what is called 'perceptual relativity'.  Practice and knowledge makes improved discrimination possible, so two men can perceive the same thing in the same conditions but not reach the same identification.  But my point was just that drawing a picture always makes data easier to understand when the data forms lines or curves or loops, and that includes easier for the kind of scientists and engineers that can read the data in tabular form.  Again I cannot agree that there is any problem here for Rand's theory of concepts to overcome.

 

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1 hour ago, Eiuol said:

... As I pointed out, orientation is qualitative. ...

I'm just not seeing why all qualities must be epistemological artifacts.

The quirk about orientation compared to regular attributes of an entity is that it is relative to some reference, either oneself as observing subject or some relevant thing in the environment.  Orientation then is a relationship not an attribute.  It still exists in the form of some angular rotation with respect to that reference and could be measured.  Saying that something is "facing up" is dropping/omitting the measurement because it is within a certain range.  So in conclusion orientation is no more qualitative than color, and describing a thing as "facing up" is similar to claiming it is "red".  This is not just an analogy because "red" is also a relationship between subject and object not an intrinsic attribute of an entity.

Qualities (in this context qualitative thinking as opposed to quantitative thinking) are epistemological artifacts because the only way to get rid of the quantitative character which constitutes all of existence is to omit it, omission being an epistemological operation. All that exists are concretes with their measurable attributes and relationships.  Orientation is an existent and is measurable and in any particular manifestation is a concrete.

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1 hour ago, Grames said:

It still exists in the form of some angular rotation with respect to that reference and could be measured.

I'm fine with saying that orientation is a relationship, not an attribute - but that's because I agree that orientation must be in respect to something else. How does that support your position though that all qualitative things are epistemological artifacts? After all, you can't think about a length either unless you've compared it to some other entity. Length is intrinsic to an entity, sure, yet omitting particular measurements of length is dealing with something relational because you would be dealing with "long" and "longer". 

Of course orientation can be measured quantitatively, I'm claiming that you can also do qualitative measurement omission. I'd rather say that for a concept to be verifiable, quantitative measurement must be at some level possible. The problem I'm running into is how you would explain coming up with the concept "shadow", or the concept "sour". You could come up with sour by trying a variety of sour things (comparing the blueberry to a lemon for example), but you could also do it by trying a sour thing and then a sweet thing (trying a lemon, then eating chocolate cake). Sweet and sour are comparable as far as both being flavors, but their commensurability ends there. They are not on the same range of intensity; there is sweet and sweeter, and there is sour and more sour. But becoming more sour is not the same as becoming less sweet. Neuroscientifically, this is because each flavor refers to a specific chemical combination. This is in contrast to color, where your eyes detect an intensity of wavelength that is not sharply divided each color. 

Basically, if it can be valid to come up with concepts with qualitative methods, you could then say that some sort of spatial thinking method is as valid as quantitative measurement omission.

5 hours ago, SpookyKitty said:

But figuring out a totally new pattern you've never seen before would be an instance of concept formation.

Patterns are not concepts, or at least this isn't what this thread would be about (at least as far as Rand's ideas). I've agreed with a lot of what you said, but this looks like a dead end for your position. I see how you mean that it isn't induction now, but even my own experience with pattern recognition, I don't recognize patterns as concepts (you can develop concepts of patterns, though). 

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8 hours ago, SpookyKitty said:

Recognizing a pattern you've already seen would be an instance of induction. But figuring out a totally new pattern you've never seen before would be an instance of concept formation.

Are you sure about this? My understanding is that recognizing is deduction while figuring out a new pattern is induction.

You use deduction based on the concepts that you have previously created by using induction.

To recognize requires traveling through the category "tree", i.e. heuristics.

2 hours ago, Eiuol said:

Patterns are not concepts, or at least this isn't what this thread would be about (at least as far as Rand's ideas).

Aren't patterns equivalent to "definitions", as in you pattern match to recognize the pattern.

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9 hours ago, Easy Truth said:

Aren't patterns equivalent to "definitions", as in you pattern match to recognize the pattern.

To fix up what I said, I should say that concepts are made up of patterns. A definition would be an explicit statement of the pattern of a given concept. But the pattern itself is not a concept. 123123123 has a pattern, but "repeated counting from 1 to 3" would not be a concept.

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On 2/24/2020 at 10:53 PM, Eiuol said:

I'm fine with saying that orientation is a relationship, not an attribute - but that's because I agree that orientation must be in respect to something else. How does that support your position though that all qualitative things are epistemological artifacts? After all, you can't think about a length either unless you've compared it to some other entity. Length is intrinsic to an entity, sure, yet omitting particular measurements of length is dealing with something relational because you would be dealing with "long" and "longer". 

Excuse me but could you please clarify if you think length is a quality or a quantity?  What are examples of qualitative thinking and quantitative thinking with respect to length?

My answer to those questions is that metaphysically what exists is entities with quantities of extension, and length is an human concept which refers to those quantities abstracted from the entities.  If attribute, characteristic, property, and quality are all taken as synonyms then the relationship between quality and quantity becomes clear.

The summary case of why all qualitative things are epistemological artifacts is that they are hierarchically dependent upon pre-existing quantitative things, and derived from them by dropping the quantity (measurement omission).  In chapter 2 of ITOE Rand goes through the gamut of the parts of speech describing how the measurement omission applies to entities/nouns, to materials, to motion, then adverbs, prepositions, adjectives, pronouns, conjunctions and ends with the flourish of claiming love can be measured.  That was what she needed to do for validating the relationship of concepts to reality.

If there is some aspect of thought, such as visualizing spatial manipulations, that is neglected by this theory that is because that is not part of the philosophical problem at hand.  If you think it does touch on the problem, please elaborate.

Taste works almost exactly the same way color perception works, specialized cells detect particular basic tastes just as specialized cells detect particular basic colors.  The basics and their combinations produce the range of what is possible to perceive with that sense.  Color and taste are both relationships.   

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3 hours ago, Grames said:

if you think length is a quality or a quantity? 

I think length is a quantity. As far as forming the concept length, I would say it is completely quantitative because it is a concept of measurement. You could think of length qualitatively once the concept has been formed, or going from abstract to abstraction, and all that. My disagreement only comes in when I propose that there are qualitative (or to put in a better way, non-quantitative) aspects of perception of entities that are not measuring anything quantitatively, and that those aspects may be used to form (most) concepts instead of the quantitative measurements.

3 hours ago, Grames said:

If there is some aspect of thought, such as visualizing spatial manipulations, that is neglected by this theory that is because that is not part of the philosophical problem at hand.  If you think it does touch on the problem, please elaborate.

I will need to refresh my memory about chapter 2, but I recall that I never found it very satisfactory as far as forming concepts, even though I found a great for validating concepts. I will have to think about this more to give you a good answer. I wanted to convey first what I think is a problem, and then the solution to it. Maybe not exactly a problem, but a weakness.

3 hours ago, Grames said:

The basics and their combinations produce the range of what is possible to perceive with that sense. 

But this doesn't explain how sweet and sour are not on the same range, yet that distinction is sufficient to distinguish two entities and then form the concept flavor. Flavor neurons aren't just attuned to a specific sub-range, they are attuned to completely different ranges, we only recognize them as flavors because we experience them on our tongue. 

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2 hours ago, Eiuol said:

I think length is a quantity. As far as forming the concept length, I would say it is completely quantitative because it is a concept of measurement. You could think of length qualitatively once the concept has been formed, or going from abstract to abstraction, and all that. My disagreement only comes in when I propose that there are qualitative (or to put in a better way, non-quantitative) aspects of perception of entities that are not measuring anything quantitatively, and that those aspects may be used to form (most) concepts instead of the quantitative measurements.

I agree. 

Regarding length, one can distinguish between extension and length. The first is an attribute of many entities. The second is, strictly speaking, a relationship rather than an attribute. For example, the pencil's length is 6 inches determined by measuring it, for example, laying a ruler alongside the pencil and observing numbers on the ruler. Using this distinction, the child in Ayn Rand's example in ITOE (page 11) grasped extension, not length.

Edited by merjet
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Length, as a measurement is another stage.

A pencil is longer than a matchsticks. It is shorter than broomstick. The pencil may be slightly longer or shorter than 3 matchsticks. This is the gateway to inches, millimeters etc. In another sense, length, as a concept isn't quantitative as if counting the number of units.

Yet, measurement omission is what Rand refers to the process of forming a concept. Extension is a property of all perceptual entitles we can see. But slide over to justice for a bit where it is a matter of considering all the available evidence known. Not less than or more than the known evidence available. This separates facts from evidentiary facts.

What about getting under the hood of qualitative?

Consider Oxford's definition here:

Relating to, measuring, or measured by the quality of something rather than its quantity.

Might this be relevant, and perhaps illuminate a broader usage that may have been used and intended than pointing out how it doesn't fit into the currently conceived packaging requirements?

I am not seeing a "what is wrong with Rand" on this point or that point here, If Rand is not asking herself the right questions to lead herself to the right answers, what are the questions she left unasked, and what are the descriptions of the observations that lead to the answer that unequivocally demonstrates the contradiction contended.

If the differences are akin to prescriptive law versus descriptive law and executing a difficult to detect equivocation, then the Atilla's and Witchdoctor's are going to prevail whenever they encounter individuals ignorant of the bait and switch of congress creating laws for a nation segueing into what creates laws for the universe.

 

 

 

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10 hours ago, Eiuol said:

But this doesn't explain how sweet and sour are not on the same range, yet that distinction is sufficient to distinguish two entities and then form the concept flavor. Flavor neurons aren't just attuned to a specific sub-range, they are attuned to completely different ranges, we only recognize them as flavors because we experience them on our tongue. 

Sweet and sour are on the same range by virtue of being perceived by the same sense mode.  Vision is the the same as taste in this respect.  The body neither knows nor cares about the order of colors on a spectrum, it just has specialized cells for different colors. 

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2 hours ago, dream_weaver said:

If the differences are akin to prescriptive law versus descriptive law and executing a difficult to detect equivocation, then the Atilla's and Witchdoctor's are going to prevail whenever they encounter individuals ignorant of the bait and switch of congress creating laws for a nation segueing into what creates laws for the universe.

Never fear, the Gods of the Copybook Headings always put things aright again.

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21 minutes ago, Grames said:

Never fear, the Gods of the Copybook Headings always put things aright again.

I enjoyed that. It doesn't fully assuage the comparison between the psychological truism alluded to in Numbers 14:18 and this passage found within the Chapter of Atlantis inside of Atlas Shrugged:

The Lord is long-suffering, his mercy, forgiving iniquity and transgression persists,
And the Gods of the Copybook Headings had said: "Justice has not ceased to exist."

The sins of the fathers, bequeathed to their sons, encrypted a message long spurned,
And the Gods of the Copybook Headings replied: "A blind eye to Justice has turned"

The future descendants may well will to ask, "What onus does this thrust upon us?"
While the Gods of the Copybook Headings might sigh: "A mutual exchange, such as thus.

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22 hours ago, Grames said:

My answer to those questions is that metaphysically what exists is entities with quantities of extension, and length is an human concept which refers to those quantities abstracted from the entities.  If attribute, characteristic, property, and quality are all taken as synonyms then the relationship between quality and quantity becomes clear.

The summary case of why all qualitative things are epistemological artifacts is that they are hierarchically dependent upon pre-existing quantitative things, and derived from them by dropping the quantity (measurement omission).  In chapter 2 of ITOE Rand goes through the gamut of the parts of speech describing how the measurement omission applies to entities/nouns, to materials, to motion, then adverbs, prepositions, adjectives, pronouns, conjunctions and ends with the flourish of claiming love can be measured.  That was what she needed to do for validating the relationship of concepts to reality.

Ok, see this is what I have a problem with. Strictly speaking, there are no "quantities" in reality since every thing that actually exists is a particular. So one cannot literally have "two" (or more) of any particular thing. Therefore, quantities are abstractions, and cannot be used in the process of concept formation without concept-stealing.

What I was saying earlier was that the first step of concept formation (the one where we move beyond concrete representations of concrete entities), is not the passive process of measurement omission, but the active process of interpolation (the explicit, conscious, mental construction of entities that we have never actually observed from the mental representations of entities that we have actually observed).

For example, whenever I have read about Rand's description of the formation of the concept "length", in my mind, I visualize two "long" objects (pencils, say), laid next to each other and then I mentally construct a third pencil that is longer than both, and a pencil longer than that, and so on. But I still don't fully feel as though I have grasped the concept of "length", but rather, only the length of pencils. When, however, I grasp the spatial relationships among the lengths of the pencils, only then do I feel like I have grasped "length" as an abstraction. Because now that I have an awareness of the spatial relationships involved alone, I can apply the concept of length to things other than pencils, such as football fields, cars, and so forth. Note that this happens entirely without any sort of quantitative reasoning, not even implicitly.

My claim is that spatial reasoning is fundamental because, while I can imagine thinking without numbers, I cannot, no matter how hard I try, think without space. Even when comparing numbers I tend to think things like : "Oh, 2 is less than 3 because 2 is to the left of 3 on the number line".

And this ties back into the discussion about quantiative vs. qualitative. That a given length x is longer than some other length y is a qualitative distinction. On the other hand, that a given length x is longer than some other length y by 2.3 inches is a quantitative distinction. And I would disagree with Eiuol that length is a quantity. Length can be measured by a quantity, but it is not itself a quantity.

Edited by SpookyKitty
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13 hours ago, Grames said:

Sweet and sour are on the same range by virtue of being perceived by the same sense mode.

Then you have destroyed what it means to be quantitative. A range implies that two things can be measured with the same kind of measurement. Sweet and sour cannot be measured with the same kind of measurement. Indeed, they are perceived by the same sense mode, but this is exactly what I mean by qualitative aspects that are not dependent on some prior (implicit) measurement.

13 hours ago, Grames said:

The body neither knows nor cares about the order of colors on a spectrum, it just has specialized cells for different colors. 

This is not precise enough.

I'm going to assume that you already know that cones of the eye are not sensitive to specific colors per se, but sensitive to a range of wavelengths, ranges of wavelengths that we name as colors by convention. But those cones are not sensitive to anything else about color, particularly the impact of luminosity and saturation. That part of perception occurs further in visual processing. For this reason, we can't say that cones are "just" specialized for certain colors. Instead, they are "just" specialized for certain wavelengths. In some way, your body does "care" that the colors are on a spectrum, that's what makes it possible to compare colors in a fully commensurable way!

Not to mention that specialization to "just" different colors would only add further support to what I'm saying: your body is capable of detecting differences of kind (without reliance on a quantitative feature) in addition to differences of quantitative measurement. Color perception is so complex that qualitative differences might be a better picture to the whole story. 

2 hours ago, SpookyKitty said:

And I would disagree with Eiuol that length is a quantity. Length can be measured by a quantity, but it is not itself a quantity.

I was confident enough to say that it is a quantity, but I think after reading your post just now, I wouldn't call it a quantity anymore (I like your last sentence). It doesn't alter the point I was getting at though, so everything else I wrote stays the same.

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4 hours ago, SpookyKitty said:

Ok, see this is what I have a problem with. Strictly speaking, there are no "quantities" in reality since every thing that actually exists is a particular. So one cannot literally have "two" (or more) of any particular thing.

A "unit" is not simply a "particular thing." "A unit is an existent regarded as a separate member of a group of two or more similar members." (ITOE, Ch. 1)

If you reject Rand's concept of "unit," then we could debate it. But misrepresenting her theory and ideas solves nothing.

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22 minutes ago, MisterSwig said:

A "unit" is not simply a "particular thing." "A unit is an existent regarded as a separate member of a group of two or more similar members." (ITOE, Ch. 1)

If you reject Rand's concept of "unit," then we could debate it. But misrepresenting her theory and ideas solves nothing.

I don't remember saying anything about units.

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5 minutes ago, SpookyKitty said:

I don't remember saying anything about units.

I know. I did a search. And it looks like you've only used the word three times before on this forum, despite being shown how you misrepresent Rand's theory and definition of concepts. Just saying it might be an issue. You know I like you, but you seem to have an allergic reaction to this topic. The OP talked about "units" like it was an obsessive compulsion, and you act like the idea doesn't exist.

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33 minutes ago, MisterSwig said:

I know. I did a search. And it looks like you've only used the word three times before on this forum, despite being shown how you misrepresent Rand's theory and definition of concepts. Just saying it might be an issue. You know I like you, but you seem to have an allergic reaction to this topic. The OP talked about "units" like it was an obsessive compulsion, and you act like the idea doesn't exist.

Ummm... yeah... cuz that's totally a thing that normal, sane people do...

Here:

unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit

unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit

unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit

unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit

unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit

unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit

unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit

unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit

 

Does that make you feel better?

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