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

[Ogg_Vorbis]

In her Intro to Objectivist Epistemology Ayn Rand stated that the problem of universals is "philosophy's central issue." Would someone please point me to the part of that book where she solved it? And with her focus on concept-formation, why shouldn't she be considered a Conceptualist? Take for instance the concept of a straight line. Where is one in reality? You will be hard-pressed to find it. You will find many lines that appear to be straight, but upon closer examination you will find that they are not straight after all, they always deviate from the 'straight and narrow.' The concept of a straight line refers to nothing in reality.

[softwareNerd]

ITOE itself is the book, because that's where Rand solves her solution to the problem of universals: in short that they are objective (neither arbitrary, nor "out there in the real world" for use to absorb). They are human creations. We create them to help us think about the world. We cannot find them out in the real world; yet, they are useless if we simply make up whatever we want.

So, instead of asking: "where's the straight line?", ask this: "have I ever used that idea"? For instance, have I told someone that I'd like one picture to be hung in a straight horizontal line with another? If I've done something like that, have I spoken complete gobbledegook? Could I just as easily have asked for the two pictures to be hung so that they as asitized (no such word) with each other? If not -- i.e. if the "straight horizontal line" was talking about something in reality while "asitized" was not, then you have your referent in reality.

[DavidOdden]

Would someone please point me to the part of that book where she solved it?

From start to finish. You can explain which part of the book you find unsatisfactory. If you are objecting that she doesn't get into a long, academic rant about the so-called problem of universals, that's not a valid objection, since her goal is to present epistemology, not to do a lit-crit review of previous philosophers. If you're interested in the application of Objectivism to the academic problem, I think you'd have to develop the historical analysis yourself (or find someone who has done it). Remember, she wasn't doing a history of philosophy.

And with her focus on concept-formation, why shouldn't she be considered a Conceptualist?

Are you implying that she isn't? Again, there are package-deal aspects of "Conceptualism" that she may not wish to embrace, so are you objecting that she doesn't embrace an existing package deal, or is there a substantive objective?

The concept of a straight line refers to nothing in reality.

It does: here are some examples.

[Ogg_Vorbis]

ITOE itself is the book, because that's where Rand solves her solution to the problem of universals: in short that they are objective (neither arbitrary, nor "out there in the real world" for use to absorb). They are human creations. We create them to help us think about the world. We cannot find them out in the real world; yet, they are useless if we simply make up whatever we want.

So, instead of asking: "where's the straight line?", ask this: "have I ever used that idea"? For instance, have I told someone that I'd like one picture to be hung in a straight horizontal line with another? If I've done something like that, have I spoken complete gobbledegook? Could I just as easily have asked for the two pictures to be hung so that they as asitized (no such word) with each other? If not -- i.e. if the "straight horizontal line" was talking about something in reality while "asitized" was not, then you have your referent in reality.

But the concept of a straight horizontal line wasn't talking about something in reality, so why shouldn't I simply continue asking "where's the straight line"? The horizontal line between the pictures only looks straight, and while this is good enough for gubmint work it doesn't do anything to answer the problem of universals. No matter how many 'line' examples you may muster up, the only thing they have in common is utility, not straightness, when after all it was the concept of a straight line I was concerned with not the concept of utility. Interesting. I'm not sure of that connection being made between utility and objectivity, or how concepts with no referents "out there in the real world" can be objective.

I have another question about Rand's statement, "concepts are abstractions or universals." Why is it that when I actually research these terms I do not find any equivalence between them? --

"concept" - an abstract or general idea inferred or derived from specific instances.

"universal" - a property held in common by all members of a class of entities.

[Ogg_Vorbis]

From start to finish. You can explain which part of the book you find unsatisfactory. If you are objecting that she doesn't get into a long, academic rant about the so-called problem of universals, that's not a valid objection, since her goal is to present epistemology, not to do a lit-crit review of previous philosophers. If you're interested in the application of Objectivism to the academic problem, I think you'd have to develop the historical analysis yourself (or find someone who has done it). Remember, she wasn't doing a history of philosophy.Are you implying that she isn't? Again, there are package-deal aspects of "Conceptualism" that she may not wish to embrace, so are you objecting that she doesn't embrace an existing package deal, or is there a substantive objective?It does: here are some examples.

You don't understand what I mean by a straight line. By definition, the line must travel continuously in the same direction, never deviating from the course. What I saw on that page are squiggly lines which, for some strange reason, we think as straight. But I don't believe that our need or desire to *think* them as straight actually makes them straight, and it certainly doesn't even make them appear to be straight. The illustrations only give approximations of straightness -- whatever that looks like. Has anybody actually seen a straight line? How then is its concept formed?

As for the rest, I could simply point out the fact that a theory of concept-formation is not an epistemology, and that ITOE was no work on epistemology at all. Perhaps ITOE is introductory to a work on epistemology that has never appeared, so I'm still waiting to see what an Objectivist epistemology consists of. Rand can't very well solve the problem of universals in a mere introductory work that doesn't deal with the topic of knowledge itself, only with concept-formation. And no, I don't believe that solving such problems is a matter of mere academic and historical interest, nor do I see how analyzing the history of philosophy could possibly solve it, it would just be an unoriginal exercise in finding and eliminating dead-end approaches already extant.

But in fact I do believe Rand thought she had solved the problem of universals. Simply put,

"concepts are abstractions or universals,"

that statement being an assertion of her solution.

And since universals are equivalent to concepts, with the theory of concept-formation you have the solution to a problem that, in Rand's view, never should have existed in the first place if only someone hadn't separated the ideas of 'concept' and 'universal'. But since concepts are not universals any more than a concept is a property, the problem is valid and remains a problem.

[agrippa1]

But the concept of a straight horizontal line wasn't talking about something in reality, so why shouldn't I simply continue asking "where's the straight line"? The horizontal line between the pictures only looks straight, and while this is good enough for gubmint work it doesn't do anything to answer the problem of universals. No matter how many 'line' examples you may muster up, the only thing they have in common is utility, not straightness, when after all it was the concept of a straight line I was concerned with not the concept of utility. Interesting. I'm not sure of that connection being made between utility and objectivity, or how concepts with no referents "out there in the real world" can be objective.

The straight line concept is derived from the positional relation of entities. Positional relation is defined in terms of direction and distance. Distance is defined in terms of standard unit and is measured in a straight line. Straight line, conceptually, is defined as the shortest distance between two points, and has the characteristic of being "straight." So the example of straight line that you find in infinite examples in reality is in the distance and shortest path between any two points you can indicate.

[Ogg_Vorbis]

The straight line concept is derived from the positional relation of entities. Positional relation is defined in terms of direction and distance. Distance is defined in terms of standard unit and is measured in a straight line. Straight line, conceptually, is defined as the shortest distance between two points, and has the characteristic of being "straight." So the example of straight line that you find in infinite examples in reality is in the distance and shortest path between any two points you can indicate.

Given a specific example, how do you know which path is the shortest?

[agrippa1]

I have another question about Rand's statement, "concepts are abstractions or universals." Why is it that when I actually research these terms I do not find any equivalence between them? --

"concept" - an abstract or general idea inferred or derived from specific instances.

"universal" - a property held in common by all members of a class of entities.

You lost me. Are you asserting that properties are not derived from specific instances of entities? If so, where do properties come from?

Given a specific example, how do you know which path is the shortest?

You measure the distance between the two with a string, and you notice after a couple of attempts that the shortest measurement corresponds to the string having a characteristic that you conceptualize as "straight."

[softwareNerd]

But the concept of a straight horizontal line wasn't talking about something in reality, ...

I hope you did not get that assumption from my response. Definitely, if the term "straight line" means just as much to you as the terms "syzdygt" and "filfeezeesh", Objectivism would tell you stop using the term. In general, it is quite useless to use terms when you do not know their meaning. Edited February 17, 2008 by softwareNerd

[DavidOdden]

By definition, the line must travel continuously in the same direction, never deviating from the course.

Assuming that you did read ITOE, you then understand that definitions arise inductively from the concrete that the concept subsumes, and the concretes aren't deduced from a definition. Your objection that the lines "deviate" and therefore aren't straint only means that you just think that straight lines are physically perfect. You read the part on concepts of method, right?

Has anybody actually seen a straight line? How then is its concept formed?

By visually inspecting examples such as the one I pointed you at, and generalizing the essential characteristics. It's like extracting "4" from observation of "4 cats", "4 sticks", "4 cows" and so on. No mathematical idealizations are ever seen directly in that form (e.g. you cannot directly see a pure, abstract "7").

As for the rest, I could simply point out the fact that a theory of concept-formation is not an epistemology, and that ITOE was no work on epistemology at all.

On that point, you're simply mistaken. As I said, the "problem of universals" is of no significance in an Objectivist epistemology.

Rand can't very well solve the problem of universals in a mere introductory work that doesn't deal with the topic of knowledge itself, only with concept-formation.

Is your objection that it isn't a complete, exhaustive epistemology? That isn't a valid objective, especially given the title of the book.

But since concepts are not universals any more than a concept is a property, the problem is valid and remains a problem.

What is a "universal"; why is it deserving of any attention? The reason why Rand devotes little attention to the word is that it's a philosophical mess, and it's better to focus on what a "universal" is, namely an abstraction. She explains, philosophically, what "universals" are. If you think that universals are not concepts, then that would explain the nature of your error, that she is not talking about some other sense of so-called "universals".

[Ogg_Vorbis]

You lost me. Are you asserting that properties are not derived from specific instances of entities? If so, where do properties come from?

A property is an attribute derived from observing classes of entities; a property is a "class instance" such that it can be said

that all members of class X share the same property. And indeed they must share the property in order to be considered part

of the same class. In this way we can assert the same properties for members we have never encountered and may never encounter. A property is considered a universal if it satisfies the form, All members of class a have property b.

Particular entities have attributes, but when considered members of the same class these attributes are known as properties. The problem of universals deals with the question of properties, not attributes.

The question then is, how does a property follow all the members of a class? For example, if you have two red books, the property 'redness' is shared between them as members of the class of red books. However, upon closer examination you

may notice that they are not precisely the same color red, that one instance of red is a little darker than the other. In order to classify the books under the same category of red it is necessary to ignore subtle perceptual distinctions. Here's another example: again you are given two books, both books are identical in title, author, cover, publisher, and year of publication, such that you can say that they are both Atlas Shrugged written by Ayn Rand, paperback edition, etc. However, one of the books has its front cover torn off. How are the books identifiable under the same class, and why can they still be considered the same book?

You measure the distance between the two with a string, and you notice after a couple of attempts that the shortest measurement corresponds to the string having a characteristic that you conceptualize as "straight."

Is that straightness accurate to the millimeter, nanometer, or picometer?

Edited February 17, 2008 by Ogg_Vorbis

[Ogg_Vorbis]

I hope you did not get that assumption from my response. Definitely, if the term "straight line" means just as much to you as the terms "syzdygt" and "filfeezeesh", Objectivism would tell you stop using the term. In general, it is quite useless to use terms when you do not know their meaning.

I got that much out of your original post, but I'm saying that your point about the meaning of a straight line relied on a concept external to the problem, that of utility. And while I agree that utility is a property shared by all such intellectual devices as straight lines, that was not the original question. Besides, utility is a property held in common by many devices that are not straight lines.

[softwareNerd]

... utility ...

The point is that utility implies something real.

[Acount Overdrawn]

Is that straightness accurate to the millimeter, nanometer, or picometer?

I don't have ItOE on me, but in the appendix there's a similar objection raised on "exactness." I can't quite think of what was said, but wasn't it to the effect of "this is exact to within such and such measurements (e.g. millimeters)"? And wouldn't this apply to "straightness" as well--that there's a context for straightness, in that any deviations can only go such-and-such nanometers or whatever until it can no longer be considered "straight"? Of course, a person can determine the context for "straightness" in a given instance, but this doesn't mean that "straightness" doesn't exist--it means that it is contextual.

[agrippa1]

Is that straightness accurate to the millimeter, nanometer, or picometer?

Yes.

And this speaks to the problem of universals, as you state it above. The property of "redness" depends on how precisely you define (ostensively) "red," as well as the context of identification. For instance, if you pointed to a bookshelf and said, "see those two red books over there?" I look, and based upon my personal conceptualization of the "ideal" red, look for two books that match that ideal closer than the other books. If I see a red book and a burgundy book on a shelf of blues and greens, I identify those as the "red books" you are referring to. There is no conceptual confusion there. Moving the fringe, if I look and see one red book and one orange book, I may have to come back with "You mean the red and the orange one?" which is a process of communication in which we synchronize our definitions of concepts. If you were to reply "no those are both red" then I might calibrate my communications with you, in a sort of unique dialect, in which the term "red" as used by and to you, subsumes my concepts "red" and "orange." (Preferably, I would point out the difference between the colors of the two books, and try to come to an agreement on the meaning of "red" and "orange" but if you were color-blind, my redefinition of the term would be the only way to synchronize our concepts)

In regards to the straight line, the same process of definition holds true. If I drew three lines on a piece of paper, one curved and two generally "straight" (I will assume that your confusion is theoretical, and not conceptual), and asked you to measure the two straight lines, you would look at the three lines, identify the two which hold more closely to your concept of "straight" and measure them. If two of the lines were straight, accurate to the picometer, and one was straight, accurate only to the nanometer, you would have no confusion as to which lines I meant, assuming those accuracies were apparent to you. If they weren't, or if the difference did not meet your conceptual threshold for differentiation (in terms of "straightness"), you might ask me what I mean by "straight."

A particular "universal" is a property that is conceptualized by your rational mind, not necessarily by all rational minds. If you're looking for a "universal" that is universal to all men, in absolutely, precisely defined terms, you are not going to find it. We all conceptualize properties based on our perceptions and rational processes, so there is naturally some level of disparity between any two men's concepts, as held in their minds, and as synchronized by their terms. (In a manner similar to the observation that two clocks never agree with absolute precision, but both say sufficiently the same thing in terms of "what time it is.")

Edit: typos and more words

Edited February 17, 2008 by agrippa1

[Ogg_Vorbis]

Assuming that you did read ITOE, you then understand that definitions arise inductively from the concrete that the concept subsumes, and the concretes aren't deduced from a definition. Your objection that the lines "deviate" and therefore aren't straint only means that you just think that straight lines are physically perfect. You read the part on concepts of method, right?By visually inspecting examples such as the one I pointed you at, and generalizing the essential characteristics. It's like extracting "4" from observation of "4 cats", "4 sticks", "4 cows" and so on. No mathematical idealizations are ever seen directly in that form (e.g. you cannot directly see a pure, abstract "7").On that point, you're simply mistaken. As I said, the "problem of universals" is of no significance in an Objectivist epistemology.Is your objection that it isn't a complete, exhaustive epistemology? That isn't a valid objective, especially given the title of the book.What is a "universal"; why is it deserving of any attention? The reason why Rand devotes little attention to the word is that it's a philosophical mess, and it's better to focus on what a "universal" is, namely an abstraction. She explains, philosophically, what "universals" are. If you think that universals are not concepts, then that would explain the nature of your error, that she is not talking about some other sense of so-called "universals".

I agree in that the concept of a straight line is, like the number 7, a mathematical idealization. And since they are not existents (which, according to ITOE, are concretes), they are formal, intellectual constructs. A concept of method requires a purposive course of action, i.e., a method has to have a purpose and a function. And yet all concepts I can think of have a purposive directedness or utility. The concept "tree" is a concept of method used for communicating to you about a tree.

Rand explained the problem of universals by citing the concept 'man.' But she never really got around to stating the actual problem, focusing instead on attributes that are not identical (such as fingerprints). But the problem involves properties which are allegedly identical: if reason is a distinguishing property of man separating him from animals, then how do we know that the rational faculty in one man is the same as the rational faculty in any other men, such that all men may be classified under the same category of rational animal? The general classification 'man' does not necessarily speak to any particulars whatsoever. And unlike the concept of a straight line, I don't hold the concept 'man' to be a mathematical idealization at all.

Yes, it is a sticky problem, and it won't go away simply by asserting, "a concept is an abstraction or universal." And it is deserving of attention because Rand bothered to mention it. And, need I remind you, '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.'

As for the title of the book, if she had called it "A Brief Pictorial History of Motocross Racing," would that have made it a book on motocross racing? And so here I am, still sitting on my thumbs waiting for an Objectivist theory of knowledge and not just a theory of concept-formation.

[dbc]

But the problem involves properties which are allegedly identical: if reason is a distinguishing property of man separating him from animals, then how do we know that the rational faculty in one man is the same as the rational faculty in any other men, such that all men may be classified under the same category of rational animal? The general classification 'man' does not necessarily speak to any particulars whatsoever. And unlike the concept of a straight line, I don't hold the concept 'man' to be a mathematical idealization at all.

First, it would be helpful if you told us to what you refer when you speak of one man having "the same" rational faculty of another man. Regardless, Rand tells us that the fact that men possess rational faculty is a characteristic that justifies us in regarding them as members of the same class. The degree of a man's intellegence (assuming that is what you were refering to) is not an essential characteristic.

Edited February 17, 2008 by dbc

[dbc]

As for the title of the book, if she had called it "A Brief Pictorial History of Motocross Racing," would that have made it a book on motocross racing? And so here I am, still sitting on my thumbs waiting for an Objectivist theory of knowledge and not just a theory of concept-formation.

As she stated in the Foreword, Rand intended that ITOE be a "summary of one of its [Objectivist epistemology's] cardinal elements--the Objectivist theory of concepts."

Dan

[agrippa1]

The concept of a straight line refers to nothing in reality.

The concept of a perpetual motion machine refers to nothing in reality. It is the construct of three concepts which do exist in reality: Perpetual (in context of a time frame), motion, and machine. The fact that a perpetual motion machine does not exist, does not invalidate the concepts which were combined in order to create the new concept of such a non-existent machine.

Similarly, the concept of a "straight line" is the construct of the the attribute "straight" and the concept "line." I can define straightness comparatively, by demonstration, and I can find examples of straightness (a piece of twine suspending a weight) that idealize the concept of "straight." The concept "line" is based on the perception of demarcation between two entities or two regions of an entity, or the border of a single entity. It was probably concretized as a result of drawing figures, and refers to the representation in graphic terms of either a concrete or an abstract concept.

The fact that a perfectly straight line may not "exist" in nature does not invalidate the concepts from which the concept "straight line" was constructed.

[softwareNerd]

... if reason is a distinguishing property of man separating him from animals, then how do we know that the rational faculty in one man ...

Are you saying the biologists are wrong to group you and me into a single species, and that they could just as well group me with say one peacock and you with some other peacock, and that in reality there are no observations of similarity that biologists use? Are you saying that you are just as similar to a rock, or a lion, regardless of what measure you use? Edited February 17, 2008 by softwareNerd

[agrippa1]

And so here I am, still sitting on my thumbs waiting for an Objectivist theory of knowledge and not just a theory of concept-formation.

Could you define "knowledge?"

[DavidOdden]

And since they are not existents (which, according to ITOE, are concretes)

I think if you re-check, you will see that that is false. I advocate using direct quotations, which tends to catch those errors. Straight lines, numbers, etc are all existents.

The concept "tree" is a concept of method used for communicating to you about a tree.

No, "tree" is a concept which reduces to particular wooden entities. Don't confuse the things you can do with a concept -- communicate or obfuscate X -- with a concept which is in fact a method.

But the problem involves properties which are allegedly identical: if reason is a distinguishing property of man separating him from animals, then how do we know that the rational faculty in one man is the same as the rational faculty in any other men, such that all men may be classified under the same category of rational animal?

Your concern is misplaced; and I see you returning to that theme of "definition". The fact of identification is primary, and definition is secondary. You don't need to know that the rational faculty in one man is the same as the rational faculty in any other men, all you need to be able to do is identify a man.

And so here I am, still sitting on my thumbs waiting for an Objectivist theory of knowledge and not just a theory of concept-formation.

And yet, you can't name any aspect of an epistemology that is missing from ITOE. I'll help you with the one thing I know of -- she did not develop the distinction between possible, probably and certain, which was done in OPAR. She did dispose of the so-called "problem of universals", by proposing a theory of concept formation (which then leaves no unresolved matters of substance in the "problem of universals").

[Ogg_Vorbis]

Yes.

And this speaks to the problem of universals, as you state it above. The property of "redness" depends on how precisely you define (ostensively) "red," as well as the context of identification. For instance, if you pointed to a bookshelf and said, "see those two red books over there?" I look, and based upon my personal conceptualization of the "ideal" red, look for two books that match that ideal closer than the other books. If I see a red book and a burgundy book on a shelf of blues and greens, I identify those as the "red books" you are referring to. There is no conceptual confusion there. Moving the fringe, if I look and see one red book and one orange book, I may have to come back with "You mean the red and the orange one?" which is a process of communication in which we synchronize our definitions of concepts. If you were to reply "no those are both red" then I might calibrate my communications with you, in a sort of unique dialect, in which the term "red" as used by and to you, subsumes my concepts "red" and "orange." (Preferably, I would point out the difference between the colors of the two books, and try to come to an agreement on the meaning of "red" and "orange" but if you were color-blind, my redefinition of the term would be the only way to synchronize our concepts)

In regards to the straight line, the same process of definition holds true. If I drew three lines on a piece of paper, one curved and two generally "straight" (I will assume that your confusion is theoretical, and not conceptual), and asked you to measure the two straight lines, you would look at the three lines, identify the two which hold more closely to your concept of "straight" and measure them. If two of the lines were straight, accurate to the picometer, and one was straight, accurate only to the nanometer, you would have no confusion as to which lines I meant, assuming those accuracies were apparent to you. If they weren't, or if the difference did not meet your conceptual threshold for differentiation (in terms of "straightness"), you might ask me what I mean by "straight."

A particular "universal" is a property that is conceptualized by your rational mind, not necessarily by all rational minds. If you're looking for a "universal" that is universal to all men, in absolutely, precisely defined terms, you are not going to find it. We all conceptualize properties based on our perceptions and rational processes, so there is naturally some level of disparity between any two men's concepts, as held in their minds, and as synchronized by their terms. (In a manner similar to the observation that two clocks never agree with absolute precision, but both say sufficiently the same thing in terms of "what time it is.")

Red and orange are precisely distinguishable from each other: red is a color in the wavelength range of roughly 625–740 nm; orange is a color at a wavelength of about 585 – 620 nm. (Source = wikipedia.)

The question for you seems to involve relativity and perspectivism. Straightness is defined relative to a standard of measure. But since that in itself only stands relative to some more or less fine degree of measure, an absolute degree of measure would be infinitely precise. I am not demanding that true knowledge conform to this perfectionistic standard, only that a relative measure must stand in comparison to some absolute standard, despite the fact that no such standard can ever be found in reality. In Rand's terms, the concept of a straight line must omit the particular measurements, retaining just a few essentials: two points joined by a line that never deviates as it traverses whatever distance stands between them. So even if you allow for the slightest possible deviation you still do not have, by definition, a straight line, because it is the latter immutable definition that guides your thinking, not some arbitrary, relative standard of straightness that doesn't properly "define away" the particulars (nanometers, etc).

I don't believe that red and orange were originally defined scientifically, only intuitively (or ostensively). On such a subjective grounds everybody must simply find some basis for agreement. However, the problem of universals only asks if it is the same color classifiable under the same category 'red' when pondering two red books. Perhaps the colors should be called 'red1' and 'red2', since no two colors of red appear exactly identical. There is then no intersubjectivity question, the problem of universals isn't concerned with that anyway. The question is why we always consider red as red, or better, why the redness in the one book falls under the same category of redness in all red books, and how we learned to generalize 'redness' in the absence of anything but intuitive, perceptual guidance, where concept-formation falls flat on its face. Rand thought that it was due to some sort of 'implicit measurement,' [itoe, 14] but this was going on long before anybody even had an inkling that color consists of measurable wavelengths of light.

[Ogg_Vorbis]

As she stated in the Foreword, Rand intended that ITOE be a "summary of one of its [Objectivist epistemology's] cardinal elements--the Objectivist theory of concepts."

Dan

That's true, she did state that. I wonder what the other cardinal elements are?

The point is that utility implies something real.

And 'straightness' implies an impossibility.

[dbc]

And 'straightness' implies an impossibility.

What is that you mean by "straight"? Doesn't straight refer to a particular shape? A relationship between two or more points? What, specifically, is the "impossibility" you refer to?

Dan