Universals and Measurement

[BaalChatzaf]

If there is something wrong with that method and the premise of the tentativeness of scientific knowledge then that's what needs to be discussed. What also needs to be discussed is philosophical absolutism and the psychological and political and other human needs it serves.

--Brant

The only philosophical absolutism that makes sense to me is our insistence on internal logical consistency. We absolutely insist that our arguments be sound, that is logically valid and based on true premises, when truth is determinable.

In short, no logical balderdash allowed.

This includes the Beloved Principle of Identity. Consistency implies that a thing is what it is and not what it isn't. We also do not like solopsist fantasies so we base our philosophies on the premise they something Out There exists that isn't us. This leaves a lot of wiggle room and opportunities for variation and variety.

Ba'al Chatzaf

Edited October 29, 2007 by BaalChatzaf

[Ellen Stuttle]

[...] please explain why you are ignoring the fact that Popper states clearly that his objection is to using intuition as a scientific method. Here are his quotes once again from my post above. Notice my phrase below: "Popper does not understand the term 'essence' without it being grasped by intuition." At least he doesn't in that essay.

[....] from Popper's essay, Two Kinds of Definition (my bold):

Aristotle followed Plato in distinguishing between knowledge and opinion. Knowledge, or science, according to Aristotle, may be of two kinds - either demonstrative or intuitive. Demonstrative knowledge is also a knowledge of 'causes'. It consists of statements that can be demonstrated - the conclusions - together with their syllogistic demonstrations (which exhibit the 'causes' in their 'middle terms'). Intuitive knowledge consists in grasping the 'indivisible form' or essence or essential nature of a thing (if it is 'immediate', i.e. if its 'cause' is identical with its essential nature); it is the originative source of all science since it grasps the original basic premisses of all demonstrations.

. . .

But how to obtain these basic premisses? Like Plato, Aristotle believed that we obtain all knowledge ultimately by an intuitive grasp of the essences of things. 'We can know a thing only by knowing its essence', Aristotle writes, and 'to know a thing is to know its essence'. A 'basic premiss' is, according to him, nothing but a statement describing the essence of a thing. But such a statement is just what he calls a definition. Thus all 'basic premisses of proofs' are definitions.

. . .

But the most difficult question is how we can get hold of definitions or basic premisses, and make sure that they are correct - that we have not erred, not grasped the wrong essence. Although Aristotle is not very clear on this point, there can be little doubt that, in the main, he again follows Plato. Plato taught that we can grasp the Ideas with the help of some kind of unerring intellectual intuition; that is to say, we visualise or look at them with our 'mental eye', a process which he conceived as analogous to seeing, but dependent purely upon our intellect, and excluding any element that depends upon our senses. Aristotle's view is less radical and less inspired than Plato's, but in the end it amounts to the same. For although he teaches that we arrive at the definition only after we have made many observations, he admits that sense experience does not in itself grasp the universal essence, and that it cannot, therefore, fully determine a definition. Eventually he simply postulates that we possess an intellectual intuition, a mental or intellectual faculty which enables us unerringly to grasp the essences of things, and to know them. And he further assumes that if we know an essence intuitively, we must be capable of describing it and therefore of defining it.

Michael,

I'm concluding that you're being thrown off here by not understanding the Aristotelian program. Aristotle wanted to establish indisputably true basic premises which could then be used as the universals ("All men are mortal," e.g.) of a syllogism for guaranteeing correct inference. For "demonstrative" and "intuitive" in the first sentence you quoted above, if you substitue "deduction" and "induction," this is closer in modern language to what Aristotle was trying for. He was seeking an earlier version of the same thing Objectivism is trying for -- and which you've proclaimed time and again in your posts is the nature of knowledge -- an induction/deduction loop such that the root premises, arrived at by induction, then provide a basis for guaranteed deduction. I think if you push what Rand says about definitions, you end up very close to Aristotle's view. Rand first says that she's thinking of the essential characteristic(s) as "epistemological," but she then brings in metaphysics by saying that metaphysically the greatest number of other characteristics depend on the essential characteristic(s). This is a causal statement; but how does she -- how does anyone -- ascertain and demonstrate what such a characteristic(s) might be? She doesn't really have a method for doing that. She says the process is one of induction; but how is she going to prove that she's arrived at the correct supposedly metaphysical characteristic(s) on which the most others depend? Brass tacks is that it's going to have to be known not by direct sense experience but by some form of intellectual grasp. Which leaves her, really, in the same boat as Aristotle of having to resort to a method other than observation in formulating the correct, the "true," definition.

Ellen

___

[Michael Stuart Kelly]

I'm concluding that you're being thrown off here by not understanding the Aristotelian program. Aristotle wanted to establish indisputably true basic premises which could then be used as the universals ("All men are mortal," e.g.) of a syllogism for guaranteeing correct inference. For "demonstrative" and "intuitive" in the first sentence you quoted above, if you substitue "deduction" and "induction," this is closer in modern language to what Aristotle was trying for. He was seeking an earlier version of the same thing Objectivism is trying for -- and which you've proclaimed time and again in your posts is the nature of knowledge -- an induction/deduction loop such that the root premises, arrived at by induction, then provide a basis for guaranteed deduction. I think if you push what Rand says about definitions, you end up very close to Aristotle's view. Rand first says that she's thinking of the essential characteristic(s) as "epistemological," but she then brings in metaphysics by saying that metaphysically the greatest number of other characteristics depend on the essential characteristic(s). This is a causal statement; but how does she -- how does anyone -- ascertain and demonstrate what such a characteristic(s) might be? She doesn't really have a method for doing that. She says the process is one of induction; but how is she going to prove that she's arrived at the correct supposedly metaphysical characteristic(s) on which the most others depend? Brass tacks is that it's going to have to be known not by direct sense experience but by some form of intellectual grasp. Which leaves her, really, in the same boat as Aristotle of having to resort to a method other than observation in formulating the correct, the "true," definition.

Ellen,

In other words, am I correct in my assumption that you believe Rand's theory of concept formation is based on intuition as the basic form of gaining knowledge?

Michael

[Ellen Stuttle]

Ellen,

In other words, am I correct in my assumption that you believe Rand's theory of concept formation is based on intuition as the basic form of gaining knowledge?

No, you aren't; furthermore, I don't think you're getting even what's being described as Aristotle's method. I think Aristotle and Rand were more significantly similar than different, and that you aren't really grokking Popper's discussion, and that I don't know how to explain it to you. You read the same words I read -- I guess; at least I'm assuming you read them -- and get a different meaning from what I get. (I notice, too, that you leave out passages which I think are important in explaining what Popper is talking about.) Impasse is where it's at.

Ellen

___

[Michael Stuart Kelly]

The problem with these threads and posts is that they aren't centered on the scientific method, but Popper this and Rand that and so and so that.

Brant,

This is absolutely correct in my case. I object to Rand's ideas being mischaracterized, and then the mischaracterization criticized as if this came from her.

I actually disagree with some points of ITOE, but I don't wish to discuss them until we are all talking about what she actually wrote and meant, not something projected from a misunderstanding or statement taken out of context. My belief is that she wrote enough that needs to be corrected and/or fleshed out to satisfy critics. Nobody needs to make up anything.

I will state unequivocally that Rand made not one ounce of contribution to the scientific method and she cannot be reversed engineered to that.

I do not know of how much she contributed or not. I do know that there are several scientists on record I have read over the years stating their agreement with her epistemology and its value to their work. I would have to look to find them, but they exist. I even read about some software engineers developing their programs and (if I am not mistaken) programming language based on the principles given in ITOE.

So I do not know about historical impact. There is some impact just by the existence of these scientists. But if the gist of what you are claiming is that Rand's epistemology somehow contradicts scientific method, we disagree big time.

Also, if you are claiming that the arguments on OL in support of Rand's epistemology are meant to "reverse engineer" her ideas to pump them up in importance, I would be interested in reading something to that effect. Could you provide some kind of quote? (Lamentably, quotes from her exist to this effect, but I am asking about OL posters.)

Michael

[Michael Stuart Kelly]

No, you aren't; furthermore, I don't think you're getting even what's being described as Aristotle's method. I think Aristotle and Rand were more significantly similar than different, and that you aren't really grokking Popper's discussion, and that I don't know how to explain it to you.

Ellen,

So long as you contend that intuition and measurement have little or nothing to do with the difference in the meaning of essence between Aristotle and Rand, we will remain at this impasse. I cannot delete these words I read from Popper and Rand in my mind simply to serve your theory.

Incidentally, how do you account for Popper repeatedly saying that essence according to Aristotle is grasped through intuition? Just ignore it?

Michael

[Michael Stuart Kelly]

Ellen,

For the sake of ease of reference, here is your post where you cite Rand on essence.

Michael

I haven't had time yet to find out where the discussion's gotten to since I last posted. Meanwhile, however, I looked up further material from Rand's ITOE (in her chapter on "Definitions") pertaining to her use of "essence"/"essential characteristic." I expanded the quotes which I first posted in my #230 of the "Scorecard" thread (here) and re-posted as #329 of that thread (here). The expanded set is given below. I think this series makes abundantly clear that she thought of the differentia ("rational" in the case of her definition of "man") as identifying the "essence"/"essential characteristic" of a concept; also that it makes abundantly clear why Popper would have considered her approach, along with Aristotle's, "essentialism."

Here's another quote which well illustrates her sharp divergence from Popper on the nature and role of definitions:

[emphasis in original]

The truth or falsehood of all of man's conclusions, inferences, thought and knowledge rests on the truth or falsehood of his definitions.

An objective definition, valid for all men, is one that designates the essential distinguishing characteristic(s) and genus of the existents subsumed under a given concept--according to all the relevant knowledge available at that stage of mankind's development. [iTOE, 61 original; 46 expanded]

[Notice she says two parts there: the essential characteristic AND the genus; thus she isn't considering the genus to be the essential distinguishing characteristic.]

The rules of correct definition are derived from the process of concept-formation. The units of a concept were differentiated--by means of a distinguishing charactersitic(s)--from other existents possessing a commensurable characteristic, a "Conceptual Common Denominator." A definition follows the same principle: it specifies the distinguishing characteristic(s) of the units, and indicates the category of existents from which they were differentiated.

The distinguishing characteristic(s) of the units becomes the differentia of the concept's definition; the existents possessing a "Conceptual Common Denominator" become the genus.

[....] The differentia isolates the units of a concept from all other existents; the genus indicates their connection to a wider group of existents.

[in later quotes she says the essential characteristic differentiates from ALL other existents; obviously the genus doesn't do that but instead, as she says, connects to a wider group.]

[....] In the definition of man ("A rational animal"), "rational" is the differentia, "animal" is the genus. [iTOE 53 original, 41-42 expanded]

When [the maturing person (she says at about the time of adolescence)] grasps that man's distinctive characteristic is his type of consciousness--a consciousness able to abstract, to form concepts, to apprehend reality by a process of reason--he reaches the one and only valid definition of man, within the context of his knowledge and of all mankind's knowledge to date: "A rational animal."

[....]

Now observe, on the above example [that of the stages she describes in defining "man"], the process of determining an essential characteristic: the rule of fundamentality. When a given group of existents has more than one characteristic distinguishing it from other existents, man must observe the relationships among these various characteristics and discover the one on which all the others (or the greatest number of others) depend, i.e., the fundamental characteristic without which the others would not be possible. This fundamental characteristic is the essential distinguishing characteristic of the existents involved, and the proper defining characteristic of the concept.

Metaphysically, a fundamental characteristic is that distinctive characteristic which makes the greatest number of others possible; epistemologically, it is the one that explains the greatest number of others.

For instance, one could observe that man is the only animal who speaks English, wears wristwatches, flies airplanes, manufactures lipstick, studies geometry, reads newspapers, writes poems, darns socks, etc. None of these is an essential characteristic: none of them explains the others; none of them applies to all men; omit any or all of them, assume a man who has never done any of these things, and he will still be a man. But observe that all these activities (and innumerable others) require a conceptual grasp of reality, that an animal would not be able to understand them, that they are the expressions and consequences of man's rational faculty, that an organism without that faculty would [not be a man--and you will know why man's rational faculty is his essential distinguishing and defining charactersitic.

If definitions are contextual, how does one determine an objective definition valid for all men? It is determined according to the widest context of knowledge available to man on the subjects relevant to the units of a given concept.

[....]

An objective definition, valid for all men, is one that disignates the essential distinguishing characteristic(s) and genus of the existents subsumed under a given concept--according to all the relevant knowledge available at that stage of mankind's development.

[....]

This does not mean that every man has to be a universal scholar and that every discovery of science affects the definitions of concepts: when science discovers some previously unknown aspects of reality, it forms new concepts to identify them (e.g., "electron"); but insofar as science is concerned with the intensive study of previously known and conceptualized existents, its discoveries are identified by means of conceptual sub-categories. For instance, man is classified biologically in several sub-categories of "animal," such as "mammal," etc. But this does not alter the fact that rationality is his essential distinguishing and defining characteristic, and that "animal" is the wider genus to which he belongs.

[iTOE, ?-59 original, 44-47 expanded]

Let us note, at this point, the radical difference between Aristotle's view of concepts and the Objectivist view, particularly in regard to the issue of essential characteristics.

[Popper of course, had he known of Rand's theories, wouldn't have considered this a "radical difference"; both Aristotle and Rand propose the idea of "essences."]

It is Aristotle who first formulated the principles of correct definition. It is Aristotle who identified the fact that only concretes exist. But Aristotle held that definitions refer to metaphysical essences, which exist in concretes as a special element or formative power, and he held that the process of concept-formation depends on a kind of direct intuition by which man's mind grasps these essences and forms concepts accordingly.

Aristotle regarded "essence" as metaphysical; Objectivism regards it as epistemological.

Objectivism holds that the essence of a concept is that fundamental characteristic(s) of its units on which the greatest number of other characteristics depend, and which distinguishes these units from all other existents within the field of man's knowledge. Thus the essence of a concept is determined contextually and may be altered with the growth of man's knowledge. The metaphysical referent of man's concepts is not a special, separate metaphysical essence, but the total of the facts of reality he has observed, and this total determines which characteristics of a given group of existents he designates as essential. An essential characteristic is factual, in the sense that it does exist, does determine other characteristics and does distinguish a group of existents from all others; it is epistemological in the sense that the classification of "essential characteristic" is a device of man's method of cognition--a means of classifying, condensing and integrating an ever-growing body of knowledge. [iTOE, 68 original, 52 expanded]

___

[Michael Stuart Kelly]

Rand first says that she's thinking of the essential characteristic(s) as "epistemological," but she then brings in metaphysics by saying that metaphysically the greatest number of other characteristics depend on the essential characteristic(s). This is a causal statement; but how does she -- how does anyone -- ascertain and demonstrate what such a characteristic(s) might be? She doesn't really have a method for doing that.

Ellen,

It's odd that you ask this question and make this affirmation (that Rand "doesn't really have a method for doing that"). You even talk about "greatest number of other characteristics," quote Rand on this and give her examples. If you look, the method is right in front of you. Once again, I will state it: measurement.

What is "greatest number" if not a measurement?

Let's look at the Rand quote again (ITOE, 2nd, pp. 45-46, and I added the preceding paragraph, since it included the word "fundamentality" - my bold):

Now observe, on the above example, the process of determining an essential characteristic: the rule of fundamentality. When a given group of existents has more than one characteristic distinguishing it from other existents, man must observe the relationships among these various characteristics and discover the one on which all the others (or the greatest number of others) depend, i.e., the fundamental characteristic without which the others would not be possible. This fundamental characteristic is the essential distinguishing characteristic of the existents involved, and the proper defining characteristic of the concept.

Metaphysically, a fundamental characteristic is that distinctive characteristic which makes the greatest number of others possible; epistemologically, it is the one that explains the greatest number of others.

For instance, one could observe that man is the only animal who speaks English, wears wristwatches, flies airplanes, manufactures lipstick, studies geometry, reads newspapers, writes poems, darns socks, etc. None of these is an essential characteristic: none of them explains the others; none of them applies to all men; omit any or all of them, assume a man who has never done any of these things, and he will still be a man. But observe that all these activities (and innumerable others) require a conceptual grasp of reality, that an animal would not be able to understand them, that they are the expressions and consequences of man's rational faculty, that an organism without that faculty would not be a man—and you will know why man's rational faculty is his essential distinguishing and defining characteristic.

The thing that almost screams out to be observed (within the context of this discussion) is that fundamentality is a measurement. "Greatest number" and "all" and "none" and "any or all" are measurements. Even "innumerable" is a measurement. (I am using measurement in Rand's meaning, which is especially appropriate since I am discussing her work.)

Look at her examples of characteristics of man: "speaks English, wears wristwatches, flies airplanes, manufactures lipstick, studies geometry, reads newspapers, writes poems, darns socks, etc." Rand is only talking about one type of characteristic in these examples: actions. There are many other characteristics a man has (or that are possible to him) that are not included in "rational" such as having a gall bladder, reproducing by sex, and a host of others I am sure you can imagine. What do the actions Rand mentioned (if projected) have in relation to these other characteristics I mentioned? There are more of them, i.e., a measurement is computed in the mind (in gross terms). The characteristics (actions) Rand mentioned can only exist if a rational faculty exists. Eliminate the rational faculty and a huge number of human characteristics (actions) disappear from the realm of the possible. This "huge number" of characteristics is larger than the number of characteristics emanating from any other aspect of man.

This is a measurement.

"Essential characteristic" for Rand ALWAYS presumes the phrase "all or greatest number."

Notice that Rand nowhere says that a characteristic cannot exist in a defined existent if it is not dependent on the essential characteristic. She does not even exclude a characteristic that is unique to a single member of a group. The law of identity (from which causality emanates) includes the entire range of characteristics, going from essential ones explaining all or the greatest number of characteristics for the group to a unique one for a single member.

Now, of course, according to your contention, all this is pretty much similar to Aristotle's intuition for mentally grasping essences, and Popper meant both Aristotle's method (intuition) and Rand's (measurement).

Right.

Thinking the way I do and noting these differences must be due to (what is that favorite characterization of yours for my epistemological prose?—oh, yes...) my "kinda, sorta exegetical style."

Michael

[BaalChatzaf]

There are more of them, i.e., a measurement is computed in the mind (in gross terms). The characteristics (actions) Rand mentioned can only exist if a rational faculty exists. Eliminate the rational faculty and a huge number of human characteristics (actions) disappear from the realm of the possible. This "huge number" of characteristics is larger than the number of characteristics emanating from any other aspect of man.

Our intellect is a direct result of our genome. Therefore the genome is THE underlying characteristic. We are what our genes make us. Even our ability to make choices is a result of our genes. No genome. No intellect and therefore no rationality.

Rationality is NOT a self standing characteristic of humans. It is an accident in the Aristotelean sense. Our rationality is a side effect, an epiphenomenon of our genetic makeup.

Ba'al Chatzaf

[Michael Stuart Kelly]

Our intellect is a direct result of our genome. Therefore the genome is THE underlying characteristic. We are what our genes make us. Even our ability to make choices is a result of our genes. No genome. No intellect and therefore no rationality.

Rationality is NOT a self standing characteristic of humans. It is an accident in the Aristotelean sense. Our rationality is a side effect, an epiphenomenon of our genetic makeup.

Bob,

This is interesting (and I have some observations), but it is another discussion. (And incidentally, nobody in Objectivism that I know of claims that rationality is a "self standing characteristic of humans." I don't know where on earth you got that. Even a genome is not a "self standing characteristic of humans.")

The discussion on the table is whether Rand's concept of essence is the same as, or greatly similar to, Aristotle's. To me this boils down to whether measurements are made by intuition or not. I do not call the mental capacity to identify (i.e., distinguish similarities and differences between existents) and measure existents "intuition." I do not even find it to be "greatly similar" to intuition.

Michael

[merjet]

The thing that almost screams out to be observed (within the context of this discussion) is that fundamentality is a measurement. "Greatest number" and "all" are measurements.

How do you reconcile this with Rand's position that entities are the primary existents? I'm not expecting a reply, but offering you some food for thought. Aristotle held that the primary existents were "substances", arguably not exactly the same thing, but close. (He used "substance" in another sense as well, like the more common one now.) Take your pick -- Aristotle or Pythagoras.

I do know that there are several scientists on record I have read over the years stating their agreement with her epistemology and its value to their work. I would have to look to find them, but they exist. I even read about some software engineers developing their programs and (if I am not mistaken) programming language based on the principles given in ITOE.

An article in JARS was about this topic (Adam Reed, Vol. 4, No. 2, 2003). Several years ago a revolution in computer programming occurred, and the new way came to be called object-oriented programming (OOP). As Reed notes, several textbooks on OOP make reference to Ayn Rand’s epistemology. He says OOP and Rand's epistemology have much in common, not that Rand had anything to do with OOP. Reed also gives a brief description of OOP, but here I will describe it with a different way, one that supports the commonality.

Computer languages prior to the OOP revolution are usually described as procedural. However, I do not believe that provides a great contrast to OOP. The steps in OOP are less linear and less uniform (think user interfaces), but OOP is still procedural. In my view OOP is more about data structures and program organization.

Prior to OOP the typical language offered two main data types – alphabetic and numeric. The latter came in two main types -- integer and floating point (non-integer). All types could be structured in vector or array form. OOP offers the programmer the opportunity to build their own data types, by combining the given, basic ones. These came to be called "objects". For example, as a programmer for a business, one might define an object SUPPLIER, which is a combination of several data types. One could be its name (alphabetic), another how much money the business owes it (numeric), an assigned unique ID (numeric), an array of products the supplier has (numeric and/or alphabetic).

While one could manage without an OOP language to keep track of the different kinds of data for several suppliers, it would be much more difficult since different data types, and arrays of different sizes, must be maintained separately. An OOP language affords the opportunity to combine the given, basic data types into one big one.

Another difference is that in the procedural era, there were often main programs and subroutines. A subroutine was called as needed by the main program, after which control returned to the main program. However, the subroutine could not be called by another main program. If the programmer wanted another main program to use the same subroutine, the latter had to be duplicated. A key feature of OOP is that subroutine-like programs are made to be stand-alone and can be called by multiple main programs.

Both of these features are about organization. There is more to OOP than this, but this suffices to show the commonality. "Objects" are central to the organization of OOP. Entities are the primary existents for Rand and thus central. In OOP attributes and methods are tied to "objects". For Rand attributes and actions are tied to entities.

Edited October 29, 2007 by Merlin Jetton

[tjohnson]

[Off Topic]

And now there another kind of programming - web based. I have never done OOP but I used to do procedural in BASIC and FORTRAN. Now I do php programming and it's cool because it's in a client-server environment and every php file is a standalone program but can also fork to another so there really is no hierarchy, except usually the web server will parse index.php by default if no other file is specified.

[merjet]

I'm not familiar with PHP, but its OOP nature is addressed here.

http://en.wikipedia.org/wiki/PHP#Data_types

[Ellen Stuttle]

Now, of course, according to your contention, all this is pretty much similar to Aristotle's intuition for mentally grasping essences, and Popper meant both Aristotle's method (intuition) and Rand's (measurement).

Right.

According to my contention, all this -- by which I mean what Rand actually wrote, in full, complete sentences and thoughts included -- is "pretty much similar" to Aristotle's approach to definitions, and, had Popper known of Rand's views (which he certainly had never heard of at the time the essay was written, since Rand's views were 20+ years short of being published then, and which I know of no indication he ever learned of), he'd have thought of her views, if he was being consistent, as another case in point.

Thinking the way I do and noting these differences must be due to (what is that favorite characterization of yours for my epistemological prose?—oh, yes...) my "kinda, sorta exegetical style."

LOL. Yeah, kinda, sorta that, Michael. Plus the selective recreations of your readings. For instance, words like "depend [on]," "makes possible," "explains," "require" -- words indicating a causal thesis. And even taking your approach to Rand as the Great Cataloguer, you'd have to tally up every characteristic of the human and then...what? What would a sheer tally tell you?

Another example of your selective reading -- and this one just in the last less-than-twelve hours -- is your query to me (from your post #131):

Incidentally, how do you account for Popper repeatedly saying that essence according to Aristotle is grasped through intuition? Just ignore it?

I think I know how Sisyphus might have felt. And I think I shall cease attempting to push this particular rock up a hill.

Ellen

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[Michael Stuart Kelly]

Ellen,

I just love the way you ignore the words "intuition" and "measurement" with Rand and Popper and even make fun of them. I certainly have seen nothing resembling an argument against them coming from you so far. And for some darn reason they just won't go away, will they?

On the other hand, I have provided measurement ("greatest number of characteristics") for the elusive method you claim Rand did not have for identifying essence, giving this in Rand's own words that you have even quoted (but somehow missed).

I have also provided Popper's own words showing that he only identified essence with intuition when discussing Aristotle, and you somehow missed this, too. From the way you write about what Popper really would have thought, it almost seems as if you are in denial of what he actually wrote.

It's too bad these observations undo your channeling of "what Popper would have thought had he known" and how Rand got it all wrong, but things happen.

EDIT: I have never denied that there exists causality within the components of an entity or existent. For instance, a heart causes blood to pump through veins. Rationality causes the possibility of production and conceptual actions. I think it is silly to try to deny this or claim that observing this is based on intuition (like Popper claims Aristotle thought—and I admit Aristotle might have had an excuse, but as I keep pointing out, this has nothing to do with Rand's approach). I have seen no instance in my own readings of Popper where he denies causality or claims that it is based on intuition. I have even quoted him on mentioning "laws of nature," yet I do not think he arrives at them through intuition. I specifically remember (and have quoted him) on concluding that intuition is not reliable knowledge. From what I have read and quoted, Popper's standard for judging and identifying essence is that knowing it can only be done by intuition. Had he somehow miraculously known Rand's work, I see no reason to suppose he would have used a different standard, although you seem to think so when you channel him.

Michael

[BaalChatzaf]

On the other hand, I have provided measurement ("greatest number of characteristics") for the elusive method you claim Rand did not have for identifying essence, giving this in Rand's own words that you have even quoted (but somehow missed).

The technically correct way of saying this is "most inclusive set of characteristics". You could have two sets of characteristics of the same cardinal number but one might be more inclusive than the other. Inclusion is a way of -comparing- sets which is not the same as -measuring- sets. Set comparison is a partial ordering. Measuring implies a linear ordering which is more restrictive. In a linear ordering one of three conditions hold: a < b or a = b or a > b. This does not apply to sets. Given a pair of sets A and B, it is possible that A does not include B nor does B include A. In short, set comparison is not linear.

You might want to consult David Kelley's book on logic -The Art of Reasoning-. Not a bad book of its kind. Your thinking needs some sharpening. You mean well but you sometimes miss the mark.

Ba'al Chatzaf

[Michael Stuart Kelly]

Bob,

As I mentioned above, I am using Rand's meaning when I discuss what Rand means in her works.

Frankly, I do not think using that standard is missing the mark at all.

Michael

[Guyau]

Stephen,

Is it really the case, as Rand seems to think, that all nominalists and conceptualists believe that abstractions have "no basis in reality"?

In addition to my remarks and references here

http://rebirthofreason.com/Forum/ArticleDi...ns/1772.shtml#1

a couple more helps are these:

“Nominalism in Metaphysics”

Gonzalo Rodriguez-Pereyra

http://plato.stanford.edu/entries/nominalism-metaphysics/

There are other forms of nominalism about universals, two of which are Predicate Nominalism and Concept Nominalism. The realist about universals admits that the predicate ‘scarlet’ applies to a scarlet thing. But he says that the predicate ‘scarlet’ applies to it in virtue of its being scarlet, which is nothing else than its instantiating the universal scarletness. Similarly he says that the thing in question falls under the concept scarlet in virtue of being scarlet, which is nothing else than the thing instantiating the universal scarletness. But for Predicate Nominalism there is nothing like scarletness. According to this theory a thing is scarlet in virtue of the fact that the predicate ‘scarlet’ applies to it. Similarly, according to Concept Nominalism (or Conceptualism), there is nothing like scarletness and a thing is scarlet in virtue of its falling under the concept scarlet. These two views entail that if there were no speakers or thinkers, things would not be scarlet.

“The Picture of Reality as an Amorphous Lump”

Matti Eklund

http://www.people.cornell.edu/pages/me72/cdm.pdf

~~~~~~~~~~~~

It seems to me that Rand’s position is closer to resemblance nominalism than to concept nominalism. Ockham is generally taken as under the latter. He took similarity to be a second intention, not first. Rand takes perceptual similarity to be given in the world, not from second intention. Nonetheless, for reasons touched in the first link of this note, I locate Rand’s Objectivist view on universals outside either realism or nominalism.

I hope to dig into this further in the future, Neil. It would be interesting to figure out which philosophers Rand was taking to be conceptualists (concept nominalists). Ockham (and pals)? The British empiricists? Contemporaries such as Goodman and Quine?

[Flagg]

I hope to dig into this further in the future, Neil. It would be interesting to figure out which philosophers Rand was taking to be conceptualists (concept nominalists). Ockham (and pals)? The British empiricists? Contemporaries such as Goodman and Quine?

Biggest compliment I saw her give was to Witty, whose theory of concepts is somewhat similar to Rand's - she said it was a perfect description on how a mind out of focus operated. I think it was too harsh of a judgment, though.

[Flagg]

Rand's system relies on three propositions taken as axioms[2]. (E) Existence exists. (I) Existence is identity. (C ) Consciousness is identification. Rand's set of axioms conveys the fundamental dependence of consciousness on existence. Existence is and is as it is independently of consciousness, whereas consciousness is dependent on existence and characters of existence (Rand 1957, 1015–16; 1966, 29, 55–59; 1969, 228, 240–41, 249–50).

First of all, the order of precedence of the term "existence exists" is ill-defined without the proceeding notion that defines what existence is in the first place. I tend to work from two axioms: (I) Identity exists; (II) Consciousness (identification) exists.

As part of the meaning of (I), Rand contended (Im): All concretes, whether physical or mental, have measurable relations to other concretes (1966, 7–8, 29–33, 39; 1969, 139–40, 189, 199–200, 277–79)[3]. Every concrete thing—whether an entity, attribute, relation, event, motion, locomotion, action, or activity of consciousness—is measurable (Rand 1966, 7, 11–17, 25, 29–33; 1969, 184–87, 223–25).

Right, but relational measurement itself has an identity, which isn't up in the chain yet. That's why I use what I listed above. B)

All concretes can be placed within some concept class(es). All concretes can be placed under concepts.

That's tautological, since you've already shown "concretes" is a concept that sweeps over reality completely, i.e. implicitly you have shown that the axiomatic concept of the Law of Identity applies to all.

Suppose you were a disembodied mind (OK, pretend you have some means inherent to your mind) in a universe where all that existed other than you was a proton. Then the only conclusion you can discern from recognizing the proton and recognizing that you are conscious of it is: both have an identity. They meet at no specific quality other than the fact that they have quantifiable quality, since no points of specific quality exist between the identity of your mind and the identity of the proton. But here you make an omission of sorts even though no similar concretes allow you a "ratio" - you omit all specifics, because there is no perceived similarity between the proton (an object of mass) and your mind (an abstract particular, so to speak), and you cannot go further in your omissions than that. What you are left with is the only concept possible: that to be is to be something, or more specifically, that to be is to have qualities.

Such mathematical structure obtaining in all concrete reality is metaphysical structure. It is structure beyond logical structure; constraint on possibility beyond logical constraint. Yet it is structure ranging as widely as logical structure through all the sciences and common experience.

It is not beyond logical constraint - it serves as the very basis for that notion. Existence is identity.

The minimum measurement and suspension powers required of the conceptual faculty by Rand's theory of concepts calls for neuronal computational implementation. Is such implementation possible, plausible, actual? This is a topic for the future, bounty beyond the present study.

Well, since we both understand mathematics, I'll venture to say "yes" ;)

Hope this guy comes back, or I'm about to blow quite a bit of time

[Flagg]

Applied to concept units in their substitution sense, measurement omission means release of the particular identities of the class members so they may be treated indifferently for further conceptual cognitive purposes[7]. This is the same indifference at work in the order-indifference principle of counting. The number of items in a collection may be ascertained by counting them in any order. Comprehension of counting and count number requires comprehension of that indifference.

That\'s correct. As I mentioned with my own thoughts on the conceptualization of the Law of Identity, omission may include more than mathematical quantifiables.

The release of particular identity for making items into concept-class substitution units is a constant and necessary part of Rand\'s measurement-omission recipe. But this part is not peculiar to Rand\'s scheme. What is novel in Rand\'s theory is the idea that in the release of particular identity, the release of which-particular-one, there is also a suspension of particular measure values along a common dimension.

Correct.

But the numbers have intrinsic character—even or odd, whole or fraction, rational or irrational, analytic or transcendental—quite independently of our choices, such as choice of number base.

That\'s right; a rational being with six total fingers who utilized base-six would count a basket of 100 bananas in a different way, but the set of his target of counting would correspond one-to-one with mine, should I be counting the same bananas (in base-10). The fact that the numbers are different due to the choice of bases is a nonessential epistemological difference for that very reason.

Affordance of Ratio or Interval Measures

Shapes must possess such pairs of magnitudes in some measure but may possess them in any measure.

Not zero-measure. Can\'t count a square, or a line segment, or a point, as a cube.

Observe that Rand\'s measurement-omission theory does not entail what number of dimensions for the magnitude relations among concretes is appropriate for the concept. Length requires 1D, shape requires 2D. Rand\'s theory works for any dimensionality and does not entail what the dimensionality must be, except to say that it must be at least 1D. Observe also that the conception of linearity to be applied here to each dimension is not the more particular linearity familiar from analytic coordinate geometry or from abstract vector spaces. It is merely the linearity of a linear order[9].

This is correct. And my above sentence cures the headache the former part of this quote posits.

That is a numerical rule of combination appropriate to concatenations of the concrete magnitude structure in the case of length.

Wouldn't this just be Rn, n = number of qualities to quanitfy?

The magnitude structure of the concretes falling under the concept length also affords ratios that are independent of our choice of elementary unit. The ratio of the span of my left hand, thumb-to-pinky, to my height is simply the number it is, regardless of whether we make those two measurements using sixteenths of an inch as elementary unit or millimeters as elementary unit.

This is correct.

Grades can be concatenated, although the proper mathematical reflection of this concatenation is not simple addition[11].

Grades depend on trigonometry, which presupposes its ultimate origin in a right triangle, meaning it\'s a ratio corresponding with the proper function acting on the angle in question. Its precedent is thus a fraction, which is multiplication, which may be extended - definitely or indefinitely depending on the numbers in question - to summation of integers.

Finest objectivity requires measurement scales appropriate to the magnitude structures to which they are applied. What does appropriate mean in this context? It means that all of the mathematical structure of the measurement scale is needed to capture the concept-class magnitude structure of concretes under consideration. It means as well that all the magnitude structure pertinent to the concept class is describable in terms of the mathematical structure of the measurement scale[12].

Precisely. That\'s my whole issue with the Teleological Argument for the Existence of God, by the way, when they harp on the \"smallness\" of certain constants. The units, of course, are not relational to their everyday application, and thus will appear to be quite precise when they may not have been such at all.

If one uses a different scale for one quantifiable, though - even within reason - won't that bunk the shape of the entire concept here?

What is the magnitude structure of concretes that is appropriately reflected by ratio-scale characterization? It is a magnitude structure whose automorphisms are translations[13]. Translations are transformations of value-points (i.e., points, which may be assigned numerical values) of the magnitude structure (the ordered relational structure of the concept-class concretes) that shift them all by the same amount, altering no intervals between them.

This means: since a ratio is independent of specific measurement, it is crystalline and unchangeable. Much easier to work with than that length-scale structure above that's all amorphous.

What about concretes involving both length- and ratio-scale characteristics, such as a sauna, for instance?

Physical temperature, certain aspects of sensory qualities, and certain aspects of utility rankings are examples of concretes whose magnitude structures afford what are now called interval measures, but evidently do not afford ratio measures[16]. The magnitude structure underlying the concept class temperature affords only an interval scale of measure. Such magnitude structures do not afford concatenations, unlike the natures of length or mass, but they do afford ordering of differences of degree, and they afford composition of adjacent difference-intervals[17].

Right; such things are not extended in space, yes - it makes sense such things fit under interval scale. What is a "composition of adjacent difference-intervals?"

Such magnitude structures do not afford ratios of degrees that are independent of choice of unit, but they afford ratios of difference-intervals that are independent of choice of unit and choice of zero-point[18]. Ratio scales have one free parameter, requiring we select the unit, such as yard or meter. These scales are said to be 1-point unique. Interval scales have two free parameters, requiring we select the unit, such as ˚F or ˚C, and requiring we select the zero-point, such as the freezing point of an equally portioned mixture of salt and ice or the freezing point of pure ice. These scales are said to be 2-point unique[19].

Two points to consider here:

(1) Again - what about concepts entailing both ratio and length? How are those constructed?

(2) Ratio may be used for temperature if the relation of the relative thickness and motion of the particles comprising an object are compared with later states of thickness (or thinness!) and motion of particles.

The magnitude structure of concretes affording interval-scale characterization is one whose automorphisms are fixed-point collineations, preeminently stretches[20]. Stretches are transformations of the value-points of a magnitude structure such that one point remains fixed and the intervals from that point to all others are altered by a single ratio.

Isn\'t this a contraction? And wouldn\'t this only apply to a change of a single unit potentially, i.e. could someone mess with one scale of one quantity in your storage set of concepts and have the concept-structure all damaged as a result, unlike what is possible for ratio structures?

Rand\'s measurement-omission analysis of concepts and concept classes applies perfectly well to cases in which the measurement scale appropriate to the pertinent magnitude structure of concretes is interval scale. The temperature attribute of a solid or fluid must exist in some measure, but may exist in any measure[21].

Right. But if it is not interval scale, then one can structure it under the assumption that there's one anyway.

An analogous conclusion obtains for multidimensional magnitude structures of concept classes. Rand\'s theory does not entail that all 2D or 3D magnitude structures have not only order structure, but affine structure, as Euclidean and Minkowskian geometry have[22]. That is, Rand\'s theory does not entail that multidimensional magnitude structures of concept classes afford a metric definable from a norm (a measure on vector structure)[23].

Why would such a structure be necessary, metaphysically? I don't see how it would relate to something like brain storage, since we're talking about objects more than likely to exceed 3-D. I understand the mathematical interest in it, though.

Won't affine structure only apply to those structures constructed from ratio relations?

Edited April 13, 2009 by Flagg

[Flagg]

The measure values required for Rand's theory need not be interval units. As Rand realized, merely ordinal measurement suffices for her measurement-omission scheme (1966, 33). I say that the magnitude structure captured by ordinal measurement is the minimal structure implied for metaphysics if, as I supposed at the outset, all concretes fall under one or more concepts for which Rand's measurement-omission analysis holds. What is the magnitude structure captured by ordinal measurements?

Just a bunch of lines with concrete points of constant separation of otherwise unimportant unit length separating the ordered points in the imagined graph, partially ordered. "Cubes" in Rn, in other words. That's my guess, let's see how silly I look at the end of this thing.

The magnitude structure affording merely ordinal measurement is a linear order whose automorphisms are the order-automorphisms of (same-order subsets of) the real numbers in their natural order. Such a magnitude structure affords characterization by a lattice (a type of partially ordered set) formed of sets and subsets of possible Dedekind-cuts of its linear order. This linear order might be scattered or dense; ordinal measurement is possible in either case[25].

Why not just a poset? Why the need to allow for Dedekind cuts and the like? Is this to establish limit points for orderings? I don't quite understand why it can't be modeled by a poset as I explained above.

The magnitude structure affording merely ordinal-scale measurement affords metrics. Each of the three scales adduced above to capture degrees of hardness bears a metric defined by the absolute values of those scales' numerical differences. A magnitude structure affording a (separable) metric belongs to the topological category known as a (separable) uniformity. Topologies that are uniformities in this sense are Hausdorff topologies, but they need not be compact nor (topologically) connected[26]. The topological character of the magnitude structure entailed for all concretes by Rand's measurement-omission theory of concepts is the character of a uniformity.

Hausdorff space is immediate here, of course. I suppose this alleviates the headache of Dedekind cutting and the imposing thundercloud of denseness above, but I guess I don't know what's going on with the previous example at all. Are you asserting that this particular structure presupposes a declared (discrete point) choice of scale, while the above structure does not presuppose that? If so, why does selecting this choice of scale alleviate the headache from the above structure, and how does the above's non-choice of metric entail the possibility of Dedekind cutting and denseness, etc., while this does not?

The magnitude structure entailed by Rand's theory has the algebraic character of a lattice, which has more structure than a partially ordered set (or a directed set) and less than a group (or a semi-group). In terms of the mathematical categories, Rand's magnitude structure for metaphysics is a hybrid of two: the algebraic category of a lattice and the topological category of a uniformity. Rand's structure belongs to the hybrid we should designate as a uniform topological lattice.

OK - the only reason why I think you're asserting this is that the lattice represents the ordinal order-structure for both a ratio and a length-related original conceptual structure, whereas the simpler uniform topo represents the concepts that are relational like the scratching rocks, where ratio and length do not apply. Is this correct?

Concerning multidimensional magnitude structures of concept classes, I concluded in the preceding subsection that Rand's theory entails neither affine nor absolute structure. What is entailed: concept classes with a 2D or 3D magnitude structure will have the structure of at least an ordered, distance geometry[27]. Significantly, it is implied that planes and spaces concretely realizable will have at least that much structure.

Probably only "plane" and "space" themselves fit in accordance with the minima indicated in the last sentence. Correct?

Whichever concept is considered as an instance of the superordinate concept, not only will that subordinate concept and its instances stand as a substitution instance of the superordinate, each instance of the subordinate will have some particular measure value along a specific dimension. And that particular value is suspended for the concept, thence for the superordinate concept.

So the subordinate part is omitted in measurement, allowing the superordinate to act according to its given precedent in context since the subordinate is unimportant? This would seem to cure the problem for practical consideration, but in general, is it still possible for this odd crossover category (math sense) to really be clear on the concrete level?

Analytically, identity precedes similarity[28]. For purposes of her theory of concepts and concept classes, Rand defined similarity to be "the relationship between two or more existents which possess the same characteristic(s), but in different measure or degree" (1966, 13). I concur. Occasions of scratch-hardness are similar to each other because they are all occasions of scratch-hardness, exhibiting that hardness in various measurable degrees. This much accords with Rand's definition and use of similarity in the theory of concepts.

Right.

To say that ball shapes are more like one another than they are like cup shapes is to say something beyond what is claimed in saying: Shapes that balls have are themselves and not something else, such as shapes that cups have.

The latter deals with the identity of the perceptual, while the former the identity of the relevant concepts.

But such an employment of Rand's conception of similarity as sameness of some characteristic, but difference in measure, is incorrect in application to the comparative similarities of the various strengths of solids, thence to their superordinate concept strength of a solid.

Right, because strength involves different measure methodology (linear, relational, ordinal) while shape involves only one linking measure for its subordinate concepts.

. . . . There is no single, common measure of property of a solid that all specific properties of solids have in common. Rand supposed in error that there were, for she supposed it always the case that there is some same, common measurable dimension supporting the conceptual common denominator for any superordinate concept (1966, 23)[29]. That supposition is here rejected, and measurement-omission analysis of superordinate concepts is here corrected in this respect.

Understood.

So I should amend Rand's definition of similarity as follows: Similarity is the relationship between two or more existents possessing the same characteristic(s), but in different measurable degree or in different measurable form.

Why not just chuck the different measurements? They are, after all, measurements to omit; the difference in unit or form is not essential to the quality you abstracted.

The corresponding definition of concepts would be: Concepts are mental integrations of two or more units possessing the same distinguishing characteristic(s), with their particular measurements omitted or with the particular measurable forms of their common distinguishing characteristic(s) omitted.

Well, you need to do this or else you won't be able to conceptualize the Law of Identity, right? I mean, I suppose that's gotta be the "top of the tower," probably isolated from everything else.

Every concrete falls under both sorts of concept.

In other words, concretes have extension in space and degree (whatever measure this may mean) of density, to put it very broadly.

What is the magnitude relation under which all concretes must stand such that conceptual rendition of them is possible? They must stand in the relation of a uniform topological lattice, at least one-dimensional. This is the magnitude structure implied for metaphysics, for all existence, by the theory of concepts in Rand's epistemology. The same magnitude structure is implied by that theory with my friendly amendment.

Good.

Universals as (abstractions that are) concepts are concept classes with their linear measure values omitted. If the concept is a superordinate, then the linear measurable form might also be omitted, that is, be allowed to vary across acceptable forms. Universals as collections of potential concept-class members are recurrences on a linear order with their measurement values in place[32]. For either sense of the term universals, they are an objective relation between an identifying subject and particulars spanned by those universals (Rand 1966, 7, 29–30, 53-54; 1965, 18; 1957, 1041).

(Continued below)

Good job, but by what standard do we judge "acceptable" forms?

[Flagg]

It would imply that every concrete can be placed in concept classes whose linear measures are not only ordinal-scale, but interval- or ratio-scale as well[43].

From what I gather, you're implying the "other direction" in this post and thus grounding the theory like Newton did gravity. Kinda scary...

Very good job on this paper, and a fun read! It's great that you identified your fallacy at the end here, but I would add the following: how could neurological analysis deny an epistemic process? Perhaps electric pathways lighting up in the structures of our brains may cross specific memories just over the places that link their essentials and omit consideration of their particulars ...

[thomtg]

This entry is a trackback cross-reference to a discussion on "The Opposite of Nothing ..." at Post #292 about your subsection "Superordinates and Similarity Classes" in Post #4.

[Guyau]

In “Universals and Measurement,” one of the ways in which I characterized the distinctive magnitude structure for metaphysics implied by Rand’s measurement-omission analysis of concepts was according to mathematical category. I reached this result:

The magnitude structure entailed by Rand’s theory has the algebraic character of a lattice, which has more structure than a partially ordered set (or a directed set) and less than a group (or a semi-group). In terms of the mathematical categories, Rand’s magnitude structure for metaphysics is a hybrid of two: the algebraic category of a lattice and the topological category of a uniformity. Rand’s structure belongs to the hybrid we should designate a uniform topological lattice. (JARS 5[2], 280; AOM)

What qualifies as the mathematical structure that is called a category? A category consists of three things: (i) a class of elements, which are called objects (ii) a set of morphisms from any one of those objects to another of them, (iii) a rule for composing a new morphism from any two morphisms, where this composition is associative. Included in the set of morphisms under (ii), there must be an identity morphism. There are certain further notions that are available in every category, such as the notions of monomorphism, epimorphism, isomorphism, and subobjects.

To specify a category, we must specify the objects, their morphisms, and the compositions of morphisms; and we must show that all the requirements of a category are met. Here are some categories. In the category of sets, the objects are sets, the morphisms are mappings from one set to another, the monomorphisms are one-to-one mappings, the epimorphisms are onto mappings, and so forth. In the category of vector spaces, the objects are vector spaces, the morphisms are linear mappings from one vector space to another, and so forth.

Examples of algebraic categories: sets, partially ordered sets, lattices, Boolean algebras, semigroups, groups, abelian groups, rings, fields, vector spaces, associative algebras, Lie algebras. Examples of topological categories: topological spaces, Hausdorff topological spaces, and uniform spaces. (Topological spaces have a notion of “points sufficiently close; neighborhood of point.” Uniform spaces have in addition a notion of “comparatively close; comparative size of neighborhoods.”) Examples of hybrid categories: topological groups and topological vector spaces.

The category I have targeted as reflecting the metaphysical magnitude structure implied by Rand’s measurement-omission form of concepts is the hybrid category resulting from combination of the algebraic category of lattices and the topological category of uniform spaces. In this category, the objects are lattices, and the morphisms are uniformly continuous lattice homomorphisms. The category of lattices (and uniform lattices) includes the binary operations of meet and join as well as morphisms, called lattice homomorphisms. These map one lattice to another, are order-preserving, and satisfy category requirements.

~~~~~~~~~~~~~~~~

PS

I was introduced to category theory through the text:

Mathematical Physics

Robert Geroch (Chicago 1985)

Edited January 29, 2010 by Stephen Boydstun