Two Kinds of "Induction": Important similarities and trivial differences


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(I've brought this over from the other thread, mainly because it's grown rather long and off topic, but also because it's now clear, thanks to REB's comment, that a lot of the debate is simply due to a muddle over terms.)

OK, so at last I get a moment to refer back to Roger's crucial post. It is important for two reasons. Firstly because it clears up a long-standing verbal confusion, and secondly, beneath the verbal smoke, it highlights two areas of surprising agreement:

Roger:

Hume is not even talking about the same thing that Peikoff and I are.

"Hume's problem" is over what Roger calls "enumerative generalisation"; the fact that you can't validly go from X swans are white -> All swans are white.

Roger and Peikoff, on the other hand, are talking about "induction" in the Objectivist sense - a process of observational-integrative generalisation. Details of this are sketchy to non-Objectivists; however they claim it is completely different from "enumerative generalisation," so we should take them at their word.

Hence we now have a fundamental and highly unproductive confusion cleared up.

Roger:

We are saying that enumerative generalization is NOT induction. Nor is it deduction. Nor therefore is it "deductively valid."

Now to me this is the first point of striking agreement, which I will repeat despite risking incensing Roger ( I think he got annoyed previously only because the confusion over the term "induction" was muddying the waters, and he didn't see this himself).

Roger and Peikoff are saying "enumerative generalization" is not deductively valid.

Now, with the terms corrected, we see clearly that this is also Hume's view.

Thus, Roger and Peikoff and Hume all agree on this key point at least. The difference is that while Hume clung to "enumerative generalisation" despite its deductive invalidity, Roger and Peikoff replace it with "observational-integrative generalisation",* or "induction." (We should note however that their "induction" is no more deductively valid than Hume's, but that they argue that it doesn't need to be)

The second point of agreement is also important, if slightly harder to see. It lies in the practical consequences of each theory.

The practical consequence of Hume's criticism of "enumerative generalisation" is that no matter how many experiences we have, we'll never have enough make an infallible universal law. We are not omniscient; there is always the possibility new facts and events outside of our experience will disprove our theory. Thus, a "universal law" is an abstract ideal we can almost certainly never achieve, although we can do our best to try to attain it.

Similarly, the practical consequence of Roger and Peikoff's "observational-integrative generalisation" is that no matter how many experiences we have, we'll never arrive at an infallible universal law either. It also holds that we are not omniscient; there is always the possibility new facts and events outside of our experience will disprove our theory. Thus, also for the Objectivist camp, a "universal law" is also an abstract ideal that we can almost certainly never achieve.

It is hard to deny that this is a pretty close position. However, philosophers are only too clever at making mountains out of molehills. Perhaps it is time to wheel out one of my favourite warnings, from Freud, about the dangers of the "narcissism of minor difference."

The remaining difference between the two sides on this (other than some terms, that is**) is indeed minor, and seems to be merely psychological; that is, in the attitude to the situation. The Objectivists seem to view the ideal of a comprehensive universal law as a kind of Platonic siren, luring unwitting explorers into the oblivion of impossibility, and to be therefore shunned and anathematised. My own view is less negative. I tend to see an ideal like a universal law as a mighty goal to be aimed at; the hardest, highest and fewest of all pursuits, something that a man, if sufficiently brilliant, determined, and insanely lucky might just against all odds get within his grasp. The rub is this: For the privilege of the very possibility of this, the price he pays is that he never quite knows for sure that he has it.

I say it's worth it.

Roger:

You want an apology? All right. You didn't "put words in my mouth," so I'm sorry for saying that.

Thank you.

Roger:

What I am still incensed about, though, is your continual attempts to lump me and Peikoff in with Hume, saying that "we all agree" that "induction is not deductively valid."

I hope you see my point clearly now with much of the verbal smoke blown away.

*BTW this seems to be another way of saying "concept formation." Is there any major difference? If not, why not throw away the term "induction" altogether then?

**For example, the Objectivists call this state of affairs "certainty" and even "absolute certainty", whereas everyone else calls it "uncertainty." This is the converse of the previous problem with "induction" where we had the same term for two different situations. Here we have two different terms, and opposites at that, for the same underlying situation. However, as the situation with "induction" demonstrates, the confusion is merely verbal and no deeper.

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I think it would help also to have Roger's post #312 from the old thread copied here.

I'll copy it, but, Roger, if you see this and want to copy it yourself so your avatar shows on the post, I'll delete this copy.

Ellen says that I have not replied to her question in this post. I have highlighted it, as well as another point on which I want to comment for (possible) clarification...

Roger,

Does Peikoff give a definition of what he means by "induction"? [Edit: He gives a statement which sounds like a definition in the quote from him below. However, I'm not seeing how that definition would produce reflections on the kinds of scientific issues hinted at in your post.] From what you describe in your post #115, it sounds to me as if what he's talking about is what I'd call theory formation and testing rather than the traditional meaning of making a universally quantized statement (an "all") statement on the basis of a group of uniform observations (I've observed X number, all of which have had a particular quality).

In regard to the point 2 you listed:

2. Induction begins with first-level, self-evidence generalizations to which all other generalizations must be ultimately reduced.

Am I correct in thinking that he's making the claim that we perceive causal connection? That was my understanding of his claim in a statement I've given a couple times, which I take to be his key contention relating concept formation and induction.

A generalization is no more than the perception of cause and effect conceptualized. [....] Induction is measurement-ommission applied to causal connection.

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1. Peikoff's model of induction is very much like "theory formation and testing." He stresses that generalization must always be supplemented with further observation and integration, even if that amounts not to a quest for constant observation of a specific kind of phenomenon, but instead simply being open to experience and data that does not integrate with the generalization, so that a wider context has been revealed, leading to a possible need to expand or revise the generalization. As said numerous times, it is not enumerative generalization, which is invalid. (Lucky guesses notwithstanding.)

2. Yes, causality is a perceptual (i.e., perceivable) phenomenon. If a roll a ball across the floor, I perceive that the ball is rolling and I perceive that I made the ball roll. Something's making something happen is (often, anyway) every bit as perceivable as something's happening.

REB

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Likewise for Bob K.'s post #313. (I'll copy it; Bob, if you want to copy it yourself, I'll delete this copy.)

2. Yes, causality is a perceptual (i.e., perceivable) phenomenon. If a roll a ball across the floor, I perceive that the ball is rolling and I perceive that I made the ball roll. Something's making something happen is (often, anyway) every bit as perceivable as something's happening.

REB

No. No. You -inferred- the cause. You did not see (i.e. perceive) what (if anything) initiated the motion. All you perceived was something in motion. You ought to distinguish between what you witnessed and what you concluded. In a court of law, a conclusion stated by a witness concerning what is being questioned, is not admissible. A good attorney will object to the conclusion and claim it is not a -fact- that is witnessed.

Ba'al Chatzaf

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Ellen:

http://plato.stanford.edu/entries/induction-problem/#Hum

"The term 'induction' does not appear in Hume's account."

He used the description "causal inference."

Ellen hits on another crucial point.

For a vital distinction can get overlooked between:

1) The particular cause of an event(or series of them)

2) Our knowledge of that cause (or what we infer to be the cause)

This goes to the various attempts to argue from the Law of Identity, which I will examine later.

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... the confusion is merely verbal and no deeper.

Daniel,

After all the long posts and twisting side-roads, this is a conclusion I started arriving at when I first read Popper. I wrote back at the beginning of May (to another poster who fell into a jargon kneejerk reaction):

Actually, I just read that essay, and getting around all the hot button terms, it is in agreement with Rand's views on many points. Two premises jump out at me: facts exist independently of knowledge, and the purpose of knowledge is to correspond to facts. Popper's criticism is not against that. It is basically against "essentialism," which Rand called "moderate realism" for some reason.

. . .

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.

Look at what Rand wrote on the same page above:

For the purposes of this series, the validity of the senses must be taken for granted...

That happens to be Popper's premise if you read him correctly. Where you might get confused is that Popper mentioned "nominalist" and so did Rand:

3. The "nominalists," who hold that all our ideas are only images of concretes, and that abstractions are merely "names" which we give to arbitrary groupings of concretes on the basis of vague resemblances.

Now if you want to make some kind of argument based on that, there might be something to it. But the more I read, the more I believe this also is more semantics than meat. Still, I suggest you reread Chapter 5 of ITOE, then reread Popper's essay. You will see that his idea of scientific definition is very similar, although his rhetoric is just as bombastic as Rand's...

I have mentioned to you several times that I am discovering that the ideas between Objectivism and CR are similar with differences in jargon. We always seem to come to a dead end over the jargon, though. ("I am now glad that you agree with me that ..." thereafter follows jargon problems, then further disagreements.)

I am delighted to see that the ideas are finally getting through, "getting past the words" so to speak, although there are still some misunderstandings and/or points that do not align.

One huge trouble area I see is over the phrase "universal law." In my understanding, the very existence of categories is "universal law" because nature is so constructed that it lends itself to being categorized (with concepts).

But I am starting to think the real issue is that both CR and Objectivism are against the primacy of consciousness, but from different angles. Both CR and Objectivism hold that information is changed with learning and experience of new elements. Thus what is changed is the way we think about things, not the things in themselves.

Another confusion is over Hume. Objectivism sees Hume's induction problem as an attempt to deny causality. Maybe CR sees Hume's argument as a form of proving that reality does not submit to the mind, or even more, that the mind does not finally arrive at some kind of Truth with a capital "T" that signifies limitations on what is possible to reality.

These are just a few problems and there are many. I do think that a critical examination of the fundamental concepts (or ideas) of both CR and Objectivism—without competition over which jargon or which starting point or which person is better or worse—would be very fruitful.

Michael

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[....] I wrote back at the beginning of May (to another poster who fell into a jargon kneejerk reaction):
Actually, I just read that essay, and getting around all the hot button terms, it is in agreement with Rand's views on many points. Two premises jump out at me: facts exist independently of knowledge, and the purpose of knowledge is to correspond to facts. Popper's criticism is not against that. It is basically against "essentialism," which Rand called "moderate realism" for some reason.

Rand didn't call "essentialism" "moderate realism"; she called Aristotle's variant of "essentialism" "moderate realism," which is the term by which it's been designated for a long time. Rand didn't make up the term. The "moderate realism" of Aristotle is distinguished from the "extreme realism" of Plato. Both are forms of "essentialism," as is Rand's own theory of concepts.

Rand was not against "essentialism"; she WAS an "essentialist." Although she described the difference between her view of "essences" and Aristotle's view as "radical," from Popper's perspective the difference is only that of two variants of the same error.

I re-quote some of the material I quoted from Rand herself ("Scorecard" thread, here) describing her theory of the "essence" or "essential characteristic" of a concept:

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]

Now observe...[ellipsis in the Lexicon] 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. [iTOE, 59]

Man's essential characteristic is his rational faculty. ["What Is Capitalism?" CUI, 16]

[she says that explicitly elsewhere, too, but I'm not finding the quote at the moment. She also someplace discusses "rationality" as making possible and explaining the greatest number of other characteristics of man.]

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, as I said above, would not have considered this a radical difference, only a difference between two variants of "essentialism." Rand was as much an essentialist, as Popper decries that type of definitional procedure, as was Aristotle.]

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]

Ellen

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Both are forms of "essentialism," as is Rand's own theory of concepts.

Ellen,

I should have said the kind of essentialism Popper was discussing in the essay (Aristotle's version) instead of just essentialism when I said "moderate realism" and gave Rand's quote. I did not mean that she called ALL forms of essentialism (including Plato's form) "moderate realism," just Aristotle's form. I thought the context and quote made that clear but apparently it did not for you.

You can insist on your theory if you like about Rand's theory of concepts being essentialism, but it is dead wrong. I certainly will not take it seriously and I doubt many others will either, at least not those who actually understand Objectivist concept formation. The manner Rand was using the word essential as in "essential characteristic" was a LOT different than the essence embodied in a thing as given in the ancients.

(For the record, I personally have been flirting with essentialism in thinking about top-down organization, but that is another matter.)

Here is the short version. In classical essentialism, things have conceptual (sort of) essences within them. In Objectivism, concepts (categories made in our heads) have essences, not things (out there), and these are determined by measurement. "Essence" in this context is a form of ordinal measurement meaning "measurable necessary feature more distinctive than xxx," not "unique spirit" or something like that. This is the same word used with another meaning.

By your standard, since Popper used the word "essential" to describe falsifiability and seems to think things are different from each other and not a simple mush, we can call him an essentialist, too.

Michael

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Both are forms of "essentialism," as is Rand's own theory of concepts.

You can insist on your theory if you like about Rand's theory of concepts being essentialism, but it is dead wrong. I certainly will not take it seriously and I doubt many others will either, at least not those who actually understand Objectivist concept formation. The manner Rand was using the word essential as in "essential characteristic" was a LOT different than the essence embodied in a thing as given in the ancients.

Michael,

I was afraid you wouldn't understand the point, and I signed on specifically to try to state it a bit further -- I'll be away from home almost all day tomorrow (if predictions pan out).

The difference between Popper and Rand in regard to definitions isn't of either of the types Daniel talked about in his initial post. It isn't a case of (1) two different processes (or at least two superficially different processes -- I still think Peikoff's theory might amount to "enumeration") being described by the same term ("induction") or of (2) the same lack of being sure what tomorrow's evidence will bring being described by diametrically opposed terms ("certainty"/"uncertainty"). This one is a case of a REAL difference. Rand is an example of the "essentialist" definition-type to which Popper objected.

Furthermore, no, she doesn't differ much from the ancients in the respect Popper was talking about. Recall, she says (I'll add emphasis):

[my emphasis]

Now observe...[ellipsis in the Lexicon] 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. [iTOE, 59]

She is, there, stating the nucleus of a CAUSAL hypothesis; this is very much stating that the "essence" is more than just an epistemological way of keeping track of how we're divying up the world.

Here is the short version. In classical essentialism, things have conceptual (sort of) essences within them. In Objectivism, concepts (in our heads) have essences, not things (out there), and these are determined by measurement.

Well...there you touch on another, related problem: Just what IS that entity-of-sorts "in our heads" she was talking about when she spoke of a "mental integration"? In the Objectivist theory of concepts, there are three layers: (1) the units out there; (2) the "concept," a "mental integration" (in here), the referents of which are the units out there; and then (3) the label, the word, used to track the "mental integration." Just what is the supposed nature of this "mental integration"? I don't think there's any such entity-of sorts. The issue will be a very long topic.

By your standard, since Popper used the word "essential" to describe falsifiability and seems to think things are different from each other and not a simple mush, we can call him an essentialist, too.

Michael, no, Popper's views on definitions weren't such that he could be described as an "essentialist" (using this term as he meant it); the issue isn't merely using the word "essential." The issue is a particular type of theory about the nature of definitions.

Do recall RAND wrote:

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.

Do you think she was so completely ignorant of what she was saying as not to have understood that her definitional principles were Aristotelian in type?

Ellen

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Just what is the supposed nature of this "mental integration"?

Ellen,

The integration is akin to a math operation. It uses measurement. Once you understand that, you will probably see why it is not essentialism.

About Aristotle and definitions, you are making the same mistake the guy I was originally talking to made. He presumed that Rand did not discard any part of Aristotle's epistemological theory.

From ITOE, 2nd., "Foreword to the First Edition," p. 2:

2. The "moderate realists," whose ancestor (unfortunately) is Aristotle, who hold that abstractions exist in reality, but they exist only in concretes, in the form of metaphysical essences, and that our concepts refer to these essences.

Notice the phrase: "whose ancestor (unfortunately) is Aristotle." This was the exact same thing Popper was criticizing in his essay on two types of definition. But in his essay, he called it "essentialism." Both Popper and Rand rejected this for the same reasons. Rand rejected Aristotle's essence here.

Her phrase that you quoted is one of those places where she used a word with more than one meaning. (She sometimes did this and I am making a list of them to include in an article later.) I can assure you that she did not consider "thingness" to be an epistemological essence. Her epistemological essence is the prominent feature of a thing as follows: A category is constructed by deciding on a prominent feature of the referent, measuring it against a standard, then discarding all measurements, and tacking a name on it at the end to give it an identifiable physical form.

Essence to Aristotle was the whole shebang. To Rand, this meant merely one feature of the whole shebang.

The hardest part I am seeing that people don't understand about the CDD (conceptual common denominator) is that it has to be measurable and it is used in relation to the perspective of the agent. That is why, for instance, she claims man to be a rational animal for universal purposes in all contexts and rational primate (and even other divisions) for scientists. The essence here (the measurable prominent feature, the "essential characteristic," the CDD) for all purposes is awareness and the essential characteristic is the highest measured awareness. It is NOT "manness" as it would be for essentialists.

In ordinal measurement, a conceptual awareness is more advanced than a strictly perceptual awareness. One is more than the other. A measurement is made and that is what causes the distinction (from the CDD in the genus).

There are other features that can be measured and they also belong to "animal" but they are not as fundamental to survival (which is the best standard for life) as awareness is. The more specific and varied these other features become, the closer to the scientific perspective and further away from the "all contexts" perspective one gets.

Michael

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Both are forms of "essentialism," as is Rand's own theory of concepts.

You can insist on your theory if you like about Rand's theory of concepts being essentialism, but it is dead wrong. I certainly will not take it seriously and I doubt many others will either, at least not those who actually understand Objectivist concept formation. The manner Rand was using the word essential as in "essential characteristic" was a LOT different than the essence embodied in a thing as given in the ancients.

The difference between Popper and Rand in regard to definitions isn't of either of the types Daniel talked about in his initial post. It isn't a case of (1) two different processes (or at least two superficially different processes -- I still think Peikoff's theory might amount to "enumeration") being described by the same term ("induction") or of (2) the same lack of being sure what tomorrow's evidence will bring being described by diametrically opposed terms ("certainty"/"uncertainty"). This one is a case of a REAL difference.

If you still think this, you really have more than Leonard Peikoff (and Ayn Rand) to content with. You are really bucking the entire tradition of Aristotelian logic and philosophy of science.

1. I assume that motivated readers and Rand fans have or have access to H. W. B. Joseph's An Introduction to Logic (1906), so I'll just recommend that they read (or re-read) pages 177-180 and chapter 18 "Of Induction" and chapter 19 "Of the Presuppositions of Inductive Reasoning: The Law of Causation." But one brief quote from pp. 400-401:

J.S. Mill in System of Logic wrote: "Why is a single instance, in some cases, sufficient for a complete induction, while in others myriads of concurring instances, without a single exception known or presumed, go such a very little way towards establishing an universal proposition? Whoever can answer this question knows more of the philosophy of logic than the wisest of the ancients, and has solved the problem of Induction." Joseph comments: "However we may think of the knowledge possessed by the wisest of the ancients, the question which Mill asks is no doubt an important one. By what right do we ever generalize from our experience? and how can we tell when we have a right to do so?" After discarding syllogism and enumeration, Joseph continues: "The answer is that all induction assumes the existence of connexions in nature, and that its only object is to determine between what elements these connexions hold. The events of our experience are no doubt particular, but we believe the principles which they exemplify to be universal; our difficulty lies in discovering what principles they exemplify; in that, a close study of particular facts will help us; but were we to be in doubt whether there are any such principles or not, no amount of study of particular facts could resolve our doubt." (nifty little application of the Stolen Concept Fallacy :-)

2. A less widely known Aristotelian logician, and currently out of print, is Peter Coffey, The Science of Logic, An Inquiry into the Principles of Accurate Thought and Scientific Method (1912), volume 2:

page 27

We have already repeatedly distinguished between the mere concrete, collective, enumerative universal, and the really scientific universal which is an abstract judgment, embodying some more or less necessary principle or law (95, 195 [vol. 1]). It is this latter that scientific induction proper aims at establishing.

page 29-30

[Enumerative induction] will not be valid unless the enumeration is complete. The enumeration must be [Greek expression] as Aristotle expresses it; else the argument will be fallacious: there will be an illicit process of the subject of the conclusion. St. Thomas likewise insists that as long as we base our conclusion on enumeration the latter must be complete. So long then as we concentrate our attention on the mee enumeration of instances, and disregard their nature, we can never be certain of our conclusion until we are certain that our enumeration is actually complete.

Secondly, even where the enumeration of instances is complete, the process does not lead to scientific knowledge, i.e., the knowledge of a strictly universal conclusion embodying what can be called a law. And the reason is manifest. The conclusion expresses a simple addition of instances, and is, therefore, simply a collective proposition whose subject is an actual whole; whereas the strict universal proposition, the abstract universal, can be reached only by generalization of the abstract judgment which establishes some sort of necessary connexion of attributes between subject and predicate. Adding parts to parts, to form a natural whole, gives us a collective idea. Considering an object in the abstract, apart from its individualizing characteristics, putting it into relation with its concrete realizations, actual or possible, indefinite in number, seeing that it is predicable of all, is to universalize and to make scientific progress. For "all science is of the universal and necessary" [Aristotle, Posterior Analytics, i, 5 (5-7)]; i.e., it is expressive of necessary, and therefore universal, relations between the objects of our thought. The strict universal is no mere actual collection; it isapplicable to an indefinite number of instances. Therefore, this kind of induction [enumeration] does not put us in possession of scientific or necessary truth.

page 33 (my favorite passage from Coffey)

We find it sometimes stated by modern logicians that the only way of ascending from the particular to the general, explicitly treated by Aristotle, and the only way known to the mediaeval Scholastic logicians, was that of enumerative induction, "complete" and "incomplete"; that we find in these authors no trace of the method of modern scientific induction, the method of attaining to the universal by analysing a limited number of instances and seeking therein a connexion of content, of attributes, a causal connexion, in the nature of the phenomena considered." And why have various modern logicians held that scholastic logicians thought the essence of induction was enumeration? Coffey quotes Joyce, Logic: "The error seems to have arisen from the fact that the most famous of the Scholastics (St. Thomas, Albert the Great, Scotus) do not employ the term induction as the distinctive name of the inference by which we establish universal laws of nature. Following the terminology of Aristotle...they called it proof from experience. The significance of the term induction was somewhat vague. It covered all argument from the particular to the general...It was by a later generation that the term induction was restricted to its present signification. Incautious readers, finding in certain passages the inductive syllogism described as the formula of inductive argument, jumped too hastily to the conclusion that the mediaeval philosophers rested their knowledge of the laws of nature on no basis but enumeration."

Coffey continues on pp. 33-34:

Now, from the very fact that Aristotle and the Scholastics considered it possible to reach a truth about "all," actual and possible, known and unknown, by an aquaintance with "some," they must have recognized a method of ascent to the "all," other than enumeration. And so they did: viz., the method nowadays known as Physical or Scientific Induction.

When, therefore, we hear it stated that Scientific Induction is an achievement of the modern mind, we must not infer that it was entirely unknown to the ancients. That to modern thought the honour was reserved of seizing upon the full significance of the method, and of applying it with such marked success, even the most ardent defenders of Aristotle and the Scholastics need not deny. But that the principle of this method was known to the latter, their works give unmistakable evidence. [And he cites Aristotle, Aquinas, and Scotus.]

So, can we please have an end to this myopic focus on how Peikoff must be (or should be suspected of being) confused between enumeration and true induction? And how Objectivists are the ones who are trying to distort the traditional usages of concepts and terms? If you must tar and feather anyone on this issue, at least have the courtesy and accuracy to smear the entire Aristotelian establishment. And realize also that the genesis of the modern tendency to saddle Aristotelians with induction as essentially a process of enumeration is itself...an over-generalization by those in a bit much of a hurry to discard the supposed strait-jacket of Aristotelian logic and philosophy of science.

REB

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Both are forms of "essentialism," as is Rand's own theory of concepts.

You can insist on your theory if you like about Rand's theory of concepts being essentialism, but it is dead wrong. I certainly will not take it seriously and I doubt many others will either, at least not those who actually understand Objectivist concept formation. The manner Rand was using the word essential as in "essential characteristic" was a LOT different than the essence embodied in a thing as given in the ancients.

The difference between Popper and Rand in regard to definitions isn't of either of the types Daniel talked about in his initial post. It isn't a case of (1) two different processes (or at least two superficially different processes -- I still think Peikoff's theory might amount to "enumeration") being described by the same term ("induction") or of (2) the same lack of being sure what tomorrow's evidence will bring being described by diametrically opposed terms ("certainty"/"uncertainty"). This one is a case of a REAL difference.

If you still think this, you really have more than Leonard Peikoff (and Ayn Rand) to content with. You are really bucking the entire tradition of Aristotelian logic and philosophy of science.

1. I assume that motivated readers and Rand fans have or have access to H. W. B. Joseph's An Introduction to Logic (1906), so I'll just recommend that they read (or re-read) pages 177-180 and chapter 18 "Of Induction" and chapter 19 "Of the Presuppositions of Inductive Reasoning: The Law of Causation." But one brief quote from pp. 400-401:

J.S. Mill in System of Logic wrote: "Why is a single instance, in some cases, sufficient for a complete induction, while in others myriads of concurring instances, without a single exception known or presumed, go such a very little way towards establishing an universal proposition? Whoever can answer this question knows more of the philosophy of logic than the wisest of the ancients, and has solved the problem of Induction." Joseph comments: "However we may think of the knowledge possessed by the wisest of the ancients, the question which Mill asks is no doubt an important one. By what right do we ever generalize from our experience? and how can we tell when we have a right to do so?" After discarding syllogism and enumeration, Joseph continues: "The answer is that all induction assumes the existence of connexions in nature, and that its only object is to determine between what elements these connexions hold. The events of our experience are no doubt particular, but we believe the principles which they exemplify to be universal; our difficulty lies in discovering what principles they exemplify; in that, a close study of particular facts will help us; but were we to be in doubt whether there are any such principles or not, no amount of study of particular facts could resolve our doubt." (nifty little application of the Stolen Concept Fallacy :-)

2. A less widely known Aristotelian logician, and currently out of print, is Peter Coffey, The Science of Logic, An Inquiry into the Principles of Accurate Thought and Scientific Method (1912), volume 2:

page 27

We have already repeatedly distinguished between the mere concrete, collective, enumerative universal, and the really scientific universal which is an abstract judgment, embodying some more or less necessary principle or law (95, 195 [vol. 1]). It is this latter that scientific induction proper aims at establishing.

page 29-30

[Enumerative induction] will not be valid unless the enumeration is complete. The enumeration must be [Greek expression] as Aristotle expresses it; else the argument will be fallacious: there will be an illicit process of the subject of the conclusion. St. Thomas likewise insists that as long as we base our conclusion on enumeration the latter must be complete. So long then as we concentrate our attention on the mee enumeration of instances, and disregard their nature, we can never be certain of our conclusion until we are certain that our enumeration is actually complete.

Secondly, even where the enumeration of instances is complete, the process does not lead to scientific knowledge, i.e., the knowledge of a strictly universal conclusion embodying what can be called a law. And the reason is manifest. The conclusion expresses a simple addition of instances, and is, therefore, simply a collective proposition whose subject is an actual whole; whereas the strict universal proposition, the abstract universal, can be reached only by generalization of the abstract judgment which establishes some sort of necessary connexion of attributes between subject and predicate. Adding parts to parts, to form a natural whole, gives us a collective idea. Considering an object in the abstract, apart from its individualizing characteristics, putting it into relation with its concrete realizations, actual or possible, indefinite in number, seeing that it is predicable of all, is to universalize and to make scientific progress. For "all science is of the universal and necessary" [Aristotle, Posterior Analytics, i, 5 (5-7)]; i.e., it is expressive of necessary, and therefore universal, relations between the objects of our thought. The strict universal is no mere actual collection; it isapplicable to an indefinite number of instances. Therefore, this kind of induction [enumeration] does not put us in possession of scientific or necessary truth.

page 33 (my favorite passage from Coffey)

We find it sometimes stated by modern logicians that the only way of ascending from the particular to the general, explicitly treated by Aristotle, and the only way known to the mediaeval Scholastic logicians, was that of enumerative induction, "complete" and "incomplete"; that we find in these authors no trace of the method of modern scientific induction, the method of attaining to the universal by analysing a limited number of instances and seeking therein a connexion of content, of attributes, a causal connexion, in the nature of the phenomena considered. [And why have various modern logicians held that scholastic logicians thought the essence of induction was enumeration? Coffey quotes Joyce, Logic: "The error seems to have arisen from the fact that the most famous of the Scholastics (St. Thomas, Albert the Great, Scotus) do not employ the term induction as the distinctive name of the inference by which we establish universal laws of nature. Following the terminology of Aristotle...they called it proof from experience. The significance of the term induction was somewhat vague. It covered all argument from the particular to the general...It was by a later generation that the term induction was restricted to its present signification. Incautious readers, finding in certain passages the inductive syllogism described as the formular of inductive argument, jumped too hastily to the conclusion that the mediaeval philosophers rested their knowledge of the laws of nature on no basis but enumeration."]

Coffey continues on pp. 33-34:

Now, from the very fact that Aristotle and the Scholastics considered it possible to reach a truth about "all," actual and possible, known and unknown, by an aquaintance with "some," they must have recognized a method of ascent to the "all," other than enumeration. And so they did: viz., the method nowadays known as Physical or Scientific Induction.

When, therefore, we hear it stated that Scientific Induction is an achievement of the modern mind, we must not infer that it was entirely unknown to the ancients. That to modern thought the honour was reserved of seizing upon the full significance of the method, and of applying it with such marked success, even the most ardent defenders of Aristotle and the Scholastics need not deny. But that the principle of this method was known to the latter, their works give unmistakable evidence. [And he cites Aristotle, Aquinas, and Scotus.]

So, can we please have an end to this myopic focus on how Peikoff must be (or should be suspected of being) confused between enumeration and true induction? And how Objectivists are the ones who are trying to distort the traditional usages of concepts and terms? If you must tar and feather anyone on this issue, at least have the courtesy and accuracy to smear the entire Aristotelian establishment. And realize also that the genesis of the modern tendency to saddle Aristotelians with induction as essentially a process of enumeration is itself...an over-generalization by those in a bit much of a hurry to discard the supposed strait-jacket of Aristotelian logic and philosophy of science.

REB

Thanks for a splendid and substantial post! Now, back to reread it to make certain I understood it.

Alfonso

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I wrote:

The practical consequence of Hume's criticism of "enumerative generalisation" is that no matter how many experiences we have, we'll never have enough make an infallible universal law. We are not omniscient; there is always the possibility new facts and events outside of our experience will disprove our theory. Thus, a "universal law" is an abstract ideal we can almost certainly never achieve, although we can do our best to try to attain it.

Similarly, the practical consequence of Roger and Peikoff's "observational-integrative generalisation" is that no matter how many experiences we have, we'll never arrive at an infallible universal law either. It also holds that we are not omniscient; there is always the possibility new facts and events outside of our experience will disprove our theory. Thus, also for the Objectivist camp, a "universal law" is also an abstract ideal that we can almost certainly never achieve.

What emerges from this direct comparison of the practical consequences of Rand's theory is that we see that it lands, contrary to the all intents and purposes of its author, in an obviously skeptical theory of knowledge.

I am not the only one to suggest this. Fred Seddon summarised Rand's position neatly as "We can know P, but P may be false."*

A simple example will suffice. It was once thought - for many hundreds of years - that the sun went around the earth. According to Objectivism, we would be fully entitled to say we knew this to be true, as this was in the context of the limited human knowledge at the time. (More than that, we would be entitled to say we would be absolutely certain of it)

Now, this theory turned out to be false. In fact, the opposite is true: the earth goes around the sun. We are now able to say, in this new context, that we know this (and are "absolutely certain" of it).

Thus Rand's theory does indeed suggest that we can know P, but P may not be true.

(One might remark in passing just how low the bar is set for both "truth" and "certainty" in Rand's "contextual" theory, in that we can claim both to an "absolute" degree for opposing theories!)

The key point is, however, that Seddon is right in terms of consequences, if not intent. On examination, there is far more common ground between Objectivism and something like Critical Rationalism in practice than Objectivists suspect.

*The remark occurs in his review of "Ayn Rand Contra Human Nature." I in turn severely criticised Seddon's review here. While I note the clear skeptical implications, I doubt this was Rand's intent.

Edited by Daniel Barnes
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Do you think she was so completely ignorant of what she was saying as not to have understood that her definitional principles were Aristotelian in type?

Ellen

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That is a question we cannot answer. We can only know what Rand wrote and said, and the logical consequences therefrom. We cannot know all that she knew or did not know. That is true in general of anyone. What you see is what you get.

Ba'al Chatzaf

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I wrote:
The practical consequence of Hume's criticism of "enumerative generalisation" is that no matter how many experiences we have, we'll never have enough make an infallible universal law. We are not omniscient; there is always the possibility new facts and events outside of our experience will disprove our theory. Thus, a "universal law" is an abstract ideal we can almost certainly never achieve, although we can do our best to try to attain it.

Similarly, the practical consequence of Roger and Peikoff's "observational-integrative generalisation" is that no matter how many experiences we have, we'll never arrive at an infallible universal law either. It also holds that we are not omniscient; there is always the possibility new facts and events outside of our experience will disprove our theory. Thus, also for the Objectivist camp, a "universal law" is also an abstract ideal that we can almost certainly never achieve.

What emerges from this direct comparison of the practical consequences of Rand's theory is that we see that it lands, contrary to the all intents and purposes of its author, in an obviously skeptical theory of knowledge.

I am not the only one to suggest this. Fred Seddon summarised Rand's position neatly as "We can know P, but P may be false."*

A simple example will suffice. It was once thought - for many hundreds of years - that the sun went around the earth. According to Objectivism, we would be fully entitled to say we knew this to be true, as this was in the context of the limited human knowledge at the time. (More than that, we would be entitled to say we would be absolutely certain of it)

Now, this theory turned out to be false. In fact, the opposite is true: the earth goes around the sun. We are now able to say, in this new context, that we know this (and are "absolutely certain" of it).

Thus Rand's theory does indeed suggest that we can know P, but P may not be true.

(One might remark in passing just how low the bar is set for both "truth" and "certainty" in Rand's "contextual" theory, in that we can claim both to an "absolute" degree for opposing theories!)

The key point is, however, that Seddon is right in terms of consequences, if not intent. On examination, there is far more common ground between Objectivism and something like Critical Rationalism in practice than Objectivists suspect.

*The remark occurs in his review of "Ayn Rand Contra Human Nature." I in turn severely criticised Seddon's review here. While I note the clear skeptical implications, I doubt this was Rand's intent.

Oh, Kant rare.

Skepticism is the active doubt that something is true. If you have specific reason to doubt that a specific conclusion is true, your skepticism is warranted. If you have no specific reason to doubt it, your skepticism is not warranted.

The acknowledgement that people sometimes make errors and their beliefs are sometimes later shown to be incorrect is ~not~ the doctrine of skepticism. It's the doctrine of human fallibility.

Knowledge and certainty are contextual. About the only acontextual items of knowledge with certainty I am aware of are the Laws of Logic. They designate basic facts of reality that cannot be otherwise.

Everything else that we know ~might~ be otherwise -- but unless we have evidence to suggest that it is, we are not warranted in doubting our conclusions.

REB

P.S. -- Rene and David, sitting in a tree, d-o-u-b-t-i-n-g. :-)

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Do you think she was so completely ignorant of what she was saying as not to have understood that her definitional principles were Aristotelian in type?

Ellen

___

That is a question we cannot answer. We can only know what Rand wrote and said, and the logical consequences therefrom. We cannot know all that she knew or did not know. That is true in general of anyone. What you see is what you get.

Ba'al Chatzaf

Oh, Kant rare.

Rand completely understood that she was adopting Aristotelian principles of definition, as were her followers Leonard Peikoff and David Kelley in their logic lectures and logic textbook, respectively.

I don't pose a breach between people's understanding and their words and actions, unless they give me reason to suppose there is one.

Probably the one time my confidence in this perspective was badly shaken was when Rand in "Art and Cognition" blatantly contradicted herself about architecture, which she said does not re-create reality, nonetheless being a form of art, which (by her definition) does re-create reality. How she could have put this all on the same page, without at least temporarily having a screw loose, is beyond me.

REB

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Roger:

Probably the one time my confidence in this perspective was badly shaken was when Rand in "Art and Cognition" blatantly contradicted herself about architecture...How she could have put this all on the same page, without at least temporarily having a screw loose, is beyond me.

Interesting. This is the same feeling I get when I see the phrase "contextual absolute."

Edited by Daniel Barnes
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Roger:

Skepticism is the active doubt that something is true
.

Roger, the formulation is this: We may know P, but P may not be true.

This specifically includes active doubt.

If you have specific reason to doubt that a specific conclusion is true, your skepticism is warranted. If you have no specific reason to doubt it, your skepticism is not warranted.

I believe this argument, which is a standard one, fails for extremely simple reasons. I have already explained why, but to save trawling back through the thread I will repeat it (you may have replied to it too)

This is why: no-one had any reason to doubt that the sun went around the earth. (or, more properly, it seemed to them as "self-evident" as the opposite does to us today. It was a great shock to mankind to find out that this "self-evident" truth was quite the opposite of reality.)

From this, and a near infinite number of examples like it from both human history and our own personal experience we obtain our warrant for skepticism. There is plenty of evidence that beliefs we have no specific reason to doubt can and do regularly turn out to be false; enough even to destroy that argument inductively...;-)

The acknowledgement that people sometimes make errors and their beliefs are sometimes later shown to be incorrect is ~not~ the doctrine of skepticism. It's the doctrine of human fallibility.

It is one and the same thing. Although there are a few different branches of skepticism, the root is that all human knowledge is fallible; it contains the possibility of error.

At any rate, the bottom line is that the proposition we may know P, but P may not be true is perfectly compatible with a philosophy like Karl Popper's Critical Rationalism, which is fallibilist, and widely regarded as skeptical. Hence there is a clear family connection.

I believe there is certainly room for confusion around this issue, but this is because Rand's rhetoric, and her intentions are one thing, and the real consequences of her position are quite the opposite of how it appears. Shockingly, it turns out the earth actually goes around the sun!...;-)

Knowledge and certainty are contextual. About the only acontextual items of knowledge with certainty I am aware of are the Laws of Logic. They designate basic facts of reality that cannot be otherwise.

Well now I would agree that the Laws of Logic are the nearest things to "acontextual items of knowledge", or rules that we can use to produce something like "absolute certainties" in abstract. And these rules can be applied to the world with useful results. But of course they do not hold in all cases.

Everything else that we know ~might~ be otherwise -- but unless we have evidence to suggest that it is, we are not warranted in doubting our conclusions.

There is so much evidence to the contrary of this argument itself that it cannot possibly stand, I think.

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Roger:

Probably the one time my confidence in this perspective was badly shaken was when Rand in "Art and Cognition" blatantly contradicted herself about architecture...How she could have put this all on the same page, without at least temporarily having a screw loose, is beyond me.

Interesting. This is the same feeling I get when I see the phrase "contextual absolute."

For obviously an "absolute" is something that is invariant, no matter where in space or time (like an "absolute law" of physics)

Yet the "contextual" means its something that varies, depending on the context.

"Contextual absolute" therefore amounts to a "varying invariant."

It's basically contradictory.

Edited by Daniel Barnes
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Oh, Kant rare.

What? Kant and I part company on the matter of apodictic synthetic a priori judgments, which is at the foundation of Kantian philosophy. There are no such judgements. If I follow anyone it is Hume and Hobbes. Hume was a WSYIWYG philosopher from the git-go. If you recall, Kant came up with the Critique in order to refute Hume.

Do watch your language, sir.

Ba'al Chatzaf

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The practical consequence of Hume's criticism of "enumerative generalisation" is that no matter how many experiences we have, we'll never have enough make an infallible universal law. We are not omniscient; there is always the possibility new facts and events outside of our experience will disprove our theory. Thus, a "universal law" is an abstract ideal we can almost certainly never achieve, although we can do our best to try to attain it.

Similarly, the practical consequence of Roger and Peikoff's "observational-integrative generalisation" is that no matter how many experiences we have, we'll never arrive at an infallible universal law either. It also holds that we are not omniscient; there is always the possibility new facts and events outside of our experience will disprove our theory. Thus, also for the Objectivist camp, a "universal law" is also an abstract ideal that we can almost certainly never achieve.

What do you mean by saying that “there is always the possibility new facts and events outside of our experience will disprove our theory?” Suppose that no new facts will disprove the theory that the earth revolves around the sun. In that case, is it still “possible” that new facts will disprove it? No, because in that case, it’s impossible. But then how can you say that there is always the possibility that new facts will disprove it? Clearly, you cannot. You can say it only if there is some reason to doubt the theory — some evidence to think that it might be false.

What emerges from this direct comparison of the practical consequences of Rand's theory is that we see that it lands, contrary to the all intents and purposes of its author, in an obviously skeptical theory of knowledge.

I am not the only one to suggest this. Fred Seddon summarised Rand's position neatly as "We can know P, but P may be false."*

I don’t think Rand would say that we can know P, but that P may be false. She would say that if there is some reason to doubt P — some reason to believe that P may be false — then we cannot claim to know P.

A simple example will suffice. It was once thought - for many hundreds of years - that the sun went around the earth. According to Objectivism, we would be fully entitled to say we knew this to be true, as this was in the context of the limited human knowledge at the time. (More than that, we would be entitled to say we would be absolutely certain of it)

Now, this theory turned out to be false.

Yes, it turned out to be false, but only in relation to our discovery that in fact the earth revolves around the sun. If we couldn’t say that our present theory were true, we couldn’t say that our previous theory is false.

In fact, the opposite is true: the earth goes around the sun. We are now able to say, in this new context, that we know this (and are "absolutely certain" of it).

Yes, we are absolutely certain of it, because we have no reason to doubt it. Do you think there is some reason to doubt that the earth revolves around the sun?

(One might remark in passing just how low the bar is set for both "truth" and "certainty" in Rand's "contextual" theory, in that we can claim both to an "absolute" degree for opposing theories!)

Not simultaneously. We are justified in claiming a theory as true, if all the evidence supports and none contradicts. But once there is evidence disproving it, we can no longer claim it as true. We can claim that we thought it was true and that we were justified (within the context of our knowledge) in thinking so, but we cannot claim that it was true. It was certainly false to say that the sun revolves around the earth, even though we were justified in saying so based on the evidence available to us at the time. But we are no longer justified in saying so, because we now have evidence disproving it. We are never justified in simultaneously claiming opposite theories as true.

[Moderator's note: I used my handy-dandy editing powers to fix Bill's formatting so that the quotations showed up properly. Otherwise, his post is as he submitted it....reb, 9/24/07]

Edited by Roger Bissell
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Ba'al:

Kant and I part company on the matter of apodictic synthetic a priori judgments...Kant came up with the Critique in order to refute Hume.

Yes. It seems Kant developed the "synthetic a priori" in order to rescue Newton from the consequences of Hume's critique.

It almost certainly fails (Newton's theory eventually turned out to be false anyway, thus corroborating Hume). A large part of Kant might be rescued though by evolutionary theory, which states that a much of our expectations about the world, rather than the laws of the world itself, are inborn. Kant was simply wrong in not realising that our inborn expectations themselves may err, and are not laws.

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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]

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