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

[Dragonfly]

Does non-metric topology use any units?

I don't know what you mean by the vague term "units", but non-metric refers to spaces without metric, which means you can't measure anything (a metric is that what makes measurement of the distance between points in that space possible). Really, you can't smuggle measurement in via the back door.

[BaalChatzaf]

Bob,

Math is not used in measuring ingredients in making chocolate chip cookies? Math is not used in counting how many are made? I don't understand.

You use the word differently from the way I do.

Notice that, did you? Rand did too.

Michael

Some mathematical systems have to do with numbers. Others do not. Mathematics is not inherently about numbers. It is about abstract systems of objects and the operations and relations that obtain in such systems. This is the position taken by the Formalist School, one of several schools of thought on what mathematics is.

Ba'al Chatzaf

Edited October 1, 2007 by BaalChatzaf

[Michael Stuart Kelly]

Dragonfly,

I don't know this field, but are there any mathematical formulas with symbols and do the symbols stand for something? Measurement does not have to be geometrical measurement for Rand to be measurement. And if there are no formulas and symbols, how is math applied?

Merlin,

I skimmed your articles. Nyquist brought up some similar points in ARCHN. I need to read them more thoroughly before I can make an intelligent comment on them. (Actually, I do have an idea for the one on RoR, but I prefer to let it cook for now.) Also, just because Dragonfly answered my question, I am still interested in your answer.

Michael

[Michael Stuart Kelly]

Some mathematical systems have to do with numbers. Others do not. Mathematics is not inherently about numbers.

Bob,

Who said anything about numbers? I asked about units.

Michael

[BaalChatzaf]

Some mathematical systems have to do with numbers. Others do not. Mathematics is not inherently about numbers.

Bob,

Who said anything about numbers? I asked about units.

Michael

You define units trivially. By you, a unit is a component of discourse. EVERY SUBJECT UNDER THE SUN has units in this trivial sense.

Ba'al Chatzaf

[Ellen Stuttle]

Merlin,

This is just a note pertaining to the (at least apparent) contradiction you pointed out in Rand's wording, that between "implies all" and "explains the greatest number" (your post #185).

On detailed "parsing" of the contrasting passages, I think that she isn't really contradicting herself but instead is using the word "essential" in a different way in one of the passages than she uses it elsewhere in the chapter, with the result that she's confusing and looks as if she's contradicting herself.

I think the tangle hinges on a mix-up between "essential" for the purpose of defining a concept and "essential characteristic(s)."

Rand considered both species and genus essential parts of a proper definition; and she indicates that a definition is required in order fully to have a concept.

Repeating (this is quoted in my post #187):

"Words transform concepts into (mental) entities; definitions provide them with identity. (Words without definitions are not language but inarticulate sounds.)" (pg. 11)

But when she speaks of the "essential characteristic(s), which she also calls "distinguishing characteristic(s)" and "fundmental characteristic(s)," she's referring only to the differentia, not to the whole definition.

"The distinguishing characteristics(s) of the units becomes the differentia of the concept's definition; the existents possessing a "Conceptual Common Denominator" become the genus." (pg. 41)

It's the "essential" or "distinguishing" characteristic(s) which she says is(are) ascertained by "the rule of fundamentality."

Now observe, on the above example [the example was that of 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 [that is, differentia-establishing characteristic; see the above quote] 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.

Thus...

I think she isn't really contradicting herself, though she is using confusing wording, when she says that:

A definition must identify the nature of the units, i.e., the essential characteristics without which the units would not be the kind of existents they are. But it is important to remember that a definition implies all the characteristics of the units, since it identifies their essential, not their exhaustive, characteristics; since it designates existents, not their isolated aspects; and since it is a condensation of, not a substitute for, a wider knowledge of the existents involved." (pg. 42)

I think what she means, in that particular quote, is both differentia and genus, although when she says "essential characteristic" elsewhere, she means just the differentia.

Thus in regard to the thumb, she would be saying (if my interpretation is correct) that "rational animal" implies a thumbed creature, not that "rational" (the essential in the sense of fundamental and differentia-establishing characteristic) implies a thumbed creature. Thus she could still consistently say that "rational" "explains the greatest number" of other characteristics.

(It remains, I'd be willing to bet, that she unfairly faulted the "noted" anthropologist for saying something that wasn't being said. It sounds to me as if the article was pondering the evolutionary explanation for the big brain's developing, and she interpreted backward timewise, that is, from the standpoint of presuming the existence of humans as they are today; thus she faulted the author for "blanking out" the existence of exactly the feature of the human the emergence of which the author was trying to explain.)

Ellen

___

Edited October 1, 2007 by Ellen Stuttle

[Ellen Stuttle]

Michael,

Re Rand on "specialized definitions": She isn't saying that there are two kinds of definitions; instead that specialized definitions are subcategories.

There's no discussion of the subject of specialized definitions in the Definitions chapter of ITOE. Where the subject comes up is in the Workshop, and there only briefly. She's quite explicit, however, in saying (a) that a specialized definition is a subdivision; and (b ) that a specialized definition musn't be substituted "for the basic philosophical definition which is valid for all men in all stages of knowledge."

AR: [....] Philosophical problems have to be solved on a level of knowledge available to a normal adult at any period of human development; so that philosophical concepts are really not dependent on the development of individual sciences. And "primate" or "mammal" would be a very specialized subdivision of a concept according to a particular science.

Prof. A: Then would it be wrong for a biologist to define man as "a rational primate," or would that be correct in his context?

AR: It would be correct in his context, if he remembers that he is speaking here from a professional context. And, as you know, they subdivide even further. Any subdivision within a given science is proper provided it is not substituted for the basic philosophical definition which is valid for all men in all stages of knowledge.

I.e., philosophy rules, and the sciences must obey. ;-)

Ellen

___

[BaalChatzaf]

I.e., philosophy rules, and the sciences must obey. ;-)

Ellen

___

Thank your Lucky Transistors that this is not the case.

Ba'al Chatzaf

[Michael Stuart Kelly]

Ellen,

I thought when I stated that one kind of definition complements the other the idea of subdivision was clear.

In simple terms, from a philosophical viewpoint, one observes an existent and opens a mental file on it. The existent is called the referent and the file is called the concept. A category is put on file in the mind, so to speak.

Science does not put information into that file and make an entirely new file for the same existent in the same instant. Although research brings new knowledge of new existents, therefore new files for them are opened, the original file stays the same and the existent remains the same. The referent is still that particular kind of existent. That is the philosophical meaning at the root. (Interestingly, the philosophical definition can change over time, but the original concept-referent relationship does not change.)

No matter how much science studies an existent, the existent will still be what it is and the original concept for it will still mean that kind of existent. There is no way more knowledge can undo that fact.

So in that sense, yes, philosophy rules. This to me is a silly a way to say it, though. It is like saying that after you have traveled miles, your decision to go and your first step rules because you wouldn't be where you are without them.

Rules what?

That's silly. It's the same journey.

Michael

[Steve Gagne]

The answer is 476.

[merjet]

Yes, there is advanced math that doesn't involve measurement, e.g. non-metric topology.

Merlin,

Does non-metric topology use any units?

Michael

Yes, "unit" meaning "member of a set", but not meaning "a basis of measurement". I comment about Rand's ambiguous use of "unit" in the 2nd link in msg #198.

[BaalChatzaf]

Yes, there is advanced math that doesn't involve measurement, e.g. non-metric topology.

Merlin,

Does non-metric topology use any units?

Michael

Yes, "unit" meaning "member of a set", but not meaning "a basis of measurement". I comment about Rand's ambiguous use of "unit" in the 2nd link in msg #198.

Using Topoi one can even eliminate set theory. I suppose elements of a set would correspond roughly to Michael's "units". But even those can be made to go away.

The fact that any mathematical theory has objects and relations means they constitute units in a trivial sense. Anything expressible in some sort of human language or another has units, so mathematics is not special in that sense.

Ba'al Chatzaf

[Alfonso Jones]

Alfonso,

There is a theory (not coming from you, obviously) that Rand was an ignoramus for defining mathematics as "the science of measurement" (ITOE, p. 7). Those who generally claim this are math and science oriented. I am merely wondering if there is any math without units and if there is any structured handling of units that does not involve some kind of measurement.

I'm just trying to figure out why Rand was an ignoramus.

After I figure that out, I can look at why she used measurement as the fundament of concept formation.

Michael

I'm not as knowledgeable about ITOE as I would like to be. But I think the concept of "unit" as defined by Rand on page 2 ("A unit is an existent regarded as a separate member of a group of two or more similar members.") is NOT to be confused with "units" as in "What units are you speaking of - miles or kilometers?" I'm not saying you're making that error - but I wonder about some of the things I have seen posted.

I think that Rand was extremely insightful about many things. The notion that she was an "ignoramus" in the area of math is a little silly. I wish I could recall where I have read of Rand taking tutoring in math toward the last years of her life, and her own statement of her motivation for doing this and her evaluation of her competence.

Alfonso (who has a PhD in Mathematical Statistics, and has done a bit of theoretical math in his past)

[Daniel Barnes]

Alfonso:

The notion that she was an "ignoramus" in the area of math is a little silly. I wish I could recall where I have read of Rand taking tutoring in math toward the last years of her life, and her own statement of her motivation for doing this and her evaluation of her competence.

I think someone (Merlin?) answered this, Alfonso. She took some private algebra tuition very late in life. Middle school level, not high school, let alone anything advanced. As I recall the tutor is said to have commented on how mindblowingly good she was at it. The source for this quote may be dubious however. It may be like the story about Rand completely destroying a professor of philosophy one night in argument, which as I recall Chris Sciabarra investigated and could find no foundation for.

[Steve Gagne]

Yes, there is advanced math that doesn't involve measurement, e.g. non-metric topology.

Merlin,

Does non-metric topology use any units?

Michael

Yes, "unit" meaning "member of a set", but not meaning "a basis of measurement". I comment about Rand's ambiguous use of "unit" in the 2nd link in msg #198.

Using Topoi one can even eliminate set theory. I suppose elements of a set would correspond roughly to Michael's "units". But even those can be made to go away.

The fact that any mathematical theory has objects and relations means they constitute units in a trivial sense. Anything expressible in some sort of human language or another has units, so mathematics is not special in that sense.

Ba'al Chatzaf

Bob, can you point me at a book on that subject?

Even so, the answer is still 476. That's how many angels can dance on the head of a pin. I mean, how many times have you advocated for your Reality Lite viewpoint, and not insisted on it here? If you want to discuss how we get mental content, then you don't discuss math, you don't discuss physics, you don't discuss set theory, you don't discuss Aristotle. "Popper said...." "Aristotle said......" "Rand said....." "Plato said...." "J.S.Mill said......" but not one of these people did anything but hypothesize in the absence of evidence. What would YOU say?

Experimental psychology is the scientific field that actually identifies how we get our mental content, how we do concept formation: i.e., learning. And it is not so verbal-centric that it ignores the 2-year pre-verbal period of learning we all go through from 5 months of gestation onward, wherein we acquire concepts such as "me-feel" (focus), "me"-"not-me" ("identity"), "me-do"-"not-me-do" ("causation"), "not-me-do"-"me-feel" ("pain/pleasure principle"), etc., etc., etc. It is because all these essential "axiomatic" concepts are learned, are formed, are inferred, at the pre-verbal level that later definitions appear circular or to tend toward infinite regression. You just can't remember how you got where you are, so you make it up as you go.

The late experimental psychologist Robert Gagne (1916-2002, not an immediate relative) isolated 5 different types of learning, and proposed a process for applying the nine necessary conditions for learning (in the form of instruction -- his theories in learning have been applied to the military, kindergartens, home study programs, etc., with great success). From his work we find that the simplest answer to the question of the origin of mental content is, "It is learned."

Though in some respects simplistic, based on postulation rather than evidence, and showing signs of what I have called elsewhere "knowledge stubs", Ayn Rand's hypotheses concerning concept formation echo significant parts of what has been theorized by Gagne et al. And if these principles are taken seriously, one realizes that our "knowledge" is the experienced concrete, generalized and integrated with what we have known before. This is learning, this is concept formation. It makes foolish any assertions about distinctions in types of "induction", because it's all the same thing. And there is no guarantee of automatic infallability.

I suspect that would be the type of answer you would want, were you to be consistent to the principles you've advocated here.

Edited October 2, 2007 by Steve Gagne

[Michael Stuart Kelly]

The fact that any mathematical theory has objects and relations means they constitute units in a trivial sense. Anything expressible in some sort of human language or another has units, so mathematics is not special in that sense.

Bob,

In Objectivist epistemology, mathematics is not "special" as in "cut off from reality." It is merely one form of the same knowledge of the same brain of the same entity. According to Objectivism, ALL conceptual knowledge is mathematical at root.

Michael

[Roger Bissell]

Alfonso,

There is a theory (not coming from you, obviously) that Rand was an ignoramus for defining mathematics as "the science of measurement" (ITOE, p. 7). Those who generally claim this are math and science oriented. I am merely wondering if there is any math without units and if there is any structured handling of units that does not involve some kind of measurement.

I'm just trying to figure out why Rand was an ignoramus.

After I figure that out, I can look at why she used measurement as the fundament of concept formation.

Michael

..."Ignoramus" usually means "ignorant and stupid." So I would only call Rand ignorant in math. Face the facts. Late in life she studied algebra -- a middle school subject for better students. I'd guess she didn't even take high school math (geometry, trig, etc.), let alone basic college level math (linear algebra, calculus, etc.) and advanced college math (advanced calculus, differential equations, probability and statistics, real analysis, abstract algebra, topology, etc.)...

I'm still trying to get clarity on to what extent anyone, let alone Rand, deserves to be labeled either "ignorant" or an "ignoramus" (ignorant and stupid) in regard to her acquaintance with mathematics.

I would happily "face the facts" about Rand's educational attainments in mathematics, but I would like to know a little more about what source is being used for the claim that Rand didn't study algebra, etc., in high school, but only in late in her life.

I quote from Barbara Branden's biography, The Passion of Ayn Rand, which Merlin surely (?) has read, though probably (?) Bob has not:

The subject she most enjoyed during her high school years, the one subject of which she never tired, was mathematics. "My mathematics teacher was delighted with me. When I graduated, he said, 'It will be a crime if you don't go into mathematics.' I said only, 'That's not enough of a career.' I felt that it was too abstract, it had nothing to do with actual life. I loved it, but I didn't intend to be an engineer or to go into any applied profession, and to study mathematics as such seemed too ivory tower, too purposeless--and I would say so today." Mathematics, she thought, was a method. Like logic, it was an invaluable tool, but it was a means to an end, not an end in itself. She wanted an activity that, while drawing on her theoretical capacity, would unite theory and its practical application. That desire was an essential element in the continuing appeal that fiction held for her: fiction made possible the integration of wide abstract principles and their direct expression in and application to man's life. She wanted to define a moral ideal, to present her kind of man--and to project, through fiction, the living reality of that ideal. She wanted to project it, using as her tool the precise, unsentimental mind of a mathematician. [p. 35]

This does not sound like Rand was being praised for her mathematical ability at multiplying fractions or calculating percentages. From this alone, especially her referring to mathematics' abstractness and impracticality (other than in applied form as in engineering), my own "guess" (using Merlin's methodology) is that, in high school Rand studied algebra, geometry, and at least trigonometry, before truncating her mathematical studies -- and that in her final few years, what she was delving into was differential and integral calculus, differential equations, etc. As Peikoff indicates in a Q-A session in his lectures on "Induction in Physics and Philosophy," in her last years, Rand was pursuing the hunch that there were many deep connections between higher mathematics and epistemology of the sort that she had already alluded to in Introduction to Objectivist Epistemology regarding concepts-formation and algebra. He specifically mentioned "calculus and differential equations."

This is yet one more reason why all of you people who are trying so vigorously to rip Leonard Peikoff -- or Ayn Rand -- another asshole should instead spend some of your seemingly boundless energy listening to his lectures on induction. And maybe read/re-read Barbara's biography a bit more carefully. Pessimist that I am, I will be surprised if any of you actually do so; it's apparently far easier and more fun to be negative and scornful of someone you know from recycled second-hand misimpressions and snippets.

REB

[Roger Bissell]

Alfonso,

There is a theory (not coming from you, obviously) that Rand was an ignoramus for defining mathematics as "the science of measurement" (ITOE, p. 7). Those who generally claim this are math and science oriented. I am merely wondering if there is any math without units and if there is any structured handling of units that does not involve some kind of measurement.

I'm just trying to figure out why Rand was an ignoramus.

After I figure that out, I can look at why she used measurement as the fundament of concept formation.

Michael

Rand's defining mathematics as "the science of measurement" is too narrow. One of the rules for a proper definition -- e.g. see David Kelley's logic book -- is that it not be too broad or narrow. Indeed, "the science of measurement" doesn't even encompass arithmetic in my view. "Science of quantity" is far better, but still too narrow.

I think it's amazing and amusing -- and somewhat curious -- that Rand's definition of "mathematics" is so similar to that of the philosopher who coined the term naming the ethical philosophy Rand hated most: altruism. Auguste Comte defined mathematics as "the science of indirect measurement."

As Spock would say: "Fascinating!"

REB

[Alfonso Jones]

This is yet one more reason why all of you people who are trying so vigorously to rip Leonard Peikoff -- or Ayn Rand -- another asshole should instead spend some of your seemingly boundless energy listening to his lectures on induction. And maybe read/re-read Barbara's biography a bit more carefully. Pessimist that I am, I will be surprised if any of you actually do so; it's apparently far easier and more fun to be negative and scornful of someone you know from recycled second-hand misimpressions and snippets.

REB

Let me say, with a meaning I think the readers and denizens of Objectivist Living Forum will find familiar - AMEN! I have been at times extremely disappointed by Peikoff - "Fact and Value" comes to mind. But I've been listening to Understanding Objectivism as of late. And I've gotten a good amount of insight out of that. I'm going to check the dates on the CDs I have - I'm coming to suspect that Peikoff has acquired an emotional/pontificating side over the years which was not so present during Rand's lifetime or shortly after her death.

I'll take REB's advice and listen to Peikoff on induction. Are you thinking of the lectures on Inducton in Physics and Philosophy, or do you have another reference, REB?

And anybody who hasn't read Passion of Ayn Rand carefully betrays a lack of interest in Rand and Objectivism, while anyone reading Passion of Ayn Rand and concluding Barbara Branden is primarily interested in spreading negatives about Ayn Rand displays a tin ear and an inability to comprehend Barbara's extremely lucid prose.

Alfonso

[Dragonfly]

This is yet one more reason why all of you people who are trying so vigorously to rip Leonard Peikoff -- or Ayn Rand -- another asshole should instead spend some of your seemingly boundless energy listening to his lectures on induction. And maybe read/re-read Barbara's biography a bit more carefully. Pessimist that I am, I will be surprised if any of you actually do so; it's apparently far easier and more fun to be negative and scornful of someone you know from recycled second-hand misimpressions and snippets.

Second-hand impressions? In earlier posts I've domumented with quotes a lot of Peikoff's howlers in the fields of physics and mathematics (in his DIM lectures and in The Ominous Parallels), which are always conveniently ignored by his apologists. These alone are enough reason to dismiss anything he wrote about science. Is there anyone who takes his The Ominous Parallels seriously? I've dissected his The analytic-synthetic dichotomy elsewhere. I'm getting tired of hearing about his wonderful lectures. Lectures are not a source I can take seriously, especially not when they cost hundreds of dollars. So far the evidence for Peikoff's prowess has been rather underwhelming. The only second-hand impressions I get are those from his admirers who ad nauseam tell me how wonderful his lectures are.

[tjohnson]

In Objectivist epistemology, mathematics is not "special" as in "cut off from reality." It is merely one form of the same knowledge of the same brain of the same entity. According to Objectivism, ALL conceptual knowledge is mathematical at root.

Micheal, do you not consider the human nervous system a part of "reality"? If I say that pure mathematics is special because mathematical objects exist only in our nervous systems this does not mean it is cut off from "reality". It simply means that it is about the "reality" in our nervous systems, ie. how our brains work.

[merjet]

Bissell's guess may be correct, but it remains speculative that Ayn Rand took geometry and trig without specific evidence or at least knowing what a high school education in Russia was like about 1920. If she did take them, it strikes me as odd that she studied algebra late in life. Also, the following webpage lists Ayn Rand's college courses. None in math.

http://www.nyu.edu/projects/sciabarra/essays/randt2.htm

So it's pretty clear she was relatively uneducated in math, and I don't regard use of "ignorant" as improper.

Here is a dictionary definition.

ignorant - 1. having little knowledge, education, or experience

- 2. lacking knowledge (in a particular area or matter)

Some may take the term to be offensive. But I would not be offended if somebody said I was ignorant in chemistry. I took chemistry in high school and one college course in it, but have forgotten most of it since.

Edited October 2, 2007 by Merlin Jetton

[Ellen Stuttle]

As to why Rand used measurement as fundamental to concept formation, I can only speculate. Perhaps it was "marketing". Perhaps she accepted a corrupted definition of measurement -- see here: http://rebirthofreason.com/Articles/Jetton...asurement.shtml

In any case it's clear to me that much of concept formation does not require measurement omission. There is some measurement omission, but it is overwhelmed by qualitative omission. I cover the topic much more extensively here: http://www.objectivistcenter.org/events/ad.../JettonOaM3.PDF

Thanks for the links. I read the RoR article and discussion with much interest. Oh, how I agree with you about the fogs, fuzzinesses, and mess-ups trying to physicize psychology produced. (I'm taking your morals-charges angle tongue-in-cheek; I don't think it was a "corrupters'" plot; but I think it was a mistake, one which goes way back to the psychophysics approach to perception.)

Seems to me the way Rand actually used "measurement" in her theory comes down to just "comparison" in any sort of way.

I'll read the other link when I can. Sounds like you're still accepting her notion of a "concept" as a form of "entity" -- an "integrate" ("A concept is a mental integration of two or more units...," she says.)

(Having trouble trying to resist reading the posts.)

Ellen

___

[Roger Bissell]

This is yet one more reason why all of you people who are trying so vigorously to rip Leonard Peikoff -- or Ayn Rand -- another asshole should instead spend some of your seemingly boundless energy listening to his lectures on induction. And maybe read/re-read Barbara's biography a bit more carefully. Pessimist that I am, I will be surprised if any of you actually do so; it's apparently far easier and more fun to be negative and scornful of someone you know from recycled second-hand misimpressions and snippets.

REB

Let me say, with a meaning I think the readers and denizens of Objectivist Living Forum will find familiar - AMEN! I have been at times extremely disappointed by Peikoff - "Fact and Value" comes to mind. But I've been listening to Understanding Objectivism as of late. And I've gotten a good amount of insight out of that. I'm going to check the dates on the CDs I have - I'm coming to suspect that Peikoff has acquired an emotional/pontificating side over the years which was not so present during Rand's lifetime or shortly after her death.

I'll take REB's advice and listen to Peikoff on induction. Are you thinking of the lectures on Inducton in Physics and Philosophy, or do you have another reference, REB?

And anybody who hasn't read Passion of Ayn Rand carefully betrays a lack of interest in Rand and Objectivism, while anyone reading Passion of Ayn Rand and concluding Barbara Branden is primarily interested in spreading negatives about Ayn Rand displays a tin ear and an inability to comprehend Barbara's extremely lucid prose.

Alfonso

Hey, Alfonso, good post. I agree with you about Peikoff's "emotional/pontificating" tendencies. I think that after Rand's death, he was becoming more, shall we say, tolerant and open-minded -- especially as evidenced by the lecture series you mentioned, which I enjoyed very much. But then, when Barbara's biography came out, he swung back the other way. I don't know if it was all self-motivated, or if he was under pressure to crack down from Schwartz and/or Binswanger, etc., but it was a very perceptible reversal in direction, and all of the destructive events that followed seem to stem from the (over)reaction by Peikoff and ARI to The Passion of Ayn Rand -- the Kelley Split, the Reisman Split, the Branden bashing, the Sciabarra bashing, the Campbell bashing, and the Kelley/IOS/TOC/TAS bashing. It's not been a very pretty sight, but it really is quite typical of movements, as the siege mentality takes over. Circle the wagons, boys.

Also, I agree that Peikoff's writing and lecturing has been uneven. I find nothing wrong with his "Analytic-Synthetic Dichotomy," nor with his "DIM Hypothesis" (except the authoritarian application he tries to make with it). But I have winced and groaned and cursed at the sloppiness in OPAR, as when, for instance, he carefully distinguishes between an axiom and a corollary, then refers to volition, validity of the senses, and causality all as both axioms and corollaries! Arrrrgh.

I'll be happy to suggest an approach to his lectures on induction. If you have plenty of $$, start with "Objectivism through Induction," then follow it up with "Induction in Physics and Philosophy." The first series has a lot of painstaking derivation of key Objectivist tenets in an inductive manner, so it is great training and practice, as well as insight. However, if you're on a budget, I'd say skip OTI and go right to the IPP series. It is a more theoretically integrated discussion of induction, and though most of the examples are from physics, there is at least one extended example from philosophy. And if you're really on a budget, you can wait for David Harriman's book on IPP to come out, and in the meantime, you can check out his essays on the history and philosophy of physics in The Objective Standard.

REB

P.S. -- I'm surprised General Semanticist hasn't chimed in and accused you of having the "tin ear." After all, everything is relative, don't you know? :-)

[Dragonfly]

As to why Rand used measurement as fundamental to concept formation, I can only speculate. Perhaps it was "marketing". Perhaps she accepted a corrupted definition of measurement -- see here: http://rebirthofreason.com/Articles/Jetton...asurement.shtml

In any case it's clear to me that much of concept formation does not require measurement omission. There is some measurement omission, but it is overwhelmed by qualitative omission. I cover the topic much more extensively here: http://www.objectivistcenter.org/events/ad.../JettonOaM3.PDF

Excellent articles and a must read for every Objectivist who wants to discuss measurement and measurement omission.