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

[BaalChatzaf]

I have already written a rather lengthy explanation that the problem is the consequences of Aristotle's essentialist method of definition, not his essentialist metaphysics. Plus a further elaboration. I've already pointed this out to you. Plus its the whole point of the "Two Kinds of Definitions" essay in the first place.

The argument is not about whether Rand believed in metaphysical essences or not. Never has been! Get with the program....

I find your essays right on point and very well crafted.

Of all the philosophers of science (those who study and comment on what scientists actually due) the ones most respected by the scientists themselves, seem to be Popper and Kuhn. In a course in astrophysics that I took last year at Princeton, the professors actually spent a bit of time presenting Popper's views. It is rather unusual for physicists to pay much mind to philosophers.

Ba'al Chatzaf

Edited September 30, 2007 by BaalChatzaf

[Daniel Barnes]

Ba'al:

I find your essays right on point and very well crafted.

Praise from Caesar is praise indeed.

[BaalChatzaf]

Ba'al:

I find your essays right on point and very well crafted.

Praise from Caesar is praise indeed.

No, No. The other guy is Caesar. I am Titus Pullo. But the baby is mine.

Ba'al Chatzaf

Edited September 30, 2007 by BaalChatzaf

[tjohnson]

Physics works while our measurements in general give consistent results, and that leads us to postulate that there is something "out there", independent of our consciousness.

After sleeping on it I think Dragonfly has summed it up quite well here. The key word above is 'postulate'. I would slightly reword this by saying physics works while our measurements in general give consistent results, and that leads us to postulate that there is a certain structure "out there", independent of our consciousness. In fact, the structure in question is arrived at from the interaction of the stimuli and our nervous systems. We notice structure at a perceptual level and then we mirror it at a verbal level.

We assume this postulated structure would apply back in the time of the dinosaurs as well as everywhere in the universe but this is an assumption none the less for we have no way of verifying it. For example think of the theory of evolution - we can not observe evolution, we can only observe natural selection. There is a large assumption involved to go from observing natural selection to saying we evolved from a single celled organism over a period of billions of years. We postulate the existence of electrons which have certain ascribed properties because it allows us to explain certain phenomena and we can postulate whatever structure we want in attempts to account for new experimental results.

[BaalChatzaf]

Physics works while our measurements in general give consistent results, and that leads us to postulate that there is something "out there", independent of our consciousness.

After sleeping on it I think Dragonfly has summed it up quite well here. The key word above is 'postulate'. I would slightly reword this by saying physics works while our measurements in general give consistent results, and that leads us to postulate that there is a certain structure "out there", independent of our consciousness. In fact, the structure in question is arrived at from the interaction of the stimuli and our nervous systems. We notice structure at a perceptual level and then we mirror it at a verbal level.

We assume this postulated structure would apply back in the time of the dinosaurs as well as everywhere in the universe but this is an assumption none the less for we have no way of verifying it. For example think of the theory of evolution - we can not observe evolution, we can only observe natural selection. There is a large assumption involved to go from observing natural selection to saying we evolved from a single celled organism over a period of billions of years. We postulate the existence of electrons which have certain ascribed properties because it allows us to explain certain phenomena and we can postulate whatever structure we want in attempts to account for new experimental results.

Consider the alternatives. Would a reasonable person assume that the variety of life on this planet have been here forever or had appeared only a short while ago? As to natural selection, it has been observed in -real time-. Mutation among microbes has been observed over a matter of hours, not decades, centuries or thousands of years. Of course when Darwin postulated natural selection, he did just that postulate. We now know from direct observation that is brilliant conjecture/hypothesis was right on the money. And he didn't get it by induction either. He got it buy comparing nature to animal and plant breeders of whose art he knew a great deal. Darwin abduced natural selection from Malthus' analysis proving that more offspring our produced than can survive and from the animal breeders who keep animals with the characteristics they wanted and culled the rest. It was a brilliant analogy and it was right on the money. Hypotheses start off as guesses, but they are rapidly re-enforced by honest to goodness observation and measurement.

J.J. Thompson postulated some kind of emanation from cathodes. They were originally called cathode rays, on the supposition that they were some kind of light. But whatever it was that was streaming out of hot cathodes could be diverted by magnets so it was clear it was not light. The next best guess was some kind of charged particle. This guess was checked when "cathode rays" could be bent by the presence of positively or negatively charged bodies. Again, it was a brilliant conjecture/hypothesis which was stiffened up by careful measurement and observation. We now accept electrons as fact (even though we cannot see them) because of all the interactions that have been observed and by the fact no other explanation accounts for what is seen. For similar reasons no one alive today (except maybe you) doubts that atoms exist.

Ba'al Chatzaf

[tjohnson]

we can not observe evolution, we can only observe natural selection.

As to natural selection, it has been observed in -real time-. Mutation among microbes has been observed over a matter of hours, not decades, centuries or thousands of years.

Perhaps you did not read my post carefully, evolution is not the same as natural selection.

[BaalChatzaf]

we can not observe evolution, we can only observe natural selection.

As to natural selection, it has been observed in -real time-. Mutation among microbes has been observed over a matter of hours, not decades, centuries or thousands of years.

Perhaps you did not read my post carefully, evolution is not the same as natural selection.

Evolution is the result of

1. genetic variation.

2. natural selection of those variants which produce reproductive success by natural culling of those variants which do not have comparative reproductive success.

Did you learn your evolution from The Count along with your physics?

Ba'al Chatzaf

Edited September 30, 2007 by BaalChatzaf

[tjohnson]

Did you learn your evolution from The Count along with your physics?

Tell me, did you become a sarcastic asshole on Sept. 11, as well as a lunatic, or were you always like that?

[BaalChatzaf]

Did you learn your evolution from The Count along with your physics?

Tell me, did you become a sarcastic asshole on Sept. 11, as well as a lunatic, or were you always like that?

Since I could talk.

Ba'al Chatzaf

[merjet]

Combining these two claims, the essential characteristics implies all the characteristics of the units. Ergo, in the case of man and contra MSK, 'rational' or 'animal' implies a thumb.

Merlin,

Contra? I thought I said precisely that.

Really? My response was to the the bold part in the following, which is contra Rand's saying "the essential characteristics implies all the characteristics of the units."

Here is one place where the problem lies. Rand is not saying that all other characteristics in reality, i.e., metaphysically, depend on the fundamental one. She is saying that the details falling within the concept depend on it. This is because the concept refers to something that exists and we have already learned many things about it. Here is an example. "Out there" the fact that man has a thumb does not depend on him being rational. Thumb and rational are not even connected. Rand's words could be interpreted to mean this, but that is not what she is getting at.

I believe "a definition implies all the characteristics of the units" is far overstated. A correct formula seems to be that the definition refers to the units, and the reference is to all the units' characteristics, not just the ones condensed into the definition. Essential characteristics can't imply contingent characteristics, e.g. the definition of 'boat' doesn't imply it has sails.

Not only is this claim of Rand's overstated, it conflicts with what she says three pages later. "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 45) "Implies all" and "explains the greatest number" are inconsistent.

[Michael Stuart Kelly]

Really? My response was to the the bold part in the following, which is contra Rand's saying "the essential characteristics implies all the characteristics of the units."

Here is one place where the problem lies. Rand is not saying that all other characteristics in reality, i.e., metaphysically, depend on the fundamental one. She is saying that the details falling within the concept depend on it. This is because the concept refers to something that exists and we have already learned many things about it. Here is an example. "Out there" the fact that man has a thumb does not depend on him being rational. Thumb and rational are not even connected. Rand's words could be interpreted to mean this, but that is not what she is getting at.

Merlin,

That is qualified with "out there" and explained by my former post. See here:

When I use the term "out there" or "metaphysical" in this context, I mean the actual existence of something, irrespective of the observing agent. Without the observing agent, nothing can be implied. "To imply" is a mental operation.

To try to be clearer, "out there" (in the sense I just explained) if one lopped off the thumb of an human being, the rationality would remain and if the rationality were removed (but some motor operations still retained), a functional thumb would remain. That is what I meant by not connected. One does not flow from the other. In terms of evolution, the thumb probably did aid in the emergence of a conceptual faculty (which is debatable), and there is the fact that they are both attached to the same entity, but that is about all. Thumbs do exist on non-rational beings and some rational beings do not have them.

Now enter the agent. He observes. He sees more thumbs than rational faculties as features of separate entities and he sees that rational faculties are usually features of entities that have thumbs. Although he could see a human being without hands or arms at times, but they appear defective because of the sheer number he has observed. Saying "rational animal" after that implies thumbs because of such observation, not because some kind of essence of thumbness is contained within the essence of rationalness.

That is the way I understand "implies."

Not only is this claim of Rand's overstated, it conflicts with what she says three pages later. "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 45) "Implies all" and "explains the greatest number" are inconsistent.

You are absolutely correct in pointing out this inconsistency. This is a point where Rand was not clear. Still, I think some sense can be made out of this, depending on the attitude one adopts. Here is a caricature of the extreme ends.

One can point to it and say, "See? Rand was inconsistent here so all her ideas are crap."

Or one can point to it and say, "Whoever sees a contradiction here simply doesn't understand and is a Rand-hater."

There is another way that I find useful to contemplate. One can also point it out and say, "On the surface, this passage is inconsistent. Let's look behind the words into the concepts and meanings and see if it makes sense, but is merely poorly worded—or see if it doesn't make any sense at all."

When I do that, I actually do start to see some sense. "Greatest number" is a measurement. "All" is also a measurement. Neither can exist without units. So regardless of whether she is speaking about metaphysical facts or epistemological processes, she is actually speaking about epistemological processes applied to metaphysical facts. I do not see how this can be otherwise. Measurement is a mental process.

Now, from one angle, looking at the entity itself and trying to remove the epistemological process as much as possible, her "distinctive characteristic which makes the greatest number of others possible" is actually a correct description of how the hierarchy of some characteristics exists within entities. This can be seen running throughout all that exists. It is there so it can be observed. When looking at the epistemological process of how to determine a distinctive characteristic so a concept can be formed, her "one that explains the greatest number of others" also works, since it reflects or symbolizes something that actually exists (how the parts of a whole work). Lets say that the context here is constructing the concept and focusing on the existent (or better, group of existents). The epistemological process involved is forming the file folder (concept).

Now fast-forward this to the already formed concept and me using it, either to make other concepts or to learn more about the existent it represents. In this case, the distinctive characteristic portion of the concept will work like the shorthand and memory jog I mentioned and include everything that I have observed about the entity, not just one that explains the greatest number of the others. This is because the concept both is information and contains information, and it is not the thing it refers to. So by naming that thing (or better, that group of things) and establishing a file folder for it, I automatically put in it everything I know about that thing. Where else am I going to store that information? Thus, in using an already formed concept, the epistemological process involved is storage. Just because a folder is not made up of a fact does not mean that it cannot hold that fact within it.

Some people, especially those with already formed arguments against Rand, could say what I am doing here is rationalizing in order to show that Rand was not wrong. But I am honestly not doing this. I have no problem saying when I believe she was wrong. I honestly see where in one perspective (use of already formed concept) "all" is correct and in another (formation of concept) "the greatest number" is correct. And I do think Rand's wording on this point leaves much to be desired.

Michael

[Ellen Stuttle]

Michael,

I apologize in advance for the length of this post. Since it's the last extended post I'll have time for till after Thanskgiving, I tried to get a lot into it.

I'll also say in advance that I haven't yet read any of the posts which have accumulated since I last signed on early Friday am. This is picking up with where I'd gotten to then.

In light of the quotes you selected (in your post #152) from Popper's "Two Kinds of Definition," I re-re-read that essay. I felt doubly confirmed in my own initial assessment that Rand's approach to definitions is a case in point of what he calls the "essentialist" approach. On the other hand, I think I've come to see where you're getting the idea that she's not an example of what he means. I think it's because you're focusing on a different issue than I am.

The issue which looms large for you -- as it did for Rand -- in comparing her views to Aristotle's is that of their respective answers to what's been called "the problem of universals": how do we come to have ideas of generalized categories to begin with; how do we form "concepts" in the first place?

But please notice that Popper's essay is not titled "Two Kinds of Concept-Formation." It's titled "Two Kinds of Definition." And recall that Rand herself credited Aristotle with having "first formulated the principles of correct definition" (pg. 52, Exp. 2nd Ed.).

Before I turn again to the issue of definitions, I'll say some brief words on the subject which you've kept emphasizing in your replies, the role of "measurements" in Rand's theory of concept-formation. Although you've addressed me on this topic as if you think of me as a tardy learner in need of special ed, I assure you that I well know the intricacies of her theory. The reason I show no interest in what she says about "measurements" and their omission is because it's my very considered view that her theory is mostly wrong.

I give Rand A-for-effort, and I think she does have some valuable insights. But to begin with, she was hampered by an outmoded theory of perception (basically the Helmholtzian approach combined with some misunderstood James). Since it's vital to a theory of cognition to get perception right, she has a strike against her from the start, and I don't think things improve as she proceeds.

The subject is a long one. Indeed, I'm in process (slowly) of writing a long analysis of what I consider to be the errors in her theory. I don't want to try to synopsize in a post. I'm merely alerting you to the extreme unlikelihood of your convincing me that what she calls "measurement" is key.

Next, returning to the subject of definitions and why what she's talking about is what Popper describes in his essay as left-to-right.

I'll start this time with Rand's definitions (plural) of "concept." She gives two of these in her chapter "2. Concept-Formation" (her italics in both):

(1) A concept is a mental integration of two or more units which are isolated according to a specific characteristic(s) and united by a specific definition.

(2) A concept is a mental integration of two or more units possessing the same distinguishing characteristic(s), with their particular measurements omitted.

The first definition indicates that without "a specific definition," one doesn't even fully "have" a "concept," i.e., that a definition is required. A little further on, she explicitly confirms that she means this implication, since she writes (her italics):

Words transform concepts into (mental) entities; definitions provide them with identity. (Words without definitions are not language but inarticulate sounds.) We shall discuss definitions later and at length.

She next gives a couple examples, that of "length" and "table." (I'll leave aside critiquing her analysis.)

In concluding the brief introductory exposition, she says (in part), "As [the child's] knowledge grows, the definitions of his concepts grow in complexity. (We shall discuss this when we discuss definitions.)

She then gives definition (2) of "concept." The second wording (as well as making reference to your beloved "measurements") speaks of "distinguishing characteristic(s)."

Let's now turn to the chapter on defintions.

Sorry to quote at length again, but the detail is needed to make clear how she's thinking of the issue of definitions and their relationship to the concept's "distinguishing [a/k/a 'essential' and 'fundamental'] charactistic(s)."

(all italics hers)

A definition is not a description; it implies, but does not mention all the characteristics of a concept's units. If a definition were to list all the characteristics, it would defeat its own purpose [of providing an easily usable condensation]. 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.

This leads to a crucial question: since a group of existents may possess more than one characteristic distinguishing them from other existents, how does one determine the essential characteristic of an existent and, therefore, the proper defining characteristic of a concept?

The answer is provided by the process of concept-formation.

[in the next couple paragraphs she says that this process is contextual but has no proper element of the subjective. Instead:]

If [the person's] grasp is non-contradictory, then even if the scope of his knowledge is modest and the content of his concepts is primitive, it will not contradict the content of the same concepts in the mind of the most advanced scientists.

The same is true of definitions. All definitions are contextual, and a primitive definition does not contradict a more advanced one: the latter merely expands the former.

As an example, let us trace the development of the concept "man."

[she goes through steps according to a sequence which she would consider proper for the growing child, culminating with:]

When he grasps that man's distinctive characteristic is his type of consciousness [...] he reaches the one and only valid definition of man, within the context of his knowledge and of all of mankind's knowledge to date: "A rational animal." [my highlight]

[she spells out what "rational" means "in this context and goes on to say that each of the way-stage definitions she gave -- "speaks, does things no other living beings can do, walks on two legs, has no fur, moves and makes sounds" was valid "in a given context of knowledge" and was included implicitly in the next expanded context.]

[The pattern she's described, she then says:]

[...] is the pattern which makes intensive study and, therefore, the growth of knowledge--and of science--possible.

I pause there for station identification and to call your attention, Michael, to something I hope you're noticing, having just recently re-read the Popper essay yourself:

The process described is not what Popper describes physicists (or other "hard" scientists) as doing. Instead, he says that if such a scientist gives a verbal definition of the concepts of the discipline, this definition is just a sort of placeholder reminder; nothing rests on its precision; and scientists don't sit around debating the "correct" meaning, let alone "the one and only valid" meaning of their terms. (See the Popper quotes in the PS to this.)

Please recall in this context the story I told (post #82) about what happened when I wanted a simple definition of "energy" to use in a book understandable by mid-gradeschoolers. A whole group of physicists, including one (Peter Havas) of major repute in physics circles, having become interested by the little problem I'd posed, sat around for a couple hours trying out various suggestions, and not finding any with which all of them felt fully satisfied. Yet all quite understood what they were talking about with their formulae and theories. I'll add that what they're thinking of when they speak of "energy" isn't really, as Rand says it ought to be (as per her discussion of "man"), the same "concept" a child could grasp on the child's level.

Another thing I'll point out to you here pertains to her use of "condensation" in the first paragraph I quoted (where she says a definition implies "all the characteristics of a concept's units"). You described that word choice, in your post #158, as "not her finest moment, since it confuses more than it explains." From this I gather that you find "condensation" infelicitous to her own meaning.

She, however, did not find the word choice infelicitous but instead just what she meant, since she emphasized the description twice six pages further on (her italics):

(all italics hers)

A definition is the condensation of a vast body of observations--and stands or falls with the truth or falsehood of these observations. Let me repeat: a definition is a condensation. As a legal preamble (referring here to epistemological law), every definition begins with the implicit proposition: "After full consideration of all the known facts pertaining to this group of existents, the following has been demonstrated to be their essential, therefore defining, characteristic..."

Furthermore, it's just this idea that a definition condenses all one's knowledge of the specified referents which is the base of Leonard Peikoff's essay rejecting the analytic/synthetic dichotomy, an essay which there's no question Rand approved of since it was published in The Objectivist.

Furthermore, recall again a statement I've quoted enough times it's probably been memorized:

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

Let's consder that in light of her depicting "a rational animal" as "the one and only valid definition of man, within the context [...] of all of mankind's knowledge to date [...]."

If I were to take these combined contentions seriously, I'd have to conclude that nothing whatsoever which I believe I know about the human being could be true, since I've never in my life used "a rational animal" as my definition of "man" (a human being). Instead, from the time I was in grade school and first studied biological classification (having become fascinated by the theory of evolution), I've used the biological "Homo sapiens sapiens." I quite know what creature I'm talking about. Indeed, I think the definition is more useful than "rational animal," which I think has numerous problems (which I'll leave aside).

Nor am I the only one whose knowledge of humankind would be declared null due to not using "the one and only valid" definition. As you've been told by Bob K. and Dragonfly, were a modern biologist to try to give an "essential" definition of "human being" (though biologists don't think like that, in terms of "essential definition"), "possessing a human genome" would best suit the purpose as it identifies most reliably which creatures are meant.

Returning to Rand's discussion: she comes up with a neat little example which illustrates (though of course it wasn't intended to do so) the difference between her approach to defining and that of scientists.

I first remind you of this statement, quoted in an earlier post (or two):

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.

Immediately after emphasizing that "a definition is a condensation" and describing, as quoted, "a legal preamble" (in epistemological law) with which "every definition begins," she continues:

In the light of this fact, consider some modern examples of proposed definitions. A noted anthropologist, writing in a national magazine, suggests that man's essential distinction from all other animals, the essential characteristic responsible for his unique development and achievements, is the possession of a thumb. (The same article asserts that the dinosaur also possessed a thumb, but "somehow failed to develop." What about man's type of consciousness? Blank out.

She doesn't cite the source so that we might check for ourselves, should we desire to, what exactly was said in the article. Nor does she name the anthropologist so that we might assess for ourselves, should we desire to, whether the description "noted" is accurate. However, the historical context in which a claim sort of like what she describes would have been made by "noted" anthropologists happens to be one with which I'm familiar.

Recall that ITOE was first published in July 1966-February 1967. Over the preceeding about a decade, there had been some important paleo-anthropology discoveries of skeletons; these discoveries started a process which has been much expanded since then of our acquiring a fairly good picture of the evolutionary history of our own species. The specimens weren't humans but seemed possibly in the lineage; a question being asked a lot was: What had spurred the development toward the big brain? What factors were the triggers that led to humans having the exceptional brain size and complexity making human characteristics possible? In other words, the paleo-anthropologists weren't asking "What is a human?" but "Why did humans develop?, How did we become what we are?" In Randese, "metaphysically," what were the key factors which made us possible at all?

During this same era of speculation, there was a widely held premise which turned out to be false. (I won't resist crowing here: I always thought it would turn out to be false.) The premise was that first the nascent capacity to make systematic use of tools had developed with concomitant increase in brain size and then, enabling freeing of the hands for unencumbered tool use, the upright posture had followed.

Notice, in regard to "the nascent capacity to make systematic use of tools," the issue wasn't, as Rand describes, that of having "a thumb" but instead of having an opposable thumb. The opposable thumb was indisputably a gargantuanly important development in making us us. You can try it out for yourself to see why: Hold your thumb in line with the other fingers and pick up, say, a stick, a ruler, a pencil. With your thumb curved around along with the other fingers, you're mighty limited in how much manipulating, maneuvering of the object you can do. Now pick it up using the grip which curling your thumb in opposition to your fingers gives you. Voila, an enormously increased range and delicacy of manipulative movements is possible.

So the theory was, first there was the start of systematic tool-using made possible by the opposable thumb, along with increased brain size for coordinating the movements, then the upright posture developed. It's thus easy to see how reasonable it was -- and not at all blank-outish, given this theory -- to wonder, then why didn't the dinosaurs develop in the way humans did? To hear Rand tell it, the anthropologists were ignoring the significance of "man's type of consciousness." Not so; they were attempting to explain how "man" ever acquired a human type of consciousness.

The example well illustrates the difference between the way a scientist goes about thinking and the way she did.

(Just to tell a little more of the story of discovery: Further finds made clear that the direction of development was the reverse: first the upright posture, then the big brain. And the dinosaurs couldn't have developed in the way humans did because they were stuck with an anatomy which wouldn't have permitted the numerous intricate changes in the positioning of the skull that allowed the expansion in relative size of the human cranium, thus accomodating a larger brain.)

Well...I've already gone on at length; there's much more I could say illustrating the difference between how scientists do things and how Rand said one must do things to have objectively correct concepts. I hope I've said enough so that if you re-consider Popper's essay, this time you'll see why his description of the "right-to-left" approach to definitions isn't what Rand would have us do.

In any event, I must now discontinue any extensive posting until after Thanksgiving.

Ellen

PS: Here are a couple passages which I think especially demonstrate the difference:

Two Kinds of Definition

How then do the sciences make sure of the meanings of their terms? Various replies to this question have been suggested, but I do not think that any of them is satisfactory. The situation seems to be this. Aristotelianism and related philosophies have told us for such a long time how important it is to get a precise knowledge of the meaning of our terms that we are all inclined to believe it. And we continue to cling to this creed in spite of the unquestionable fact that philosophy, which for twenty centuries has worried about the meaning of its terms, is not only full of verbalism but also appallingly vague and ambiguous, while a science like physics which worries hardly at all about terms and their meaning, but about facts instead, has achieved great precision. This, surely, should be taken as indicating that, under Aristotelian influence, the importance of the meaning of terms has been grossly exaggerated. But I think that it indicates even more. For not only does this concentration on the problem of meaning fail to establish precision; it is itself the main source of vagueness, ambiguity, and confusion.

Even where a term has made trouble, as for instance the term 'simultaneity' in physics, it was not because its meaning was imprecise or ambiguous, but rather because of some intuitive theory which induced us to burden the term with too much meaning, or with too 'precise' a meaning, rather than with too little. What Einstein found in his analysis of simultaneity was that, when speaking of simultaneous events, physicists made a false assumption which would have been unchallengeable were there signals of infinite velocity. The fault was not that they did not mean anything, or that their meaning was ambiguous, or the term not precise enough; what Einstein found was, rather, that the elimination of a theoretical assumption, unnoticed so far because of its intuitive self-evidence, was able to remove a difficulty which had arisen in science. Accordingly, he was not really concerned with a question of the meaning of a term, but rather with the truth of a theory. It is very unlikely that it would have led to much if someone had started, apart from a definite physical problem, to improve the concept of simultaneity by analysing its 'essential meaning', or even by analysing what physicists 'really mean' when they speak of simultaneity.

___

Edited October 1, 2007 by Ellen Stuttle

[Michael Stuart Kelly]

Ellen,

I am grateful the tone is changing. And I am grateful that you are challenging Rand's theory as hard as you are doing. Your post requires a well thought-out response, so I will only mention a few things for now.

You imply very clearly that "human genome" somehow contradicts "rational animal" or that "rational animal" excludes arriving at "human genome" as a definition.

That supposition is false, but it is a type of supposition that I see people make all the time about Rand's theory of concepts. There are two kinds of definition for her, philosophical and scientific. People who arrive at the supposition you are making never understand this difference. And I have even seen some, when they finally did understand, close their eyes to it and keep on criticizing Rand according to the same error they recognized.

In short, there is no way on earth a person without highly specialized instruments or highly specialized knowledge can even arrive at the idea of genome (a scientific definition), much less state what it is. Should a person or civilization bumble along in life without a definition of human being until such time as the human genome is discovered and mapped? That is silly to even postulate.

Going from the other end, I have not studied the genome, but I seriously doubt that manufacturing a normal human being in a test-tube from a genome (if and when such were possible) would exclude either "rational" or "animal" (rational animal being the philosophical definition). I would be flabbergasted to see a rubber rabbit come out of that test-tube.

Actually, one type of definition complements the other, but the difference between the philosophical and scientific need to be understood and/or accepted in order to understand that point.

I have several things of this nature to comment on, but I will take some time with my answer.

You are right about Popper saying that a name is a loose or vague term as some kind of placeholder. I never intended to imply the contrary, if I so implied. I was looking at placeholder for what let's say and seeing similarities between this "what" and Rand's theory of concepts. I continue to see several similarities.

Also, in a formula kind of manner, Rand's definition formula follows Aristotle's, but this does not imply she accepted intuitive knowledge or special revelation as knowledge (the heart of the essentialism Popper was complaining about). On the contrary, Rand specifically rejected those, as did Popper.

On a related matter, just as a curiosity, I would be interested in knowing if there is any kind of math that does not involve units.

Much more later.

Happy Thanksgiving when if finally comes around.

Michael

[BaalChatzaf]

On a related matter, just as a curiosity, I would be interested in knowing if there is any kind of math that does not involve units.

Michael

How do you mean "units"? Do you mean something like the integer 1, such that any integer equals the sum of enough 1's? Do you mean a multiplicative identity (call it u) such that u*x = x for all x and where * is a binary operator in the system? Do you mean the cardinal number of a non-empty set S such that for all x, y in S x = y (this is a fancy way of saying S has exactly one member, i.e. its cardinal number is 1)? Do you mean a measure of some sort such that all values are denominated in that measure or unit? Such as pounds or inches. If by a unit you mean a discrete quantity there are many branch of mathematics where the values of the variable are not integral multiples of some unit value, for example the real number system.

Or the boolean algebra of sets. There are only two "special" sets in such an algebra. One is the empty set which is contained in all other sets and the other is the "universe set" which contains all other sets. Neither are units in the usual sense but they are identity elements with respect to set intersect and set union respectively. In a boolean algebra there are the singleton sets such that all sets in the algebra are subsets of the union of singleton sets. In this case the set algebra has many units and not a unique unit such as the integer 1.

Please say what you mean when you write or utter "unit".

Ba'al Chatzaf

[Alfonso Jones]

On a related matter, just as a curiosity, I would be interested in knowing if there is any kind of math that does not involve units.

Michael

How do you mean "units"? Do you mean something like the integer 1, such that any integer equals the sum of enough 1's? Do you mean a multiplicative identity (call it u) such that u*x = x for all x and where * is a binary operator in the system? Do you mean the cardinal number of a non-empty set S such that for all x, y in S x = y (this is a fancy way of saying S has exactly one member, i.e. its cardinal number is 1)? Do you mean a measure of some sort such that all values are denominated in that measure or unit? Such as pounds or inches. If by a unit you mean a discrete quantity there are many branch of mathematics where the values of the variable are not integral multiples of some unit value, for example the real number system.

Or the boolean algebra of sets. There are only two "special" sets in such an algebra. One is the empty set which is contained in all other sets and the other is the "universe set" which contains all other sets. Neither are units in the usual sense but they are identity elements with respect to set intersect and set union respectively. In a boolean algebra there are the singleton sets such that all sets in the algebra are subsets of the union of singleton sets. In this case the set algebra has many units and not a unique unit such as the integer 1.

Please say what you mean when you write or utter "unit".

Ba'al Chatzaf

If one is going to say that set theory (or point set topology, to pick another favorite example - I obtained some of my education in point set topology from folks in the R. L. Moore school of thought, if that is familiar to you, Ba'al) involves "units" then I'm not certain WHAT area of learning does NOT involve units. You are asking, in my opinion, the right question --- "Please say what you mean when you write or utter 'unit.'"

Alfonso

[Michael Stuart Kelly]

Alfonso,

All areas of learning involve units because they involve concepts and concepts are based on integrating units.

Bob,

"Unit" merely means a thing or symbol and another like it exists. I have seen that so far in everything you mentioned. Is there any math without this?

Michael

[Alfonso Jones]

Alfonso,

All areas of learning involve units because they involve concepts and concepts are based on integrating units.

Bob,

"Unit" merely means a thing or symbol and another like it exists. I have seen that so far in everything you mentioned. Is there any math without this?

Michael

Exactly, Michael. So, I wonder what you meant when you asked:

"On a related matter, just as a curiosity, I would be interested in knowing if there is any kind of math that does not involve units."

Would this mean, in the light of what you say in the post above, "I would be interested in knowing if there is any kind of math that does not involve any area of learning?"

Am I missing something here?

Alfonso

[Michael Stuart Kelly]

Alfonso,

My next question would be if there is any kind of unit manipulation that does not involve measurement of some sort.

Michael

[Alfonso Jones]

Alfonso,

My next question would be if there is any kind of unit manipulation that does not involve measurement of some sort.

Michael

I don't know if we're connecting here. My point is that you asked a question about if there was any field of math which does not involve "units." I don't know how that question is meaningful, in the sense that ANY FIELD OF LEARNING seems to involve units. Have I misunderstood you, or were you really just asking the question as in my paraphrase in my previous post?

Alfonso

[Michael Stuart Kelly]

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

[BaalChatzaf]

Alfonso,

All areas of learning involve units because they involve concepts and concepts are based on integrating units.

Bob,

"Unit" merely means a thing or symbol and another like it exists. I have seen that so far in everything you mentioned. Is there any math without this?

Michael

Given that meaning of the term anything that can be spoken, written or read involves linguistic units. This is true in -any- field, not particularly mathematics. I was asking about units in a mathematical context. You use the word differently from the way I do. Making chocolate chip cookies requires units too.

Ba'al Chatzaf

[Michael Stuart Kelly]

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

[merjet]

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.

"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.).

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

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

[Daniel Barnes]

Merlin:

In any case it's clear to me that much of concept formation does not require measurement omission.

Yes. If most concepts are "abstractions from abstractions" what are you supposed to be "measuring" at that point anyway?

[Michael Stuart Kelly]

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

Merlin,

Does non-metric topology use any units?

Michael