Ch. 2 "Concept-Formation" - The theory of how human babies acquire concepts

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Chapter 2 Study Questions

• From reading the entire chapter "Concept-Formation," how would you improve on Ayn Rand's generalized definition on page 10 for your own understanding of what a concept is?
• On minor issues about the text,

                - Is "isolation" the same as "differentiation"?10b, 5b, 13d)
                - Is "isolation" the same as "abstraction"? (10b-c)
                - What are the two examples given at 10c examples of?
                - Is "identical" the same as "the same"? (2b, 17c)
                - What does it mean for a concept to be abstract? (1c, 18b-c)
                - What does it mean for a concept to be universal?(1c, 17d-18a)
                - Is "meaning" and "reference" the same with regard to concepts? With regard to words?
                - How are attributes to be distinguished from qualities? From characteristics? (10b, 17b 264d)

• Using either of the two definitions given (10b or 13c), identify the genus and the differentia of the concept "concept."
• Illustrate Rand's theory of concept-formation on a near-verbal infant-child who is about to learn his first slew of concepts. Trace through (in adult words) the cognitive process he would go through mentally to form the following concepts: "shirt," "smooth," "rolling," and "under." How might his parents or babysitter help him to expedite the process in each case?
• Distinguish the following sorts of characteristics: commensurable characteristics, distinguishing characteristics, conceptual common denominator.
• Can a blind man from birth grasp the concept "blue"? Can a color-blind man grasp the concept "red"? (15a)
• What is the relationship between the principle of measurement-omission and the concept "similarity" in the context of concept-formation? (13c-14d)

[ThomTG]

My comments on two items:

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To follow up on a comment from Ed concerning Rand's statement on page 8:

Now what is the purpose of measurement? Observe that measurement consists of relating an easily perceivable unit to larger or smaller quantities, then to infinitely larger or infinitely smaller quantities, which are not directly perceivable to man. (The word "infinitely" is used here as a mathematical, not a metaphysical, term.) The purpose of measurement is to expand the range of man's consciousness, of his knowledge, beyond the perceptual level: beyond the direct power of his senses and the immediate concretes of any given moment.

Ed cited the measurement problem at the subatomic level as a limit to what knowledge man's range of consciousness can acquire by means of his measurements at that level.

My reply relies on Rand's three criteria of the standard of measurement from the previous page: "The requirements of a standard of measurement are: that it represent the appropriate attribute, that it be easily perceivable by man, and that, once chosen, it remain immutable and absolute whenever used."

I conclude from this that "the appropriate attribute" to measure velocity or to measure the location of atomic-level entities become an inappropriate standard to measure any such statistics at the subatomic level. The task of physicists is to discover new, more "appropriate attributes" to measure this level of reality. It is therefore erroneous to cite merely the inapplicability of measurement from existing standards of measurement as a limitation on man's range of consciousness to know all levels of the universe. Rather than discovering the means of measuring reality, the fallacy here is a form rewriting reality to suit man's means.

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This item has three subitems:

If there is still any doubt that a name is not and cannot be a concept, let me lay it to rest. "Pen421" names a concrete. "Pen421" qua name has but one "meaning," namely, referring to that concrete so named. The fact that the particular concrete is a pen is not part of the meaning of the name. Penness is not part of the meaning of "Pen421"; the former may be part of the meaning of "pen" but not of the latter. This is a matter of an intellectual division of labor.

"Pen421" simply names a concrete. It presents to the mind a something. That's it. But that is enough for this next development: "Pen421 is a pen." This statement asserts a fact about a concrete. For this statement to be meaningful, the subject has to refer to some concrete. Then it is the job of the predicate to signify meaning, in this case, the concept "pen"; and it is the job of the copula to connect the two to render a meaningful mental integration.

If "Pen421" were meaning-laden to include penness, there would be no need for a syntactic language ever to be developed. Just one word would convey all truths needed about the particular. Whether the thing is a pen, is metallic, angular, black-inked, and on, could all be evoked by the mere invocation of "Pen421."

So, human beings do need bot concepts and names for conceptual cognition. And each kind has its own proper role in cognition. Rand's parenthetical remark at the top of page 11 is highly significant.

As to the problem of "John Smith" being ambiguous, let us make clear first the underlying principle. Names name a single concrete. When a so-called name fails to name one thing unambiguously, it fails its role as a name. It becomes an invalid name, philosophically speaking. It is thus up to the namer/baptizer to rename it. And indeed, in normal, everyday contexts, people do this all the time. In a third-grade classroom where every child is called only by his first name, when and if there is a collision in names, for example, when there are two Samanthas, the teacher will name one as Samantha S., and the other as Samantha B. So, in the same way in the larger society, the ambiguous "John Smith" can still identify the particular individual, as Rich suggested, when it is added with a date and place of birth.

On another line of thought about names, Brion or maybe Rich suggested that there must be an implied concept in the meaning of a name in order to name a single concrete. I would identify this issue more as the issue of names versus descriptions. For example, isn't it the case that "the man holding a glass of water in the middle of the room" names the same individual named "John" who stands in the middle of the room holding a glass of water? So, isn't it equivalent to assert that "John is a professor" as to assert that "the man holding a glass of water in the middle of the room is a professor"? So, doesn't that mean that "John" as a name really means "the man holding..."? Here, I would only refer back that, as "Pen421" does not mean "pen," so "John is the man holding..." is a meaningful statement; but the two terms are not the same.

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[ThomTG]

Re: A Problem of Propositional Regimentation

Here is a question stemming from our last meeting regarding the discussion of the term "Superman" as naming that man from Krypton named Kal-El. My question is, how does one regiment in proper propositional form the statement to the effect that "Clark Kent is Superman"? How is one to interpret this statement such that it can become a unit of thought in a conceptual method of cognition?

It seems easy enough to regiment to standard form the sentence "Superman is Kryptonian." Equally easy is the task to transcribe "Clark Kent is a reporter." Even easier still, even if evidentially more difficult to verify, is the regimentation for the statement that "a Kryptonian is a reporter." Why is the latter easier? Because it takes the particular-affirmative form, while the first two need to take the singular-affirmative form. (For a tutorial in standard forms, see this site here.)

But what is the form that will accommodate the sentence "Clark Kent is Superman"? How is it to be regimented?

[ThomTG]

Re: Understanding as Contextual

In re-reading ITOE Ch. 2 today in preparation for studying Ch. 3, I find it fascinating that Ayn Rand repeats herself FOUR times in explaining the process of concept-formation, each time adding more richness to the description, building on what was said before, and relying on the reader's ability to raise himself from one level of understanding to the next.

The first time, she outlines the subprocesses and lays out the beginning and ending conditions. (ITOE 10-11b)

The second time, she illustrates the principle of measurement-omission, showing how similarity arises derivatively from quantitative differences in measurement, and showing the necessity--i.e., the nonoptionality--of having measurements in the process of abstraction. (ITOE 11b-13b)

On the third iteration, she identifies explicitly the commensurable characteristic as the basis from which a distinguishing characteristic is discovered to isolate the existents, showing from where is to be derived the unit of measurement, and grounding foundationally our ability to detect similarity perceptually (thus, avoiding the so-called bootstrap problem in cognition). (ITOE 13c-14c)

On the fourth iteration, she identifies that commensurable characteristic of the concept as the technical concept "CCD," what logicians also call "the principle of classification," mentioning it to prepare the context for future abstractions from existing abstractions, while highlighting the subtle concept of implicit measurement during abstraction with examples from babies and animals. (ITOE 14d-16b)

Thereafter, respecting the reader's context of understanding, she gave no less than seven varied examples on how the process works to form concepts of different aspects of reality. I am totally impressed by her concise thoroughness.

[ThomTG]

Re: A Problem of Propositional Regimentation
...
But what is the form that will accommodate the sentence "Clark Kent is Superman"? How is it to be regimented?

Since no one considered it, here is my answer--so as to tie up this loose end. My answer is, because the sentence as stated is elliptical, it cannot be regimented literally as is. The sentence needs to be reconstituted before either regimentation or transcription.

As stated currently, the sentence is impossible to regiment, because it fits into none of the Aristotelian forms. All truth-bearing sentences require a general term for a predicate. That is, the predicate term of a proposition must be a concept, not a name. And "Superman" is a name.

Yet the sentence is still grammatical and meaningful. The question then is, what is the meaning of this sentence?

It turns out that the "'is'" in the sentence is not the copula "is" of predication but that elliptical form of the relation "the same as"--or, synonymously, "equal to"--and in which case, the relation, being binary, takes two subjects terms. And "Clark Kent" and "Superman" qualify. It is not the names that are problematic but the verb that needs to be reconstituted explicitly.

So reconstituted, the original sentence becomes either "Clark Kent is the same as Superman," or, equivalently, "Superman is the same as Clark Kent." In these versions, the "'is'" is once again the "is" of predication, which predicates the "the same as" relationship to both singular terms. Thus interpreted, either version of the reformulated sentences can be regimented with the singular-affirmative propositional form.

For each new sentence, the simple subject regiments to become the subject term, and everything after the "'is'" regiments to become the relational predicate term. Though the resulting four terms are all different expressions, they doubly integrate to the same unit of thought corresponding to a fact of comic-book reality, namely, that Clark Kent and Superman are one and the same man.

From this example, one may draw a generalization. Not all "'is''s" are the same. In fact, so far as I can discern, there are three meanings of "'is'":

• "   the "is" of identity-also known as the "is" of predication
  (e.g., "Kal-El is a Kryptonian.")
• "   the "is" of existence-tautological, in every case
  (e.g., "Superman is"; "Existence is"; "Consciousness is"; "'A is A' is.")
• "   the "is" of equivalence-elliptical in transformational syntax
  (e.g., "Clark Kent is the Kryptonian.")

The way I list these here is not the same as Aristotle's predicables, but I think it covers the same range of what can be predicated.

[David M. Brown]

I'm not sure I fully understand the problem--I guess I have to review logic and the proper forms of premises--but presumably every attribute of a subject can be predicated in some proper form of a subject. The focus on the copula while perhaps not Clintonesque doesn't strike me as the key; we can always understand "is" on a common-sense basis. (I think there was something in text on Bertrand Russell that spoke of his solution to a comparable problem of unpacking a proposition to get it into the right form, though I don't remember where this discussion is off the top of my head.)

Anyway, how about this: The names by which persons are called are attributes (attributes that arise in a [social-psychological] context, i.e., that are not intrinsic to the person like height, but, still, attributes). Premise. There is a man is known by the name of Clark Kent. (The subject is a particular man, and we predicate called-by-name-Clark-Kent-itudinousness of him). Premise: The same man is known by the name of Superman when he is not wearing his glasses. Conclusion: There is a man known by the names of both Clark Kent and Superman (or: Clark Kent is Superman).

Perhaps because I'm not privy to the original discussion I'm not addressing the problem that was raised?

[David M. Brown]

Re the question raised by Ed about subatomic measurement, if it is a fact that we cannot take a measurement within a particular range (because the perturbing act of measuring, or the impossiblity of measuring position and momentum with the same degree of precision simultaneously), how can this be solved by the positing of a new "appropriate attribute"? I assume the reference here is to the uncertainty principle (which I take it is only an epistemological issue for this group, not a metaphysical one). We do measure certain things on a subatomic scale unproblematically (that is, once the tough experimental investigation has been accomplished), in terms of billionths of a meter or the like.

The fact that we can only take measurements within a particular range or within particular limits is true on the macro level also. We know that something is a foot long, but only under special circumstances do we trouble to find out and are able to find out that it is 1.000002 feet long with reference to whatever glass-cased slab of metal serves as the standard of what a foot is (and we usually have the luxury of the item's standing still with reference to us as we apply the ruler). No matter what the context is, there is a certain degree of precision of measurement beyond which we cannot go, even in principle (if that principle has to do not with the ability to keep subdividing mathematically but with actual constraints on investigating physical reality).

If we definitely cannot pin down where and when an electron is within the particular range that is exluded by observation-related perturbation, does it matter, given all the measurements and other information we have about subatomic matter (and as long as we're not supposing that inability to measure a quantum system in certain respects must mean, a la the Copenhagan interpretation, "that a quantum system simply does not possess a definite value for its position and momentum at the same time")? When the aliens from Alpha Centauri invade earth, is it the hitherto elusive data about locus and momentum of particular pivotal electrons going to be what will enable us to disable from afar the aliens' gigantic matter disintegrator?

What we can't measure, we can't measure--a constraint not dissolved by positing hitherto undiscovered "appropriate attributes." We can measure location-plus-momentum-of-particle-within-a-certain-range. We can't measure location-plus-momentum-of-particle-simultaneously-with-equal-precision. Or so the physicists say. I can barely measure a room.

[ThomTG]

I agree that every measurable attribute of a subject can be predicated of that subject. But the concrete, measured attribute itself cannot be predicated of any subject, which is the issue here.

In a sentence, what may stand in the subject, and what in the predicate? Aristotelian logic answers: primary and secondary things in the subject, and only secondary things in the predicate. Translated into modern terms, it's both concrete existents and abstract concepts that may be in the subject term, but it's only abstract concepts that may be in the predicate term.

Now, if we take Ayn Rand's classification of visual-auditory symbols as true for now, then we have "proper name" and "word". (ITOE 10d) Names denote concrete existents (including fictional ones), and words denote abstract concepts. Thus, in logic, names cannot be in the predicate term of any sentence expressing a proposition. The "is" of predication forbids it.

Now while I agree with you, David, that names can be considered as attributes in social-psychological context, as in a name-rank-serial-number attribute in a data-processing entry, we cannot escape the function of names, namely, to bid us to identify the existent. Even when you say, "The man wearing glasses is Clark"; the actual subject is "Clark" and is the specifier of a particular existent in the class of men wearing glasses.

So when someone says "Clark Kent is Superman," we have a language problem. Which or where is the predicate?

This is where I think mathematics as the science of measurement has helped 20th century logicians to identify certain implicit quantities in measuring propositions. Since Aristotle's time, we have known how to assert truths about most things: entities, attributes, actions, but not relationships--until recently, 1967. It's truly an egg of Columbus that a relationship presupposes the existence of two other existents; thus, in asserting a thing as being in an abstract relation, we are implicitly asserting at least another thing in a relationship. The solution to asserting truths about relationships--a solution Aristotle did not discover but only hinted at obliquely--is to acknowledge multiple subject terms in a single assertion about which a relationship is predicated.

So in the above sentence, "Clark Kent is Superman," the "is" is not the "is" of predication but is an elliptical form standing in for the relation "the same as," a relation that presupposes two existents.

While a proper name is not the same as an abstract relationship, you were on the right track though. You supplemented a name and turned it into a relationship. "To be called by" or "to be known by" is a relationship in equal relational quantity to "to be married to" and to "the same as." Each relation takes two names to complete the assertion.

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I agree that every measurement of some attribute by some means has a range of precision. This fact about a known attribute does not change with the discovery or the positing of a new "appropriate attribute" of some entity, subatomic or otherwise. My original comment to Ed is meant to refute the idea that any limit on precision is a limit to man's range of knowledge at the subatomic level.

How do I interpret "appropriate attribute" to mean? Everyday objects have a color, one of red, green, purple, and so on. Color is an attribute appropriate for physical, macroscopic objects, but it becomes a category mistake as an attribute of temporal objects (black Fridays notwithstanding) or subatomic objects. Not being able to measure the color of a neutron does not limit our range of knowledge of neutrons. Neutrons can be known in a new way with attributes appropriate to this subatomic level; for example, the rate of decay from neutron to proton, β− decay, or the likelihood of a nuclear transmutation, can be measured as an appropriate attribute. Of course this new measure also has a range of precision by the current methods, but its limitation does not preclude our knowing more in the future about neutrons and protons when physicists discover new attributes suitable for measurement.

I agree, therefore, that even if we can't measure location-plus-momentum-of-particle-simultaneously-with-equal-precision at the subatomic level, it says nothing about our power to whip out a matter decayfetor to zap the space invaders' disintegrators.