What about all those concepts with only one member in the class?

I posted the following comments in two parts at a blog devoted to criticizing Ayn Rand's philosophy of Objectivism. Here I am re-posting what I said with a few edits.

Some of what I say below may not make sense unless you know something about Rand's theory of concepts, which as she initially presented it in a short treatise is highly compact. The concept theory is probably her most technical work in philosophy. However, the Second Expanded Edition of Rand's Introduction to Objectivist Epistemology includes a lengthy edited transcript of a workshop about the theory in which she answers a wide range of detailed questions about her explanation and specific formulations. That edition is the place to start if you have an interest in this subject. Although Rand characterizes a concept in several overlapping ways in the treatise, her considered definition in light of her theory is "a mental integration of two or more units possessing the same distinguishing characteristic(s), with their particular measurements omitted."

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Neil writes: "This entire approach (two instances plus perhaps a 'foil') [as inherent in the process of valid concept formation] is highly unlikely to be correct. Every once in a while I read an article about how someone finds a new mammal in Borneo or wherever. Apparently there is no problem 'conceptualizing' it even though only one animal has been found."

Describing an entity and forming a new concept of it are not the same thing. If I create a table with a unique doohicky-flange, and I intend never to make another such, I don't need to form a concept of a special subcategory of table in the tradition of end tables, coffee tables and dining room tables. But if I plan to mass-produce my new kind of table and sell it, I can call it a DH Table or whatever. Of course, I can imagine other DH Tables before I actually produce them. I don't need to have other units of a concept before me perceptually in order to have them in mind. If I did, all higher-order concepts that in order to be formed require more than what is right in front of my eyes (justice, government, planetary systems, historical eras) would have to be declared out of conceptual bounds from the get-go.

Neil does not elaborate his example. Is the single animal discovered in Borneo unique in the world, and regarded by the biologist who studies it as unique in the world? Is it merely a deformed instance of an already-known species? Or does the biologist believe that there is or has at some point been more than one of this previously unknown kind of animal? Does he believe that he is looking at a member of a species?

There is no point in forming a concept of a species of this animal unless there is cause to suppose that it is in fact a member of a species--i.e., one of a group of others like it. The biologist is then forming a concept based on his assumption that there are two or more animals like this. The fact that the existence of other members of the species is only assumed until the biologist can find more members or evidence of more members does not mean that conceptualizers need only one unit of a kind of thing to form a concept of that kind of thing. The concept would refer now to any units that one discovers in the future that are sufficiently like the already observed referent of the concept to also be included in the class the members of which are referred to by the concept.

To what extent the provisionally formed concept of the new species in Neil's example is satisfactory can only be determined when more members of the species are actually found. Moreover, the biologist's provisional concept can be as plausibly formed as it is to begin with only because the rest of the living world is not a blank to him. The biologist can suppose that whatever may be the traits of other members of the species, if the sole member thus far discovered is a normal member of the species, then the traits of the other members will vary only within certain definite limits. But why is the biologist able to make this assumption? He doesn't simply deduce the constraints in a cognitive vacuum, without ever having differentiated and integrated anything in the plant and animal kingdoms ever before. He relies on an extensive background knowledge. Yet the fact and utility of such background knowledge is simply neglected in Neil's example. "More than one" species of animal has already been found. Millions have been found. Millions currently flourish on the earth. And they typically consist of more than one member. When forming his concept of the new species with, so far, only one known member, the biologist can compare the single known member of the new species with what he knows of other species, especially the most closely related other species.

Let there be an alien race that knows nothing of plants and animals; the aliens are fed magically by manna, let's say. In any case, for whatever strange reasons the aliens have lived in splendid biological isolation. Let's also stipulate that they form concepts the way humans do. They have the same kind of consciousness that we do. What they lack is our knowledge and acquaintance with flora and fauna.

Let the aliens one day invent space flight and land on a planet where they discover a single blade of grass--that's it. All the rest is rocks and sand and sky and the two suns. Can our alien adventurers now form a concept of what kind of class this entity belongs to, without any further investigation and without bringing any knowledge that could have been gained only by prior familiarity with plants and animals? Can they form the concept without even a single other blade to which they can compare the blade they've found, let alone without a single other example of a plant to which they can compare it? How is the single blade similar to and how is it different from any other possible members of the species? Same length but different colors? Different colors but same length? Is it a part of something else? Does it have any form of consciousness? Is it normal to be stuck in the ground like that?

The alien discoverers of the single blade have lacked even a concept of species as a kind of organism. Human beings may have trouble distinguishing one species of warbler from another, but the aliens have had no concept of species at all. They've been differentiating themselves only from rocks and sun and rain, not from other organisms. They've never seen other organisms. Perhaps they can imaginatively project different versions of themselves. But none of their science fiction has been exploiting information about elephants, tigers, mosquitoes or cucumbers. The alien astronauts may infer that the blade is alive, for they do have another example of a living thing--themselves--to which they can see the blade is like in that respect. In the expectation of eventually finding other blade-things, they may form a concept of it that they define as "living thing stuck in ground." Since that's the only other kind of living thing they are aware of, the concept, despite its lack of precision, successfully distinguishes the blade-thing and any other blade-things they come across from everything else they know about so far.

If the spacefarers then discover other living things, organisms that are not only alive but markedly different from the blade-thing, the new organisms would probably only briefly if at all be subsumed under the concept that the aliens had formed with the hope of finding at least one other living thing not themselves. Suppose the aliens go around a ridge and see a frog and a flower and a mosquito, maybe even more than one of each. If the aliens expect to be referring to these organisms, they need more concepts. They need to distinguish the plants and animals not only from the aliens themselves but from each other. The aliens must certainly regard the frogs as similar to each other as well as different from the flowers, the mosquitoes and the blade-thing. The same is true for members of the other species that the aliens are discovering. Moreover, this discovery of species with more than one instance makes it more plausible that they will someday find another blade-thing; i.e., that there is a practical point to having a concept, and a word, for blade-things.

If you want to know whether differentiation and integration are fundamental and inescapable requirements of forming concepts and acquiring knowledge of the world, watch what your mind does as you form concepts and gain knowledge. Look first at the normal cases, not the borderline or unusual cases that can be explicated by reference only to the usual case of valid concept formation. When it is cognitively useful to group things together on the basis of their fundamental similarities, I need a concept that enables me to refer to units of that group. I don't need a concept to refer to a unique thing qua unique thing. I need a concept for designating possession. I need a concept for houses. I need a concept for numbers. I need a concept for streets. I don't need a concept for "my house on 101 Mulberry St.," however partial I may be to calling it The Mulhouse. If a biologist says he has discovered a new species even though he has only observed one example of the species, he expects that there are or have been other animals sufficiently like it to be properly considered a member of that new species. There is no need (except for purposes of imagination), and it would be cognitively counterproductive, to form the concept of a species if there evidently is no species, no group, no prospective units, plural.