IOE, Chapter Five
Definitions
by Bryan Register
Date: 10 Apr 1995
Forum: Moderated Discussion of Objectivist Philosophy
Copyright: Bryan Register
'A definition is a statement that identifies the nature of the units subsumed under a concept.'
Upon re-reading chapter five of ITOE, I found it to have a few pages of substantive work at the beginning, followed by several pages of wandering criticism and discussion of a number of faintly related issues. I plan to integrate the relatively disconnected bits as well as I can with the main themes and ignore any material which I can't connect with the essence of the chapter, and end up with a problem and a couple of questions that I think may pose challenges to Rand's scheme here.
For Rand, definitions serve to differentiate different concepts by identifying the essential characteristics of given concepts. Some concepts, axiomatic and sensual, are undefinable in terms of words. To define existence or red, one points at an existent or some red. But for all more abstract concepts, definitions are possible though not always necessary. It may be unnecessary to define very simple concepts like table, because one can point easily enough at a table and one knows what one means when one says 'table', so a definition probably will serve no cognitive purpose. All this matter of defining something by direct reference to reality is called ostensive definition.
What is the purpose of definitions in those concepts that do require or at least allow for them? Definitions consist of words, and words, as we know, refer us to concepts. So the definition of a concept is a reference to other concepts. Ultimately, our definitions will always point back to the percepts the integration of which are the concepts. This allows us to have the full structure of our conceptual system at hand, and know the connections of this system to reality. This would seem to be where deductive logic comes from: our concepts subsume one another and refer to each other allowing us to form syllogisms and other logical statements.
How then are valid definitions formed? A definition consists of a genus and a differentia, as Aristotle stated. (These next few paragraphs of ITOE are very unclear to me, so this is one of the bits that are more likely to be criticized). The genus is a concept from which the concept in question was differentiated. The differentia is the line along which the concept in question was differentiated; it seems to me that the differentia states the CCD of the concept.
For example, life is a process of self-sustaining and self-generating action. Animal is a kind of life which employs locomotion. Man is a rational animal. The genus here of animal is 'life', the differentia is 'kind which employs locomotion.' The genus of man is animal, the differentia is rationality. (This example poses one of the questions with which I intend to end the discussion.)
I don't know how well the interpretation I just gave jives with Rand's second paragraph here: 'The distinguishing characteristic(s) of the units becomes the differentia of the concept's definition; the existents possessing a 'Conceptual Common Denominator' become the genus.'
However, I think my interpretation is definitely right given the next paragraph: 'Thus a definition complies with the two essential functions of consciousness: differentiation and integration. The differentia isolates the units of a concept from all other existents; the genus indicates their connection to a wider group of existents.'
(Both paragraphs on page 41, these two and the paragraph before seem to comprise the discussion of the form of definitions. The first and last of these are very clear, but the middle one doesn't make much sense to me. Do not all the existents possessing a CCD become the whole concept? and is not the distinguishing characteristic the CCD? Or am I hopelessly confused on the nature of the CCD?)
A definition is not a list. The point being made on page 42 which leads into the discussion of valid definitions would, I think, be made stronger by pointing out the consequences of the crow again. A definition can be only so long before we can no longer hold it in mind at once. Thus a list will not serve. So there must be a single (or very few) characteristic taken out of the mass of qualities of the existents referred to by the concept; a DEFINING characteristic. However, in order to define the CONCEPT, the definition must imply all the rest of the qualities of the existents subsumed by the concept. This characteristic (or very small group thereof) is the ESSENTIAL characteristic of the many existents.
Later in the chapter, Rand contrasts her view with that of Plato and Aristotle; this seem the most reasonable place to bring that in. For Plato, the essential characteristic of an entity was (this is very rough) the fact that it is an instance of a form -- its essence was that form, with the form being transcendent and immaterial. For Aristotle, all entities in a class are united by an essence which is non-transcendent, but still inherent in the entity. For Rand, all entities in a class are united by an essence which is a product of the human mode of understanding. This is her claim to objectivity, rather than intrinsicism (usually known -- by everyone other than Rand, so far as I can see -- as essentialism), that she bears in mind both the context of the observer and the independent reality which he observes. But I get ahead of myself.
Because the essence of a group of entities is that fact about them which implies all facts about them, definitions are open-ended and open to revision -- but not to 'correction', unless an error has been made. (By correction, I mean here a change which contradicts an earlier definition. It is likely that there is a better word for this.) One can form a definition based on a very limited amount of information which will be valid, but once one has more information one must revise one's definition.
For instance, take the atom. Once upon a time, an atom could be reasonably defined as 'the smallest instance of an element which retains the qualities of that element.' Then it was discovered that there were nuclei in atoms and variously charged particles. So the definition might become 'a particle which possesses a dense, positively charged center surrounded by negative charges.' Then it was discovered that electrons have specific orbits, so the definition might have 'which circle in specific orbits about the nucleus' added to the end.
Now, none of those definitions were false. A modern physicist thinking in terms of an atom as defined by being the smallest instance of an element which retains the qualities of that element would not be wrong, per se. But he would be horribly lacking in ability to connect 'atom' to other concepts; would not know the true defining essence of atoms at his level of knowledge.
(If I may put in an aside: I think the problem Kuhn raised in The Structure of Scientific Revolutions might be impacted by Rand's open-ended concepts. Kuhn asserts that scientific revolutions are non-rational gestalt switches between different conceptual orderings, but if concepts aren't the set-in-stone dogma which Kuhn viewed them as, then no such non-rational switches are necessary.)
So the essence of a group of entities is that fact about them which implies all other qualities which they possess. This essence is epistemological, being formed not only by the means and limitations (finite carrying capacity, the crow again) of human cognition but also by the limits of an individual's context of knowledge -- and, equally or more importantly, by the inherent metaphysical similarities of the entities in question.
Rand maintains that concepts can be true and false. It is at this point (p 48) that I think what may be a very serious problem arises. 'Truth is the product of the recognition... of the facts of reality.... He organizes concepts into propositions -- and the truth or falsehood of his propositions rests, not only on their relation to the facts he asserts but also on the truth or falsehood of the definitions of the concepts he uses to assert them, which rests on the truth or falsity of his designations of essential characteristics. 'Every concept stands for a number of propositions.... A definition is the condensation of a vast body of observations -- and stands or falls with the truth of these observations.'
Truth is the correspondence of a proposition to reality; a proposition is true of it accurately describes reality, false if inaccurate. A definition can be true or false only if it is a proposition, and Rand claims that it is. But how does this work? A definition states something like 'man is a rational animal.' This proposition is true if man is indeed the rational animal. But how could one check the truth of this proposition? By pointing at men and claiming that they have all kinds of characteristics of which the essential is rationality. But since 'man' does not exist save as that which is defined as the rational animal, one can't refer to the entities and actually hit men with one's reference except by going by the definition which is exactly what one is checking in the first place.
My point here is also illustrated, I think, by the actual way we form concepts. We do not start with 'man' and figure out what defines him. We start with men and figure out that they need to be mentally integrated and how. We start, then, with rational animals, proceed to 'rational animal', and finish off with 'man.' (Or am I hopelessly confused? I do not rule out the possibility.) With the process running this way, the 'propositions' of definitions will always be vacuously true.
I think this can be solved by backing down from the claim that definitions are propositions that can be true and false. Definitions are something other than propositions (what? definitions, I think, and nothing else) and cannot be true or false. They can be valid or invalid, with validity being the quality of maximizing unit-economy by being that definition which implies the most other qualities of the entity-grouping in question, and invalidity being an identification of essential characteristics which does not in the least unify the entities in question. (Note my appeal to the crow again.) This does the same job Rand wants her truth/falsity to do (beat up on defenseless nominalists) without involving her in the rather painful circles of vacuous truth I think I showed above.
I will skip the discussion of essentialists dropping consciousness and subjectivists dropping existence, as we have all heard it before.
So just a couple more questions are these:
1. Justice is classically defined as 'giving each man his due.' No genus, no species that I can see. Is justice being poorly defined here, or is this an exception, or is there a genus and species that I'm not seeing?
2. In an earlier example, I derived man from animal from life. Like justice, life seemed to have no genus and species. It also doesn't seem to be something which can be traced back to a larger-scale concept (explaining the lack of genus.) Same question as for justice, but with the additional: is life a primitive concept, despite being defined? Do such things exist? (I would have asked for justice, but I think it's pretty clearly not primitive.)
Bryan Register
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