MonoRealism Philosophy Site

Immaculate Conceptions

Part C: Defining

Size Doesn't Matter

Concepts combine things in reality which are different. Even electrons vary in their speed, spin etc. Implicit in this is the knowledge that the things to which our concepts apply have many qualities which vary from one to the other, often including the degree of their defining characteristic(s). Thus, implicit in the nature of concepts is the recognition that each referent of a concept differs quantitatively from the others. That is, implicit in grouping things into concepts is the recognition that those things have various qualities in some quantity, but we ignore the actual quantities (except in so far as we define a range of possible values). For example, all men have some height, but it can be anything from around 4 to 7-odd feet.

This idea of measurement omission is a central part of the Objectivist theory of concepts (see especially, Ayn Rand's Introduction to Objectivist Epistemology, from which the quotes in this section are taken). Rand defined concepts as "a mental integration of two or more units possessing the same distinguishing characteristic(s), with their particular measurements omitted." This identifies how we can unite different things by their essential similarities, even if those essentials – and their other qualities – are not quantitatively identical. It is not that the measurements don't exist: "The principle is: the relevant measurements must exist in some quantity, but may exist in any quantity". Rand intriguingly compared this to algebraic variables, which similarly have some value which could be "anything".

Rand further expanded on the relationship of measurements and concepts:

Observe the multiple role of measurements in the process of concept-formation, in both of its two essential parts: differentiation and integration. Concepts cannot be formed at random. All concepts are formed by first differentiating two or more existents from other existents. All conceptual differentiations are made in terms of commensurable characteristics (i.e., characteristics possessing a common unit of measurement). No concept could be formed, for instance, by attempting to distinguish long objects from green objects. Incommensurable characteristics cannot be integrated into one unit.

Tables, for instance, are first differentiated from chairs, beds and other objects by means of the characteristic of shape, which is an attribute possessed by all the objects involved. Then, their particular kind of shape is set as the distinguishing characteristic of tables – i.e., a certain category of geometrical measurements of shape is specified. Then, within that category, the particular measurements of individual table-shapes are omitted.

... When, in the process of concept-formation, man observes that shape is a commensurable characteristic of certain objects, he does not have to measure all the shapes involved nor even to know how to measure them; he merely has to observe the element of similarity.

Similarity is grasped perceptually; in observing it, man is not and does not have to be aware of the fact that it involves a matter of measurement. It is the task of philosophy and of science to identify that fact.

Note again the fundamental link between senses and reason: we perceive via our senses, and understand via our reason. We form concepts based on perceived reality: and the perceived similarities must be validated by reason. Our knowledge cannot proceed from either mindless perception or rationalistic ponderings divorced from perception: only the mind applied to perception is the path to truth.

The importance of Rand's theory of concepts is its profound and original break with the standard errors of mysticism, skepticism and subjectivism:

None of [the traditional theories of concepts] regards concepts as objective, i.e., as neither revealed nor invented, but as produced by man's consciousness in accordance with the facts of reality, as mental integrations of factual data computed by man – as the products of a cognitive method of classification whose processes must be performed by man, but whose content is dictated by reality.

This is the key to a valid epistemology (theory of knowledge). The duality of reality and consciousness is not a flaw or an impediment, but merely determines a method of cognition – a method which is both valid and necessary, because it derives from the nature of that duality. We are conscious beings living in reality, and our knowledge can only proceed from the application of the former to the latter. Objectivity as the result of the application of consciousness (via reason) to reality (via senses) is the fundamental key to how we know, and thus the only proper basis of epistemology.

The Word

Earlier I mentioned that we identify concepts using words. This deserves more detailed treatment.

A word is a label for a concept. As such words serve a dual purpose. Primarily, they are how we use concepts in the privacy of our own minds. When I am thinking conceptually, I use words. Secondarily, they are how we communicate conceptual knowledge. That is what you are reading now.

(Imagery has its own purposes, for example in creative invention or to illustrate complex relationships and networks – where the linear nature of words is a limitation. However, even then any explanation and validation relies on words. For example, one draws a diagram – and explains it by pointing to and describing its parts: with words.)

Because words are labels for concepts, they are not arbitrary. They have the same bearing on reality as the concepts they label. This is another area where subjectivist philosophers have run aground – oddly, communicating their nonsense by means of words, which proves my point quite adequately. Of course the actual sound of a word or its shape on paper are usually "arbitrary" in the sense that they have no necessary link with what they describe. But while the link between the concept and its word is arbitrary in that sense, and agreed upon socially for the sake of communication, the meaning of words is not arbitrary, but grounded in reality.

The link between a word – a sequence of sounds – and a concept – the reality it labels – is its definition. If you think about the hierarchy of concepts, it is clear that there are two complementary types of definition.

First is its "top-down" deductive definition, which places it in the proper context of knowledge. This is its "genus and species" definition, which names the next higher concept (its "genus") and identifies what distinguishes it from the other concepts or things in its genus. The classic example is the definition of "man" as a "rational animal": which notes that we are an animal – with all that implies – while identifying the quality which most fundamentally and causally distinguishes us from other animals – our power of reason.

Second is its "bottom-up" ostensive ("pointing out") definition, which reflects the inductive process through which concepts are originally formed. Thus to define "star", one needs merely point at the stars in the sky; to define "dog", at members of that species.

It is clear that all valid deductive definitions ultimately must rest on ostensive definitions, because all valid concepts are grounded in observable reality. While this is plainly true of visible things such as dogs, it is also true of invisible entities such as electrons, whose existence is inferred more indirectly – but still inferred from observable reality.

A Defining Moment

The nature of valid definitions derives from that of valid concepts.

Why, for example, is "a rational animal" a good definition of "man", whereas "a farming animal" isn't? Man is the only animal who farms, after all. The answer is that a correctly formed concept identifies essential or fundamental distinguishing traits, and therefore so must the definition of the concept's word. Yes, man is the only animal who farms – but that is because he is the only animal which is rational, rationality being a precondition for farming. Indeed, rationality is the precondition for everything concrete which we have and animals don't: things such as complex language, advanced tool-making, road-building and writing.

Note however that there may be more than one valid definition, depending on the context in which you are working. Defining man as a rational animal is correct philosophically, but is of little use to a palaeontologist studying our fossil forebears. The palaeontologist is forced to deal with a limited part of a human being, and so to identify what are and are not human remains, must choose a definition based on what is available. Usually this is related to rationality, in fact: things related to brain size and function, or bipedalism (which in man is closely linked to the emergence of intelligence). On the other hand, a comparative zoologist might consider man to be "an intelligent ape", "animal" being too broad a genus for his purposes.

However, such specialist or contextual definitions merely complement the primary definition. Man is a rational animal and even a palaeontologist needs to know that – when dealing with other people as people, as opposed to dealing with old bones.