How to Define a Concept

Conceptual analysis is the philosophical study of concepts. It can be approached in a variety of ways, but one common strategy is to try to formulate a theoretical definition that clarifies the concept and improves our understanding. In order to do this, of course, we need to know how to construct useful definitions. There are at least three ways to define a concept:

  1. Defining with synonyms
    Perhaps the easiest and most obvious way to define a word is to identify another word or phrase with the same meaning (or a similar meaning). Defining with synonyms isn’t an effective approach to conceptual analysis, ordinarily, but it does have other important uses in philosophy. Lexical definitions are often specified in this way, and stipulative definitions are sometimes introduced with synonyms as well, e.g. when a new term is defined as shorthand for a long or cumbersome phrase. Synonyms can also serve as useful precising definitions. For example, some people use the word ‘faith’ to mean belief without evidence, while others use the word to mean evidence-based trust.In an appendix to my other e-book, Faithful Science: A Christian’s Guide to the Study of Creation, I argue that the word ‘faith’ in most biblical contexts is closer in meaning to ‘trust’ than it is to ‘belief.’
  2. Defining with genus and differentia
    The ancient Greek philosopher Aristotle developed an especially versatile way of defining concepts. His approach was first to specify a genus (general category) to which the concept belongs, then identify some differentia—properties or features that distinguish the concept from other members of the genus. The method of definition by genus and differentia can be used for any of the purposes mentioned on the previous page: it can be used to construct lexical, precising, stipulative, or theoretical definitions. The method has been employed in practically every field of academic study, from the humanities to the sciences and even mathematics. For example, a square can be defined as a polygon with four equal sides and four right angles. The differentia of having four equal sides and four right angles distinguish squares from all other shapes in the genus of polygons.
  3. Defining with necessary and sufficient conditions
    A third way of defining concepts is to identify a set of necessary and sufficient conditions, as will be explained below. This type of definition usually is harder to construct than a definition with synonyms or with genus and differentia, yet it is often more illuminating than the other methods, producing a deeper understanding of the concept thus defined. For this reason, attempting to identify necessary and sufficient conditions is arguably the most effective approach to conceptual analysis.

    4. Necessary and Sufficient Conditions

    Necessary conditions are conditions that must be met in order for something to be the case. For example, the presence of clouds is a necessary condition for rain to occur: there must be clouds in order for it to rain. Similarly, truth and belief are necessary conditions for knowledge—conditions that are required in order to have knowledge. In order to know that it is raining, you must believe that it is raining and your belief must be true. You can’t know something that is false, nor can you know a truth that you don’t believe.

    Sufficient conditions are conditions that are enough to ensure that something is the case. Rain is a sufficient condition for cloudiness, because the occurrence of rain is enough to guarantee that clouds are present. In contrast, the presence of clouds is not a sufficient condition for rain to occur, because it can be cloudy without raining. Likewise, truth and belief are not sufficient for knowledge, because you can believe a truth without really knowing it. If your belief that it will be sunny tomorrow is just a lucky guess, rather than a well-founded belief based on good evidence (such as a weather forecast), then you don’t really know it will be sunny even if your belief turns out to be true.

    To define a concept using necessary and sufficient conditions, we need to specify a set of individually necessary and jointly sufficient conditions in which the concept applies. A set of conditions is individually necessary when each condition in the set must be satisfied. For example, in order for something to be a square, it must satisfy each of the following conditions:

    Each of those conditions, individually, must be satisfied in order for something to be a square. If something fails to satisfy any one of those six conditions, then it’s not a square.

    On the other hand, none of those conditions is sufficient on its own. Merely having four sides, for example, isn’t enough to ensure that a something is a square. It could be any kind of quadrilateral—a trapezoid, perhaps. Similarly, having four sides of equal length isn’t enough. The shape could be a rhombus instead. When all six of the above conditions are taken together, however, they are sufficient. Anything that satisfies all of those conditions is definitely a square. No further conditions are needed. So, the above six conditions are jointly sufficient—that is, they constitute a sufficient condition when taken together.

    Each of the above six conditions is necessary for something to be square, and together they are sufficient. That set of individually necessary and jointly sufficient conditions provides a definition for the concept of a square: a square can be defined as anything that meets those six conditions. Individually necessary and jointly sufficient conditions can be expressed using the phrase “if and only if.” For example, we can say that something is a square if and only if it lies on a flat plane and has exactly four straight sides of equal length that form a closed path and meet at right angles. The phrase if and only if is used frequently in philosophical writing, especially when defining concepts, and is often abbreviated iff.

    Philosophers often try to define foundational concepts—such as knowledge—in a similar way, by identifying a set of individually necessary and jointly sufficient conditions. Even when such attempts fail, their failure may lead to new insights, as we’ll see on the next page.