Oh, joy. Are we here to define ‘define’? That depends on what you mean… But no, not really. We’re here to look at some central types of definitions and see some ways in which they differ from each other. For every definition it is the case that they consist of a definiendum – that which is to be defined – and a definiens – that which is giving the meaning (or reference) of some expression or term. In this way, they are similar to explanations which also consist in analogous two parts. They come in different kinds, much like explanations, and we’ll now have a look at a few of them to have a more fine-grained understanding of their constituent parts.
Lexical definitions are definitions that, when accurate, reflect the common usage of a term or expression. That is to say, if we define ‘circle’ as something like ‘a two-dimensional figure with every point equidistant from an arbitrarily chosen and fixed center point’ we have provided a definition which can be either true or false. In this case it’s true. A lexical definition might, however, be false. This happens when a suggested definition does not reflect a term’s or expression’s common usage. Say, for instance, that we define ‘circle’ as ‘a two-dimensional figure which consists in three sides’. We’ve given the definiendum ‘circle’ the definiens of a triangle. This is plainly (or should that be ‘planely’?) false. Lexical definitions thus attempt to capture the common usage of a term, such as those collected in dictionaries and the like. They can, as such, be evaluated in terms of truth and falsehood.
Stipulative definitions, on the other hand, mainly prescribe a certain meaning onto a term or expression in a given context. They are not so much true or false as they are suitable or unsuitable. Say that someone wishes to define the term ‘large’ in the context of a specific natural museum’s mineral collection. This could mean samples having a volume of such-and-such a size, much larger than we would have as a standard for what constitutes a large sample in the department where they house replicas of different kinds of mice. A museum guide might then define ‘large’ as e.g. ‘a sample of a volume greater than one cubic meter’ and go on about describing the various minerals to the visitors. The suggested definition does not have to reflect common usage, but is rather a way of signaling how the term or expression is to be understood in the given context. They can be provided to alleviate issues of vagueness and ambiguities, but do not automatically do so. In this case, it might be a suitable definition. Using the supplied definiens in the context of the department where they house the replicas of different kinds of mice, however, might not be as suitable. Neither of the respective definitions in the given contexts is, however, true or false as such.
Ostensive definitions are definitions that are accomplished by pointing out some object or property and either give it a name, or use its already given name. Perhaps we could argue that the prototypes of the meter or kilogram were pointed to in this way at some point in the past, or at least that it is conceivable that we could say that a ‘meter’ is the length of this object to which I am now pointing. This is not an intensional definition that fixes a meaning of the definiendum, but an extensional one that makes use of the reference of some expression.
There are, of course, other kinds of definitions that could be listed here. Moreover, there are undoubtedly features of each that have not been captured in full. As such, this list could be viewed as incomprehensive. Hopefully, in the given context, this is an appropriate quality, however.
Definitions come in many different kinds. Some of them are lexical and so are intended to report common usage of terms and expressions. Stipulative definitions instead are intended to prescribe a usage of a term or expression in a given context. They are both intensional types of definition. That is to say, they provide a conceptual meaning in the definiens to the provided definiendum. Ostensive definitions are extensional and make use of the reference of an expression. They all function in various ways, but serve to elucidate the meanings of concepts and the things these concepts refer to.