A definition is not the meaning of a word, but a way to convey it.
In short: We often mistake definitions for the essence of things, but they are merely tools for communication. Whether you are pointing at a rabbit or calculating the properties of a triangle, definitions function as semantic bridges. Understanding their structure—from genus to differentia—reveals how we organize our entire conceptual world.
At its core, a definition links a term—the definiendum—to a phrase or action that carries its meaning, known as the definiens. These are not the meanings themselves, but vehicles for them. Definitions generally fall into two camps: intensional, which define by specifying necessary conditions for membership in a set, and extensional, which attempt to list the members of that set. For instance, defining a prime minister by their role within a cabinet is intensional, while listing every past and present prime minister is extensional.
Classical philosophy, rooted in Aristotle, long sought to capture the 'essential nature' of things through definitions. This led to the distinction between nominal definitions, which explain what a word means, and real definitions, which claim to express the underlying nature of an object. However, modern analytic philosophy has largely moved away from this pursuit of essence. Thinkers like Russell dismissed the very concept of essence as muddled, while others, such as Kripke, have re-examined essentialism through the lens of modal logic and possible worlds.
In formal fields like mathematics, definitions serve a different purpose: they do not describe existing concepts but construct them. A mathematical definition provides a precise, unambiguous condition that qualifies what a term is and is not. These can be stipulative—temporary definitions meant to guide a specific discussion—or descriptive, which must align with general usage. Some definitions, as noted by C.L. Stevenson, are even persuasive or coercive, designed to shift beliefs or legal duties rather than simply clarify language.
The complexity of language often introduces ambiguity. Homonyms share spelling and pronunciation but have unrelated origins, while polysemes share a common origin despite having multiple, related senses. Whether we are using ostensive definitions—pointing to an example—or genus-differentia structures to narrow down categories, we are constantly navigating a system where the same word can hold vastly different meanings depending on the context and the field of study.
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- Summary by Intellect · source: Definition
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