You can start by explaining what it means for something to have a definition by reducing to the idea of a 'concept':

''

The classical theory of concepts, also referred to as the empiricist theory of concepts,[2] is the oldest theory about the structure of concepts (it can be traced back to Aristotle[3]), and was prominently held until the 1970s.[3] The classical theory of concepts says that concepts have a definitional structure.[1] Adequate definitions of the kind required by this theory usually take the form of a list of features. These features must have two important qualities to provide a comprehensive definition.[3] Features entailed by the definition of a concept must be both necessary and sufficient for membership in the class of things covered by a particular concept.[3] A feature is considered necessary if every member of the denoted class has that feature. A feature is considered sufficient if something has all the parts required by the definition.[3] For example, the classic example bachelor is said to be defined by unmarried and man.[1] An entity is a bachelor (by this definition) if and only if it is both unmarried and a man. To check whether something is a member of the class, you compare its qualities to the features in the definition.[2] Another key part of this theory is that it obeys the law of the excluded middle, which means that there are no partial members of a class, you are either in or out.[3]

The classical theory persisted for so long unquestioned because it seemed intuitively correct and has great explanatory power. It can explain how concepts would be acquired, how we use them to categorize and how we use the structure of a concept to determine its referent class.[1] In fact, for many years it was one of the major activities in philosophy - concept analysis.[1] Concept analysis is the act of trying to articulate the necessary and sufficient conditions for the membership in the referent class of a concept.[citation needed] Arguments against the classical theory

Given that most later theories of concepts were born out of the rejection of some or all of the classical theory,[4] it seems appropriate to give an account of what might be wrong with this theory. In the 20th century, philosophers such as Rosch and Wittgenstein argued against the classical theory. There are six primary arguments[4] summarized as follows:

It seems that there simply are no definitions - especially those based in sensory primitive concepts.[4]
It seems as though there can be cases where our ignorance or error about a class means that we either don’t know the definition of a concept, or have incorrect notions about what a definition of a particular concept might entail.[4]
Quine's argument against analyticity in Two Dogmas of Empiricism also holds as an argument against definitions.[4]
Some concepts have fuzzy membership. There are items for which it is vague whether or not they fall into (or out of) a particular referent class. This is not possible in the classical theory as everything has equal and full membership.[4]
Rosch found typicality effects which cannot be explained by the classical theory of concepts, these sparked the prototype theory.[4] See below.
Psychological experiments show no evidence for our using concepts as strict definitions.[4]

Prototype theory

Main article: Prototype theory

Prototype theory came out of problems with the classical view of conceptual structure.[1] Prototype theory says that concepts specify properties that members of a class tend to possess, rather than must possess.[4]Wittgenstein, Rosch, Mervis, Berlin, Anglin, and Posner are a few of the key proponents and creators of this theory.[4][5] Wittgenstein describes the relationship between members of a class as family resemblances. There are not necessarily any necessary conditions for membership, a dog can still be a dog with only three legs.[3] This view is particularly supported by psychological experimental evidence for prototypicality effects.[3] Participants willingly and consistently rate objects in categories like ‘vegetable’ or ‘furniture’ as more or less typical of that class.[3][5] It seems that our categories are fuzzy psychologically, and so this structure has explanatory power.[3] We can judge an item’s membership to the referent class of a concept by comparing it to the typical member - the most central member of the concept. If it is similar enough in the relevant ways, it will be cognitively admitted as a member of the relevant class of entities.[3] Rosch suggests that every category is represented by a central exemplar which embodies all or the maximum possible number of features of a given category.[3] Theory-theory

Theory-theory is a reaction to the previous two theories and develops them further.[3] This theory postulates that categorization by concepts is something like scientific theorizing.[1] Concepts are not learned in isolation, but rather are learned as a part of our experiences with the world around us.[3] In this sense, concepts’ structure relies on their relationships to other concepts as mandated by a particular mental theory about the state of the world.[4] How this is supposed to work is a little less clear than in the previous two theories, but is still a prominent and notable theory.[4] This is supposed to explain some of the issues of ignorance and error that come up in prototype and classical theories as concepts that are structured around each other seem to account for errors such as whale as a fish (this misconception came from an incorrect theory about what a whale is like, combining with our theory of what a fish is).[4] When we learn that a whale is not a fish, we are recognizing that whales don’t in fact fit the theory we had about what makes something a fish. In this sense, the Theory-Theory of concepts is responding to some of the issues of prototype theory and classic theory.[4]""