To Define or Not to Define…

We use definitions in a wide range of human activities. Law, science and technology are areas in which definitions have prominent roles, but we also find them in almost every other context where we consider it important to understand each other correctly. When we define a concept (the definiendum), we construct a phrase (the definiens) with which it is equivalent or at least exchangeable. For a definition to be useful, the definiens must have some advantage over the definiendum, such as being easier to understand, analyse, operationalise or demonstrate. The most common form of a definiens is a set of individually necessary and jointly sufficient conditions. The prevalence of this form has a simple logical explanation: It would seem plausible that most definitions are based on a set of conditions that can be either true or false, and furthermore that the definiens is a well-formed propositional formula that can be constructed from these conditions with truth-functional operators. It then follows from the conjunctive normal form theorem that the definiens is equivalent with an expression that is the conjunction of one or more clauses, where each clause is a disjunction with at least one disjunct and each disjunct is either one of the conditions or the negation of one of the conditions. Each of the clauses will then be necessary for the definiendum to be true, and their conjunction will be sufficient for it to be true. Under the presuppositions just mentioned, we can assume that all definitions have this form. 1 It is commonly referred to as the ‘classical’ approach to definitions. Another way to express the equivalence between definiendum and definiens is that it should be impossible to formulate a statement that contradicts the definiendum but does not contradict the definiens, or the other way around. If such a statement can be constructed, then it constitutes counterexample and is taken to prove that the definition does not hold. It is common practice, in philosophy and elsewhere, to ‘consider a definition satisfactory if, after careful reflection, we can think of no possible examples in which either the defined word truly applies to something but the defining words do not, or the defining words truly apply to something but the defined word does not’ (Cornman et al. 1982, 18). Definitions are used for both descriptive and normative purposes. In linguistics, definitions are used descriptively to specify the practices of language users. In mathematics as well as the natural, social and behavioural sciences, definitions usually have the normative purpose of establishing and maintaining terminological practices that facilitate scholarly communication and cooperation. In philosophy, where definitional work is called ‘conceptual analysis’, it is often unclear whether a definition has a descriptive or a normative purpose. Presumably, most philosophers would agree with Robert Audi's characterisation of philosophical concept analysis as ‘an attempt to provide an illuminating set of necessary and sufficient conditions for the (correct) application of a concept’ (Audi 1983, 90), but they would not agree on whether the relevant criterion of correctness refers to actual usage in some group of users or to some ideal usage that differs from actual usage. For instance, philosophers discussing the definition of knowledge may differ in what they want to achieve with a ‘correct’ definition. They can strive to identify what people in general mean by that word, what philosophers mean by it, what we should mean by it according to some objective standard or what we should mean by it in order to optimise our terminology. The philosophical use of definitions is far from uncontroversial. The most famous internal criticism is Ludwig Wittgenstein's observation that a concept may ‘have no one thing in common in virtue of which we use the same word for all – but there are many different kinds of affinity between them’. Such a ‘family resemblance’, he claimed, represents ‘a concept with blurred edges’ and no sharp boundaries (Wittgenstein 1953/2009, 38–40). Another highly influential criticism of philosophical concept analysis is based on experimental psychology. Beginning in the 1970s, psychologists have conducted empirical studies of the nature of human concepts and categorisations. Their findings do not tally with the classical view of definitions (Rosch 1973; Rosch and Mervis 1975). Subjects consistently exhibit a ‘typicality effect’, that is, they perceive different items that fall under a concept as more or less typical of the concept. A robin is considered to be a more typical bird than an ostrich, and an apple a more typical fruit than a fig. Subjects were quicker to categorise a typical than a more peripheral member of a category, and their categorisation of the less typical members was less consistent and less confident than that of the more typical members. The early studies of typicality effects were mainly devoted to concepts referring to concrete objects, such as colours, animals and plants. However, they have been followed by studies showing similar effects for abstract concepts of the type that can occur in philosophical discussions, such as ‘work of art’, ‘science’, ‘crime’, ‘work’, ‘just decision’, ‘female’ and ‘male’ (Hampton 1981; Arcuri et al. 2001). [T]he assumptions which drive conceptual analysis are not empirically founded and clash with prevalent psychological theories of concept representation.[… T]he search for a simple, non-disjunctive definition of a given philosophical concept that accords with all of our intuitions and admits of no counterexamples is a hopeless enterprise – there simply is no such thing. (Ramsey 1992, 59 & 65) To account for the experimental results, Eleanor Rosch proposed an alternative model in which categories are characterised by ‘prototypes or prototypical instances that contain the attributes most representative of items inside and least representative of items outside the category’ (Rosch 1978, 30). She used the term ‘prototype’ for such representative items but also said that ‘to speak of a single entity that is the prototype is either a gross misunderstanding of the empirical data or a covert theory of mental representation’. A prototype could be ‘described as well by feature lists or structural descriptions as by templates’ (ibid., 40). Unfortunately, the terminology is unclear. Some still use the word ‘prototype’ for ‘the best example of a given category’ (Albertazzi 2003, 256). Others have found it impossible to conceive of a prototype as ‘a real individual’ and see it instead as ‘the result of a mental construction’ and thus as an entity that ‘may well never be actualized in reality as any real instance’ (Violi 2003, 107). Prototypes can then be defined as ‘features abstracted from category members’ (Jylkkä 2008, 24), as ‘a concept's abstract average of typical instances’ (Pölzler and Hannikainen 2022, 2) or as a representation of ‘weighted dimensions and features’ (Del Pinal 2016, 2900). Authors who use the term ‘prototype’ to denote features of category members often use the term ‘exemplar’ for a category member that typifies the concept (Lombrozo 2011; Divjak and Arppe 2013). Both in exemplar theories and prototype theories of meaning, the applicability of a concept comes in degrees. In exemplar theories, these are degrees of similarity to the exemplar(s). In prototype theories, they are degrees of conformity to the features included in the prototype. Attempts have been made to unify prototype and exemplar theory, treating them as the extreme ends in a scale of models with different degrees of abstraction (Divjak and Arppe 2013). A proposal has also been made to formalise prototype theory with the help of fuzzy sets (Osherson and Smith 1981). Empirical information about the structure of mental representations of concepts has usually not been taken to have any impact on definitional practices in science. For instance, the fact that experimental subjects consider some objects to be more typical fruits than other fruits, or more typical birds than other birds, has seemingly not led anyone to claim that biologists should replace their current binary concepts of fruits or birds by graded concepts of fruitness or birdness that comply with the typicality effects observed in these experiments. The reason for this is that definitional work in science (outside of psychology) is not undertaken in order to find out what types of concepts we currently have. Instead, its purpose is to construct terminologies that are as useful as possible for scientific work. For instance, we use definitions of key terms such as ‘species’, ‘substance’ and ‘climate’ that facilitate the formulation of informative generalisations. There are strong reasons why sharp definitions are preferred in science. They make it easier to compare different observations and they also facilitate scientific communication and cooperation. The fact that our everyday concept of a bird is inexact and seemingly best represented by prototypes or examplars is no reason why biologists should use the same concept. It should, however, be recognised that even for a concept that has a sharp classical definition, supplementary information about prototypes or examplars can be useful. A major reason for this is that prototypes and exemplars tend to exhibit cues that facilitate recognition and identification. We do not use the scientific definition of a ‘dog’ to determine if we should use that term about an animal we encounter. If an animal is sufficiently similar to the dogs we have met before, then we call it a dog, otherwise not. The dogs we have seen before serve as exemplars for our concept of a dog. Another example can be drawn from medical science. A physician often makes at least a preliminary diagnosis based on (proto)typical symptoms. Many infectious diseases can be recognised and diagnosed from symptoms, although the definition refers to a particular pathogenic agent (Amoretti et al. 2017). The characteristic symptoms of the disease serve as a prototype. One could expect the approach to definitions to be about the same in philosophy as in science. Just as scientists, philosophers need to develop and refine conceptual tools for research. These definitions may have another structure than the mental representations of our everyday concepts, but that is no reason not to use them. As noted by Matti Eklund, ‘when physicists study reality they do not hold on to the concepts of folk physics but use concepts better suited to their theoretical purposes. Why should things stand differently with what philosophers study?’ (Eklund 2014, 293). In actual fact, however, the prevalent approach to definitions in philosophy differs drastically from that in other academic disciplines. Conceptual analysis is commonly treated as a process of discovery rather than construction. Philosophical discussions about the definition of concepts such as justice or knowledge are not just aimed at constructing sharp and well-defined concepts that are suitable for philosophical work. Instead, much of these discussions are conducted under the (usually unstated) assumption that the task is to uncover the exact delimitation of a preexisting concept. The way to achieve this is to extract intuitions from human minds. If this is what philosophical definitions are about, then information about the actual structure of human concepts is most certainly relevant. This is the reason why psychological findings such as typicality effects are widely considered to be problematic for philosophical conceptual analysis. However, the ‘discovery’ approach to philosophical concepts that underlies this criticism is far from unproblematic. It is difficult to explain why suitable philosophical concepts should be preexisting and why they should in that case be retrievable by probing into our intuitions. It is therefore advisable to work under the assumption that, just like other researchers, we have to construct a terminology suited to our needs. Furthermore, since we need precise concepts, such constructions should preferably have the exactness that is obtainable with the classical approach that makes use of necessary and jointly sufficient conditions. It follows from this that if we have philosophical use for an everyday concept that cannot be defined in the classical way, then we should look for ways to modify the concept so that it can be defined in that way. This has long been recognised. Several prominent philosophers have argued that we may have to modify our concepts in order to make them definable in a precise way. Rudolf Carnap proposed a process of explication, which he described as ‘transforming a given more or less inexact concept into an exact one or, rather, in replacing the first by the second’ (Carnap 1962, 3. Cf.: Brun 2016; Justus 2012). Similarly, W. V. O. Quine maintained that the purpose of conceptual analysis should not be to ‘make clear and explicit what the users of the unclear expression had unconsciously in mind all along’. Instead, the purpose should be to ‘fix on the particular functions of the unclear expression that make it worth troubling about, and then devise a substitute, clear and couched in terms to our liking, that fills those functions’ (Quine 2014, 238). The term ‘revisionism’ has sometimes been used to denote the standpoint that the meaning of common terms may have to be adjusted in order to make them useful for philosophical purposes (Deutsch 2021). However, in order to create a workable philosophical terminology, it is not sufficient to modify existing non-philosophical concepts. Just as in other scholarly disciplines, we also have to create and denominate new concepts that have no representation in ordinary language. Quite a few such concepts have been constructed by philosophers, for example utilitarianism, supererogation, credence and supervenience. The construction of new concepts goes beyond what is usually meant by ‘explication’ and ‘revisionism’. The term ‘conceptual engineering’ is more appropriate since it covers both the repair of existing concepts and the construction of new ones (Blackburn 1999, 119; Cappelen 2018; Koch et al. 2023). In addition to our need for well-defined philosophical concepts, we also have good reasons to pay attention to everyday concepts that are not accessible to precise definitions. The most important reason for this is that we need to be connected with non-philosophical discussions of topics that we also discuss in philosophy. For instance, suppose that we conclude that the everyday concept expressed with the word ‘beauty’ has to be modified (perhaps explicated) in order to be useful in philosophical aesthetics. We will then still need to know what is commonly meant by the everyday concept so that we can compare it to the modified concept that we have found to be more useful in philosophy. There may also be some philosophical terms that it does no harm to use even if they lack precise definitions. ‘Marxist’ and ‘Kantian’ may be examples of this. As always, definitional efforts should be apportioned according to the need for precision. The author has nothing to report. Data sharing is not applicable to this article as no datasets were generated or analysed during the current study.