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«Abstract: Practical methods are introduced for the construction of definitions, both for philosophical purposes and for uses in other disciplines. ...»

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How to define – a tutorial

Sven Ove Hansson *

Abstract: Practical methods are introduced for the construction of definitions, both

for philosophical purposes and for uses in other disciplines. The structural and

contentual requirements on definitions are clarified. It is emphasized that the

development of a definition should begin with careful choice of a primary

definiendum, followed by the selection of appropriate variables for the definition.

Two methods are proposed for the construction of the definiens, the case list method and the method of successive improvements. Four classes of concepts are discussed that are particularly difficult to define: vague concepts, value-laden concepts, controversial concepts, and inconsistent concepts.

Keywords: Concepts, Definition, Formal philosophy Resumo: Introduzem-se aqui métodos práticos para a construção de definições, tanto para propósitos filosóficos quanto para usos em outras disciplinas.

Clarificam-se os pré-requisitos que se aplicam sobre a estrutura e o conteúdo das definições. Enfatiza-se que o desenvolvimento de uma definição deve começar com a escolha cuidadosa de um definiendum principal, seguido da seleção de variáveis apropriadas para a definição. Propõem-se dois métodos para a construção do definiens, o método da enumeração de casos e o método dos aperfeiçoamentos sucessivos. Discutem-se quatro classes de conceitos que são particularmente difíceis de se definir: conceitos vagos, conceitos que envolvem julgamentos de valor, conceitos controversos e conceitos inconsistentes.

Palavras-chave: Conceitos, Definição, Filosofia formal

1. Introduction Careful analysis and development of our own terminology is an essential part of modern philosophy. Definitions and conceptual analysis provide us with philosophical tools in the form of precise concepts that can be used in philosophical arguments. In addition, definitions are an important part of our contributions to other disciplines. In interdisciplinary co-operations, it is often the role of philosophers to work out precise definitions and distinctions.

* Department of Philosophy and the History of Technology. Royal Institute of Technology (KTH). Stockholm, Sweden. E-mail: soh@kth.se Princípios, Natal, vol. 13 nos. 19-20, jan./dez. 2006, p. 05-30.

Sven Ove Hansson The present paper is a tutorial on how to construct useful definitions, both for philosophical purposes and for use in other disciplines. Section 2 provides a background on different uses of definitions, and Section 3 introduces the basic structural and contentual requirements on a definition. After this follow four

sections that show, step by step, how to develop a definition:

choosing a primary definiendum (Section 4), selecting the variables of the definition (Section 5), and after that constructing a definiens either according to the case list method (Section 6) or the method of successive improvements (Section 7). The next four sections focus on classes of concepts that are particularly difficult to define: vague concepts (Section 8), value-laden concepts (Section 9), controversial concepts (Section 10), and inconsistent concepts (Section 11).

2. The uses of definitions Definitions can be either lexical (descriptive) or stipulative. In principle, the difference is simple. A lexical definition reports actual linguistic usage. Therefore, it can be correct or incorrect (i.e., true or false, although that terminology is seldom used). A stipulative definition reports how the definer is going to use a term, or how she recommends others to use it. A stipulative definition cannot be correct or incorrect, but it can be enlightening or confusing, fruitful or barren, adequate or inadequate.

It is often difficult to draw a sharp line between lexical and stipulative definitions. How, for instance, should we classify the extensive philosophical literature on the meaning of “knowledge”?

Do the authors aim at a lexical definition describing what we mean by “knowledge” in ordinary language, a lexical definition of what “knowledge” means in philosophy, a stipulative definition for a fruitful concept in philosophy, or perhaps even a real definition (i.e.

a definition of the essence of what it is to know something, rather than a definition of the word “knowledge” or the concept knowledge)? 1 In practice, this is often far from clear. A major In what follows I will focus on nominal definitions, i.e definitions of terms in the language or concepts that can be expressed in the language.

How to define – a tutorial 7 reason for this is that stipulative definitions are circumscribed by linguistic practice. The common saying that you can stipulate arbitrarily is just a myth. Of course there is a sense in which you “can” choose to define “believe” to mean “know with certainty” or “compound” to mean “atom”, but such a venture is almost sure to be unsuccessful. Chances are minuscule that others will adopt your definition, and – what is worse – chances are also small that they will keep track of how you use the words. To be successful, a stipulative definition should correspond to needs of precision and clarity among those who use the term in question.

Lexical and stipulative definitions tend to differ in how they treat the ambiguities and unclarities of ordinary language. A lexical definition should, at least in principle, exhibit actual uses even when they are unclear or even confused. If a term has several different meanings or uses, they should be listed and distinguished between.

In contrast, stipulative definitions are usually developed in order to eliminate ambiguity and vagueness.

There are at least three different attitudes that a stipulative definer can take to the lack of clarity in ordinary language. First, one can choose to do essentially as in lexical definitions, namely to accept but clarify what is confused or obscure in ordinary usage.

This approach is justified when it can be shown that the lack of clarity is not a disadvantage given the purpose of the definition.

Secondly, one can restrict the meaning of the word, for

instance in the following way:

With “person” we will mean here a human being who is conscious or capable of gaining consciousness.

This definition excludes legal persons. Such a restriction on the term “person” may be useful for instance in moral philosophy, but it is probably not useful in legal philosophy or in legal contexts generally.

Thirdly, one can split the concept by introducing new terms that distinguish between different meanings of the word under

scrutiny, for instance in the following way:

Sven Ove Hansson With “person-H” we will mean a human being who is conscious or capable of gaining consciousness. With “person-L” we will mean a legal entity that can, according to the legal system in force, be a contracting party in a legally binding contract or have rights that are acknowledged by the legal system.

In this case it would also be adequate to use the established term “legal person” instead of “person-L”, and similarly, “human person” instead of “person-H”.

Definitions may either be briefly stated as preconditions for a study, or they may be the major topic of an investigation that has the development of a definition as its purpose. Although the former case is more common, we will be more concerned here with the latter case.

It a good practice to state, as a precondition for an argument or an investigation, what one means by the central terms and (whenever applicable) what deviations one makes from common usage. Such definitions should either be presented in an introductory part of the text or introduced when the term in question is used for

the first time. They have the role of terminological commitments:

With a counterfactual sentence we will mean a sentence of the form “If A then B” in which A is false.

With a consensus decision we will mean a group decision in which none of the participants in the final vote voted against the winning alternative.

The term “reason” will be used here in accordance with Kant’s usage of the German term “Vernunft”.

By “intuitionism” we will mean moral intuitionism.

The first two of these are full definitions. The last two are incomplete definitions. They explain how a term will be used by reference to definitions by others, or to a particular well-known usage of the term.

How to define – a tutorial 9 If you make terminological commitments, you should also follow them through, i.e. use the defined terms as you have defined them. It is often more difficult than what one initially believes to be consistent in this respect. A good way to avoid such inconsistency is to check through the text at a late stage to verify that one has honoured one’s own terminological commitments.

3. The structure of a definition A definition has three constitutive parts. It consists of the definiendum (that which is to be defined), the definiens (that which defines) and a defining connective 2. Hence in the definition “A bachelor is an unmarried man”, “a bachelor” is the definiendum, “an unmarried man” the definiens and “is” the defining connective.

In this case, it will be understood from the context that “is” is used as a defining connective (and not in the same sense as in “My uncle is an unmarried man”). When needed, this can be clarified for instance with the notation “isdef”. In more precise contexts, “if and only if” (often abbreviated: iff) is often used as the

defining connective:

A man is a widower if and only if some woman died while married to him.

However, “if and only if” is not either specific for defining.

It may for instance be true that “A person is a full professor of the philosophy department of this University if and only if that person is male, above 45 years old, and an employee of the department”. But even if this is true it is certainly not a definition.

There are two major ways to clarify that “if and only if” is definitional: The index “def” can be used:

A man is a widower iffdef some woman died while married to him.

The word “definition” is used here to cover the whole complex consisting of these three parts. It can also be used as a synonym of “definiens”.

Sven Ove Hansson Or, the definitional character of the sentence can be stated in

a heading or in some other way in the surrounding text:

–  –  –

The definiens of a definition should have the same meaning as the definiendum has (or is given). It is common for proposed definitions to fall short of this requirement in ways that can be discovered without detailed knowledge of the meanings of the terms. The reason for this is that sameness in meaning can only be obtained if the definition satisfies three important formal congruence requirements, namely linguistic congruence, categorial congruence, and congruence in variables.

Perhaps most obviously, definiendum and definiens should be linguistically congruent. Hence a noun should not be defined by a verb phrase, or a plural noun by a singular noun, etc.

–  –  –

By categorial congruence is meant that definiens and definiendum belong to the same general category of concepts. A state of mind should not be defined as a state of the external world, an evaluative concept should not be defined as a descriptive one, etc. There is of course no general list of categories that can be appealed to when checking categorial congruence. A good education in philosophy furnishes us with useful distinctions that can be used to identify relevant categories in each particular case.

–  –  –

In the first of these two examples, the left-hand definition defines preference as an objective relational property of two objects.

The right-hand, improved definition, treats preference as a potential element of a state of mind. (The definiens of the left definition would have been more appropriate for the definiendum “betterness”.) In the second example, the problem with the left-hand definition is that it does not clarify what category the definiendum belongs to. In the right-hand definition it is made clear that remorse is an attitude or an emotion, i.e. some kind of state of mind.

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