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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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Parent 1983, p. 253). From an analytical point of view, MacCallum’s proposal (and the fourth of the above definienda) has the advantage that different views on freedom can be represented in one and the same format.

Sven Ove Hansson

6. The case-list method Given that we have chosen an appropriate primary definiendum and associated with it an appropriate list of variables, our task is now to develop a definiens that includes exactly that which it should cover, nothing more, nothing less. Two methods to do this will be presented here. They will be called the case-list method and the method of successive improvements. Both these methods take as their starting-point a preliminary definition that is then improved.

A good way to find that starting-point is often to consult a dictionary. Large dictionaries such as the Oxford English Dictionary and the corresponding large dictionaries in other languages usually provide good lexical definitions that can be used as starting-points.

It is often also useful to consult dictionary definitions of related terms in other languages. Hence, if we wish to define the English word “science”, we can learn from comparisons with the (wider) German term “Wissenschaft”.

The case-list method is best suited for lexical definitions. It begins with the compilation of two extensive lists of test cases. One of these contains cases that should be covered by the definition, and the other cases that should not be covered. Both lists should include “limiting” cases, i.e. cases that are close to the limit of what the definition should cover. The preliminary definition is checked against the two lists, and after that the definition is adjusted in order to comply better with them. This is repeated until the resulting definition conforms completely with the two lists. If the lists are representative of common usage, then the resulting definition will be an appropriate lexical definition of the term in question.

Suppose for an example that we want to define “traffic accident”, and that the two lists are as follows: (In a full discussion of this definition, the lists would have to be longer, but these short lists can be used to illustrate the method.)

–  –  –

We can then see from 2+ that the vehicle need not be a motor vehicle. However, as can be seen from 1– some kind of vehicle (not only pedestrians) have to be involved. It follows from 2– and 3– that the vehicle has to be moving and from 3+ that it does not have to be driven. All this can be summarized by replacing “motor vehicle” by “moving vehicle”. It follows from 2+ and 3+ that the event need not cause personal injury to quality as a traffic accident; material damage is enough. Thus “personal injury” should be replaced by “personal injury or material damage”. Finally, it can be seen from 4– that an event in which the damage is caused intentionally is not a traffic accident, thus we should add the word “unintentional” to the definition. These considerations give rise to the following, improved definition.

A traffic accident is an event in which a moving vehicle causes unintentional personal injury or material damage.

7. The method of successive improvements Sven Ove Hansson As already noted, the case-list method is primarily intended for lexical definitions. It can be used for stipulative definitions as well.

However, it easily leads to entangled definitions with many exception clauses. In order to achieve a stipulative definition that is reasonably simple, the method of successive improvements is usually preferable.

In this method as well, we begin with a preliminary definition that can have its origin in a dictionary or in some other report of common usage. If that definition is not found to be satisfactory, we identify its major (or most obvious) deficiency. The next step is to carefully consider how this deficiency can be avoided and whether the improvement is worth other possible drawbacks such as making the definition more complex. The resulting definition is evaluated, discussed and possibly amended. In this way we approach a new definition through a series of successive improvements. The process is halted when a definition has been obtained that we do not manage to improve without overweighing drawbacks, typically in terms of complexity.

As an example of this method we can define the political concept of “discrimination”. (Hansson 2005) Probably the most obvious feature of discrimination is that certain persons receive worse treatment than others. We can therefore begin with the

following tentative definition:

(1) A person is subject to discrimination if and only if she receives worse treatment, or less of some advantage, than others.

This definition is obviously too wide. An employee who steals from the workplace will probably receive worse treatment from the employer than her colleagues, but we would not call that discrimination. Generally speaking we do not call a deservedly worse treatment discrimination. The definition can be adjusted to

accommodate this insight:

How to define – a tutorial 21 (2) A person is subject to discrimination if and only if she receives worse treatment, or less of some advantage, than others, without sufficient justification to select her for such inferior treatment.

Clearly, “sufficient justification” is open to interpretation, but that is not necessarily a drawback. We cannot require of a definition of discrimination that it contains in itself the answer to whether or not discrimination is at hand in a particular case. It should, however, tell us what needs to be determined in order to answer that question. Whether or not the inferior treatment is welldeserved seems to be something that has to be determined for this purpose.

However, discrimination does not refer to undeservedly inferior treatment in general. A person who criticizes minimum wages for being too low would not typically describe this as a case of discrimination 4. In other words, we need to distinguish discrimination from general inequality. The difference can be seen from the typical cases of discrimination that we usually refer to, such as discrimination of women, ethnic and religious groups, sexual minorities etc. A crucial issue is the selection of persons for these different treatments. Someone can, for instance, complain that women are discriminated against since they have most of the lowpaid jobs, without having any complaint against the existence of such low-paid jobs. Hence, whereas “inequality” refers to differences in treatment or conditions, “discrimination” refers primarily to selection for such treatment or conditions. This should be reflected in a definition of discrimination.

In the cases that have attracted public attention, discrimination affects the members of certain groups, such as those just mentioned. Adverse treatment can also affect a single person, but this is not normally called discrimination. (We have other words such as “harassment” to denote individual mistreatment.) In a Unless, of course, as a way to point out that those who receive minimum wages predominantly belong to some group, such as an ethnic group, that is at disadvantage also in other respects.

Sven Ove Hansson stipulative definition, a terminological decision has to made whether or not the meaning of the term should be extended to cover unfair treatment of an individual that does not depend on her being a member of some group. Let us assume here that we decide not to extend the term in this way. We can then amend the definition as


(3) A person is subject to discrimination if and only if she receives worse treatment, or less of some advantage, than others, because she belongs to a group that has been selected for such treatment without sufficient justification.

The phrase “without sufficient justification” will have to be retained in the revised definition because there may be groups of persons (such as justly convicted criminals) who are subject to worse treatments than others for good reasons.

Definition (3) is a reasonable definition of “discrimination”, but it is not necessarily a final definition. In order to determine whether to stop here or to further modify the definition it is useful to consider carefully each of the key terms of the definiens. We can exemplify this by considering the phrase “worse treatment, or less of some advantage” in definition (3).

One of the most intriguing issues about discrimination is in what areas of human life non-discrimination should be enforced.

Many acts that treat members of a discriminated group unfairly take place in the private sphere, in which we do not enforce the standards of fairness and equal treatment that are upheld in the public sphere.

Our choices of friends and acquaintances are examples of this. A white family that never invites non-whites to visit their home may be prejudiced and bigoted, but we would nevertheless consider them to be acting completely within their rights when choosing the company they want. “The pleasure of my company may, or may not, be one of the great goods, but it is for me to decide on whom to bestow it, however ardently you may yearn for it”. (Lucas 1985) Nevertheless, many such permissible small private evils can add up to a great social evil. When defining “discrimination” we will have How to define – a tutorial 23 to decide whether or not unfair treatment in the private sphere should be included. If we choose not to include it, then definition (3) will have to be amended.

The final choices in a case like this will depend on the purpose of the definition. It is advisable not to “load” a definition with too many details. Therefore, depending on the purpose of the definition it may be advisable to let a relatively simple definition such as (3) stand, after careful consideration of possible further provisos that would make it more precise at the price of also making it less straightforward.

The above descriptions of the case-list and successive improvement methods may give the impression that the construction of a definition is a routine activity. Therefore, it should be added that in many cases, a fair amount of ingeniousness is needed to construct a workable definition. An interesting example of this is the definition of “game”. Wittgenstein (1953) claimed that there is no set of characteristics that is common to everything that we call a game. Therefore, he said, the best that we can do is to give a list of characteristics such that all games have some of these characteristics. (This is still the standard example of a “family resemblance”.) It took a quarter of a century until Bernard Suits (1978) presented a unifying definition of a game, of precisely the type that Wittgenstein claimed to be impossible. A game is, according to this definition, an activity in which one pursues a goal that can be described independently of the game (such as getting a ball into a hole in the ground) but willingly accepts rules that forbid the most efficient way to achieve that goal (such as placing the ball in the hole by hand). (Cf. Hurka 2004 p. 251-252)

8. Defining vague concepts The definition of a vague term is often problematic. We have the choice between constructing a vagueness-preserving or a vaguenessresolving definition. In the former case, the definiens will be vague just like the definiendum. This can be perceived as unsatisfactory. In the latter case, the definiens will be more precise than the Sven Ove Hansson definiendum. This means that the definiens will not mirror the meaning of the term to be defined, which can also be seen as unsatisfactory.

For practical purposes we can distinguish between two types of vagueness, namely one-dimensional and multi-dimensional vagueness. Vagueness is one-dimensional if it refers to a property for which we have a well-defined scale. The vagueness consists here in the lack of a precise point on the scale where the property starts to hold. As an example we can consider the property of a chemical substance to be water-soluble. The relevant scale here is solubility in water, that is well-defined. We can easily determine how watersoluble a substance is, and compare it in that respect to other substances. The vagueness inherent in the concept concerns how soluble a substance has to be in water in order to count as watersoluble. Similarly, to be bald is to have few hairs, but it is not welldetermined how few the hairs on a head must be for the person to count as bald.

In cases like these, i.e. cases of one-dimensional vagueness,

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