Some important distinctions and topics

 

Clarity and precision

 

The purpose of definitions is to increase the efficacy of scholarly work and exchange. They serve this purpose by determining the semantics of expressions. In order to be effective means of communication, terms should be precise. When we define the term "institutional fact" by saying that such facts "have much to do with people's way of thinking, and tend to involve normativity", then the term remains vague, due to the qualifying phrases "have much to do" and "tend to involve". Being vague, it will be an ineffective means of communication; talk of "institutional facts" will tend to remain vague, involve misunderstanding, etc. Definitions should be precise.

 

We may have a clear conception of a what a term means, but not succeed in conveying this clear conception. In such a case, the situation is more or less identical with the ine in which we have no clear conception at all. Except of ourselves, all participants of the debate will lack a precise conception of what the term aims at. Again, communication involving the use of that term will tend to be vague, to involve misunderstanding, etc. Therefore, definitions should be transparent, clear.

 

 

Adequacy

 

 

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Definition of intension and extension

 

Expressions have meaning, and many of them refer to something. The meaning of an expression is the intension it expresses. What the term refers to is its extension. Every expression seems to have meaning (otherwise it would not be an "expression"). Yet not every kind of expression does seem to have an extension; "perhaps", "soon", "unfortunately", "Come!" and "Why?", for example, do not seem to refer to anything.

 

To define an expression can mean to determine its intension (meaning), and/or to determine its extension (reference).

(1) A definition of the extension of an expression would be: "'Members of the European Union' are Austria, Belgium, Bulgaria, Croatia, Republic of Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Poland, Portugal, Romania, Slovakia, Slovenia, Spain and Sweden."

(2) A definition of the intension of an expression is: "'Communication' means 'transmission of information'."

 

 

Ostensive definition

 

A definition of the extension of an expression can be "ostensive", which means, by pointing at entities which are supposed to belong to this extension. We do this in workaday life, for example, when we introduce people: "This is Mrs Crook ... This is Dr Quine ... Ms Davidson .. Freddy, our dog ... Ms Dummett ..."

 

 

Explicit vs. inexplicit definition

 

Often, the central terms used in a text are not devoted statements of definitions identitified as such. In such a case, the semantics of terms must be figured out indirectly. All indications which allow conclusions to the semantics of such terms can be subsumed under the notion of "implicit", or "inexplicit" definition.

 

Yet the distinction between "explicit" and "implicit", or "inexplicit" definition, well-established though it is, is rather unclear. It is unclear, for example, where in the following chain the distinction should be applied. (a) "We hereby define 'bachelor' as 'unmarried man'"; (b) "'Bachelor' will mean 'unmarried man'"; (c) "'Bachelors' are 'unmarried men'; (d) "Bachelors are unmarried men"; (e) "Given that bachelors are unmarried men, Napoleon was not a bachelor".

 

So the borderline between "explicit" and "implicit"/"inexplicit" definition is not quite clear. Nevertheless, it is of the greatest importance for the quality of scholarly work to be aware that there are important indications of the semantics of terms apart from solemn statements of definition marked as such--and that these indications must most carefully be exploited, in order to avoid misinterpretation and confusion. 

 

 

Partial definition

 

Not always is a definition (intended to be) exhaustive. Inexplicit definition, for instance, usually involves partial definition. Also, the development or careful analysis of the semantics of terms often involves partial definition. For example, the analysis of "knowledge" involves the definition of "knowledge" as 'true justified belief" is close enough. If it is not, it odes not follow that the definition "Knowledge is true justified belief" is not a definion; it merely follows that this is merely a partial definition.

 

 

Recursive definition

 

Sometimes it is hard to define a term in one fell swoop. In some of these cases, people apply what they call a "recursive" definition. You start by specifying part of the extension of an expression; and you then go on, in one or more additional steps, to specify further parts of the extension by recourse to that part of the definition which was already given. Here is a recursive definition of "natural number":

   (a) 1 is a "natural number". 

   (b) If a given number is a "natural number", then x+1 is a "natural number", too.