The requirement of precision and clarity

The purpose of definition

The ordinary purpose of definition is to determine the semantics of expressions (their meaning, and what they refer to, if anything). The goal of definition, ordinarily, is to make the expression defined an effective means of scholarly communication.

The requirements of precision  and clarity 

Lack of precision is an impediment to effective communication. Therefore, precision is a requirement on scholarly definition. Since it is impossible to specify the semantics of a term precisely without expressing it clearly, clarity is another requirement. 

Definitorial circularity: harmless

The requirement of precision and clarity is probably the reason why definitorial circularity counts as a mistake as wasteful and embarrassing as hardly any other. Definitorial circularity arises when the term being defined (the definiendum) is actually used in the defining phrase (the definiens), or at least is needed to clarify the definiens. (It is a frequent mistake, even among distinguished philosophers, to confuse or intermingle definitional circularity with other circularities, such as circular argumentation, or circular explanation-- this mistake must urgently be avoided.) LINK->EXAMPLE]

The reason for the horror against definitorial circularity is probably the idea that when a term is being defined, then its semantics is completely unclear, and that definition which contains an unknown term is perfectly unsuccessful. Both is obviously not quite true. Definition is often applied ot terms whose semantics is at least partially clear, and definienda usually contain a plurality of partially clarifying elements.

Consider, for example, "mountain" is defined as "large natural elevation of the earth's surface; a large steep hill", and "hill" is defined as "naturally raised area of land, not as high or craggy as a mountain": this definition is bluntly circular ("mountain"/"hill"); but it serves its purpose.

To be sure, this is not only true for everyday matters, it holds for philosophical discourse quite as well. In fact, while definitorial circularity is an accusation often made, it is hard to find a single case where this "mistake" ever caused a real problem. (If you know of any, please contact us"!)

Less harmless: definiens imprecise/unclear

A much heavier problem, as a matter of fact, and one which occurs rather frequently, is lack of precision or clarity of a definiens. Consider the following definition of assertions of possibility.

(A) "___ is possible"  means 'There is a possible world in which ___ is realised‘.

The notion of something's being possible is being defined here in terms of its "being realised", and in terms of the notion of a "possible world". The problem is that the notion of something's being "realised" is far from being very clear, and the problem is even worse with the notion of a "possible world". Can a "possible world" exist?If it does, it is not just a possible world, but a real one, isn't it? If it exist, it is part of our actual world, for this comprises everything that exist, doesn't it? Where will we find it? If we cannot find it, where are we supposed to know that __ is realised in it? (Etc., etc.) The problem is not that there ar eno answers to these questions; the problem, rather, is that different authors will give very different (collections of) answers, and that for some of these questions it does not seem that a consistent answer can be given at all. So the definiens, referring to such mysterious entities aspossible worlds, is extremely unclear. The contrasts nicely with the fact that assertions of possibility are really not so exceedingly unclear. So a comparatively clear definiendum is being explained by an extremely unclear definiens: it is hard to see where the benefit of this could be.

Such imprecise or unclear definitions are stupendously frequent. Other examples include ...

(1) "a sentence is true if it is satisfied by all objects." (Tarski, "The Semantic Conception of Truth 1944, 353). Tarski focusses on the formal correctness of the definition; as to the definition's clarity: the notion of the truth of a sentence is actually fairly clear, while the notion of the "satisfaction by an object" is rather not.

(2) "An illocutionary force is uniquely determined once its illocutionary point, its preparatory conditions, the mode of achievement of its illoutionary point, the degree of strength of its illocutionary point, its prepositional content conditions, its sincerity conditions, and the degree of strength of its sincerity conditions are specified." (Searle & Vanderveken, Foundations of Illocutionary Logic 1985, 20). The definition does not specify what "illocutionary forces" are supposed to be, but only enumerate conditions for such a force's being determined--presumably due to Searle & Vanderveken's inability to specify what kind of entities are actually under consideration. Furthermore, the notions employed are far from clear (this problem persists to a considerable extent even after reading the book).

(3) "That the (putative) fact that p is an 'institutional fact' means that p is a fact that exists by virtue of the collective recognition of its existence" (Doerge & Holweger, "The Non-Existence of Institutional Facts", ms.). The notion of "collective recognition", although rather well established, turns out to be very hard to precisify itself. 

(4)   ...

In each of these cases, the definiens offered is far from being precise and/or clear; in some cases it is less clear than the definiendum is.