Browsing through the various books on databases and programming appeared over the past 20-30 years, it’s probably hard not to notice the differences between the definitions given even for straightforward and basic concepts like the ones of view, stored procedure or function. Quite often the definitions lack precision and rigor, are circular and barely differentiate the defined term (aka concept) from other terms. In addition, probably in the attempt of making the definitions concise, important definitory characteristics are omitted.
Unfortunately, the same can be said about
other non-scientific books, where the lack of appropriate definitions make the understanding
of the content and presented concepts more difficult. Even if the reader can
arrive in time to an approximate understanding of what is meant, one might have
the feeling that builds castles in the air as long there is no solid basis to
build upon – and that should be the purpose of a definition – to offer the
foundation on which the reader can build upon. Especially for the readers
coming from the scientific areas this lack of appropriateness and moreover, the
lack of definitions, feels maybe more important than for the professional who
already mastered the respective areas.
In general, a definition of a term is a well-defined
descriptive statement which serves to differentiate it from related concepts. A
well-defined definition should be meaningful, explicit, concise, precise, non-circular,
distinct, context-dependent, relevant, rigorous, and rooted in common sense. In
addition, each definition needs to be consistent through all the content and when
possible, consistent with the other definitions provided. Ideally the
definitions should cover as much of possible from the needed foundation and provide
a unitary consistent multilayered non-circular and hierarchical structure that
facilitates the reading and understanding of the given material.
Thus, one can consider the following requirements
for a definition:
Meaningful: the description should be
worthwhile and convey the required meaning for understanding the concept.
Explicit: the description must state
clearly and provide enough information/detail so it can leave no room for confusion
or doubt.
Context-dependent: the description should
provide upon case the context in which the term is defined.
Concise: the description should be as succinct
as possible – obtaining the maximum of understanding from a minimum of words.
Precise: the description should be made
using unambiguous words that provide the appropriate meaning individually and as
a whole.
Intrinsic non-circularity: requires that the
term defined should not be used as basis for definitions, leading thus to trivial
definitions like “A is A”.
Distinct: the description should provide
enough detail to differentiate the term from other similar others.
Relevant: the description should be closely
connected or appropriate to what is being discussed or presented.
Rigorous: the descriptions should be the
result of a thorough and careful thought process in which the multiple usages
and forms are considered.
Extrinsic non-circularity: requires that the
definitions of two distinct terms should not be circular (e.g. term A’s definition
is based on B, while B’s definition is based on A), situation usually met occasionally
in dictionaries.
Rooted in common sense: the description
should not deviate from the common-sense acceptance of the terms used,
typically resulted from socially constructed or dictionary-based definitions.
Unitary consistent multilayered hierarchical
structure: the definitions should be given in an evolutive structure that
facilitates learning, typically in the order in which the concepts need to be
introduced without requiring big jumps in understanding. Even if concepts have
in general a networked structure, hierarchies can be determined, especially
based on the way concepts use other concepts in their definitions. In addition,
the definitions must be consistent – hold together – respectively be unitary –
form a whole.
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