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BACK To ESSSAYS INDEX
DEFINITIONS
With respect to impressing, highbrow concepts such as
Truth, Absolute, Existence I read often: "Oxford or Webster
Dictionary calls something this and that", which closes the
matter in question ex cathedra, absolutely, without recourse.
How good are such dictionary definitions?
They have the indisputable merit of consolidating the
authority and the legitimate pride of people having such
expensive books and to stimulate the humility of guys who,
like me, cannot afford them.
Apart from that I cannot find for them any use at all, always
with respect to those highbrow concepts.
When it comes to trivial things like "bicycle", a dictionary
is ok and tells you that bicycle is "two-wheeled velocipede"
(I called a rich friend and he told me). Let's note that a
trivial term like "bicycle" may be defined in the classical
way via a superclass (velocipede) and a specific attribute
(two-wheeled). We may call that type of definition
"intensional" from "intension" denoting superclasses of
a class.
But with respect to a highbrow concept of "Truth" my friend
told me that:
truth: conformity to reality
conformity: correspondence in form or appearance
form: a particular mode in which something is manifested
manifest: reveal its presence or make an appearance
presence: current existence
existence: the state or fact of existing
existing: having existence
existence: the state or fact of existing
existing: having existence
existence: the state or fact of existing
existing: having existence
... da capo al infinitum
appearance: a mental representation
mental: of or relating to the mind
mind: the seat of the faculty of reason
reason = faculty of intellect
intellect = faculty of reasoning
faculty = mental power
mental: of or relating to the mind
mind: the seat of the faculty of reason
reason = faculty of intellect
intellect = faculty of reasoning
faculty = mental power
mental: of or relating to the mind
mind: the seat of the faculty of reason
reason = faculty of intellect
intellect = faculty of reasoning
faculty = mental power
mental: of or relating to the mind
mind: the seat of the faculty of reason
... da capo al infinitum
Maybe it's just some strange fallacy concerning "Truth", so
let's try another highbrow concept, say "Idea":
idea = object of thought
thought = idea
idea = object of thought
thought = idea
idea = object of thought
thought = idea
... da capo al infinitum
or a second entry for "thought":
thought = conception of reason
conception = idea
idea = object of thought
thought = idea
... da capo al infinitum
reason = faculty of intellect
intellect = faculty of reasoning
faculty = mental power
mental: of or relating to the mind
mind: the seat of the faculty of reason
reason = faculty of intellect
... joining the truth loop
So maybe "idea" is too ideal. Let's try something real
like "reality:
reality: the quality possessed by something real
real: coinciding with reality
reality: the quality possessed by something real
real: coinciding with reality
reality: the quality possessed by something real
real: coinciding with reality
reality: the quality possessed by something real
real: coinciding with reality
... da capo al infinitum
It looks as if the guys writing dictionaries just replaced
highbrow terms with their highbrow synonyms hoping that the
reader knows a synonym and will do the rest of the job
himself. Hardly fair, given the prices, but on the second
thought one tends to pity the fellows rather than to censure
them. It must be frustrating to say in hundred thousand
places that Truth = Truth, that Absolute = Absolute, etc.
even dressing it up with most respectable synonyms. And they
cannot do anything else.
In our world, such as it is, and I did not invent it, the
more general a domain of human reflection or activity, the
more difficult it is to be defined intensionally. Intensional
definitions may situate local areas and disciplines within
large global domains, but the largest global domains stay
entirely undefined.
One may object that at least exact sciences must have exact
intensional definitions. Well, not at all. Mathematics, the
most exact of all, stays intensionally undefined. Nobody,
and particularly no mathematician can say what he means by
Mathematics. And the mathematician will add that he could
not care less, that he does his job in what is called for
convenience Differential Topology which, for convenience,
is supposed to be a part of Mathematics, and that he was
never disturbed by Mathematics being undefined.
All one may say is that Mathematics is a collection of
disciplines studying partially intersecting subjects and
using similar methods. Creation and development of particular
areas are always triggered by some local motivation,
sometimes intellectual drive, more often necessity to solve
some concrete physical, engineering, biological, social or
psychological problem. Afterwards, they are included in
"Mathematics" in bottom-up direction, which helps other
"mathematical" areas to share top-down their achievements.
Mechanics, for instance, is not as one might think, a simple
branch applying theoretical results derived by analysts, but
a fundamental cross-roads from which part the ways towards
"mathematical" areas of analysis (partial differential
equations), of geometry (geodesics of Riemann space), of
linear algebra (relativistic tensors), etc. These local areas
are collected bottom-up into the general class "Mathematics"
which can only be described by enumeration of its elements.
Such descriptions by enumeration may be called "extensional
definitions" from "extension" meaning subclasses of a class.
They are the only useful ones with respect to general domains
and require a sincere and thorough knowledge of essential
instances of the definiendum. This may look like a vicious
circle, but in fact it is a spiral of successive, refining
approximations.
(See REFLECTION SPIRAL ).
