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DEFINITIONS

With respect to impressing, highbrow concepts
such as Absolute, Being, Existence I read often: 
"Oxford or Webster Dictionary calls something 
this and that", which closes the matter in question 
ex cathedra, absolutely, without recourse. Now, 
I would like to ask a stupid question:

How good are such dictionary definitions?

Well, 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). OK, doubtless, but not
very useful, because we are all here highly 
intelligent thinkers and know what a bicycle is 
without having to buy expensive books. Let's 
note that a trivial term like "bicycle" may be 
defined in the classical way giving a superclass 
(velocipede) and a specific attribute (two-wheeled). 
We may call that type of definition "intentional" 
from "intention" denoting superclasses of a class.

But with respect to a highbrow concept of "idea" 
my friend told me that:

1.idea = object of thought
1.1.thought = idea (that doesn't help much,
    does it?)
1.2.thought = conception of reason
1.2.1.conception = idea (there you are again)
1.2.2.reason = faculty of intellect 
1.2.2.1.intellect = faculty of reasoning
1.2.2.2.faculty = mental power eg. reason

The old peanut starts to swing, so let's leave 
it at that.

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 Being = Being, 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 define it
intentionally.
Intentional definitions may situate local areas and 
disciplines within large global domains, but the 
largest global domains stay entirely undefined.

Applied domains such as medicine or engineering 
are obviously pragmatic and intentionally undefined, 
but one may object that at least exact sciences 
must have exact intentional definitions.
Well, not at all. Mathematics, the most exact 
of all, stays intentionally 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, again 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, psychological or social problems. 
Afterwards, in the bottom-up direction, they 
are included in 'Mathematics', which helps other 
'mathematical' areas to share their achievement 
top-down.    

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 the 
classic analysis (partial differential equations), 
the geometry (geodesics of Riemann space), the 
linear algebra (relativistic tensors), etc.
Such local areas and their achievements are 
collected bottom-up into the intuitive class 
'Mathematics' which can only be defined by 
enumeration of its elements.

Such definition by enumeration may be called
"extentional" from "extention" meaning 
subclasses of a class.

Georges.