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.