Editing Vagueness (section)

==Reducing internal vagueness==
The internal vagueness of one person's message is hidden from another person, he can only guess that. We either have to accept internal vagueness, which is human, or we can try to reduce it, or completely eliminate it, which is scientific.

Demands on the accuracy of the formulation of scientific knowledge and its communication require minimizing the internal vagueness with which one connotes (vaguely, emotionally and subjectively interprets)<ref name="ReferenceA"/> linguistic constructs of the communication language, and thus improve the accuracy of the message. Various scientific procedures aim to improve the credibility and accuracy of the scientific knowledge obtained.

To formulate them, however, it is necessary to build a more precise language, with less (internal) vagueness of message than is common in daily life. This is done by purposefully (branch) constructed [[terminology]] allowing to more accurately describe the researched reality and the acquired knowledge about it. People properly educated in the field of terminology know it with little internal vagueness, so they know accurately what the individual terms mean. Basic concepts are always formed on the basis of consensus, the other derived from them by definition, to avoid to [[Circular definition]]. To improve the accuracy of research and communication (reducing the internal vagueness of connotation), tools such as classification schemes are used, such as the taxonomy of organisms by [[Carl von Linné]].

This is how descriptive (non-exact) sciences do it. Thus, they use natural human cognition (with the Russell’s filter of vagueness<ref>Russell B.: Vagueness. In: The Australasian Journal of Psychology and Philosophy 1, June 1923, pp. 84--92.</ref>) and refined natural language.

There is another continuation of the reduction of internal vagueness. The method of reducing internal vagueness to the extreme, that is '''zero''', was realized by I. Newton.<ref>Newton I: Philosophiae Naturalis Principia Mathematica in 1687</ref> It is an epochal idea, and it needs to be explained how it can be realized.
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It follows from the above-mentioned Law of maintaining accuracy of information (optimization of the truthfulness of the message) saying, if we require to eliminate the internal vagueness in the knowledge completely (to zero) then of course it must first be completely eliminated in cognition (the source of information). This means that one (Newton) must avoid the intrusion of internal vagueness, that is, to choose some filter of cognition other than vagueness. Thus we pass from the natural human world to the artificial one. We call it the '''exact world''' and we will explain why.

In the case of natural language, it is not possible to completely remove (nullify) the internal vagueness, but it is possible to build artificial formal languages (mathematics, formal logics, programming languages) that have zero internal vagueness of connotation (so they have an exact interpretation) and cannot have another in principle. (Newton for this purpose has created formal language – theory of flux - theory of flowing – infinitesimal calculus).  Languages with zero internal vagueness of their interpretation, i.e. the meaning of their linguistic constructions, have the property that all these constructions are understood by every appropriately educated person with absolutely precise, i.e. exact meaning. That is why they are part of the exact world. Thus, we have some language that is able to represent knowledge with zero internal vagueness. But these must first be acquired by adequate cognition, providing cognition also with zero internal vagueness, i.e. also from the exact world. And it is already evident that we are on the way to the creation of the scientific method that creates science belonging to the exact world, that is, an '''[[exact science]]''' is born.

It is still necessary to explain how to realize Newton`s exact cognition, that is, the cognition when the knowledge obtained from the real world is part of the exact world. The miraculous bridge between the real and exact worlds that makes this possible is called a '''[[quantity]]''' (e.g. electric field intensity, velocity, nitric acid concentration, etc.). It is common to both worlds, because in the exact world it is precisely delineated (every knowing person knows them with no doubts, so exactly), and in the real world it is an elemental '''measurable''' probe into that, and thus its elemental measurable representative. '''The quantity is the elementary building block of exact science'''. In exact sciences, it is always precisely defined, either consensually (basic set) or the other derived - [[International System of Units]].
And what about the artificial filter that allows Newton to avoid internal vagueness? For every problem of the real world that is to be grasped by Newton’s method of the exact science, it is necessary to choose a group of suitable quantities, find the natural laws that apply in the real world between them, and describe them in mathematical language. We get a mathematical knowledge (cognitive) model of a given part of the real world. A group of selected quantities forms a '''discrete Newtonian filter''' (sieve) through which man ‘’look’’ at a given part of the real world. Thus, in exact science, a given part of the real world is represented by a group of suitably chosen quantities and mathematically (programming language) described relations between them (more precisely between their names – symbols denoting them).

'''Exact science''' ''is a method that allows knowledge about the real world to be acquired and recorded so that it is part of the exact world. That is the method of modeling the real world by means of exact world, in other words, a method to mathematize the science.''

Even exact science needs to have a tool, with which it can describe the '''uncertainty''' of the results (obtained – knowledge), whether out of necessity or the need to abandon excessive precision. Since that cannot (must not) be an internal vagueness, it can only use linguistically graspable uncertainty (external vagueness). For this purpose it has for its disposal a description of fuzzy or stochastic values of quantities, and fuzzy or stochastic relations (represented by mathematical functions) between quantities.
 
The difference between the non-exact sciences (called descriptive) and the exact sciences is that the former use natural human cognition (with the Russell’s filter of vagueness) and refined natural language, and the exact sciences use cognition based on the use of Newtonian discrete filter and thus the use of quantities, and artificial formal language. Artificial formal language also brings a powerful tool to exact science, which is formal [[inference]] (information formal processing) known from mathematics.

The above-mentioned tools of exact and non-exact science are general principles, and different branches of science use them in combination with both. They have their parts exact and inexact. Purely exact sciences, such as theoretical physics or mathematics, use natural language as meta-language.

Exact science provides most trustworthy knowledge. The question can certainly be raised as to whether all science can be transformed into an exact science. The answer is not. The condition for the establishment of an exact science is to find suitable quantities, and this is possible only for a small part of the real world and for specific views of it. In other words, the filter of vagueness makes it possible to vaguely know many; Newton's discrete filter makes it possible to know only little but exactly.