Editing Vagueness (section)

=== Vagueness internal and external ===
Cognition and language (Law of maintaining accuracy of information): Communication language should have the same amount of vagueness, as have information gained by cognition (source of the information). That means, language must be tuned to appropriate cognition considering vagueness. This is one of secondary tasks of vagueness.

A person is able to speak about his inherently vague knowledge (contained in the intrapsychic cognitive model represented in hypothetical intrapsychic languages) in natural (generally informal language, e.g. Esperanto), of course only vaguely.<ref name="russell australasian"/> The vagueness of knowledge caused by the ''filter of knowledge'' is primary, we call it '''internal vagueness''' (i.e. intrapsychic). The vagueness of a person's subsequent utterance is secondary vagueness. This utterance (transformation from intrapsychic languages to external communicative languages - it is called a ''formulation'', see the [[semantic triangle]]) cannot reveal all the content of the personal intrapsychic cognitive model with all its inherent vagueness. The vagueness contained in the linguistic utterance (of external communication language) is called '''external vagueness'''.

Linguistically, only external vagueness can be grasped (modeled). We cannot model internal vagueness; it is part of the intrapsychic model, and this vagueness is contained in (vague, emotional, subjective and variable during time) interpretation of constructs (words, sentences) of '''informal language'''.<ref name="ReferenceA">Osgood C. E, Suci G., Tannenbaum P.: The Measurement of Meaning. Urbana, Illinois, University of Illinois Press, 1957</ref> This vagueness is hidden for the other human, he can only guess the amount of it. Informal languages, such as natural language, do not make it possible to distinguish between internal and external vagueness strictly, but only with a vague boundary.<ref>Bek R., Křemen J.: Logic, Cognitive Model and Reality, in: Proceedings of the 8th international symposium LOGICA  ‘94, T.Childers, O. Majer ed., publ. by PHILOSOPHIA, The institute of Philosophy of the Academy of Sciences of Czech Republic, Prague 1995, pp. 193-199.</ref><ref>Křemen, J. : Notes on Vagueness of Knowledge: Fuzzy Tools. In: Acta Polytechnica, Vol. 39, No 4/1999, pp. 81- 91. ISSN 1210-2709, Czech Technical University in Prague</ref>

Fortunately, however, informal languages use appropriate language constructs making meaning a little uncertain (e.g. ''indeterminate quantifiers'' POSSIBLY, SEVERAL, MAYBE, etc.). Such quantifiers allow natural language to use external vagueness more strongly and explicitly, thus allowing internal vagueness to be partially shifted up to external vagueness. It is a way to draw the addressee's attention to the vagueness of the message more explicitly and to quantify the vagueness, thus improving understanding in communication using natural language. But the main vagueness of informal languages is the internal vagueness, and the external vagueness serves only as an auxiliary tool.

'''[[Formal languages]]''', mathematics, formal logic, programming languages (in principle, they must have ''zero'' internal vagueness of interpretation of all language constructs, i.e. they have exact interpretation) can model external vagueness by tools of vagueness and uncertainty representation: [[fuzzy sets]] and fuzzy logic, or by [[stochastic]] quantities and stochastic functions, as the exact sciences do. Principle is: If we admit more vagueness (uncertainty), we can gain more information during cognition. See e.g. possibilities of deterministic and stochastic physic. In other cases cognitive model of certain part of real world may be simplified, such a way, that certain amount of deterministic information is possible to replace by fuzzy or stochastic one.