The analysis of a problem of definition of vague predicates

Іhor Dutsiak

As a result of the executed research a sources of paradoxes type of sorites are revealed. It is offered to bring in definitions of words with the semantics of the vagueness the information which will interfere creating of paradoxes of type of sorites. It is proposed to clarify the definition of concept of “a heap”.

semantic of vagueness

The article states the results of the research of the vague concepts defining problem. The vague concepts include such concepts which have no fixed boundary between the denotation and denotation of the adjoining concepts. These are the concepts which can be used for forming the paradoxes like "sorites paradox" or "paradox of the heap". The essence of this paradox is that while reducing the quantity of sand grains of the sand heap by removing the grains individually, we receive on every step the amount of grains that slightly differs from the previous one. The number of grains on each step of such process negligibly differs from the previous one. That is why the tendency to establish the line between the “heap” and “non-heap” is considered as unreasonable voluntarism. As a result it comes to the contradiction – one grain of sand is also a heap.

The research method considered the analysis of establishing the boundaries of vague concepts in practical usage, namely in activities involving the defining of objects as big or small. The results of the analysis are generalised for all vague concepts. It enabled us to formulate recommendations concerning the defining of vague concepts.

The research results are as follows. Mainly people should use words without pointing the fixed boundaries of the concepts except for cases when it is needed. The fixed boundaries of concepts are used in special cases. In case of defining the word "heap" it is possible to set the fixed boundary of denotation of this concept. The basis of this definition is the minimum angle of natural slope or heap integer radius to height ratio approximate to the mentioned minimum angle of natural slope.

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