## CHAPTER ONE

# THE GENERAL THEORY OF INFERENCE AND TERMS

## 2. TERMS

The terms may be represented by individual words, groups of words, letters, symbols and their combinations. It is an extralogical question, which fragments in one or another specific language are considered as terms. In order to apply the rules of logic, one should possess a certain practical skill for decomposition of the speech flow into those elements for which the rules are formulated. For instance, in order to apply to the expression 'AH metals are electrically conducting' the rules of the logical theory of quantifiers and predication, one has to be able to identify in this expression the logical operator (quantifier) 'all', the subject-term 'metal', the predicate-term 'electrically conducting' and the predicativity operator connecting these terms into a whole statement. This predicativity, operator is expressed in this case through writing the terms in a sequence. The rules of logic are applicable to terms of specific languages only according to the following scheme: if a given phenomenon is a term, such and such assertions of logic hold for it. A similar principle is valid for statements. Each term denotes or names certain objects (the word 'object' here can mean anything), i.e., it has a value. Thus, the term 'table' denotes tables; the essence of the value of this term is that it denotes exactly tables, and not other objects; precisely which objects are denoted by the term 'table' can be established by pointing to individual visible tables, by means of demonstrations of drawings or photographs of tables, through description of tables by a set of words and sentences; in physics the term 'elementary particle' denotes physical objects, the description and enumeration of which can be found in the corresponding works on physics. We shallsay that a term b is subordinated by value to a term a (or that an object a is an object b; or, to put it more briefly, that a is b) if and only if the following is valid: any object denoted by the term a can be denoted also by the term b. For instance, a term 'number' is subordinated by value to a term 'an even number' (or, an even number is a number); a term 'elementary particle' is subordinated by value to a term 'electron' (or, an electron is an elementary particle). If a is b (or a term b is subordinated by value to a term a), in symbolic form it will be written as a—b. If a is not b (i.e., not every object denoted by the term a can be also denoted by the term b), the symbolic form of it will be If a—±b and b—±a, we shall say that the terms a and b are equal in value and write it symbolically as Examples of terms, identical in value: 'diamond' and 'equilateral quadrangle'; 'table', 'der Tisch' and 'CTOJT'. The relation of subordination of terms by value may be used to define other relations of terms, in particular, the following one: a term a is called common (generic) with respect to a term b, and a term b is called special (a species) with respect to a if and only if b-^a and ~ (a-^b). For example, the term 'diamond' is a species term with respect to the term 'quadrangle', while the latter is generic with respect to the former.

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