By Zinov'ev A. A. (Зиновьев Александр Александрович)
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Sample text
While the value 'true' may be eliminated from the language, it cannot be removed from the situation in which the statements are used. It expresses the relation of the statements to the states, expresses the act of acceptance of the statements or of agreeing with what they say. So that the replacement of *x is true' with x means that the recognition of x is realized not through linguistic means (not through the predicate 'true') but in a different way (by the very fact of pronouncing or writing x, as is done most frequently).
In symbolic form this definition will be written as x = Df. , the defining statement). If one adopts a definition x = Df. y, this means the adoption of the statement x = y. More frequently (for the sake of convenience) this kind of definition is written in the following form: 'We shall say that x if and only if / . For instance, 'We shall say that a formula is provable in S if and only if it is an axiom of S or is obtained from the axioms in S according to the rules of inference in S\ This form simply implies elimination of a part of the means of definition (for example, reference to the meaning of statements); this makes the inference of the consequences from the definition easier.
We shall call such expressions local. The set of local statements includes those the THE GENERAL THEORY OF INFERENCE AND TERMS 19 truth values of which may vary depending on the individuals involved. But since the spatial and temporal location of various individuals differ in one or another way, the change of the individual to which the statement refers is the change of the spatial and temporal domain of the statement usage. Similarly, one may say that the dependence of the statements' truth values on the conditions can be reduced to spatial and temporal dependence (the change of conditions implies either change of location or change of time).