By Zinov'ev A. A. (Зиновьев Александр Александрович)
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For the sake of brevity and more clear representation, the implicit definitions are given the form of tables. It is obvious from the above that the meaning of the term 'true' depends on what kind of statements x A y, x v y, ~ x, etc. it refers to. And this term has no universal and general meaning, regardless of the statement structure. In general, it has no meaning at all by itself, if taken separately from the expressions where it plays the role of the predicates. The situation for the term 'not-true' is similar.
The following rule appears not to hold in this case. But it is valid without exception. This rule appears to be wrong because of its being confused with another 44 CHAPTER ONE statement which is indeed not valid in the general case (if u2 is u1 or if u2 follows from M1, this statement is correct). It is appropriate to differentiate between conditions and coordinates from the point of view of the possibility of formulating new rules, not coinciding with (l)-(8). For instance, the following rule is possible: where a is a variable for empirical individuals that occurs as free in x, and M is a predicate 'possible'.
These are (what we term) 'realizable' statements. The overwhelming majority of scientific expressions are realizable. Such an expression as x v ~ x is true for any statements x regardless of any empirical research; it is true exclusively for the reason that it is constructed of the statements x and ~ x by means of the operator v, and because there are certain rules for ascribing truth values to this kind of statement. On the other hand, such an expression as x A ~ x is not-true by virtue of the rules for ascribing truth values to statements with operators ~ and A .
Logical physics by Zinov'ev A. A. (Зиновьев Александр Александрович)