Логика абстракций (методологический анализ). Ч 2

Resume Part Two of the «Logic of Abstraction» continues an interval analysis of the abstract work of the mind in both the applied and theoretical fields of knowledge. The emphasis, however, is transferred from the general issues of the formation and meaning of abstractions, discussed in Part One, to the problems of developing the logical models of the latter. The author believes that it is the logical analysis that can ensure the necessary completeness of specification and identification of these abstractions and the related terminology. In particular, the classical problem of the logical meaning of relationships between identity and indiscernibility is discussed in detail for this purpose. The author presents a formulation of the logic of im/fscermftf'/fffes (as a relational system of PB-algebras), which, in Ms opinion, would allow to specify the underlying semantics of the said relationships, separating the «puncnform* meaning of identity (related to the abstractions of individuation and constancy) from the interval meaning of indiscernibility (related to the abstraction of indiscernibility and uncertainty of empirical descriptions). The author's analysis results in the conclusion that in the real process of cognition any scaling used for comparison and measurement of the objects under observation occurs within a logarithmic scale, of which the ends are absolute equality (logical identity) and absolute indiscernibility - both, in fact, unattainable. In a sense, this justifies Poincare's hypothesis of a «discontinuity jump» (le point de saut) between theory and experience, of «jumping over the abyss» we have to do on our way from empirical data to theoretical generalisations. The book also discusses some fundamental issues of logic and mathematics.