Quantum mechanics without interpretation

It is shown that the independence of the continuum hypothesis points to the unique definite status of the set of intermediate cardinality: the intermediate set exists only as a subset of continuum. This latent status is a consequence of duality of the members of the set. Due to the structural inhomogeneity of the intermediate set, its complete description falls into several “sections” (theories) with their special main laws, dimensions, and directions, i.e., the complete description of the one-dimensional intermediate set is multidimensional. Quantum mechanics is one of these theories. PACS numbers: 03.65.Bz, 02.10.Cz, 11.25.-w The concept of discrete space is always regarded as a unique alternative to continuous space. Nevertheless, there is one more possibility originated from the continuum problem: the set of intermediate cardinality represents the golden mean between the opposing concepts. But although the continuum problem has been solved [1], the status of the set of intermediate cardinality is still unclear. The commonly held view is that, according to the independence of the continuum hypothesis (CH), we can neither prove nor refute existence of the intermediate set and, therefore, CH or its negation must be taken as an additional axiom. However, it may be stated that there exists a unique definite status of the intermediate set which is consistent with the independence of the continuum hypothesis. Since, by definition, the set of intermediate cardinality I should be a subset of continuum R, the independence of CH may be understood as impossibility, in principle, to separate the subset of intermediate cardinality from continuum. In other words, the independence of CH means that for any real number x ∈ R the sentence x ∈ I ⊂ R is undecidable. Reasons of this inseparability, if any, should be investigated. This latent status is the only definite status of the set of intermediate cardinality that is consistent with the generally accepted solution of the continuum problem. However, in order to state that the status follows from the independence of CH, it is necessary to know that standard Zermelo-Fraenkel set theory