Rational Reconstructions of Modern Physics by Peter Mittelstaedt

Author:Peter Mittelstaedt
Language: eng
Format: epub
Publisher: Springer Netherlands, Dordrecht

From the logical point of view, one has to show that the ontology of unsharp properties leads to a language and logic of unsharp propositions. At this point a clear distinction must be made between two different relaxations of the concept of value definiteness. For a sharp (s) proposition A value definiteness means that either A or the counter proposition can shown to be true. In other words, there is a proof procedure that leads either to A or to . In intuitionistic logic L iand in intuitionistic quantum logic LQithis value definiteness (v) is not assumed but replaced by the relaxed value definiteness [v] which means that in general neither a proof of A nor a proof of is known. However, if accidentally a subset {A1…An} of elementary propositions is value definite in the sense of (v), then this value definiteness is inherited to all propositions which are finitely connected by the Aiand the logical connectives ∧, ∨, ¬, and →.

If sharp (s) propositions are replaced by propositions which are in general unsharp, expressed by {s}, then for an unsharp proposition A the two possibilities A and are no longer mutually exclusive. This means that the properties P(A) and P() can both be attributed to the object system S. Under these conditions, the proposition is no longer formally false, which leads to various kinds of paraconsistent logical systems. The relaxed value definiteness that is induced by the unsharpness assumption {s} will be denoted here by {v}. This weakened value definiteness means that the unsharp predicates A and will both objectively pertain to the system. This corresponds to a realizable experimental situation in a measurement process. Hence we find that there are two quite different relaxations of the value definiteness of orthomodular logic:1.intuitionistic value indefiniteness [v]

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