There is a very common fallacy, here called the separation fallacy, that is involved in the interpretation of quantum experiments involving a certain type of separation such as the: double-slit experiments, which-way interferometer experiments, polarization analyzer experiments, Stern-Gerlach experiments, and quantum eraser experiments. In each case, given an incoming quantum particle, the apparatus creates a [...]
Archives for Philosophy
From Partition Logic to Information Theory
A new logic of partitions has been developed that is dual to ordinary logic when the latter is interpreted as the logic of subsets rather than the logic of propositions. For a finite universe, the logic of subsets gave rise to finite probability theory by assigning to each subset its relative cardinality as a Laplacian probability. The analogous development for the dual logic of partitions gives rise to a notion of logical entropy that is related in a precise manner to Claude Shannon’s entropy.
From propositional logic to subset logic to partition logic
The modern category-theoretic treatment of logic, the variables in “propositional” logic should be interpreted as subsets of some given nonempty universe set U, i.e., propositional logic is subset logic. Since partitions on a set are dual to subsets of the set, the idea arises of a dual logic of partitions.