July 26th, 2012
A theory is distinct from a mere scientific explanation. Scientific explanation requires a causal explanation, which requires a law-governed explanation. Natural law describes but does not explain natural phenomena. Newton’s law of universal gravitation described, but did not explain, what caused gravitational attraction. Theories unify empirical regularities and describe the underlying process that accounts for these phenomena. Within theories are axioms, a small set of postulates, which are not proved in the axiom system but assumed to be true.
A theory goes beyond natural laws and scientific explanations in explaining the scientific explanations. A theory refers to a body of explanatory hypotheses for which there is strong support. Theories are a conjunction of axioms (of the laws of nature) and correspondence of rules specified in a formalized ideal language. This ideal language is composed of three parts: logical terms, observational terms, and theoretical terms. The logical terms were initially treated as analytic claims (particularly under the hypothetico-deductive model). Observational claims were to be unproblematic, understood as referring to incorrigible sense-data and later to publicly available physical objects. Correspondence rules were used to connect theoretical language to observational claims.
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July 26th, 2012
The level three multiverse is particular to a certain interpretation of quantum mechanics being Hugh Everett’s Many Worlds Interpretation. It is a mathematically simple model in support of unitary physics. Everything that can happen in the particle realm actually does happen. Each of the many worlds following a split represents one of the possible worlds remaining after the event which led to the split. There are no interactions between these worlds. No observer or inhabitant of them will notice anything about the other worlds.
Everett’s interpretation is not impossible due to the fact that we do not experience the continual splitting of our world. Observers would only view their level one multiverse, but the process of decoherence—which mimics wave function collapse while preserving unitary physics—prevents them from seeing the level three parallel copies of themselves. It is no more contradicted by our failure to experience the splitting than the theory that the earth rotates is contradicted by our failure to experience its movement. 
 Max Tegmark, “The Multiverse Hierarchy,” arXiv:0905.1283v1 (accessed March 15, 2011), 10.
 Some of the commentary is summarized by Karl Popper in Quantum Theory and the Schism in Physics, ed. W.W. Bartley, III (Totowa, NJ: Rowman and Littlefield, 1982): 91-2.