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|Formulation File=Necessary-mosaic-split-box-only.jpg
|Description=Necessary [[Scientific Mosaic|mosaic]] split is a form of mosaic split that must happen if it is ever the case that two incompatible [[Theory|theories]] both become accepted under the employed [[Method|method]] of the time. Since the theories are incompatible, under the [[The Zeroth Law|zeroth law]], they cannot be accepted into the same mosaic, and a mosaic split must then occur, as a matter of logical necessity.[[CiteRef::Barseghyan (2015)|pp. 204-207]]
{{PrintDiagramFile|diagram file=Necessary-mosaic-split.jpg}}
 
As shown in the figure above, the necessary mosaic split theorem follows as a deductive consequence of the [[The Second Law|second law]] and the zeroth law. Per the zeroth law, two incompatible elements cannot simultaneously remain in a mosaic, and per the second law any theory that satisfies the method of the time (and the assessment of the theory by the method is not inconclusive) is accepted into the mosaic. This creates the apparently contradictory situation where either of the two theories A) must be accepted because it satisfies the employed method and B) must not be accepted because it in not compatible with another accepted theory.
The necessary mosaic split theorem is thus required to escape the contradiction entailed by the acceptance of two or more incompatible theories. In a situation where this sort of contradiction obtains the mosaic is split and distinct communities are formed each of which bears its own mosaic, and each mosaic will include exactly one of the theories being assessed. By the [[The Third Law|third law]], each mosaic will also have a distinct method that precludes the acceptance of the other contender theory.

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