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|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)|ppp. 204-207]]

Barseghyan illustrates the necessary mosaic split theorem with the example of the French and English physics communities circa 1730, at which time the French accepted the Cartesian physics and the English accepted the Newtonian physics.[[CiteRef::Barseghyan (2015)|p.203]] These communities would both initially accepted the Aristotelian-medieval physics due to their mutual acceptance of the Aristotelian-medieval mosaic until the start of the eighteenth century[[CiteRef::Barseghyan (2015)|p.210]] but clearly had different mosaics within a few decades. According to the second law both the Cartesian and Newtonian physics must have satisfied the methods of the Aristotelian-medieval mosaic in order to have been accepted, but since both shared the same object and posited radically different ontologies they were incompatible with one another and could not both be accepted, per the second law. The necessary result was that the unified Aristotelian-medieval community split and the resulting French and English communities emerged, each with a distinct mosaic.

The most direct early source suggesting that there are circumstances in which communities necessarily obtain different beliefs about scientific subjects is the work of [[Karl Popper]], whose system of conjectures and refutations suggests that progress in science is obtained by challenging our currently accepted views by trying to refute them.[[CiteRef::Popper (1963)|p.68]] It follows that if there are situations in which a community has two theories that are both resistant to refutation then both should be accepted. This model - whereby there is a definite algorithmically determined method for theory assessment - was dominant among positivist philosophers and would prevail until the historical turn, when a model more closely reminiscent of the [[Possible Mosaic Split theorem (Barseghyan-2015)|possible mosaic split theorem]] emerged.[[CiteRef::Laudan, Laudan, and Donovan (1988)|p.5]]