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|Description=While some theories and methods can coexist in the same mosaic, others seem to be incompatible. So, the task is to understand when two theories (or two methods) can and when they cannot coexist in the same mosaic. For instance, the theories general relativity and quantum physics as it relates to how they explain singularities in black holes are inconsistent, however they remain in the mosaic. On the other hand, inconsistencies between the Aristotelian worldview and Catholic theology means both required modification before they were compatible with eachother .[[CiteRef::Barseghyan (2015)|p. 159-161]]. What conditions allow for the coexistence of elements, and what conditions require modification or rejection to take place?

|Prehistory=There are several historical episodes that appear to explicate the mechanism of theory and method incompatibility. For instance, Aristotelian physics appears to contradict some aspects of Catholic scripture in cases, one of which was regarding the status of God’s power. Scripture asserted God as an omnipotent entity, however Aristotelian physics appeared to limit some physical phenomena such as the existence of empty space. The question arose: could God create empty space? In this case, these two elements of the mosaic were inconsistent with eachother and considered incompatible as condemnation came from the church to force natural philosophers to accept the concept of empty space in the name of God’s omnipotence .[[CiteRef::Thijssen (2003)]]. The Aristotelian theory of empty space was removed from the mosaic and replaced with the absolute theological declaration. This seems to show that when incompatibility is discovered, certain theories can push out or force change in others.

The theories of general relativity and quantum physics generally deal with separate aspects of physics, however on the matter of singularities in black holes, they differ .[[CiteRef::Barseghyan (2015)|p. 159-160]]. However, this inconsistency is tolerated, and the modern scientific community appears to accept both theories as the best description of what happens in the singularity of a black hole. Potentially, this situation shows that when two theories deal with different domains that are each considered the best possible description for their respective domains, inconsistency in singular propositions is tolerated differ .[[CiteRef::Barseghyan (2015)|p. 160]].

Another example of incompatibility appears to be between Newtonian physics and Descartes’ physical theories. This appears to be a historical case of two inconsistent theories that both potentially satisfied the vague methods of the time, and illuminates a case of incompatibility that leads to a separation within the scientific community differ .[[CiteRef::Barseghyan (2015)|p. 212-213]].|History=The zeroth law, in answer to the question of the mechanism of compatibility, was originally proposed in 2012 as forbidding inconsistency in the mosaic.[[CiteRef::Barseghyan (2015)|p. 153]]. In 2013, Rory Harder argued that inconsistency-intolerance was a practical impossibility and unsupported by the historical record, resulting the current formulation of the zeroth law.