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Implicit in the theorem is the idea that each theory is assessed on an "individual basis by its compatibility with the propositions of the newly accepted theory".[[CiteRef::Barseghyan (2015)|p. 168]] If it turns out that a previously accepted theory is compatible with the newly accepted theory, it remain in the agent's mosaic.
 
Barseghyan notes that, although we normally expect a theory to be replaced by another theory in the same "field" of inquiry, this is not necessarily the case. For example, he writes, "HSC knows several cases where an accepted theory became rejected simply because it wasn’t compatible with new accepted theories of some other fields".[[CiteRef::Barseghyan (2015)|p. 171]]
 
Barseghyan summarizes '''the theory rejection theorem''' as such:
<blockquote>In short, when the axioms of a theory are replaced by another theory, some of the theorems may nevertheless manage to stay in the mosaic, provided that they are compatible with the newly accepted theory. This is essentially what the ''theory rejection theorem'' tells us. Thus, if someday our currently accepted general relativity gets replaced by some new theory, the theories that followed from general relativity, such as the theory of black holes, may nevertheless manage to remain in the mosaic. [[CiteRef::Barseghyan (2015)|p. 171]] </blockquote>
|Resource=Barseghyan (2015)
|Prehistory=
There weren’t many elements of the Aristotelian-medieval mosaic that maintained their state within the Cartesian mosaic. The conception of plenism was among the few that survived through the transition. In the Cartesian system, plenism followed directly from the assumption that extension is the attribute of matter and that no attribute can exist independently from the substance in which it inheres ...
In short, when the axioms of a theory are replaced by another theory, some of the theorems may nevertheless manage to stay in the mosaic, provided that they are compatible with the newly accepted theory. This is essentially what the theory rejection theorem tells us. Thus, if someday our currently accepted general relativity gets replaced by some new theory, the theories that followed from general relativity, such as the theory of black holes, may nevertheless manage to remain in the mosaic. [[CiteRef::Barseghyan (2015)|p. 168-170]] </blockquote>|Example Type=Historical}}{{Theory Example|Title=Theology|Description=The rejection of ''theology proper'' (the study of God, his being, his attributes, and his works) from the scientific mosaic is a historical illustration of the ''Theory Rejection theorem'' and how accepted theories in one field may become rejected due to theories in other fields. In essence, theological propositions were rejected, but were not replaced with more theological propositions. It is difficult to track the exact dynamics of theology's "exile," but it is possible that these propositions were rejected and replaced with the thesis of ''agnosticism'', or that they were rejected due to the acceptance of ''evolutionary biology''. The "exile," as Barseghyan terms it, could have also been a very gradual process, and that the rejection of theological propositions came about for different reasons in different mosaics. Despite the difficulties in tracking down the exact dynamics of the gradual rejection of theology from the scientific mosaic, Barseghyan summarizes the evidence as such: "what must be appreciated here is that a theory can be replaced in the mosaic by theories pertaining to other fields of inquiry".[[CiteRef::Barseghyan (2015)|p. 172]]|Example Type=Historical}}{{Theory Example|Title=Astrology|Description=Another example of the theory rejection theorem, specifically explaining that theories may not only be rejected because of the acceptance of new theories in their respective theories, is the case of ''natural astrology'' presented in [[Barseghyan (2015)]]. <blockquote>The exile of astrology from the mosaic is yet another example. It is well known that astrology was once a respected scientific discipline and its theories were part of the mosaic. Of course, not all of the astrology was accepted; it was the so-called ''natural astrology'' – the theory of celestial influences on physical phenomena of the terrestrial region – that was part of the Aristotelian-medieval mosaic. ... Although, for now, we cannot reconstruct all the details or even the approximate decade when the exile of natural astrology took place, one thing is clear: when the once-accepted theory of natural astrology became rejected, it wasn’t replaced by another theory of natural astrology.[[CiteRef::Barseghyan (2015)|p. 172]]</blockquote>
|Example Type=Historical
}}

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