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It is important to note that the rejection of the axioms of a theory does not necessarily lead to the rejection of its theorems. The theorems may retain their place in the scientific mosaic after the axioms from which they are derived get rejected. Each theorem 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 theorem or theorems are compatible with the propositions of the newly accepted theory, they remain in the scientific mosaic. Conversely, if the theorems are incompatible with the propositions of the newly accepted theory, they become rejected as per the theory rejection theorem.
The theory rejection theorem has another important implication. A theory can become rejected not only when replaced by theories of its own discipline, but by theories of other disciplines as well. Normally, we think that a physical theory becomes rejected when a new theory physical theory that is incompatible with the old one becomes accepted. It is possible that the physical theory becomes rejected, because a new chemical or biological theory that is incompatible with the physical theory becomes accepted.[[CiteRef::Barseghyan (2015)|p. 171]]
[DIAGRAM FROM P.171 OF BARSEYGHAN 2015 NEEDED]
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