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|Resource=Barseghyan (2015)

|Prehistory=The idea that our beliefs should not contradict each other is one of the oldest in philosophy. It can be traced, at least, to the time of Aristotle (384-322 BCE)[[CiteRef::Carnielli and Marcos (2001)]]. In classical logic, it derives from the principle of explosion, which states that a contradiction entails every other sentence. Any system of beliefs that contains a contradiction, since it compels belief in anything and everything, is therefore known as a trivialism. This deceptively simple premise is implicit in most philosophies of science, and in philosophy overall. For this reason it is rarely stated outright within a philosophical or scientific framework. However, the use of contradictions to reject particular theories is important in frameworks as diverse as Isaac Newton’s Four Rules of Scientific Reasoning (non-contradiction is the fourth)[[CiteRef::Newton (1689)]], [[CiteRef::Smith (2007)]] and [[Karl Popper]]’s 'Logic of Scientific Discovery'[[CiteRef::Popper (2005)]].

The Logical Argument: A [[Scientific Community|scientific community]] cannot always know all the logical consequences of its [[Theory|theories]] at the time of their acceptance. Logical consequences of theories often emerge later, in the course of scientific research. Therefore, scientists can never rule out the possibility that their mosaic contains a contradiction. Thus, the presence of contradiction in the consequences of the theory cannot be what determines its presence in a mosaic.

The Historical Argument: There are historical instances in which a scientific community has knowingly accepted a contradiction. One such example is the contradiction in the current mosaic between consequences of Einstein's theories of special and general relativity and quantum mechanics [[CiteRef::Harrison (2000)]]. Einstein's relativity maintains that all signals are local. That is, no signal can travel faster than light. Quantum theory, on the other hand, predicts faster than light influences. This has been known since the 1930's [[CiteRef::Einstein, Podolsky, and Rosen (1934)]], yet both quantum theory and relativity remain in the mosaic.

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