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One believes the theory, the other believes some different, incompatible theory instead.
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Conservatives have justified this failure with two incompatible theories.
It argued that unifying the currently incompatible theories of quantum mechanics and general relativity would produce a postmodern, "liberatory" physics.
Tolman found his solution to this problem of incompatible theories after his association with the Vienna Circle of Logical Positivists, whose deterministic teachings he brought to the attention of U.S. psychologists about 1920.
Neo-Nagelian accounts have attempted to solve Nagel's problem of reduction between putatively incompatible theories.
Furthermore proponents of incompatible theories often produce impressively similar observational data.
But is the pluralist alternative that incompatible theories are somehow "equally true"?
There is, of course, no problem about incompatible theories, as structures of propositions, co-existing.
According to the underdetermination thesis, incompatible theories can be consistent with available evidence.
If set theory were merely representational then both of the incompatible theories could be equally useful as representational tools, though probably for different representational tasks.
Realists reject the anti-realist claim that there are two descriptively equivalent logically incompatible theories in cases such as the space-time one.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com