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Disagreements of type 1) should be argued in the court of experiment;
reality will decide.
Disagreements of the type 2) are often concerned with individual and
institutional cultural differences. Differing conceptual models may be
equally useful (and therefore equally "true") to different physicists.
The differences can border on the religious. That is why type 2)
discussions generate so much fervor that the essence of the conceptual
differences becomes unintelligible to a sympathetic bystander (me). No
one ever gets so worked up over type 1) differences (the more "proper"
realm of physics).