John, another nice example is provided by the history of ideas in 
what is now called thermodynamics. I have an 1815 Brittanica which 
reviews the two rival theories of heat: one that it is a state of 
motion of molecules, the other that it is a fluid, called "caloric". 
It is an excellent article, running to many pages and thoroughly 
detailed, including the mathematical derivation of most of the basic 
results. And as it points out, there was (at that time) no way to 
decide which of these theories was "right", and that indeed they 
produced identical mathematical equations, so one could simply 
believe one's favorite story and still get the sums right.  (01)
Pat
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