The phrase "open mind" has nothing whatsoever to do with evidence.
It means to allow the thoughts and ideas of other people to be considered equally alongside ones own.
Considering all ideas to be equal is not a viable method of problem solving. Open mindedness has not to do with considering all ideas to be equal; it is giving all ideas equal consideration - i.e., given equal *chance* to be identified as useful to a given problem.
o·pen-mind·ed
/ˈoʊpənˈmaɪndɪd/ [oh-puhn-mahyn-did]
–adjective
1. having or showing a mind receptive to new ideas or arguments.
2. unprejudiced; unbigoted; impartial.
(
http://dictionary.reference.com/browse/open-minded)
If multiple ideas are brought up in a conversation, the relative accuracy must be considered in any worthwhile problem-solving process. Open mindedness requires taking them all as possibly true *initially*, and not rejecting them out of hand; it does not require that you then hold them all at equal value points after they have been assessed (based on the current situation and knowns).
For example, three people are lost in the woods:
Person 1: "We need to figure out where we are. We left our car on route 1 in the middle of Maine an hour ago, so we must still be in Maine."
Person 2: "Agreed. In fact, we must be 1 hour's walk or less from our car and route 1."
Person 3: "I think we are in Alaska."
All three people's ideas should be given equal initial consideration. However, after that initial consideration, person's 3 idea, while it cannot currently be proven to be incorrect (they are lost, afterall), is so unlikely to be true that it
should be devalued as a likely option.
Both ideas of Person 1 and 2 can be considered likely correct given the known aspects of the situation, however, Person 2's idea hold more useful information than Person 1, without violating logic. It can therefore be said that both Person 1 and 2 are
likely correct, but Person 2's idea is
more complete.