Both left and right are concerned with the pursuit of truth (or Truth, if you prefer. Hell, I'm a philosopher I'm happy with TRUTH), provided you exclude the extreme fringe of leftist relativist academics and right wingers who unquestioningly and unreflectively embrace religious doctrine and won't even engage with contrary evidence. Personally I think far too much attention has been paid to each of these groups, and that people who don't care about the truth can be safely ignored in debates (what else would we be discussing, if not what's true?). Methodologically, though, rightists have more respect for traditions as mechanisms for the production of knowledge than do leftists. (and i'm purposely avoiding the terms liberal and conservative here because I don't think that they have any clear meaning in contemporary American politics (to see this just consider how the republican party, an ostensibly conserrvative group, seems to be very concerned about economic "liberty" at the expense of other values.)