A school of philosophical thought which I believe can be characterised by the statement that only things which are measurable, or which can be derived logically from no assumptions, are real. Or rather, that only with such things does it mean anything to say that they are real. In other words, it is meaningless to claim something as true if its truth or falsity doesn't affect the universe (because anything which affects the universe is, in theory, measurable), unless it is necessarily true or false by logic alone.
This is essentially saying that science and pure logic (including maths) not only are the only ways of discovering truth, but that their limits define when "truth" has any meaning. So in one simple concept, we manage to do away with all those annoying unanswerable questions that have kept amateur philosophers blabbing for so long - such as the existence of a God which does not objectively affect the world, or whether my set of ethics is "better" than yours (unless one is logically inconsistent or makes demonstrably untrue assumptions about the world). It also states, for example, that to ask which of the various mathematically equivalent interpretations1 of quantum mechanics is "true" is meaningless, since they necessarily make the same predictions and so can't be differentiated. This ties in with Karl Popper's ideas of science being about what is "falsifiable".
Of course, you could say it's a bit of a cop out, just rebutting the questions of your opponents by calling them meaningless, and the fundamental acceptance of induction and deduction could also be called into question - but this is a philosophy which has definitely had a great effect on modern scientific thought.
1 - e.g. the Copenhagen interpretation which holds that the wave function is the "ultimate reality", as opposed to interpretations like Bohm's dealing with non-local hidden variables, which as I understand it is mathematically and hence scientifically equivalent, but philosophically quite different (in particular, the Copenhagen version is non-deterministic, while Bohm's is deterministic). See Ooolong's writeup at quantum non-locality for more.