>Often I do this with people who doesn't quite believe that science
>holds all the answers.
Personally, I don't think science does hold all the answers - it only holds all the * provably* true answers. If we make the (bold) assumption that the Universe is the embodiment of a formal system, then there will be truths which are not provably correct, but true nonetheless.
I've tended to imagine science as the formulation of a set of sentences within this system which are then proved or disproved. As such, it is consequently limited to things than can be proved or disproved, but obviously leaves out that which is true, but can not be proved.
However, anything which is true, but cannot be proved within the system, is also probably quite useless (from an engineering or application point of view). For example, it is possible that dowsing does work (i.e. the behaviour of the rod is effected by a body of water below it) - but only at random points in time, and under random variable conditions. It is therefore a useless art, as the conditions necessary for it to function can never be replicated.