I've just re-read what I wrote above and see that I followed If you believe something ... ask yourself why with I don't believe everything can be answered by science even in principle. So I suppose I am duty bound to explain why I believe that! To cut a very long story short, Hilbert, Gödel, Mandelbrot and in a slightly different way computational theory's NP-complete and even Riemann's geometry all show limitations of what is possible in mathematics. Not stuff we don't know: stuff whose unknowability is woven in the fabric of mathematics itself. And since mathematics is at the heart of science, there is by implication equivalent limits to science. However, this may not be significant. To use an analogy: think of the real world as a table and mathematics as a table-cloth. Even though the table cloth has edges it could still be big enough to cover the table. Alternatively it can fail to cover it to a greater or lesser extent. Whether the 'mathematical tablecloth' is big enough to cover the table that is the 'real world' is not something I know, and may only be knowable via an example where it does not. The chaotic behaviour of things like waterflow, though, make me suspect the table cloth is too small.

So that's why I think there are limits to science. But that does not deny the usefulness of science or the value of taking a scientific approach to life in general. Moreover, I also think that a Christian is under a specific obligation to do so. Mark says that when Christ was asked what was the greatest commandment he said "you must love the Lord your God with all your heart, with all your soul, with all your mind and with all you strength". Now, this is almost, but not quite, a quotation from Deuteronomy: the importance is that Christ adds in the specific instruction to use 'all your mind' which was not in the Old Testament. So it seems to me that for a Christian to deliberately decline to use whatever mental abilities they have to the best of their abilities is to deliberately avoid following what has been identified as a key part of the greatest commandment. And if that doesn't constitute sinful behaviour, I don't know what does.