Having read through quite a few of the comments lots of people seem to be drawing the conclusion 'obviously no, we have finite material resources'. I think this misunderstands the concept, as economic growth does not necessarily imply more material resources being used. In fact in developed economies the vast majority of GDP is now services (law, accounting, media etc.), which whilst obviously partly material resources based is much less material resource in intensive than say building a new car.

More interestingly over time the material resource intensity of economic activity (material resources used per $ of GDP) declines as countries develop. In the future it seems very likely that demand for creative digital and media products e.g avatars, games, films, instagram filters etc. will account for an ever larger share of GDP. If every year a company's designers creates a 'better looking / cooler' avatar range that people are willing to pay more for then we still have economic growth and assuming the avatars use the same computing power to render we would have essentially 0% growth in material resources used.

Therefore, whilst unbounded and unregulated economic growth causes lots of problems (and has for a long time), the idea it could go on for ever is not as stupid as it sounds, so long as people keep desiring more and more intangible products.