We present a novel algorithm for parsing natural language texts using fuzzy context free grammars (FCFGs). We further provide an algorithm for inferring such a FCFG based on a large corpus of tagged English text. We measure the degree to which novel sentences can be successfully parsed by our system. While the degree of generalization is still limited by the size of corpus we used, and may not be sufficient for all practical approaches, we develop methods to make the most of the corpus and extrapolate to estimate the size of a corpus needed to ensure accurate generalization.