In this work we introduce a particular case of textual entailment (TE), namely Textual Entailment by Generality (TEG). In text, there are different kinds of entailment yielded from different types of implicative reasoning (lexical, syntactic, common sense based), but here we focus just on TEG, which can be defined as an entailment from a specific statement towards a relatively more G general one. Therefore, we have T (G)→ H whenever the premise T entails the hypothesis H, the hypothesis being more general than the premise. We propose an unsupervised and language-independent method to recognize TEGs, given a pair T, H in an entailment relation. We have evaluated our proposal G → H English pairs, where we know through two experiments: (a) Test on T (G)→ H English pairs, where we know that TEG holds; (b) Test on T → H Portuguese pairs, randomly selected with 60% of TEGs and 40% of TE without generality dependency (TEnG).