 The suggestion that deductive reasoning cannot lead us to any new knowledge prompts two questions. Firstly, if not the advancement of knowledge, what is the function of syllogistic reasoning? And, secondly, what are we to say about apparently deductive reasoning which manifestly does lead us to new knowledge? To the first question, Mill answers that syllogistic reasoning allows us “test” our commitment to general propositions (System, VII: 196). In making arguments such as the one above, we cannot acquire new knowledge: for no facts beyond those which are in the premises are present in the conclusion. But the implications of holding a general premise are more clearly displayed by the syllogistic reasoning, and this, in certain instances, may cause us to re-evaluate our commitment to that premise. To the second question, Mill holds that where we do gain genuinely new knowledge—in cases of mathematics and geometry, for instance—we must, at some level, be reasoning inductively. Mill, that is to say, attempts to account for the genuine informativeness of mathematical and geometric reasoning by denying that they are in any real sense a priori. We shall return to this claim in  §3.4.