1. One of the most conspicuous points in Aristotle's doctrines as bearing upon the philosophy of Science is his account of that mode of attaining truth which is called _Induction_; for we are accustomed to consider Induction as the process by which our Sciences have been formed; and we call them collectively the _Inductive Sciences_. Aristotle often speaks of Induction, as for instance, when he says that Socrates introduced the frequent use of it. But the cardinal passage on this subject is in his _Analytics_, in which he compares Syllogism and Induction as two modes of drawing conclusions[20]. He there says that all belief arises either from Syllogism or from Induction: and adds that Induction is, when by means of one extreme term we infer the other extreme to be true of the middle term. The example which he gives is this: knowing that particular animals are long-lived, as elephant, horse, mule; and finding that these animals agree in having no gall-bladder; we infer, by _Induction_, that _all_ animals which have no gall-bladder are long-lived. This may be done, he says, if the middle and the second extreme are convertible: as the following formal statement may show. Elephant, horse, mule, &c. are long-lived. Elephant, horse, mule, &c. are all gall-less. If we might convert this proposition, and say All gall-less animals are as elephant, horse, mule, &c.: we might infer _syllogistically_ that All gall-less animals are long-lived. And though we cannot infer this syllogistically, we infer it by Induction, when we have a sufficient amount of instances[21]. I have already elsewhere given this account of Induction, as a process employed in the formation of our knowledge[22]. What I have now to remark concerning Aristotle is, that it does not appear to have occurred to him, that in establishing such a proposition as that which he gives as his instance, the main difficulty is the _discovery_ of a _middle term_ which will allow us to frame such a proposition as we need. The zoologist who wanted to know what kind of animals are long-lived, might guess long before he guessed that the absence of the gall-bladder supplied the requisite middle term; (if the proposition were true; which it is not.) And in like manner in other cases, it is difficult to find a middle term, which enables us to collect a proposition by Induction. And herein consists the imperfection of his view of the subject; which considers the main point to be the proof of the proposition when the conceptions are _given_, whereas the main point really is, the _discovery_ of conceptions which will make a true proposition possible.