In setting out the process of Demonstration, Aristotle begins from the idea of teaching and learning. In every variety thereof some _præcognita_ must be assumed, which the learner must know before he comes to be taught, and upon which the teacher must found his instruction.[8] This is equally true, whether we proceed (as in Syllogism) from the more general to the less general, or (as in Induction) from the particular to the general. He who comes to learn Geometry must know beforehand the figures called circle and triangle, and must have a triangular figure drawn to contemplate; he must know what is a unit or monad, and must have, besides, exposed before him what is chosen as the unit for the reasoning on which he is about to enter. These are the _præcognita_ required for Geometry and Arithmetic. Some _præcognita_ are also required preparatory to any and all reasoning: _e.g._, the maxim of Identity (fixed meaning of terms and propositions), and the maxims of Contradiction and of Excluded Middle (impossibility that a proposition and its contradictory can either be both true or both false.)[9] The learner must thus know beforehand certain Definitions and Axioms, as conditions without which the teacher cannot instruct him in any demonstrative science. [Footnote 8: Analyt. Post. I. i. pp. 71-72; Metaphys. A. IX. p. 992, b. 30.] [Footnote 9: Aristot. Analyt. Post. I, i. p. 71, a. 11-17. [Greek: a(/pan ê)\ phê=sai ê)\ a)pophê=sai a)lêthe/s].] Aristotle, here at the beginning, seeks to clear up a difficulty which had been raised in the time of Plato as between knowledge and learning. How is it possible to _learn_ at all? is a question started in the Menon.[10] You either know a thing already, and, on this supposition, you do not want to learn it; or you do not know it, and in this case you cannot learn it, because, even when you have learnt, you cannot tell whether the matter learnt is what you were in search of. To this difficulty, the reply made in the Menon is, that you never _do_ learn any thing really new. What you are said to learn, is nothing more than reminiscence of what had once been known in an anterior life, and forgotten at birth into the present life; what is supposed to be learnt is only the recall of that which you once knew, but had forgotten. Such is the Platonic doctrine of Reminiscence. Aristotle will not accept that doctrine as a solution; but he acknowledges the difficulty, and intimates that others had already tried to solve it without success. His own solution is that there are two grades of cognition: (1) the full, complete, absolute; (2) the partial, incomplete, qualified. What you already know by the first of these grades, you cannot be said to learn; but you may learn that which you know only by the second grade, and by such learning you bring your incomplete cognition up to completeness. [Footnote 10: Plato, Menon. p. 80.]