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Aristotle

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Epagoge is Greek for argument from induction. …. By extension, in Aristotle’s Poetics, the character projected by a speaker, artist, etc. Thus in Aristotle’s logic, the process of establishing a general proposition by induction (seeing the univers. il in the particular) or deductive reasoning in which a conclusion is derived from two premises is syllogism or Epagoge. In traditional logic, a syllogism is an inference in which one proposition (the conclusion) follows of necessity from two others (known as premises).
In his Posterior Analytics, Aristotle sets out what seems to be a rather stringent method of acquiring scientific knowledge and understanding (episteme). Aristotle argues that genuine understanding of a thing requires a grasp of why that thing is necessarily as it is. Such understanding is best facilitated by or represented in a demonstrative argument. We must proceed deductively from premises more absolutely intelligible than the conclusion to the conclusion by way of a causally explanatory middle term. The premises of demonstrations are themselves indemonstrable and serve as starting points or first principles (archai) within the given domain of inquiry. According to Aristotle, we arrive at these principles by direct derivation from experience, by what is sometimes called ” intuitive induction” (epagoge), the results of which are grasped by a special intellectual capacity, nous.
Let us follow Aristotle and say that every dialectical argument is either a syllogism or an epagoge (Topics I 12). By ‘a dialectical argument’ let us mean, as Aristotle does, any argument put forward in conversation, proceeding on premisses admitted by the other party, and not requiring any special knowledge. It follows that every Socratic elenchus is a dialectical argument. By a ‘syllogism’ let us not mean, in the narrow modern sense, an argument depending on our insight into the relation of class-inclusion; but, to translate Aristotle’s own words, any ‘argument in which, after certain propositions have been assumed, there necessarily results a proposition other than the assumptions because of the assumptions’. This broad sense of the term is certainly the only one Aristotle has in mind throughout the Topics, from which the definition comes (Topics I 1, 100A25); and probably it is also the only one he has in mind even in the Prior Analytics, although he actually studies only class-inclusion inferences there; at any rate his definition of ‘syllogism’ at the beginning of that work is only verbally different from the definition in the Topics.
Aristotle has deemed the principle ” that the same attribute cannot at the same time belong and not belong to the same subject and in the same respect” the most certain and most prior of all principles, both in the order of nature and in the order of knowledge, and as such it is indemonstrable. The principle of contradiction is involved in any act of rational discourse, and to deny it would be to reduce ourselves to a vegetative state, being incapable of uttering anything with meaning. The way we reach the principle of contradiction is by intuitive grasping (epagoge) from the experience of the particulars, by recognizing the universals in the particulars encountered, and it is different from simple induction, which, in Mill’s view, is the process through which we construct a general statement on the basis of a limited sample of observed particulars.
Refernces
http://www. ditext. com/runes/e. html
http://people. ok. ubc. ca/creative/glossary/e_list. html
http://enlightenment. supersaturated. com/essays/text/willwilkinson/aristotledialectic. html
http://etd. fcla. edu/SF/SFE0000043/thesis. pdf

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