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I was reading this article called Aristotle on the fourth figure. Thea author while exposing Aristotle theory of syllogism, identify 3 kinds of syllogisms which believes Aristotle to discuss:

- Ostensive (Categorical?) Syllogism
- Hypothetical Syllogism
- Reduction to the Absurdum

Now in my understanding the Categorical Syllogism is the central one and the main discussed. It has 3 figures (or four depending on interpretation) and it can be perfect or imperfect.

Hypothetical syllogism is the one (citing Boethius) in which conditional statements appear. It can be divided in simple and complex, but Aristotle never discussed it except for some brief comments on its existence. It was developed by his students and,improved and organized by Boethius.

Concerning the role of reduction to the absurdum, maybe I did not really get its role but I'm quite skeptic of its inclusion in the above list. Even though my researches brought up some similiar views like this one:

Reductio ad absurdum. A 'reducing to absurdity' to show the falsity of an argument or position. One might say, for instance that the more sleep one gets the healthier one is, and then, by the logical reductio ad absurdum process, someone would be sure to point out that, on such a premise, one who has sleeping sickness and sleeps for months on end is really in the best of health. The term also refers to a type of reductive-deductive syllogism.

I'm looking for some in depth clarification, can we consider the reduction to absurdum a syllogism?

If yes, in which contexts? in which case? why?

**PS:**

This question is related to this one I asked, but being the questions both broad I decided to separate them, even though the understanding of one is linked to that of the other.

HI! Thank you again for your precious answer! What do you mean for a more "basic" form of argument? What is the difference between that and the syllogistic form of argument? and in relation to the other post..I can ask myself : how the syllogistic form differs from a basic inference rule like modus ponens? Thank you again! – Gabriele Scarlatti – 2017-10-19T11:40:02.653

1It might worth pointing out that this answer is about classical reductio (if absurdity follows from not-P, infer P). There's also constructive reductio (if absurdity follows from P, infer not-P). Not everyone accepts both, so it's worthwhile to keep the distinction in mind. – possibleWorld – 2017-10-19T14:13:07.680