The Jonathan Dolhenty Archive The Radical Academy Main Menu Online Newsletter Academy Updates The M.J. Adler Archive The Dolhenty Archive Adventures in Philosophy Classic Philosophers Philosophical Critiques Philosophy Glossary Philosophy Quotations Philosophy Mini-Courses Thomas Aquinas Introductory Essays Philosophy Resources Politics Resources Religion Resources Education Resources Science Resources The Media Center Better Living Resource Center Business & Finance Resources Search Central Academy Bookstore Academy NewsStand Academy Emporium About the Academy Academy FAQs Ask the Academy Guestbook Academy Forum Calendar of Events Subscribe to Ezine Give Us Feedback Tell A Friend About Us Votecaster Cartoons & Comics Academy Chatroom
Formal Logic Select an Archive Category... Fundamentals Metaphysics Epistemology Logic/Statistics Ethics/Morality Current Affairs Main Page & Index
Academy Resources Glossary of Philosophical Terms Timeline of Philosophy A Timeline of American Philosophy Diagram: Development of Philosophic Thought Diagram: Divisions of Philosophy The Philosophy Resource Center The Religion Resource Center Books about Philosophy in The Radical Academy Bookstore Books about Religion in The Radical Academy Bookstore Click Here for New & Used College Textbooks at Discount Prices Click Here for College Education Information & Study Resources Shop Amazon Stores in the Radical Academy Bookstore Magazine Outlet Music Store Classical Music Store Video Store DVD Store Computer Store Camera & Photo Store Computer/Video Games Software Store Musical Instruments Outlet Store Cellular Phones Toys & Games Tools & Hardware Automotive Store Outdoor Living Consumer Electronics Home & Garden Kitchen & Housewares Baby Superstore Apparel & Accessories Gourmet Food Grocery Store Sporting Goods Jewelry & Watches Health & Personal Care Beauty Store Academy Showcase Specials		DEDUCTION: Part 3 - Page 1-b Figures and Moods of The Categorical Syllogism by Jonathan Dolhenty, Ph.D.   Rules for the Syllogistic Figures The First Figure M P S M S P The middle term (M) is the subject of the major premise and the predicate of the minor premise. The rule for the First Figure is: The minor premise must be affirmative and the major premise must be universal. Explanation of the Rule First Part: The minor premise must be affirmative. If the minor premise is negative, the conclusion must then be negative (according to General Rule Number 7) and the major term (P) in the conclusion would be universal. If, however, the minor premise is negative, then the major premise would have to be affirmative. Both premises are not allowed to be negative (according to General Rule Number 6). Thus the major term (P) would be particular in the major premise, since it is the predicate of an affirmative sentence. In that case, the major term (P) would be particular in the premise and universal in the conclusion. This violates General Rule Number 2. In order to avoid an illicit major, the minor premise must be affirmative. Second Part: The major premise must be universal. If the major premise is particular, the middle term (M) would be a particular term, since it is the subject of this proposition. The minor premise in this figure, however, must be affirmative, in order to be in accord with the first part of this rule. The middle term (M), because it is the predicate of the minor premise, will be particular here also. If, therefore, the major premise is particular, the middle term (M) would be particular in both premises. But this would entail an undistributed middle and violate General Rule Number 4. The only means by which to get a distributed middle is to make the major premise universal. This shows, then, that the second part of the rule is correct: The major premise must be universal. The Valid Moods of the First Figure When we consider the moods which are valid for the syllogisms of the First Figure, we find that four of the eight possible legitimate combinations are valid and four are invalid. Here are the diagrams: Moods of the First Figure A uM + pP A uS + pM uS + pP Valid A uM + pP E uS - uM uS - uP Illicit Major A uM + pP I pS + pM pS + pP Valid A uM + pP O pS - uM pS - uP Illicit Major E uM + uP A uS + pM uS - uP Valid E uM - uP I pS + pM pS - uP Valid I pM + pP A uS + pM uS + pP Undist.Middle O pM - uP A uS + pM uS - uP Undist.Middle Clearly, there are only four valid moods for the First Figure: A A, A I, E A, and E I. Each one follows the rule that the minor premise must be affirmative and the major premise must be universal. The A E and A O moods are invalid because of an illicit major brought into the conclusion. They violate the first part of the rule: The minor premise must be affirmative. The I A and O A moods are invalid because an undistributed middle is the result of the arrangement and this violates the second part of the rule: The major premise must be universal. Here are some arguments which illustrate the valid moods for the First Figure: A Every human being should have equal rights. A Women are human beings. Therefore, Women should have equal rights. A All politicians are great talkers. I Some lawyers are politicians. Therefore, Some lawyers are great talkers. E No mammals are cold-blooded. A All dogs are mammals. Therefore, No dogs are cold-blooded. E No misers are generous. I Some wealthy people are misers. Therefore, some wealthy people are not generous.   To Page 1-c of Figures and Moods of the Syllogism Enrich Your Life With a Philosophy Book... Enrich Your Life With a Philosophy Magazine... Main Page & Index
-- Top of Page -- [Homepage] [Newsletter] [Search] [Support the Academy] [Link to Us] [Contact the Academy] [Citing Articles from Our Website] [Privacy Policy & Disclaimer] Copyright 1998-99, 2000-01, & 2002-03 by The Radical Academy. All Rights Reserved.