Essential Conditions and Rules to Derive Conclusions in Syllogism

As we have discussed in the introductory post on Syllogism, it is defined as a logical science to derive appropriate conclusions from two  given statements/premises. To derive conclusions from given statements we have to follow some systematic conditions that are important and essential otherwise you might mess up with premises and their conclusions.

Note :- Read our post Introduction on Syllogism before reading reading this post otherwise you will not able to understand these conditions properly.

Rules for deriving the conclusions in Syllogism :-

1. The conclusion does not contain the middle term.                                     Example :-                                   Statements- 1. All boys are girls. 2. All girls are men.                               Conclusions- 1. are boys. 2. All men are girls. (Since both the conclusions 1 and 2 contain the middle term 'girls, so neither of them can follow).
2. No term can be distributed in the conclusion unless it is distributed in the premises.                                     Example :-                                         Statements- 1. Some dogs are goats. 2. All goats are cows.                           Conclusions- 1. All cows are goats. 2. Some dogs are cows. (Statement 1 is an I type proposition which distributes neither the subject nor the predicate. Statement 2 is an A type proposition which distributes the subject. i.e. 'goats' only. Conclusion 1 is an A type proposition which distributes the subject 'cow'.
3. The middle term (St) should be distributed at least once in the premises. Example :                                             Statements- 1.fans are watches. 2. Some watches are black.                             Conclusions : 1. All watches are fans. 2. Some fans are black. (In the premises, the middle term is 'watches'. Clearly, it is not distributed in the first premise which is an A proposition as it does not form its subject. Also, it is not distributed in the second premise which is an I proposition. Since the middle term is not distributed at least once in the premises, so no conclusion follows. 
4. No conclusion follows                                   (а) If both the premises are particular. Example :                                             Statements books are pens. 2. Some pens are erasers. Conclusions : 1. All books are erasers. 2.Some erasers are books. (Since both the premises are particular, no conclusion follows).                                        (b) If both the premises are negative.       Example :-                                         Statements- 1. No flower is mango. 2. No mango is cherry.                              Conclusions : 1. No flower is cherry. 2. Some cherries are mangoes. Since both the premises are negative, neither conclusion follows.                                                              (c) if the major premise is particular and the minor premise is negative.       Example :                                           Statements- 1.dogs are bulls. 2. No tigers are dogs.                                                 Conclusions- 1. Dogs are tiger. 2. Some bulls are tigers. Here the first premise containing the middle term 'dogs' as the Subject is the major premise and the second premise containing the middle term 'dogs' as the Predicate is the minor premise. Since the major premise is particular and the minor premise is negative, so no conclusion follows. 
5. If the middle term is distributed twice, the conclusion cannot be universal.             Example :                                         Statements- 1.fans are chairs. 2. No tables are fans.                                             Conclusions- 1. Tables are chairs. 2. Some tables are chairs. Here, the first premise is an A proposition and so, the middle term 'fans' forming the subject is distributed. The second premise is an E proposition and so, the middle term 'fans' forming the predicate is distributed. Since the middle term is distributed twice, so the conclusion cannot be universal.
6. If one premise is negative, the conclusion must be negative.                             Example :                                           Statements- 1.grasses are trees. 2. No tree is shrub.                                                 Conclusions : 1. No grasses are shrubs. 2. Some shrubs are grasses. Since one premise is negative, the conclusion must be negative. So, conclusion 2 cannot follow.
7. If one premise is particular, the conclusion is particular.                 Example :                                           Statements : 1. Some boys are thieves. 2. All thieves are robbers                           Conclusions : 1. Some boys are robbers 2. All robbers are thieves. Since one premise is particular, the conclusion must be particular. So, conclusion 2 cannot follow. 
8. If both the premises are affirmative the conclusion would be affirmative.     Example :                                           Statements- 1. women are mothers. 2. All mothers are sisters.                         Conclusions : 1. All women are sisters. 2. Some women are not sisters. 
9. If major premise be affirmative, the conclusion must be particular.        Example :                                           Statements plays are stories. 2. Some poems are plays.                                           Conclusions- 1. poems are stories. 2. All stories are poems. The first premise containing the middle term 'plays' as the subject is the major premise. Also, it is affirmative. So, the conclusion must be particular. Hence, conclusion 2 cannot follow.

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