Syllogism

Syllogism
Syllogism is a kind of logical argument that applies deductive reasoning to arrive at conclusion based on two or more propositions that are asserted or assumed to be true.

Example :

  1. All roses are flowers
  2. All flowers are beautiful
  3. All roses are beautiful

Clearly the proposition 1 and 2 are the premises and the proposition 3, which follows from the first two propositions is called the conclusion.

Term : In logic, a term is a word or a combination of words, which by itself can be used as a subject or predicate of a proposition.

Syllogism is concerned with three types:

  1. Major Term: It is the predicate of the conclusion and is denoted by P (“Predicate”)
  2. Minor Term : It is the subject of the conclusion and is denoted by S (“Subject”)
  3. Middle Term : It is the term common to both the premises and is denoted by M (“Middle”)

In the above example, beautiful is predicate of the conclusion  and roses are the subject of the conclusion; flowers are the common term for both premises hence it is the Middle.

 

Major and Minor Premises:

Of the two premises, the Major Premise is that in which the middle term is the subject and the Minor Premise is that in which the middle term is the predicate.

Rules for deriving the conclusion from two given premises

1. The conclusion does not contain the middle term.

2. No term can be distributed in the conclusion unless it is distributed in the premise.

3. The middle term (M) should be distributed at least once in the premises. Other wise the conclusion cannot follow.

For the middle term to be distributed in a premise,

  1.  M must be the subject if premise is an A proposition
  2. M must be subject or predicate if premise is an E proposition
  3. M must be predicate if premise is an O proposition.

Note that in I proposition, which distributes neither the subject nor the predicate, the middle term cannot be distributed.

Ex. Statements : 1. All fans are watches   2. Some watches are pink

Conclusion : 1. All watches are fans    2. Some fans are pink

In the premise, the middle term is not distributed in the first premise which is an A proposition as if 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 even once in the premises, so no conclusion follows.

4. No conclusion follows :

  • if both the premises are particular
  • if both the premises are negative
  • if the major premise is particular and minor premise is negative

5. If the middle term is distributed twice, the conclusion cannot be universal.

6. If one premise is negative, the conclusion must be negative.

7. If one premise is particular, the conclusion must be particular.

8. If both the premises are affirmative, the conclusion must be affirmative.

9. If both the premises are universal, the conclusion must be affirmative.

 

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