Syllogisms Examples - Lesson 3

This is the 3rd lesson of our syllogism shortcut series. If you are new to this post then first read

Lesson 1 Here and

Lesson 2 Here 

before reading this post.

In our last post we have covered 6 examples. Here we shall start from the 7th one. 

Example VII :

All Dogs are Cats ---------- (1)

Some Cats are not Pigs ------------ (2)

The first statement is a universal affirmative and hence the subject (dogs) is distributed and the predicated (cats) is not distributed. 

The second statement is particular negative and hence the subject (cats) is not distributed and the predicated pigs is distributed (Table II).

But as the middle term (Cats) is not distributed atleast once in the premises, Rule [2] is not satisfied and hence we cannot draw any conclusion.

Example VIII :

All Cats are Dogs ------------- (1)

Some Cats are not Pigs --------------- (2)

The first statement is a universal affirmative and hence "cats" is distributed and "dogs" is not distributed. The second statement is particular negative and hence "cats" is not distributed and "pigs" is distributed (as per Table II).

Here the middle term (cats) is distributed and hence we can draw a conclusion.

The conclusion should be particular negative as Rule [3] states that if a premise is negative the conclusion should also be negative. Also Rule [4] states that if a premise is particular the conclusion should also be particular. Hence the conclusion should be particular negative. 

In particular negative, we know that the subject is not distributed and the predicated distributed.

The terms "dogs" and "pigs" should come in the conclusion. Also, since "dogs" is not distributed in the premise, it cannot be distributed in the conclusion also as per Rule [7]. 

As per the above reasoning, "Pigs" can be only the subject in the conclusion and hence "Dogs" will be the predicate.

Thus the answer will be - Some dogs are not pigs

Example IX :

No Dogs are Cats -----------(1)

No Cats are Pigs ----------(2)

We cannot draw any conclusion as Rule [5] states that if both the premises are negative we cannot draw any conclusion.

Example X :

No Dogs are Cats ----------- (1)

Some Cats are not Pigs ---------- (2)

As both the statements are negative as per Rule [5]  we cannot draw any conclusion.

(The first statement is universal negative and hence the subject (dogs) is distributed and the predicate (cats) is also distributed as per Table II.

The second statement is particular negative and hence the subject is not distributed and the predicate (pigs) distributed as per Table II).

Example XI :

Some Cats are not Pigs ----------- (1)

Some Cats are Dogs -------------(2)

As the first statement is particular negative the subject (Cats) is undistributed and the predicate (Pigs) distributed. In the second premise both the subject and predicate (Cats and Dogs respectively) are not distributed since   the premise is particular affirmative (as per Table II).

No conclusion can be drawn as both the premises are particular as per Rule [6].

Example XII :

Some Cats are not Dogs ----------------- (1)

Some Cats are not Pigs ------------ (2)

We cannot get an answer from the statements as  Rule [5] states that if there are two negative statements no conclusion can be drawn. Also Rule [6] states that if there are two particular statements no conclusion can be drawn.



That's all for now friends. In our next post we shall discuss another important Reasoning topic. Happy Reading :)