SYLLOGISM : POSSIBILITIES CASE 2

                                         SYLLOGISM : POSSIBILITIES CASE 2




O-Type [Some S are not P]
I. Implication
Conclusions:
(i) All S are P [False]
The above conclusion is definitely false.
Cases of Possibility:
(i) No S are P [Doubtful]
(ii) Some S are P [Doubtful]
The above statements are cases of possibilities.
II. Conversion
We know that O-type of statements cannot be
converted. Therefore, there can be no definite
conclusion from the conversion of O-type of
statements. However, the following possibilities exist:
(i) All P are S
(ii) No P are S
(iii) Some P are S
(iv) Some P are not S
Note: Here, for the cases of possibilities, we consider
O-Type and O*-Type statements alike. For this reason
we do not take up O*-Type as a separate case.
Summary
Cases of Possibility
A-Type [All S are P]
(i) All P are S
I-Type [Some S are P]
(i) All S are P (ii) Some S are not P
(iii) All P are S (iv) Some P are not S
O-Type [Some S are not P]
(i) No S are P (ii) Some S are P
(iii) All P are S (iv) No P are S
(v) Some P are S (vi) Some P are not S
Mediate Possibilities
When we have been given any of the following types
of pair of aligned statements, cases of possibilities
exist:
A + I; A + O; E + E; E + O; I + I; I + O; O + [A or E or I
or O]
Suppose, we have the following propositions:
1. A + I
All S are P Some P are Q
2. A + O
All S are P Some P are not Q
3. E + E
No S is P No P is Q
4. E + O
No S is P Some P are not Q
5. I + I
Some S are P Some P are Q
6. I + O
Some S are P Some P are not Q
Note: Similarly, we can write a pair of aligned statements
for O + A, O + E, O + I and O + O also.
We know that from the above pairs of aligned
statements, definite conclusions cannot be drawn. But
some relationships between S and Q exist and we
cannot say definitely that the relationships do exist.
Therefore, cases of possibility arise. That is there are
the possibilities that some relationships between S
and Q exist. For any of the above pairs of aligned
statements, following are the all standard cases of
possibilities that exist between S and Q.
(a) All S are Q
(b) Some S are Q
(c) Some S are not Q
(d) All Q are S
(e) Some Q are S
(f) Some Q are not S
‘Either......or’ Cases in Possibility
We will try to understand the ‘Either.....or’ cases of
possibility by examples as given below:
Ex. 1: Statements: Some P are Q.
All Q are R.
No R is S.
Conclusions:
I. All S being P is a possibility.
II. All P being R is a possibility.
Explanation:
Some P are Q + All Q are R + No R is S = I + A + E = (I
+ A) + E = I + E = O = Some P are not S. From this OType
of conclusion there is a possibility of all S being
P. Therefore, conclusion I follows. Again, Some P are
Q + All Q are R = I + A = I = Some P are R. From this
conclusion, possibility of all P being R exists.
Therefore, conclusion II follows. But if II is possible, I
can’t be possible. How? Then All P are R + No R is S =
A + E = E = No P is S. Thus, both conclusions I and II
can’t follow simultaneously. Therefore, ‘Either I or II
follows’ will be the correct answer.
Ex. 2: Statements: Some P are Q.
All Q are R.
No R is S.
Conclusions:
I. All P being R is a possibility.
II. All S being P is a possibility.
Explanation:
Some P are Q + All Q are R = I + A = I = Some P are R 
All P being R is a possibility. Therefore, conclusion I
follows. Again, Some P are Q + All Q are R + No R is S
= I + A + E = (I + A) + E = I + E = O = Some P are not S
All S being P is a possibility. Therefore, conclusion
II follows. But, conclusions I and II both cannot be
true simultaneously. If I follows, All P are R + No R is
S = A + E = E = No P is S. Hence II can’t follow. Hence,
‘Either I or II follows’ will be the correct answer