Syllogism is a greek word which
means inference or deduction. The problems based on syllogism are on two parts:
1.
Proposition/Propositions
2.
Conclusion/ Conclusions drawn from given
proposition
WHAT IS A PROPOSITION?
A proposition is a sentence that
makes a statement giving a relation between two terms.
Parts
of proposition:
2. Predicate
TYPES OF PROPOSITIONS:
1.
CATEGORICAL PROPOSITION
The sentences which are condition
free are called as categorical propositions. For example,
“All cats are rats”
“No cat is rat”
“Some cats are rats”
“Some cats are not rats”
In other words a categorical
proposition has no condition attached with it and makes direct assertion.
2.
NON-CATEGORICAL PROPOSITION
It is different from categorical
proposition which has condition attached with it. For example,
“If M then P”
TYPES OF CATEGORICAL PROPOSITIONS:
Conversion of
Propositions:
Before solving the
problems of syllogism it is must to know the conversion rules of all A,E,I and
O types of propositions:
Conversion of A type:
“All cats are rats” can
be converted into “Some rats are cats”
That is “A type” of
propositions can be converted into “I type”
Conversion of E type:
“No cats are rats” can
be converted into “No rats are cats”.
That is “E type” of
propositions can be converted into “E type”
Conversion of I type:
“Some cats are rats”
can be converted into “Some rats are cats”
Therefore, “I type”
gets converted into “I type”
Conversion of O type:
O type of conversions
can’t be converted.
RULES FOR CONCLUSION:
In problems of
syllogism, conclusions are drawn either from single propositions or from two
propositions or from both. A conclusion from single proposition is just a
conversion of that proposition. But to get conclusion from two propositions a
certain table is used which tells what type conclusion we get from two
propositions.
CONCLUSION TABLE
I PROPOSITION
|
II PROPOSITION
|
CONCLUSION
|
A
|
A
|
A
|
A
|
E
|
E
|
E
|
A
|
(O)R
|
E
|
I
|
(O)R
|
I
|
A
|
I
|
I
|
E
|
O
|
·
Apart from above six pairs of
propositions, no other pair will give any conclusion.
·
The conclusion drawn out of two
propositions is itself a proposition and its subject is the subject of the I
proposition and its predicate is the predicate of the II proposition while the
common terms get disappeared.
·
(O)R means the conclusion is
O type but in reverse order. In this case, the subject of the conclusion is the
predicate of the proposition II and the predicate of the conclusion is the
subject of the I proposition.
·
The conclusion table gives correct
conclusions only if the two propositions are aligned properly.
WHAT IS ALIGNING?
Let
us see the following examples:
Example 1:
I.
All bats
are chair.
II.
Some bats are cats.
Example 2:
I.
Some bats are chairs.
II.
Some cats are bats.
Example 3:
I.
All bats
are chair.
II.
Allbatsare
cats.
From the above example
we notice that there is a common word in the two statements. Aligning of the
two statements means that the pair of statement must be written in such a way
that the common term is the predicate of the statement I and subject of the II statement.
Now to align example 1:
Statement I has to be
converted into
I.
Some chair are bats.
II.
Some
bats are cats.
Example 2 can be
aligned by changing the order of the sentences as
II.
Some cats are bats.
I.
Some bats are chairs.
Example 3 can be
aligned in two ways either by converting the statement I or by changing the
order of the sentences and then converting the statement II.
I.
Some chair are bats.
II.
All bats
are cats.
Or,
II.
Some cats are bats.
I.
All bats
are chair.
Therefore, as per the
requirement and nature of the sentence the alignment is done:
1.
Only by changing the order if the
sentences.
2.
Only by converting sentences.
3.
By changing the order of the statements
and then converting one of the sentences.
Thus, to solve the
problems of syllogism by analytical method there are two main steps:
·
Aligning the pair of sentences.
·
Using conclusion table to draw
conclusions.
Example:
I.
All rats are cats.
II.
All rats are men.
Alignment:
I.
Some cats are rats.
II.
All rats are men.
From the conclusion
table I+A=I type.
Hence, the conclusion
is “Some cats are men”
Further, in some
problems complementary pairs are also seen in the conclusion part in the form
of sentence given below:
I-O pair:
Some cats are rats.
Some cats are not rats.
A-O pair:
All cats are rats.
Some cats are not rats.
I-E pair:
Some cats are rats.
No cats are rats.
Apart from I-O, A-O and
E-O pair the two sentences must have the same subject and predicate. For these
pairs we write the form either (i) or (ii) follows.
Example:
Statements:
a.
Some boxes are trees.
b.
Some trees are horses.
c.
All horses are fruits.
Conclusions:
I.
Some fruits are boxes.
II.
Some fruits are trees.
III.
Some horses are boxes.
IV.
No fruits are boxes.
In the above example conclusion II follows from the
conversion of the conclusion obtained from statement (b) and statement (c)
(I+A=I). Conclusion I,III and IV do not follow because statement (a) and
statement (b) gives no conclusion. But the conclusion I and IV complementary
pair IE type. Hence of the two follows.
About Author - This article is written by Nadhini Raju, A guest contributor of BankExamsToday.com
This post have been revised here
