# Syllogism - Concept and Examples

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:
1. Subject
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.

This post have been revised here 