# What do you really mean by Statistical Syllogism?

We know that syllogism is an argument consisting of two premises and a conclu­sion. The conclusion puts together the information given in the premises.

The syllogism may either be deductive or inductive. The following are some of the examples of deduc-

tive syllogism.

Example 1 : All animals are mortal All cats are animals

.’. All cats are mortal.

Example 2 :

No teachers are uneducated Sidhartha is a teacher .’. Sidhartha is not uneducated.

(=it is not the case that Sidhartha is uneducated)

The above mentioned arguments are said to be deductive due to the reason that the conclusion necessarily follows from the premises. The conclusion is certainly true if the premises are true.

Now let us see some examples of syllogism which are inductive. Example A :

Most of the politicians are corrupt. Mr X is a politician

Mr. X is corrupt.

Example B :

Most of the socialiss are not rich Mr Y is a socialist Mr Y is not rich.

Example C :

20% of all men are vegetarians Sidhartha is a man Sidhartha is vegetarian

These syllogistic arguments are inductive in the sense that no conclusion necessarily follows. Here even if the premises are true the conclusion is only probable. This argument states that if the. premises are true the conclusion is likely to be true. In other words the conclusion is always probable.

An important point of distinction according to some modern logicians (like Salman) is that deductive arguments always use universal propositions(generalization)whereas inductive arguments often make use of statistical generalizations.

Universal propositions are expressed in the form of: “All S’s are P’s” (All dogs are mammals) or “NO S’s are P’s” (No crows are white). Statistical generalilsaions state that a proportion of members of one class are members of another class. These proposions are ordinarily expressed in the following forms:

Most S’s are P’s

(most of the teachers are learned persons)

Most S’s are not P’s

(most of the politicians are not honest)

X% of S’s are P’s

20% of politicians are highly educated.

X% of S’s are no P’s

95% of scientists are not politicians.

In a statistical syllogistic argument (or a statistical syllogism) one of the premises is a statistical generalization like the above examples. The other premise is a particular one in the sense that it uniquely denotes one individual. Thus the form of the statistical syllogism is

Example A :

Premise 1 – x% of K’s are L’s Premise 2 – a is a K a is an L

To give a concrete example-

Example B :

80% of students are sincere Rabi is a student Rabi is sincere.

In the above examples the subject in the first premise (K, student). is called the reference class. This is the class of things or persons to which a characteristic is attributed. The attributed characteristic or property is called the attributive class (L, sincere in the above examples).

The subject in the second premise refers to the individual object(person, place, thing etc.) In the above example the individual is a , Rabi(in the two examples respectively). Thus in the above example, the reference class is the class of students, the attributive class is the class of sincere beings and the individual person is Rabi.

It is important to note that the class denoted by K(students) in the first premise includes the individual (Rabi) mentioned in the second premise. This is to say that the individual ‘a’ (Rabi) in the second premise belongs to the class ‘K’ (students) of the first premise.

The class denoted by L(sincere beings) in the first premise is the characteristic or property attributed to the individual in the conclusion.

Thus, the statistical syllogism is an argument based on the principle that what is generally, but not universally, true or false of a class is also, in a like manner, true or false a particular instance. 