Syllogism Basics
Syllogism Basics
Syllogism or Logic Basics: In Logic, any categorical statement is termed as the Proposition.
A Proposition (or a categorical statement) is a statement that asserts that either a part of or the whole of, one set of objects
The set identified by the subject term in the sentence expressing that statement - either is included in, or is excluded from, another set that is the set identified by the predicate term in that sentence. The standard form of a proposition is :
Quantifier + Subject + Copula + Predicate
Thus, the proposition consists of four parts :
Illustrations: Here are certain propositions and their parts.
1. All men are animals.
All (Quantifier) Men (Subject) Are (Copula) Animals (Predicate)
2. Some pens are erasers.
Some (Quantifier) Pens (Subject) Are (Copula) Erasers (Predicate)
Four Fold Classification of Propositions : - A proposition is said to have a universal quantity if it begins with a universal quantifier, and a particular quantity if is begins with a particular quantifier. Besides, propositions which assert something about the inclusion of the whole or a part of one set in the other are said to have affirmative said to have a negative quality. Also, a term is distributed in a proposition if it, refers to all members of the set of objects denoted by that term. Otherwise, it is said to be undistributed. Based on the above facts, propositions can be classified into four types :
1. Universal Affirmative Proposition (denoted by A) : - It distributes only the subject i.e., the predicate is not interchangeable with the subject while maintaining the validity of the proposition e.g.,
All snakes are reptiles.
This is proposition A since we cannot say 'All reptiles are snakes'.
2. Universal Negative Proposition (denoted by E) : - It distributes both the subject and the predicate i.e., an entire class of predicate term is denied to the entire class of the subject term, as in the proposition. e.g.,
No boy is intelligent.
3. Particular Affirmative Proposition (denoted by I) : - It distributes neither the subject nor the predicate e.g.,
Some men are foolish.
Here, the subject term 'men' is used not for all but only for some men and similarly the predicate term 'foolish' is affirmed for a part of subject class. So, both are undistributed.
4. Particular Negative Proposition (denoted by O) : - It distributes only the predicate. e.g.,
Some animals are not wild.
Here, the subject term 'animals' is used only for a part of its class and hence is undistributed while the predicate term 'wild' is denied in entirety to the subject term and hence is distributed.
These facts can be summarized as follows :
| Statement Form | Quantity | Quality | Distributed |
|---|---|---|---|
| (A) : All S is P. | Universal | Affirmative | S only |
| (E) : No S is P. | Universal | Negative | Both S and P |
| (I) : Some S is P. | Particular | Affirmative | Neither S nor P |
| (O) : Some S is not P. | Particular | Negative | P only |
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