Syllogism

Syllogism
Syllogism is a kind of logical argument that applies deductive reasoning to arrive at conclusion based on two or more propositions that are asserted or assumed to be true.

Example :

  1. All roses are flowers
  2. All flowers are beautiful
  3. All roses are beautiful

Clearly the proposition 1 and 2 are the premises and the proposition 3, which follows from the first two propositions is called the conclusion.

Term : In logic, a term is a word or a combination of words, which by itself can be used as a subject or predicate of a proposition.

Syllogism is concerned with three types:

  1. Major Term: It is the predicate of the conclusion and is denoted by P (“Predicate”)
  2. Minor Term : It is the subject of the conclusion and is denoted by S (“Subject”)
  3. Middle Term : It is the term common to both the premises and is denoted by M (“Middle”)

In the above example, beautiful is predicate of the conclusion  and roses are the subject of the conclusion; flowers are the common term for both premises hence it is the Middle.

 

Major and Minor Premises:

Of the two premises, the Major Premise is that in which the middle term is the subject and the Minor Premise is that in which the middle term is the predicate.

Rules for deriving the conclusion from two given premises

1. The conclusion does not contain the middle term.

2. No term can be distributed in the conclusion unless it is distributed in the premise.

3. The middle term (M) should be distributed at least once in the premises. Other wise the conclusion cannot follow.

For the middle term to be distributed in a premise,

  1.  M must be the subject if premise is an A proposition
  2. M must be subject or predicate if premise is an E proposition
  3. M must be predicate if premise is an O proposition.

Note that in I proposition, which distributes neither the subject nor the predicate, the middle term cannot be distributed.

Ex. Statements : 1. All fans are watches   2. Some watches are pink

Conclusion : 1. All watches are fans    2. Some fans are pink

In the premise, the middle term is not distributed in the first premise which is an A proposition as if does not form its subject. Also, it is not distributed in the second premise which is an I proposition. Since the middle term is not distributed even once in the premises, so no conclusion follows.

4. No conclusion follows :

  • if both the premises are particular
  • if both the premises are negative
  • if the major premise is particular and minor premise is negative

5. If the middle term is distributed twice, the conclusion cannot be universal.

6. If one premise is negative, the conclusion must be negative.

7. If one premise is particular, the conclusion must be particular.

8. If both the premises are affirmative, the conclusion must be affirmative.

9. If both the premises are universal, the conclusion must be affirmative.

 

Logical Deduction

The phenomenon of deriving a conclusion from a single proposition or a set of given propositions, is known as logical deduction. The given proposition are also referred to as the premises.

There are two inferential processes of deduction:

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I. Immediate Deductive Inference

Here conclusion is deduced from one of the given propositions, by any of the three ways – Conversion, Obversion and Contraposition.

(1) Conversion:

In this inference, the subject term and the predicate term is interchanged i.e the Subject term of the premise becomes the predicate term of the conclusion and the predicate term of the premise become the Subject term of the conclusion.

The given proposition is called convertend and the conclusion drawn from it is called converse.

Table of Valid Conversions:

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Note: in a conversion the quality remains the same and the quantity may change.

(2) Obversion

In obversion, we change the quality of the proposition and replace the predicate terms by its complement.

The given proposition is called Obvertend and the conclusion drawn from it is called Obverse.

Table of Valid Obversions:

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(3) Contrapositions

To obtain the contrapositive of a statement, we first replace the subject and predicate terms in the proposition  and then exchange both these terms with their complements. Relatively simpler one!

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Note: The valid converse, obverse or contrapositive of a given proposition always logically follows from the proposition.

II. Mediate Deductive Inference (Syllogism)

First introduced by Aristotle, a Syllogism is a deductive argument in which conclusion has to be drawn from two propositions referred to as the premises.

Complete details of which is given in the next post.Click Here

An important point to remember:

While deriving logical conclusions, always remember that the following conclusions hold:

  1. The converse of each of the given premises
  2. The conclusions that directly follows from the given premises in accordance with the rules of syllogism
  3. The converse of the derived conclusions.

 

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Logic

Logic is the science of thought as expressed in language. This means that the questions on logic are to be solved as per the information given without any concern of the formal validity or truth of the statements i.e. conclusion should follow directly from the statements given. Without this unique characteristics, the Logic test becomes an instrument of teaching the candidates to follow the rules and work as per the instructions without an error.

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 – the set is 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:

1. Quantifier : The word “All” , “No” and “Some” are called Quantifiers because they specify a quantity. “All” and “No” are Universal Quantifiers as they refer to every object in a certain set, while the quantifier “Some” is a particular quantifier as it refers to at least one existing object in a certain set.

2. Subject (“S”) : The subject is that about which something is said.

3. Predicate (“P”) : It is the part of the proposition denoting that which is affirmed or denied about the subject.

4. Copula : The Copula is that part of the proposition which denotes the relation between the subject and the predicate.

Example : All Jokers are men.

Here : All -> Quantifier ; Jokers -> Subject ; Are-> Copula  ; Men -> Predicate

Four Fold Classification of the Proposition

Propositions are classified in to four types

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 cats are mammals.

This is proposition A since we cannot say “All mammals are cats.”

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 girl is beautiful.

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 and similarly the predicate term “foolish” is affirmed for a part of subject class. So both are undistributed.

Particular Negative Proposition (denoted by  “O”)

It distributes only the predicate.

e.g Some animals are not domestic.

Here the subject term “animals” is used only for a part of its class and hence is undistributed while the predicate “wild” is denied in entirety to the subject term and hence is distributed.

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Learning about classification helps to make logical deduction in the Competitive exams. How to deduce is explained in the next post. Do check.