Maharashtra Board Class 12 Logic Chapter 4 Traditional Logic PDF Download

Traditional Logic

4.1 Nature Of Propositions In Traditional Logic

The Greek Philosopher Aristotle is the founder of Traditional Logic. According to Aristotle proposition consists of terms. A Term is defined as a word or group of words which stands as the subject or predicate of a logical proposition.

For example:

1. Intelligent people are creative.

2. Bhumika is the tallest girl in the class.

3. Tejas is clever.

In the first proposition the subject term 'Intelligent people' is a group of words. In the second proposition the predicate term 'tallest girl' is a group of words and in the third example both the subject term 'Tejas' and predicate term 'clever' are single words.

Term is a part of speech representing something but it is neither true nor false. For example: man, animal, mortality, etc. However the proposition which consists of terms is either true or false. An inference can be drawn on the basis of the existing relation between these terms. According to Aristotle all propositions either assert or deny something. That about which assertion or denial is made is called the 'Subject term' and that which is asserted or denied of subject is called the 'Predicate term'. Terms may refer to a whole class or some members of a class.

For example:

1. All cows are animals.

2. Some students are not Successful.

In the first proposition 'cows' is the subject term and 'animals' is the predicate term. In the second proposition 'students' is the subject term and 'successful' is the predicate term.

The first proposition asserts that 'All cows are animals' while the second proposition denies that 'Some students are successful.'

Terms are constituents of a proposition. The two terms i.e. the subject and predicate of the proposition are unified by the means of a copula. Thus a proposition has three constituent elements, namely: subject, predicate and copula. The order of the three elements in a proposition is Subject-Copula-Predicate.

Example: 'All apples are red'.

In the above example 'Apples' is the subject, 'red' is the predicate and the word 'are' which unifies both 'apple' and 'red' is the copula.

Teacher's Note

A proposition is like a complete sentence that tells us something is true or false. Just like when your mother says 'All children must eat vegetables', this is a proposition about children and vegetables.

Exam Trick

Remember: Every proposition has three parts - Subject (who/what we talk about), Copula (the connecting word 'is/are'), and Predicate (what we say about the subject). Like: All teachers (Subject) are (Copula) intelligent (Predicate).

Points To Remember

A term is a word or group of words.
A term is neither true nor false by itself.
A proposition has three parts: subject, copula, and predicate.
The order is always: Subject-Copula-Predicate.
Propositions can be true or false.

4.2 Traditional Classification Of Propositions

In Traditional Logic Propositions are classified into two categories:

1. Conditional Proposition

2. Categorical Proposition

4.2.1 Conditional Proposition

A Conditional proposition is one in which the assertion is made subject to some expressed condition. For example: 'If diesel oil is brought near fire it will explode'.

In this example 'occurrence of explosion' is subject to the condition of 'diesel oil being brought near fire'.

Conditional Propositions are of two kinds:

i. Hypothetical Proposition

ii. Disjunctive Proposition

(i) Hypothetical Proposition:

A hypothetical proposition is one which presents a condition together with some consequence which follows from it.

In a hypothetical proposition there are two propositions. The proposition which states the condition and the proposition which expresses the consequence. The proposition which states the condition is called the antecedent and that which expresses the consequence is called the consequent.

For example: 'If metal is heated, it expands'. In this example, it does not refer to any actual instance of metal being expanded when heated, but it only states the condition that if the condition is fulfilled, the consequences will follow.

(ii) Disjunctive Proposition:

A Disjunctive proposition is one which states alternatives. This proposition asserts that the alternatives are mutually exclusive or inclusive.

For example:

1. A line is straight or curved.

2. Either Ganesh will sing or dance.

In the first example the alternatives are mutually exclusive. If we affirm that 'the line is straight' then we must deny 'it is curved' and vice versa. But in the second example the alternatives are not mutually exclusive but inclusive. By affirming the alternative that 'Ganesh will sing' we cannot deny that 'Ganesh will dance'.

Teacher's Note

A conditional proposition is like an 'if-then' statement. For example: 'If you study well, then you will pass.' This is how we speak in real life in India.

Exam Trick

Remember: Hypothetical = If-Then (antecedent and consequent). Disjunctive = Either-Or (alternatives). Think of traffic lights: 'Either red light OR green light' - these are mutually exclusive alternatives.

Points To Remember

Conditional proposition has a condition and a consequence.
Hypothetical proposition has antecedent and consequent parts.
Disjunctive proposition presents alternatives.
Alternatives can be mutually exclusive or inclusive.
These propositions tell us about relationships between conditions.

4.2.2 Categorical Propositions

Categorical proposition is a proposition of relationship between two classes referred to as the class of subject term and the class of predicate term.

By a 'class' Aristotle means a collection of all individuals, objects etc. that have some specified characteristic in common. A categorical proposition affirms or denies a predicate of a subject absolutely, i.e. without any condition. It is unconditional Proposition. For example: 'All Chillies are pungent'. The pungency of chilly is not determined by any condition.

Every Categorical proposition has both quality and quantity. Quality of Categorical proposition means that the propositions either assert something or deny something. It is either an Affirmative or Negative proposition. A Categorical proposition is affirmative when its predicate term is affirmed of the subject term and it is negative when its predicate term is denied of the subject term.

For example:

1. Some people are honest.

2. No Elephants are carnivorous animals.

The first proposition is affirmative as in this proposition the predicate term 'honest' is affirmed of the subject term 'people' and the second proposition is negative as in this proposition the predicate term 'carnivorous animals' is denied of the subject term 'Elephants'.

Every Categorical proposition has quantity. A Categorical proposition may assert or deny something about the predicate term. The assertion or denial may refer to either entire whole class or some members part of the class of subject term. A Categorical Proposition is either Universal or Particular.

It is universal when it refers to all members of the class of the Subject term and it is Particular when it refers to some members of the class of the Subject term.

For example:

1. All chess players are logical.

2. Some languages are difficult.

The first proposition is Universal as in this proposition the subject term i.e. 'the class of chess players' refers to the entire class to which it applies and the second proposition is Particular as in this proposition the subject term i.e. 'the class of languages' refers to some members of the class to which it applies.

Teacher's Note

A categorical proposition is a simple statement about things. For example: 'All apples are red' or 'Some mangoes are sweet'. This is how we describe things in our daily life in India.

Exam Trick

Remember: Categorical = Clear statement (All/Some/No). Quality = Affirmative or Negative. Quantity = Universal or Particular. Like: 'All students are hardworking' - this is Universal Affirmative.

Points To Remember

Categorical proposition makes a clear statement about classes or groups.
Quality tells if it affirms (yes) or denies (no).
Quantity tells if it is about all (universal) or some (particular).
It does not have any condition like 'if' or 'either-or'.
There are four types: A, E, I, and O.

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