jetli Aatram great talent

 Maharashtra State Bureau of Textbook Production & Curriculum Ressearch Pune,

takes immense pleasure to introduce ‘Logic’ as a subject for Standrad XI. Logic is a

science of reasoning. ‘Rationality’ is fundamental distinguishing characteristic of human

being. This unique ability helps man to draw conclusions from the available information.

Though ability to reason is an inbuilt feature of human beings, logicians have identified the

rules of reasoning. Logic deals with these rules of reasoning. In logic one studies methods

and principles of logic which enables one to distinguish between good and bad reasoning.

Training in logic sharpens our ability to reason correctly and detect fallacies in reasoning

if any. Logic, therefore is a fundamental discipline, useful to all branches of knowledge.

With the introduction of logic at Standard XI students will be able to understand, argue

and convince with considerable amount of maturity. Study of logic will enrich their ability

of logical, analytical and critical thinking.

The aim of this textbook is to explain basic principles of logic and their appllications.

We have tried to make this textbook more interesting and activity based, which will

facilitate easy understanding of the subject and create interest in the subject. The textbook

is written keeping in mind needs of students from both urban and rural areas.

Various activity based questions, exercises, puzzles given in the textbook will help

students to understand the basic concepts of logic and master the methods of logic. Q.R.

code is given on the first page of the textbook. You will like the information provided by

it.

The bureau of textbook is thankful to the Logic Subject Committee and Study Group,

Scrutiny and Quality Reviewers and Artist for their dedication and co-operation in

preparing this textbook.

Hope, Students, Teachers and Parents will welcome this textbook.

For Teachers

We are happy to introduce ‘Logic’ textbook for standard XI. As per the

revised syllabus, two new topics are added in this textbook. These are : Origin and

development of logic and Application of logic. Accordingly students will get brie

information about historical development of Western as well as Indian logic. It will

be interesting for students to know how logic has developed globally. Information

about origin and development of Indian Logic will facilitate in enhancing pride in

students mind about Indian contribution to the subject.

Logic is a fundamental subject and basis of all the branches of knowledge. The

chapter, Application of logic illustrates the importance of logic in day to day life

as well as in the important fields like - Law, Science and Computer science. This

chapter will enable students to understand the importance of logical thinking while

taking decisions in personal as well as professional life. They will also realize how

taking rational decisions at right time can lead to success and happiness in life.

Importance of logic can be highlighted by informing students, how study of logic

can help them to appear for various competitive exams, which test the reasoning

ability of students

Logic as an independent subject is introduced as standard XI. At this stage

students begin to think independently and express their thoughts and opinions. Logic

being the science of reasoning, can help students in consistent and logical thinking.

As teachers of logic it is our responsibility to train students to think rationally and

reason correctly.

As Standard XI is the first year of stydying logic, it is necessary for teachers to

take in to account students age and level of understanding. Logic studies abstract

concepts, so the important concepts in logic need to be explained step by step, in

easy to understand language and by giving examples and various activities in such

a way that, students can relate the subject to their experiences in life. Keeping this

in mind the textbook is made activity based. Teachers are expected to make use

of various examples, teaching aids and activities like debates, logical puzzles and

giving examples of good arguments and fallacies from everyday experience. In this

way teaching and learning can become interesting and enjoyable experience for

both students and teach

Competency Statements
Competency
• To acquire knowledge about the origin and development of logic.
• To understand the importance of logical thinking.

• To acquire knowledge about the fundamental concepts and principles of logic.
• To understand the types of argument and develop the ability to recognize the types of argument.

• To develop the ability of rational thinking.
• To understand the difference between sentence and proposition.
• To study the characteristics of propositions.
• To understand the types of propositions and to develop the ability to symbolize the propositions.

• To study the basic truth-tables.
• To study the method of truth-table.
• To develop the ability to apply the method of truth-table to decide whether a statement form is
tautologous or not and to decide the validity of arguments.

• To study the method of deductive proof
• To develop the ability to prove the validity of deductive argument. by the method of direct
deductive proof.
• To understand the need and importance of induction.

• To acquire knowledge about the types of inductive arguments and their use in our day to day
life and science.
• To develop the ability of recognizing the types of inductive arguments.
• To enhance argumentation skills.
• To understand the different types of fallacies.

• To devleop the ability of recognizing the types of fallacies.
• To develop the ability to reason correctly and to detect errors in others argument.
• To understand the application of logic in day

Nature of Logic

.... bad reasoning as well as good reasoning is possible, and this fact is the foundation of the practi-

cal side of logic. ---- CHARLES SANDERS PEIRCE

DO YOU KNOW THAT ..............

Logic is a branch of philosophy.

Logic developed independently in India.

Ability to reason is the unique characteristic of man.

Logic will train you to reason correctly.

You need not have formal training in logic to use the rules of logic & reason correctly.

1.1 ORIGIN AND DEVELOPMENT OF

LOGIC

Logic is traditionally classified as a branch

of philosophy. Philosophy is fundamental to

all spheres of human enquiry, and logic is the

basis that strengthens philosophical thinking.

In philosophy one needs to think clearly to deal

with the most fundamental questions related to

our life and this universe. Use of principles of

logic in thinking, reasoning and arguments is

central to the practice of philosophy.

In ancient times Logic originated and

developed in India, Greece and China. The

beginning of modern logic as a systematic study

can be traced back to the Greek philosopher

Aristotle (384-322 B.C.). Aristotle is regarded

as the father of logic. The development of logic

throughout the world is mainly influenced by

the Aristotelian logic, except in India and China

where it developed independently.

Logic originated in ancient India and

continued to develop till early modern times. The

Indian logic is represented by the Nyaya School

of philosophy. The Nyaya Sutras of Akshapada

Gautama (2nd century) constitute the core texts

of the Nyaya School. In Mahabharata (12.173.45)

and Arthashastra of Koutilya (Chanakya) we find

reference of the Anviksiki and Tarka schools of

logic in India. For his formulation of Sanskrit

grammar, Panini (5th century BC) developed

a form of logic which is similar to the modern

Boolean logic.

The Buddhist and Jaina logic also comes

under the Indian logic. Jain logic developed

and flourished from 6th century BCE to

17th century CE. Buddhist logic flourished

from about 500 CE up to 1300 CE. The main

philosophers responsible for the development

of Buddhist logic are Nagarjuna (c. 150-250

CE), Vasubandhu (400-800 CE), Dignaga (480-

540 CE) and Dharmakirti (600-660 CE). The

tradition of Buddhist logic is still alive in the

Tibetan Buddhist tradition, where logic is an

important part of the education of monks.

Mozi, “Master Mo”, a contemporary of

Confucius who founded the Mohist School, was

mainly responsible for the development of logic

in China. Unfortunately, due to the harsh rule of

Legalism in the Qin Dynasty, this line of study

in logic disappeared in China until Indian Logic

was introduced by Buddhists.

Aristotelian logic is also known as

traditional logic. Aristotle’s logic reached its

peak point in the mid-fourteenth century. The

period between the fourteenth century and the

beginning of the nineteenth century was largely

one of decline and neglect. Logic was revived in

the mid-nineteenth century

2

At the beginning of a revolutionary period

logic developed into a formal discipline. Logic

is therefore classified as a formal science.

The development of modern “symbolic” and

“mathematical” logic during this period is the

most significant development in the history of

logic. As a formal science logic is closely related

Can you answer?

1. If you attend lectures then you will understand the subject

You attend lectures

Therefore .........................

2. Wherever there is smoke there is fire

There is smoke coming out from the building

Therefore ..............

Solve the puzzles

1. A famous mathematician was walking on a street. He saw a beautiful girl on a bus

stop and he asked her, ‘what is your name? The girl recognized him as a famous

mathematician and replied that her name was hidden in the date 19/9/2001. Guess

the girls name.

2. Manikchand was looking at the photo. Someone asked him, ‘Whose picture are you

looking at? He replied: “I don’t have any brother or sister, but this man’s father is my

father’s son. So whose picture was Manikchand looking at?

to the mathematics. Development in mathematics

along with the contribution of thinkers like

Leibniz, Francis Bacon, Augustus De Morgan,

Bertrand Russell, George Boole, Peirce, Venn,

Frege, Wittgenstein, Godel and Alfred Tarski

has influenced the evolution of traditional logic

in to today’s modern logic.

1.2 DEFINITION OF LOGIC

We all can solve puzzles, give proofs

and deduce consequences as illustrated above.

This is possible because we are blessed with

the ability to reason. This is the unique ability

which differentiates man from other animals.

This ability of ours is revealed when we infer,

argue, debate or try to give proofs. We are born

rational and may not require any formal training

to reason. However our reasoning is not always

good / correct / valid. Sometimes our reasoning

is good and sometimes it is bad. It is necessary

that we always reason correctly and this is where

the role of logic is important because logic trains

us to reason correctly.

Reason has applications in all spheres of

human affairs. The study of logic, therefore,

has applications in many important fields

like Mathematics, Philosophy, Science, Law,

Computer science, Education and also in our

day to day life. Training in logic thus can help

one in all the endeavors of life.

The word logic is derived from the Greek

word ‘Logos’. The word ‘logos’ means ‘thought’.

So etymologically logic is often defined as,

‘The science of the laws of thought.’ There are

three types of sciences, 1) Natural sciences like

physics, chemistry etc. 2) Social sciences like

history, geography, sociology etc. and 3) Formal

science like mathematics. Logic is a formal

science. The etymological definition of logic,

however, is not accurate, firstly because it is

too wide and may lead to misunderstanding that

logicians study the process of thinking, which

is not correct. Thinking process is studied in

psychology. Secondly the word ‘thought’ refers

to many activities like remembering, imagining,

day dreaming, reasoning etc. and logic is

concerned with only one type of thinking i.e.

reasoning.

Another very common and easy to

understand definition of logic is – ‘Logic is the

science of reasoning.’ But this definition also

is too wide. This definition restricts the study

2
At the beginning of a revolutionary period
logic developed into a formal discipline. Logic
is therefore classified as a formal science.
The development of modern “symbolic” and
“mathematical” logic during this period is the

most significant development in the history of
logic. As a formal science logic is closely related
Can you answer?
1. If you attend lectures then you will understand the subject
You attend lectures

Therefore .........................
2. Wherever there is smoke there is fire
There is smoke coming out from the building
Therefore ..............
Solve the puzzles

1. A famous mathematician was walking on a street. He saw a beautiful girl on a bus
stop and he asked her, ‘what is your name? The girl recognized him as a famous
mathematician and replied that her name was hidden in the date 19/9/2001. Guess
the girls name.

2. Manikchand was looking at the photo. Someone asked him, ‘Whose picture are you
looking at? He replied: “I don’t have any brother or sister, but this man’s father is my
father’s son. So whose picture was Manikchand looking at?

to the mathematics. Development in mathematics
along with the contribution of thinkers like
Leibniz, Francis Bacon, Augustus De Morgan,
Bertrand Russell, George Boole, Peirce, Venn,
Frege, Wittgenstein, Godel and Alfred Tarski
has influenced the evolution of traditional logic

in to today’s modern logic.
1.2 DEFINITION OF LOGIC
We all can solve puzzles, give proofs
and deduce consequences as illustrated above.

This is possible because we are blessed with
the ability to reason. This is the unique ability
which differentiates man from other animals.
This ability of ours is revealed when we infer,

argue, debate or try to give proofs. We are born
rational and may not require any formal training
to reason. However our reasoning is not always
good / correct / valid. Sometimes our reasoning

is good and sometimes it is bad. It is necessary
that we always reason correctly and this is where
the role of logic is important because logic trains

us to reason correctly.
Reason has applications in all spheres of
human affairs. The study of logic, therefore,
has applications in many important fields
like Mathematics, Philosophy, Science, Law,
Computer science, Education and also in our
day to day life. Training in logic thus can help

one in all the endeavors of life.
The word logic is derived from the Greek
word ‘Logos’. The word ‘logos’ means ‘thought’.
So etymologically logic is often defined as,
‘The science of the laws of thought.’ There are
three types of sciences, 1) Natural sciences like
physics, chemistry etc. 2) Social sciences like
history, geography, sociology etc. and 3) Formal
science like mathematics. Logic is a formal
science. The etymological definition of logic,
however, is not accurate, firstly because it is
too wide and may lead to misunderstanding that
logicians study the process of thinking, which
is not correct. Thinking process is studied in
psychology. Secondly the word ‘thought’ refers
to many activities like remembering, imagining,
day dreaming, reasoning etc. and logic is
concerned with only one type of thinking i.e.
reasoning.
Another very common and easy to
understand definition of logic is – ‘Logic is the
science of reasoning.’ But this definition also
is too wide. This definition restricts the study

3
of logic only to reasoning but logicians are not
interested in studying the process of reasoning
as is implied by this definition too. Logicians in
fact are concerned with the correctness of the
completed process of reasoning.
The aim of logic is to train people to
reason correctly and therefore the main task of
logic is to distinguish between good reasoning
and bad reasoning. This practical aspect of logic
is accurately stated in I.M. Copi’s definition of
logic. He defines logic as – ‘The study of the
methods and principles used to distinguish
good (correct) from bad (incorrect)
reasoning.’ This definition is widely accepted
by logicians.
Reasoning is a kind of thinking in which
inference takes place i.e. a thinker passes
from the evidence to the conclusion. The term
‘inference’ refers to the mental process by
which one proposition is established on the basis
of one or more propositions accepted as the
starting point of the process. An argument is a
verbal representation of this process of inference
and logic is mainly concerned with arguments.
(In this text we shall use the words reasoning,
inference and argument as synonyms)
1.3 SOME BASIC CONCEPTS OF
LOGIC
To get precise understanding of the nature
of logic it is further necessary to understand
certain technical terms used in logic viz.
1) Argument 2) Valid argument 3) Form of
argument. 4) True / False and Valid / Invalid.
1) Argument / Inference : An argument
consists of proposition / statements. Every
argument attempts to establish a proposition
by giving another proposition / propositions
in its support. An argument may be defined
as, ‘A group of propositions in which one
proposition is established on the evidence
of remaining propositions.’ The proposition
which is established is called the conclusion and
the propositions which are stated in support of
the conclusion are called premises. For instance
in the given argument –
All artists are creative.
Sunita is an artist.
Therefore, Sunita is creative.
The propositions, ‘All artists are creative’
and ‘Sunita is an artist’ are premises and the
proposition ‘Therefore, Sunita is creative’ is the
conclusion which is established on the basis of
evidence in the premises.
Thus premise (premises) and conclusion
are the two basic constituent elements of an
argument. In every argument the conclusion
is derived from the premises and an attempt is
made to show that the conclusion is a logical
consequence of the premises.
2) Valid argument : Every argument claims
to provide evidence for its conclusion. However,
every argument is not valid. The validity of an
argument depends on the nature of relationship
between its premises and conclusion. If the
premises provide ‘good’ evidence for the
conclusion, the argument is valid otherwise it
is invalid. What is regarded as ‘good’ evidence,
however, depends upon the type of argument.
3) Form of argument : The two important
aspects of any argument are – form and content.
Every argument is about something and that is
the subject matter or the content of the argument.
In the same way every argument has some form.
Form means pattern or structure of the argument.
For instance, pots may be of various shapes or
patterns. These different shapes are the forms of
pots. These pots may be made up of any material
like clay, iron, bronze or silver. The material out
of which it is made is the content of the pot. Now
we may have pots of the same shape but made
up of different material, we may have pots of the
same material but of different forms or the pots
differing in both form and matter. In the same
way the arguments may differ in the content and
have the same form, they may have the same
content but different forms or they may differ
both in the content and the form. For example