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(2) All doctors are rich.

Sunil is a doctor.

Therefore, Sunil is rich.

The content or the subject matter of the

above given arguments is different. The first

argument is about men, wise and 

dilipkumar aatram 

The second is about doctors, rich and Sunil.

However, the form of both the arguments is

same. The first premise of both the arguments

states that a narrower class (men and doctors)

is included in a wider class (wise and rich). The

second premise of both the arguments states that

an individual (Rakesh and Sunil) is a member

of the narrower class. In the conclusion of both

the argument it is inferred that the individual

is, therefore, a member of the wider class. The

following diagram clearly reveals how the form

of both the arguments is same.

Argument – 1

Wise

Men

Men Rakesh

Wise

Rakesh

Argument 

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4) True / False and Valid / Invalid
True / False and Valid / Invalid are
important terms in logic. The terms valid / invalid
are used for arguments in logic. An argument
is either valid or invalid and never true or
false. Validity of an argument depends upon
the evidence in the premises for the conclusion.
If the conclusion of an argument necessarily
follows from the evidence in the premises then
the argument is valid otherwise it is invalid.
An arguemnt consists of propositions
/ statements. Proposition is either true or
false. The terms valid / invalid are not used
for propositions in logic. A proposition is
considered to be true if whatever is stated in the
proposition agrees with actual facts, if not it is
false. For example, ‘Washington is an American
city’ is a true proposition. And ‘London is an
Indian city’ is a false proposition.
1.4 DEDUCTIVE AND INDUCTIVE ARGUMENTS / INFERENCES
Can you find the difference in the evidence of following arguments?
1. If it rains then roads become wet. 2. All observed crows are black.
It is raining. No observed crow is non-black.
Therefore, roads are wet. Therefore, all crows are black.
Arguments are classified into two types
1) Deductive arguments 2) Inductive arguments.
This classification of argumments into deductive
and inductive is based on the nature of relationship
between premises and conclusion. Premises of
deductive arguments claim to provide sufficient
evidence for the conclusion, whereas premises
of inductive arguments provide some evidence
for the conclusion.
Deductive Argument / Inference – Every
argument attempts to prove the conclusion. The
evidence needed to establish the conclusion is
given in the premises. The evidence given in the
premises is not always sufficient. A deductive
argument claims to provide conclusive
grounds i.e. sufficient evidence for its
conclusion. If the claim that premises provide
sufficient evidence is justified, the deductive
argument is valid, if not it is invalid.
In a valid deductive argument where the
evidence is sufficient the relation between the
premises and the conclusion is of implication.
Premises imply the conclusion means, if
premises are true the conclusion is also true, it is
impossible for the conclusion to be false. Thus
the conclusion of a valid deductive argument is
always certain.
Another important feature of a deductive
argument is that, its conclusion is implicit in the
premises i.e. the conclusion does not go beyond
the evidence in the premises. This means
we don’t arrive at any new information. By
deductive argument we can know what is implied
by the premises. Deductive arguments do not
give us any new information. For this inductive
arguments are useful. Thus, the certainty of
deductive arguments comes at a cost.
In an invalid deductive argument, however,
the claim that premises provide sufficient
evidence is not justified, therefore, the relation
of implication does not hold between its premise
and conclusion. Even when the premises are true
the conclusion may be false. For example, let us
consider the following arguments.
(1) If Amit passes S.S.C. with good marks, he
will get admission in college.
Amit passed S.S.C. with good marks.
Therefore, he well get admission in
college.
(2) Meena will either go to college or study
at home.
Meena did not go to college.
Therefore, Meena is studying at hom

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(3) If Anita gets the prize then she will become
famous.
Anita did not get the prize.
Therefore, Anita will not become famous.
(4) If it rains heavyly, the college will
declare holiday.
College has declared a holiday.
Therefore, it is raining heavily.
All these arguments are deductive
arguments as the conclusions of all the arguments
don’t go beyond the evidence in the premises.
The first two arguments are valid as premises
provide sufficient evidence. The premises imply
the conclusion. If premise are true, conclusion
cannot be false. The last two arguments, though
deductive, are not valid because the claim that
premises provide sufficient evidence is not
justified. Even when premises are true, the
conclusion may be false. So there is no relation of
implication, the conclusion does not necessarily
follow from the premises.
The deductive arguments are formally
valid. A formally valid argument is one whose
validity is completely determined by its form.
In case of deductive arguments the content of
its premises and conclusion does not affect its
validity. There is no need to judge the content
of the premises and conclusion, also there is no
need to find out whether they are true or false to
determine the validity. One only needs to check
the form of the argument. If the form is valid the
argument is also valid. For example –
(1) All men are animals.
All animals are mortals.
Therefore, all men are mortals.
(2) All crows are birds.
All birds have wings.
Therefore, all crows have wings.
(3) All singers are actors.
All actors are leaders.
Therefore, all singers are leaders.
(4) All cats are rats.
All rats are lazy.
Therefore, all cats are lazy.
The form of all the above given deductive
arguments is as follows :
All X is Y.
All Y is Z.
Therefore, All X is Z.
It is obvious that the form is valid and
therefore all the arguments being its substitution
instances are also valid. It is easy to accept that
the first two arguments are valid because the
premises and conclusions of these arguments
are all true and conclusion necessarily follows
from the premises. But one may find it difficult
to accept that, the third and fourth argument is
valid as premises and conclusion of both the
arguments are false. However they are also valid.
Validity of deductive argument is conditional.
In case of a valid deductive argument if
premises are true the conclusion must be
true. So if premises of the last two arguments
are assumed as true then the conclusions of
both the arguments necessarily follow from the
premises and therefore both the arguments are
valid. If conclusion necessarily follows from the
premises then the deductive argument is valid.
Premises and conclusion of valid deductive
argument may or may not be true. When the
deductive argument is valid and its premises
and conclusion are true, such an argument is
called sound argument.
As deductive arguments are formally
valid, the validity of deductive arguments can
be determined or proved by using the rules and
methods developed by logicians.
Inductive Argument / inference ---
Inductive argument is an argument which
provides some evidence for the conclusion.
The conclusion of an inductive argument goes
beyond the evidence in the premises. There is a
guess, prediction or something new is asserted in
the conclusion for which the evidence given in
the premises is not sufficient. As the evidence in
the premises is not sufficient, the premises of an
inductive argument don’t imply the conclusion.
This means even when the premises are true the
conclusion may be false. The conclusion of an
inductive argument is always probable. W

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the argument is good (valid) or bad (invalid), the
possibility of its conclusion being false always
remains.
Technically the terms ‘valid’ and ‘invalid’
cannot be used for inductive arguments. Only
deductive arguments are either valid or invalid.
Inductive arguments can be judged as better or
worse. More the possibility of the conclusion
being true, better the argument. The addition
of new premises may alter the strength of an
inductive argument, but a deductive argument,
if valid, cannot be made more valid or invalid by
the addition of any premises. We shall use the
terms ‘good’ or ‘bad’ for inductive arguments.
For example, consider the following arguments.
(1) Whenever cat crossed my way in the past,
something bad happened on that
day.
Today morning a cat crossed my way.
Therefore, I am sure that something bad is
going to happen today.
(2) Every morning I have seen the sun rising
in the east.
It is early morning now.
So, I am sure I will find sun rising in the
east.
(3) The doctor told me that, Suresh is suffering
from cancer and he will not survive for
more than three months.
After two months I got the news that
Suresh is no more.
So, Suresh must have died due to cancer.
All the above given arguments are inductive
arguments as conclusions of all the arguments
go beyond the evidence in the premises. The
premises don’t imply the conclusion. Even
if premises are true the conclusions of all the
arguments are probable. The conclusion is
probable does not mean that the argument is bad.
In the above given arguments the first one is bad
where as the other two are good.
Like deductive arguments the validity of
inductive arguments i.e. whether the inductive
argument is good or bad, is not determined by
the form of the argument, but is decided by its
content. Inductive arguments are materially
valid. A materially valid inference is one
whose validity is completely determined by its
content. To decide whether the given inductive
argument is good or bad, one has to consider
the content / the subject matter of the argument.
The form of the first and second argument is the
same but the first one is bad whereas the second
one is good.
The amount of evidence in the premises
determines whether the argument is good. If the
evidence in the premises makes it reasonable
to accept the conclusion, then, the argument
is good otherwise it is bad. From the above
given arguments, the first arguments is a bad
one because the conclusion is based on the
superstition, there is no connection between
a cat crossing the way and good or bad events
happening in our life. In the other two arguments,
though, the conclusions may turn out to be
false, the evidence on the basis of which the
conclusions are derived is scientific. Hence the
last two arguments are good.
Though the content decides whether
an inductive argument is good, this does not
mean that the premises and conclusion of
good inductive arguments are true and of bad
inductive arguments are false. In case of the
first argument, even if premises are true and the
conclusion turns out to be true, still the argument
is bad. Similarly in case of the last argument
even if conclusion turns out to be false when the
premises are true, the argument is good because
the inference is based on the doctor’s verdict.
Like deductive arguments, whether the
given inductive argument is good or bad cannot
be determined by the methods and rules of logic.
In case of common man’s inductive arguments,
as given above, one can easily decide whether
they are good or bad. However, in case of the
inductive arguments, in various sciences, by
judging the evidence in the premises only the
experts in the field can decide whether it is good or
bad. Unlike deductive arguments, the Inductive
arguments, provide us with new information 

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thus may expand our knowledge about the world.

So, while deductive arguments are used mostly

in mathematics, most other fields of research

make extensive use of inductive arguments.

Truth and Validity of arguments – The

relation between validity or invalidity of the

argument and truth or falsity of its premises and

conclusion is not simple. As discussed earlier,

an argument may be valid when one or more

or even all its premises and conclusion are

false and an argument may be invalid with all

its premises and conclusion true. The truth or

falsity of an argument's conclusion does not

by itself determine the validity or invalidity of

that argument. And the fact that an argument

is valid does not guarantee the truth of its

conclusion.

DEDUCTIVE ARGUMENT INDUCTIVE ARGUMENT

1. Premises claim to provide sufficient 1. Premises provide some evidence for the

evidence for the conclusion. conclusion.

2. In valid deductive argument premises 2. Premises do not imply the conclusion.

imply the conclusion.

3. In valid deductive argument if premises 3. Even when premises are true conclusion

are true, conclusion must be true. may be false.

4. Conclusion of valid deductive argument 4. Conclusion is always probable.

is always certain.

5. Conclusion does not go beyond the 5. Conclusion goes beyond the evidence in

evidence in the premises. the premises.

6. Arguments are formally valid. 6. Arguments are materially valid.

7. Validity can be determined by rules 7. Correctness of arguments can be decided

and methods of logic. by an appeal to experience and not by

rules and methods of logic.

8. Deductive arguments cannot expand 8. With inductive arguments we can discover

our knowledge of the world, by deduction something new and expand our knowledge

we can only know what is implied by the of the world.

premises.

Summary

• In past logic developed independently in India, Greece and China.

• Modern logic is evolved from Aristotelian or traditional logic.

• Logic is study of methods and principles used to distinguish between good and bad reasoning.

• Arguments, Valid argument, Form of argument, True / False, Valid / Invalid are some

important concepts in logic.

• The two important types of arguments are – Deductive and Inductive arguments.

• Deductive arguments claim to provide sufficient evidence for the conclusion.

• Inductive arguments provide some evidence for the conclus