DEDUCTIVE & INDUCTIVE
ARGUMENTS
NURGALI BALAUSA 411A
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Deductive Arguments
For a deductive argument, if all its premises
are true, its conclusion is necessarily true (or
it is logically impossible for the conclusion to
be false.)
I.e., the truth of premises guarantees the truth of
conclusion.
E.g.:
1.
2.
3.
Either you work hard or you will fail the test.
You do not work hard.
Therefore, you will fail the test.
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3 Types of Possibility
Technological possibility
e.g., Going to the moon is technological possible,
but going to Mercury is not.
Physical possibility
e.g., Going to Mercury is physical possible, but
making water boil at 95 C under one atmospheric
pressure is not.
Logical possibility
e.g. Making water boil at 95 C under one
atmospheric pressure is logical possible, but
drawing a triangle with 4 angles is not.
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Deductive Arguments
When we talk about deductive
arguments, we have already
presupposed that the arguments are
successful or valid deductive arguments.
The conclusion of a valid argument is
called a valid conclusion.
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Deductive Arguments
For an unsuccessful deductive argument
(the premises are intended to guarantee
the conclusion but fail to do so), we call it
an invalid argument.
A deductive argument may be valid or
invalid, there is nothing in between.
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Deductive Arguments
Whether a deductive argument is valid or
invalid depends on its form or structure, not on
its content.
The above argument is valid because it has
this valid form:
p or q.
Not-p.
Therefore, q.
p and q are statement variables.
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Deductive Arguments
Any argument having that form will also
be a valid argument.
There are infinite possible valid
structures.
Here are some common examples:
If p, then q
p____
∴q
If p, then q
Not-q____
∴ Not-p
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Here are more examples:
If p, then q
If q, then r
∴ If p, then r
If p and q, then r
p_____________
∴ If q, then r
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Deductive Arguments
A valid argument may have false
conclusion if it has false premises.
E.g.:
CY Leung is either a genius or an idiot.
He is not an idiot.
Therefore, He is a genius.
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Deductive Arguments
In order to guarantee the truth of
conclusion, we have to make sure all the
premises are true.
When all the premises of a valid
argument are true, the argument is
called a “sound argument”.
And the conclusion of a sound argument
is called a sound conclusion.
If an argument is invalid or has false
premises, it is unsound.
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Deductive Arguments
On the other hand, the fact that an argument is
invalid does not entail that its conclusion is
false.
It just means that its conclusion does not
follow from its premises.
You can consider a valid argument structure as
a truth-keeping machine:
When you input T information into it, it will output T
information.
When you input F information into it, it will output T
or F information.
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Inductive Arguments
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A typical example of inductive argument:
Swan1 is white.
Swan2 is white.
Swan3 is white.
…
Swann is white.
________________
All swans are white.
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Another typical example:
An event of type B follows an event of type A at
time t1.
An event of type B follows an event of type A at
time t2.
…
An event of type B follows an event of type A at
time tn.
___________________________
A causes B.
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Many people think that the characteristic of
inductive arguments is arguing from particular
to general.
However, deductive arguments may also argue
from particular to general, e.g.:
I have two cats, Fluffy and Garfield.
Fluffy does not eat fish.
Garfield does not eat fish either._____
Therefore, All of my cats do not eat fish.
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Some inductive arguments may argue
from general to particular, e.g.:
Most of our students are born in HK.
Jim is one of our students.
Therefore, Jim is born in HK.
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Inductive Argument
The main difference between deductive
arguments and inductive arguments is
that, for the latter, if all its premises are
true, its conclusion is likely to be true but
still possible to be false
I.e., The truth of its premises makes it
reasonable to hold that the conclusion is
true but the content of the premises does
not include (imply) the content of the
conclusion.
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Inductive Argument
We call a good inductive argument a
strong argument, a bad inductive
argument a weak argument.
Whether an inductive argument is strong
or weak depends on its content, not on
its structure.
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Inductive Argument
These 2 arguments have the same
structure but one is strong and the other
is weak:
HK is a wealthy society. Therefore, most of
HK people are wealthy.
HK is a Chinese society. Therefore, most of
HK people are Chinese.
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Inductive Argument
Even for a strong argument, if its
premises are false, we still have no
reasons to believe in the conclusion.
If all the premises of a strong argument
are true, the argument is called a “cogent
argument.”
The conclusion is called a “cogent
conclusion.”
If an argument is weak or has false
premises, it is uncogent.
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