The document discusses deductive and inductive arguments, focusing on their structures and validity. Deductive arguments guarantee their conclusions if their premises are true, while inductive arguments suggest likely conclusions based on particular observations. The document also explains terms like sound arguments, cogent arguments, and the difference between strong and weak inductive arguments.

1. Inductive And Deductive Argument
Prepared by Osama Rahman

2. 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.
Example
Either you work hard or you will fail the test.
You do not work hard.
Therefore, you will fail the test.

3. 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.

4. 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.
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.

5. Continues….
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.

6. Continues….
A valid argument may have false conclusion if it has false premises.
Example:
CY Leung is either a genius or an idiot.
He is not an idiot.
Therefore, He is a genius.
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.

7. 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

8. Inductive Arguments
A typical example of inductive
argument:
Swan1 is white.
Swan2 is white.
Swan3 is white.
…
Swann is white.
________________
All swans are white.
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.

9. Inductive Arguments
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.
Example:
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.
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.

10. Continues….
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.
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.

11. 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.
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.