This lesson gives the basics of how to make an argument. It has lots of examples and fun pictures for students. It is

1. Tips, Pointers, and Rules to being a
Great Debator

2.  In logic ( 邏輯 ), an argument is
made up of a set of statements. The
first statements are called the
'premises‘.
 A ‘premise’ is a sentence that will
help support your argument.
 The last statement is called the
'conclusion'. The conclusion is
usually the statement that you want
somebody to accept (agree with
you), which is why you're arguing in
the first place.
 Here's an example of an argument:
 All birds have wings. (premise)
A cuckoos a bird. (premise)
Therefore, a cuckoo has wings.
(conclusion)

3.  In this particular
argument, the premises
force the conclusion.
Anyone who believes the
premises must also believe
the conclusion. This is
therefore called a 'valid'
argument, or it could be
said that the conclusion
follows 'validly' from the
premises.
 If something is valid it is
true.

4. In the previous example, both
premises are true, so the conclusion
must be true as well. By 'true', we
mean that they are statements that
accurately reflect reality.
It is possible for an argument to be
valid, yet for the premises and
conclusion to be false. For example:
All Americans eat hamburgers on
Sundays.
Tony Blair is American.
Therefore, Tony Blair eats
hamburgers on Sundays.
Both the premises and the
conclusion are demonstrably false,
and yet the argument is valid.
Anyone who believed both premises
would also have to believe the
conclusion. This shows that validity
is a feature of the form of the
argument, and has nothing to do
with its content.Can we make some examples on our own?

5.  When an argument is valid, and the premises
are true, then the conclusion must also be
true. Then the argument is called sound, or
cogent, and whoever you are arguing with is
forced to agree that you are right, or else to
resort to violence.
 Ex: Mercury destroys your nervous system.
 Sharks have a lot of mercury in their bodies.
 Eating shark can be dangerous for your
nervous system.

6.  Since validity has to do with
the form of an argument, it
is possible to identify valid
forms, and some of these
have been studied by
logicians, and have been
given names in Latin.
 Valid Argument Form
Number One - Modus
Ponens
 Modus Ponens ('proposing
mode') is the most common
form of valid argument. The
cuckoo argument and the
Tony Blair argument above
are both examples of Modus
Ponens. A generalized
Modus Ponens argument
looks like this:
 All A are B.
x is A
Therefore, x is B.
 This is what Modus Ponens looks
like with certain kinds of
statements, namely those
involving quantifiers. (A quantifier
is a word like 'all', 'some' or
'none'.) Modus Ponens arguments
can also be constructed with
conditional statements, also
called 'if/then' statements:
 If a Rimram yells, then a
Dockermarker falls.
A Rimram yelled.
Therefore, a Dockermarker fell.
 We might not know anything
about that Rimram or about
Dockermarker, but we must admit
that the argument is perfectly
valid, and that anyone who
believes the premises must also
believe the conclusion.
 With a partner make 3 valid
arguments. You have 8 minutes.

7.  Now, take a look at a different argument:
 Some vertebrates are warm-blooded. Frogs
are vertebrates.
Therefore, frogs are warm-blooded.
This argument is invalid. Both of the
premises are true, but the conclusion is
false. In a valid argument, the conclusion is
never false when the premises are true. This
particular argument is invalid because
Modus Ponens does not work with the
quantifier 'some', only with the quantifier 'all'.

8.  Invalid arguments are also
called fallacies. Let us look
at some very common forms
of fallacy:
 Invalid Argument Form
Number One - Affirming
the Consequent
 If x, then y.
y.
Therefore, x.
 Ex.
 If I am hungry, then my
stomach hurts.
 My stomach hurts.
 Therefore, I am hungry.

9.  This fallacy is a common logical
mistake, sometimes called
'abductive reasoning' (as opposed to
deductive reasoning, of which Modus
Ponens is an example). It may seem
at first glance to make sense. It is
invalid because the conclusion does
not follow from the premises, even
if it happens to be a true statement.
It is very easy to mix this form up
with the Modus Ponens form. Here's
a concrete example:
 If I am with the one I love, then I
am happy.
I am happy.
Therefore, I am with the one I
love.
 With your partner make as many
invalid arguments as you can in ten
minutes.

10.  This argument doesn't work, because
the one you love could be far away, and you
could be happy for some other reason,
perhaps having to do with food, money, or
central nervous system stimulants. Here is a
very well-known example of abductive
reasoning:
 Fire causes smoke.
There is smoke.
Therefore, there is fire.

11. As tempting as it may be to
accept this conclusion, we
only know that fire is one
cause of smoke. There may
also be other causes, so the
presence of smoke does not
necessitate that of fire. The
statements in this argument
are not explicitly phrased as
conditional statements, or as
quantified statements, but
the rules of reasoning still
apply. 'Fire causes smoke'
could be rephrased as 'If
there is fire, then there is
smoke'.

12.  If x, then y.
Not x.
Therefore,
not y.
 This is similar to Affirming
the Consequent, except
that it takes on a negative
form. Here's an example:
 All dogs have four legs.
Francis the Talking Mule
is not a dog
Therefore, Francis the
Talking Mule does not
have four legs.
 Even though both of the
premises are true, the
conclusion is false,
because dogs are not the
only animals that have
four legs.

13.  Ad homimen (meaning
'towards the person')
arguments and arguments
based on authority are very
similar fallacies. Ad hominem
arguments are very common
in politics, and authority-
based arguments are very
common in religion2
.
 In an ad hominem argument,
a statement is said to be
wrong because the person
making that statement is
foolish, or biased, or has
been wrong before. This is a
fallacy because even a
foolish, biased, often wrong
person can make correct
statements.
 Mr X says that Y is
true.
But Mr X also said
that Z was true,
and was proved
wrong.
Therefore, Y is
also untrue.

14. Citing authority is like a
positive version of ad
hominem. An argument
based on authority is one
in which a statement is
said to be true, because
the person who made the
statement is smart, or
inspired, or usually right.
This is a fallacy because
everybody can be wrong,
sometimes.

15.  Some claim that
arguments based on
human authority are
fallacious, but that
arguments based on
divine authority are
not. This claim is not
a logical one, but a
theological one, and
therefore beyond the
scope of this entry,
thank goodness.

16. Circular Reasoning
One type of fallacy
that is very
common with
longer, more
complicated
arguments is called
the circular
reasoning fallacy.
Circular reasoning
is when the
conclusion is,
itself, used as one
of the premises of
the argument. The
conclusion then
follows quite
easily, but nothing
has really been
proven.

17.  The classic example of circular reasoning
runs something like this:
 'This scripture is the inspired word of God.'
'How do you know?'
'Because it says so right here, in this
scripture.'
'Why should I believe what it says there?'
'Because this scripture is the inspired word of
God...'

18.  Here is another
argument. The
premises are both
(arguably) true, the
form seems valid, the
argument isn't
circular, and yet the
conclusion seems
false!
 Nothing is better than
eternal bliss.
 A peanut butter sandwich
is better than nothing.
 Therefore, a peanut
butter sandwich is better
than eternal bliss.
The fallacy in this argument is left as an exercise, for the
Researcher to find, with the recommendation that the
Researcher brush up on his or her knowledge of
paradoxes.

19.  Perhaps you've learned something new about
arguing from this entry, and the next time
you get in an argument, you will put this to
good use.
 Remember: true premises + valid argument
= true conclusion.
 If that doesn't seem to work, it might be wise
to back up your arguing skills with a good
working knowledge of martial arts.