Argument Structure
Arg.A.
“All men are animals and all animals are mortal and Socrates is a
man so Socrates is mortal.”
with base:
F.B: < ‘All men are animals’,
‘All animals are mortal’,
‘Socrates is a man’,
‘Socrates is mortal’ >
break it up into smaller parts.
F.1: < ‘All men are animals’,
‘All animals are mortal’,
‘All men are mortal’ >
F.2: < ‘All men are mortal’
‘Socrates is a man’,
‘Socrates is mortal’ >
< ‘United Airlines are on strike’,
‘Other airlines will carry more passengers’ >
the argument was really
< ‘United Airlines are on strike’,
‘United Airlines will not carry passengers’ >
< ‘United Airlines will not carry passengers’,
‘The airlines as a whole have to carry so many passengers’,
‘Other airlines will carry more passengers’ >
1
A premise or conclusion that is assumed but not stated is said to be
suppressed.
(NB: This differs from the definition given in the Text and is that
more usually adopted.)
2
An argument which is interpreted as containing suppressed premises
or a suppressed conclusion is called an enthymeme — the argument
is enthymematic.
Explicit
Claim /
Argument
Interpretation

Enthymematic
Argument
Suppressed Premisses
John is a native-born
American
-------------------------John is an American
citizen
Interpretation

John is a native-born
American
All native-born
Americans are
American Citizens
-------------------------John is an American
citizen
Suppressed Conclusion
No sane person
would do that
but you would
Interpretation

No sane person would
do that (i.e. X)
You would (do X)
You are insane
a.
Charity
Try to reconstruct the argument so that it is valid.
John is a native-born American
All native-born Americans are American Citizens
------------------------------John is an American citizen
is an argument in the form of
S is P
All P are Q
------------------------------S is Q
which is a valid form.
b.
Fidelity
John is Australian
---------------------John is happy
Bad reconstruction:
John is Australian
All Australians are happy
---------------------John is happy
Satisfactory reconstruction
John is Australian
Australians tend to be happy-go-lucky folk
---------------------John is happy
1.
Serial Arguments
1
2
3
Eg:
We are under attack from implacable enemies, so we need to
protect ourselves. That’s why I think the Patriot act is
required.
Number the three major statements:
(1)[We are under attack from implacable enemies], so (2)[we
need to protect ourselves.] That’s why (3)[I think the Patriot
act is required.]
Mark argument indicators:
(1)[We are under attack from implacable enemies], so (2)[we
need to protect ourselves.] That’s why (3)[I think the Patriot
act is required.]
2.
Divergent Arguments
1
2
3
We are under attack from implacable enemies, so we need to protect
ourselves. I also think that we should fight back.
(1)[We are under attack from implacable enemies], so (2)[we need to protect
ourselves.] (3)[I also think that we should fight back.]
(1)[We are under attack from implacable enemies], so (2)[we need to protect
ourselves.] (3)[I also think that we should fight back.]
Note that
We are under attack from implacable enemies. I also think that we should
fight back.
Is an argument
3.
Convergent Arguments
1
2
3
To say a reason is independent is to say that if the other
reasons fail, that reason will still provide support for the
conclusion.
A life of crime is not to be desired. Criminals are usually
quite unhappy people, and they often come to unpleasant
ends.
(1)[ A life of crime is not to be desired.] (2)[Criminals
are usually quite unhappy people] and (3)[they often
come to unpleasant ends.]
4.
Linked Arguments
1
+
3
2
In a linked argument the failure of one reason means that the
argument fails because the other reasons do not independently
support the conclusion.
Socrates is a man and all men are mortal, so Socrates is mortal.
(1)[Socrates is a man] and (2)[all men are mortal,] so
(3)[Socrates is mortal.]
Arguments that claim to provide support for a conclusion by
collecting together a large number of rather weak reasons in
support of a conclusion are best thought of as linked arguments
(rather than convergent.)
Hidden Elements
We mark hidden premises or conclusions in a diagram by
enclosing the number in square brackets, e.g.
3
United Airlines are on strike, so other airlines will carry
more passengers.
(1)[United Airlines are on strike], so (2)[other airlines will
carry more passengers.]
1
2
But if we include the hidden intermediate conclusion that was
suggested earlier, that
(3)[The airlines as a whole have to carry so many
passengers]
then we can see the argument as having the following form.
1
+
3
2
Conditionalisation
If we have an argument of the form:
A
a
B
then we can deduce the conditional statement ‘If A then B’.
This is the conditionalisation of the argument from A to B:
A
a
B
If A then B
Reductio ad absurdum (RAA):
A
a
B
(and B is known to be false)
Not B
If A then B
Not A
Here’s an example. Suppose we’re given a statement:
I know that I do not know anything.
There’s an argument against this that goes:
Suppose it’s true that I know that I don’t know anything.
If that’s the case then it’s also true that I don’t know that
I don’t know anything. So I both know and don’t know
that I don’t know anything. But that’s absurd because I
can’t both know and not know the very same thing. Thus
it can’t be true that I know that I don’t know anything.
We can identify the major statements and indicators in this
argument like this:
Suppose it’s true that 1(I know that I don’t know
anything.) If 1(that’s the case) then it’s also true that 2(I
don’t know that I don’t know anything.) So 3(I both know
and don’t know that I don’t know anything.) But 4(that’s
absurd) because 5(I can’t both know and not know the
very same thing.) Thus 5(it can’t be true that I know that I
don’t know anything.)
This argument structure looks like this:
1
2
3
5
If 1 then 3
(4 =) Not 3
Not 1
Complex Arguments
1(In
rape cases, sentences should be lighter for those who plead
guilty than for those who plead not guilty.) 2(Appearing in court
is a very distressing experience for a victim of rape.) 3(If the
defendant pleads guilty, the victim does not have to appear in
court.) 4(If sentences are as heavy for those who plead guilty as
for those who plead not guilty, all defendants will plead not
guilty), because 5(there is nothing to lose.)
5
2
3
1
4
1(Our
souls are immortal.) We know this from 2(revelation),
but we also know it by 3(philosophical argument.) 4(For
example, we can prove the immortality of the soul by simply
attending to its indivisibility), for 5(only composite things can
be destroyed) and because 6(it is pure substance) 7(the soul is
incomposite.)
6
5
+
4
2
3
1
7
REASONS AGAINST A CONCLUSION
2
2
=
~
3
not 3
Nuclear power
plants are very
controversial
We need to
generate more
electricity
~
We should build more
nuclear power plants
Reasons against a reason
4(If
we were more careful users,
we wouldn’t need more power)
~
3(We need to generate
more electric power)
Reasons against an inference
1(We
need to generate
more electric power)
5(Coal-fired
power
~
stations are much
easier to build)
3(We
should build more
nuclear power plants)