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.

 ExplicitClaim /

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 AmericanAll native-born Americans are American Citizens-------------------------------John is an American citizen is an argument in the form of  S is PAll 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.] 

1

2.                 Divergent Arguments

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

3.                 Convergent Arguments

1 2

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.]

3

4.                 Linked Arguments

1 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.

3

1 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

If A then B

(and B is known to be false)

Not 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

If 1 then 3

5

(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 4

1

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 + 7

4

2 3

1

REASONS AGAINST A CONCLUSION

2

~

3

=

2

not 3

We need to generate more electricity

Nuclear power plants are very controversial

We should build more nuclear power plants

~

Reasons against a reason4(If we were more careful users, we wouldn’t need more power)

~ 3(We need to generate more electric power)

Reasons against an inference1(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)