# 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.

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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.]

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 12

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 12 +

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 12 +

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 234234 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+75+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 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)

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