Philosophy - Philosophy Course Notes

Diagramming Arguments Method

Lecture 4

April 22, 2007

 

Standardization allows us to see a little more of the structure of an argument than just viewing the argument as a collection of sentences.

 

Using diagramming methods we can find better ways to reveal the structure of an argument.

 

Three things to consider before diagramming an argument:

1. Are any of the premises intended to link together to provide support for the conclusion or sub-conclusion?  If not, they provide convergent support.

2. Are any of the premises intended to stand alone?

3. Are any of the premises counter-considerations? Do they go against the conclusion?

 

I. Linked Premises Versus Convergent Premises

 

1. Why is it difficult to determine if premises are linked or not?

2. Premises provide linked support for a conclusion if taken together they support the conclusion, but taken individually they do not.  They have to work together to provide any support at all.

3. Premises provide convergent support if each of them individually provides support for the conclusion.

 

Example:

i) If my dog has flees, then there are flees in my bed.

ii) My dog has flees.

iii) Therefore, there are flees in my bed.

 

The first premise provides no support at all for the conclusion by itself.  Premise two might be thought to provide a little support by itself.  But taken together they provide even more support for the conclusion.

 

4. If you think one premise might be able to provide support on its own and the other would not, you are probably dealing with a case of linked support.  The flip case is possible too.  It might look like linked support but the premises actually offer convergent support.

 

5. Since arguments with linked support tend to be stronger (the strongest argument is a deductively valid one), why would someone want to even use a convergent argument?

a. Very often you are forced to give arguments without conclusive evidence.

b. So you give a cumulative argument where the weight of the evidence is taken together.

There is an important distinction between have more premises to provide support for a conclusion and having a few premises that link to provide powerful support for a conclusion.

 

II. Counter-Considerations And The Burden of Proof

 

1. Counter-considersations

Counter-considerations cannot really be easily shown in standardization.  They would be labeled 'objections' by philosophers such as St. Thomas Aquinas.

As noted above counter-considerations are premises that work against the conclusion offered.  They are arguments against the arguments given in defence of the conclusion.

 

2. What is the Burden of Proof

The burden of proof is who has to prove their case in an argument.

In a court of law a person is declared innocent until proven guilty. All the defence has to do is show that the prosecution has not established their guilt (beyond a reasonable doubt.) In this case the burden of proof is on the prosecution.  All the defence has to do is refute the arguments given by the prosecution.

When the defence presents its case it has a number of counter-considerations to challenge what the prosecution says.  Each argument presented by the prosecution is attacked.  These 'attacks' are called rebuttals.  At the end the prosecution can try to counter those rebuttals and the defense can rebut those counter-considerations.

In real life we see a mixture of linked and convergent support offered in support of a conclusion and then a variety of counter-considerations against the conclusion.

The burden of proof changes and often determining it can be a tricky proposition.

 

One good way to write an essay is to:

a. Give your reasons in support of your conclusion.

b. Offer what you might think are the objections people would raise against your premises.

c. Refute / rebut those counter-considerations.

 

III. How to Diagram an Argument

 

You need a list of self-contained declarative sentences to do this (see standardization of arguments.)  Specify the referent of pronouns in all of the premises if possible.

1. When you draw a diagram, every premise will get a circle with its number in it.

2. Each premise or conclusion gets its own number.

3. The basic idea is to draw a line from each premise to the conclusion it supports. --->

4. A sub-conclusion will have arrows that end at it and other arrows that begin from it.

5. The final conclusion would only have arrows arriving at it.

6. If have have two or more premises providing linked support instead of convergent support, put their circles close together and join them with a plus sign.  Draw one arrow only from that group of premises to the conclusion they support.

7. Draw counter-considerations with a wavy line.

8. Draw rebuttals (attacks against counter-considerations) as a line with a circle at its head instead of an arrow. Have them go to the middle of the wavy line for the counter-consideration they are working against.

 

 

 

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