Arguments & sub-arguments

Philosophy and Logic

Section 4.1

Unit 4. Analyzing Inferences

• Applied at last to real-life arguments – ex. 4.1, 4.2, & pp. 4-23 through 4-28

• Add suppressed premises– ex. 4.3, 4.4, p. 4-22.

• Give a technical definition– suppressed premise, weak/strong statement/

argument, principle of charity, strawman

Constructing an argument

The dollar will fall in value against the yen, and if the dollar falls against the yen, then the trade deficit with Japan will get worse. So the trade deficit with Japan will get worse.

FF ⊃ W

-------------------------------------W

But what if your audience does not believe that the dollar will fall in value against the yen?

The author’s burden

• You want to persuade someone that your main conclusion, Q is true.

• To do this generally you must dig down until you find premises P which that person already believes or will accept, and then show that

(P ⊃ Q)

Author’s burden (cont.)• If they don’t believe that the dollar will fall

against the yen (F), you must give an argument that F.

• More generally: almost any premise might reasonably be challenged– If it is challenged, you should be ready with a

back-up argument for that premise.– These “subsidiary” arguments are often given

with the “main” argument itself.

Why the dollar will fall

Treasury bill rates are going down, and if they do, then the dollar will fall against the yen. Hence the dollar will fall against the yen.

T

T ⊃ F

-------------------------------------

F

A more complex structure

TT ⊃ F

--------------------------F

FF ⊃ W

--------------------------W

A more complex structure

TT ⊃ F

--------------------------F

FF ⊃ W

--------------------------W The MAIN conclusion

Main argument

A more complex structure

TT ⊃ F

--------------------------F

FF ⊃ W

--------------------------W The MAIN conclusion

Main argument

A “mini” argument

A more complex structure

TT ⊃ F

--------------------------F Premise F is its conclusion

FF ⊃ W

--------------------------W The MAIN conclusion

Main argument

A “mini” argument

How to put it in words

The dollar will fall in value against the yen, since T bill rates are going down, and if they do, then the dollar falls. Now if the dollar falls against the yen, then the trade deficit with Japan will get worse. So the trade deficit with Japan will get worse.

Our problem: to go the other way

To go from the words in a real-life argument

to the main and subsidiary inferences that the passage contains.

First steps

1 Underline all of the inference indicators in the argument.

2 Identify each of the separate statements in the argument. Put brackets around each one.

3 Number each statement in the argument.

1. Inference indicators

The dollar will fall in value against the yen, since T bill rates are going down, and if they do, then the dollar falls. Now if the dollar falls against the yen, then the trade deficit with Japan will get worse. So the trade deficit with Japan will get worse.

1. Inference indicators

The dollar will fall in value against the yen, since T bill rates are going down, and if they do, then the dollar falls. Now if the dollar falls against the yen, then the trade deficit with Japan will get worse. So the trade deficit with Japan will get worse.

1. Inference indicators

The dollar will fall in value against the yen, since T bill rates are going down, and if they do, then the dollar falls. Now if the dollar falls against the yen, then the trade deficit with Japan will get worse. So the trade deficit with Japan will get worse.

1. Inference indicators

The dollar will fall in value against the yen, since T bill rates are going down, and if they do, then the dollar falls. Now if the dollar falls against the yen, then the trade deficit with Japan will get worse. So the trade deficit with Japan will get worse.

1. Inference indicators

The dollar will fall in value against the yen, since T bill rates are going down, and if they do, then the dollar falls. Now if the dollar falls against the yen, then the trade deficit with Japan will get worse. So the trade deficit with Japan will get worse.

Note: inference indicators. Not sentential connectives!

2. Identify statements

The dollar will fall in value against the yen, since T bill rates are going down, and if they do, then the dollar falls. Now if the dollar falls against the yen, then the trade deficit with Japan will get worse. So the trade deficit with Japan will get worse.

2. Identify statements

[The dollar will fall in value against the yen], since T bill rates are going down, and if they do, then the dollar falls. Now if the dollar falls against the yen, then the trade deficit with Japan will get worse. So the trade deficit with Japan will get worse.

2. Identify statements

[The dollar will fall in value against the yen], since [T bill rates are going down], and if they do, then the dollar falls. Now if the dollar falls against the yen, then the trade deficit with Japan will get worse. So the trade deficit with Japan will get worse.

2. Identify statements

[The dollar will fall in value against the yen], since [T bill rates are going down], and [if they do, then the dollar falls]. Now if the dollar falls against the yen, then the trade deficit with Japan will get worse. So the trade deficit with Japan will get worse.

2. Identify statements

[The dollar will fall in value against the yen], since [T bill rates are going down], and [if they do, then the dollar falls]. Now [if the dollar falls against the yen, then the trade deficit with Japan will get worse]. So the trade deficit with Japan will get worse.

2. Identify statements

[The dollar will fall in value against the yen], since [T bill rates are going down], and [if they do, then the dollar falls]. Now [if the dollar falls against the yen, then the trade deficit with Japan will get worse]. So [the trade deficit with Japan will get worse].

What’s one statement?

• One assertion made by the author

• Hence– “if…then…” claims should not be treated as

two separate statements.

– Ditto for “either…or…”

– But conjunctions can be split apart

3. Number the claims

[The dollar will fall in value against the yen], since [T bill rates are going down], and [if they do, then the dollar falls]. Now [if the dollar falls against the yen, then the trade deficit with Japan will get worse]. So [the trade deficit with Japan will get worse].

3. Number the claims

[(1) The dollar will fall in value against the yen], since [(2) T bill rates are going down], and [(3) if they do, then the dollar falls]. Now [(4) if the dollar falls against the yen, then the trade deficit with Japan will get worse]. So [(5) the trade deficit with Japan will get worse].

(2) T bill rates are going down(3) If T bill rates go down, then the dollar falls against

the yen----------------------------------------------------(1) The dollar will fall in value against the yen

(1) The dollar will fall in value against the yen(4) If the dollar falls against the yen, then the trade

deficit with Japan will get worse.-------------------------------------------------(5) The trade deficit with Japan will get worse.

(2) T T bill rates go down

(3) T ⊃ F If they do, the dollar falls

----------------

(1) F The dollar falls

(1) F The dollar falls

(4) F ⊃W If it does, trade deficit gets worse

----------------

(5) W The trade deficit gets worse

Our problem, in a nutshell

• At least one of the claims is both a premise (here, of the main argument) and a conclusion (of a mini argument).

• It links two inferences together.

• Q: how to represent this dual role.

One possibility: write it all out!

(2) T bill rates are going down(3) If T bill rates go down, then the dollar falls against

the yen-------------------------------(1) The dollar will fall in value against the yen

(1) The dollar will fall in value against the yen(4) If the dollar falls against the yen, then the trade deficit

with Japan will get worse.--------------------------------(5) The trade deficit with Japan will get worse.

The crucial steps

4 Note what the explicit indicators tell you. Make “sub diagrams”.

5 Put the main conclusion at the bottom of the diagram.

6 Connect all the inferences together.

7 Check the result.

4. Focus on the explicit indicators

[(1) The dollar will fall in value against the yen], since [(2) T bill rates are going down], and [(3) if they do, then the dollar falls]. Now [(4) if the dollar falls against the yen, then the trade deficit with Japan will get worse]. So [(5) the trade deficit with Japan will get worse].

[(1) The dollar will fall in value against the yen], since [(2) T bill rates are going down], and [(3) if they do, then the dollar falls]. Now [(4) if the dollar falls against the yen, then the trade deficit with Japan will get worse]. So [(5) the trade deficit with Japan will get worse].

(1), since (2) and (3). Now (4). So (5).

4a. Write out the indicator “schema”

4b. Make “sub-diagrams”

(1), since (2) and (3). Now (4). So (5). – Each explicit indicator is a “flag” for an

inference.

– Each “flag” dictates an ordering among some of the circles.

– Some of the neighbors of that flag have to be premises, and one has to be a conclusion.

4. Make sub-diagrams

“(1), since (2) and (3)” tells us that we have at least:

(2)T bill rates are going down

(3) If T bill rates go down, then the dollar falls against the yen

-------------------------------------(1)The dollar will fall in value against the yen

4. Make sub-diagrams

• The same inference can be represented as:

(2) (3)

(1)

• The bracket + arrow here stands for an inference. It means that (2) and (3) are the premises from which (1) is claimed to follow.

4. Next sub diagram, please

“Now (4). So (5).” shows that (5) must be a conclusion from at least (4):

(4) If the dollar falls against the yen, then the trade deficit with Japan will get worse.

-------------------------------------(5)The trade deficit with Japan will get worse.

4. Sub diagrams

“Sub diagram”:

(4)

---------------

(5)

Indicates that (5) is a conclusion from (4), plus, perhaps, other stuff

5. Identify the main conclusion

• We already know that it is (5) “The trade deficit with Japan will get worse”.

• Note that it is the very last claim in the passage.

• Put it at the bottom of the diagram.

6. Connect the inferences

Our sub diagrams:

(2) (3) (4) ------------

(1) (5)

6. Connect the inferences

There is only one plausible structure:

(2) (3)

(1) (4)

(5)

7. Check your results

Look at each inference (arrow) you have drawn. Ask: is that a reasonable way to argue?Is there any better way to argue, using these

claims?

Sometimes you will need to try various options. It is not always explicit!

7. Check your results

In the example, each inference is modus ponens. There isn’t any inference better than that one!

Some guidelines

1 Each inference made in a passage still has exactly one conclusion, drawn from one or more premises. The problem is that a given passage will typically contain several inferences.

2 Typically though the passage will have just one MAIN conclusion. This is the “headline” that you isolated already, in “close analysis”.

Guidelines, (cont.)

3 The MAIN conclusion should always go at the bottom of our diagrams. The main premises, from which it is drawn, are always exactly one layer above it.

4 Some of those main premises are more debatable than others, and a smart author will try to back them up. A “mini-argument” is an argument for one of the premises in the main argument.

Guidelines

5 Each mini-argument adds another inferential step or inferential layer to the structure. You should have exactly as many layers in your

diagram as there are inferences in the passage.

6 The main goal: capture all the explicit inferences. Worry about the inexplicit stuff later, if at all!

The explicit inferences

• A casting is acceptable if it portrays all of the explicit inferences which are made. – The biggest mistake is usually: adding extra

inferences.

– If you check it , you find that this extra stuff usually represents the author as making some crazy inference, or arguing in an utterly implausible way.

Guidelines on inferences

a. If you can get an inference into deductively valid form, you can stop worrying, since there is no way to make it better.

b.Failing deductive validity, you ought to find at least some repeated elements among premises and conclusion. There should be some logical connection between premises and conclusion.

c.Arguments generally move

– from assertions which the audience already believes or is willing to accept, to more dubious or controversial claims which the audience is less likely to already accept.

– Generally you should find the least controversial claims at the top, and the most controversial at the bottom.

Inferences, cont.

Inferences, concluded.

d.Similarly, arguments often move

– from specific instances, examples, or less general assertions to more general assertions which those examples or instances support.

– You should find the examples near the top, and the generalizations down below.