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Tutorial 4 - Multi-layer Arguments

Theory pages

Reasons for Reasons

One reason can provide evidence in support of another.  This is the simplest case of a multi-layer argument.

 
Discussion

Consider this reasoning from Apollo Moon Landings:

The shadows of the astronauts and their equipment in the Apollo pictures seem to point in different directions.  This suggests that artificial lighting was used and therefore the pictures were taken in a studio on earth. [Based on 5.1]

This passage contains two simple arguments:

Here are the two simple arguments mapped separately.  Notice that the first argument provides support for the second.  The contention of the first argument is in fact a premise in the second.

Here are the two arguments mapped as a single multi-layer argument.

 
New Concepts

A multi-layer argument is an argument in which there are reasons or objections bearing upon reasons or objections.

Main Conclusions

In a multi-layer argument, the topmost contention is called the main contention.  The first reason bearing upon it is known as a primary reason; the next as a secondary reason; and so forth.

 
Discussion

As we will see in Tutorial 5, the secondary reason forms a simple argument with one of the premises of the primary reason as its contention.  Thus there are many contentions; only one is the main contention

 

The main contention is the only contention which is free-standing, i.e., not also a premise in some other reason or objection.

 
New Concepts

The main contention of a multi-layer argument is the one at the top level.  It is the only contention which is not also a premise in another simple argument

Reasons for Objections

In another kind of multi-layer argument, a reason supports an objection.

Note that the reason here helps the objection, not the main contention

It provides evidence that the objection is a good one.

 
Discussion

For example, consider this reasoning from Apollo Moon Landings:

NASA claims that the Apollo astronauts landed on the moon.  However, the Apollo pictures were taken in a studio on earth. We know this because artificial lighting was used when taking them. [Based on 5.0-1]

This passage contains an objection, which is backed up by some evidence.

Here are the two simple arguments mapped separately: 

Notice that the contention of one argument is a premise in the objection.

Here are the two arguments mapped as a single multi-layer argument:

Rejoinders

Similarly, there are objections to reasons. We refer to these as rejoinders.

 
Discussion

Example:

Moon hoax believers claim that artificial lighting was used when the Apollo pictures were taken, on the grounds that the astronauts seem well-lit at times when they should be in shadow.  However reflected light from the lunar surface would easily provide enough light to illuminate an astronaut in a white spacesuit. [Based on 5.1,3]


The rejoinder provides evidence that the reason is not good evidence for the main contention - in this case because the premise should be rejected.

There are two kinds of rejoinders.  The first kind show that one of the claims in the reason is not true.  The second kind show that the claims, even if true, don't provide good evidence for their contention.

In other words, rejoinders work by providing evidence against one of the premises, or by providing evidence against the connection between the premises and their contention.  We will explore this issue much more in Tutorial 5.

 
New Concepts

A rejoinder is an objection to a reason.  A rejoinder provides evidence that a reason is not a good reason, i.e., not good evidence for its contention.

Rebuttals

A rebuttal is an objection to an objection.  It says "the first objection is not a good objection."

 
Discussion

When you see one objection below another, don't make the mistake of thinking that the lower one backs up or supports the higher one.  A rebuttal (if good) "cancels out" rather than supports the first objection.

The map above does not depict two objections to the top-level contention.  Rather, it depicts one objection to that contention, and an objection to that objection. 

Example:

Hoax believers object to the claim that Apollo astronauts landed on the Moon on the grounds that NASA can't produce pictures from the Hubble Space Telescope of the equipment the astronauts left behind.  However, NASA has provided many Hubble photographs showing objects in the landing zone. [a made-up variant on 9.4]

 
New Concepts

A rebuttal is an objection to an objection.  A rebuttal provides evidence that an objection is not a good objection, i.e., not good evidence against its contention.

Chains of Reasoning

Arguments can have more than two layers; indeed they can have many layers. Such arguments are chains of reasoning.

Here are two multi-layer arguments we saw on previous pages in this tutorial.  Notice that the main contention of the second argument is a premise in the bottom-level reason of the first. 

The two arguments combined into a single 4-level argument. An argument structure like this is a good example of a chain of reasoning.

 
Discussion

Strictly speaking, even a two-layer argument is a chain of reasoning, but the term makes more sense when applied to arguments with lots of layers.

How many layers can arguments have?  In principle, there is no limit.  In fact it is possible to design arguments which have an infinite (no finite limit) number of layers.  Mathematicians and philosophers tend to find this sort of thing particularly amusing. 

In ordinary life, the number of layers you can expect to see has a lot to do with factors such as:

It is not uncommon to find arguments with six, eight or even ten layers, but arguments with fifteen or twenty layers are very rare. 

 
New Concepts

A chain of reasoning is a multi-layer argument.  Usually the term is applied to arguments with more than two layers.

Argument Webs

Multi-layer arguments and multi-reason arguments can be combined to form complex argument webs.

 
Discussion

Consider this example:

 

Here, the two arguments are properly joined:

 

 
New Concepts

An argument web is an argument which is both multi-reason and multi-layer.

Support vs Co-premise I

The main challenge in mapping multi-layer arguments is putting claims in the appropriate place in the chain (or web). This is particularly difficult when co-premises are brought into the picture.

A common mistake is mapping a supporting reason as if it were a co-premise.

 
Discussion

Example: 

The shadows of the astronauts and their equipment in the Apollo pictures seem to point in different directions.  This suggests that artificial lighting was used and therefore the pictures were taken in a studio on earth. [Based on 5.1]

This passage contains two simple arguments.

The co-premise is really a supporting reason.  One sign that there is a problem is that the Holding Hands rule is violated.


A new co-premise has been added. Notice how the co-premises now conform to the Holding Hands rule.

Support vs Co-premise II

A similar mistake - the flip side of the previous one - is mapping a co-premise as if it were a supporting reason.

 
Discussion

The American flag is seen moving in video footage recorded when the astronauts planted it on the lunar surface. Given that there is no atmosphere on the Moon, some see this as 'proof' that the scenes were filmed on earth. [6.1]

The reasoning in this passage appears to contain two simple arguments.  In fact, however, the passage gives two co-premises of a single simple argument.

 

There is no atmosphere on the Moon is not really evidence for The American flag is seen moving...


In fact it is a co-premise in the first argument.  Note that other co-premises have not yet been articulated.

Missing Layers

Sometimes arguments are presented with a whole layer missing between the evidence and the contention.

 

There is a sizeable gap between the objection and the contention. One sign of a big gap is that the Rabbit rule is not satisfied at all, i.e., there is no overlap in significant terms or concepts between the contention and the objection. 

The argument is really a multi-layer argument, but a layer does not currently appear on the map.

One way to fix this "missing layer" problem. Notice that the objection has become supporting evidence for a higher-level objection.

 

Another way to fix the problem. In this case the objection is treated as providing evidence against a reason to believe that the astronauts did land on the Moon.

Summary - Tutorial 4

 
Key Points

Here are the four main kinds of multi-layer arguments, joined in a single argument web:

 

Here are two classic errors in constructing argument maps:

 

 
New Concepts

A multi-layer argument is an argument in which there are reasons or objections bearing upon reasons or objections.

The main contention of a multi-layer argument is the one at the top level.  It is the only contention which is not also a premise in another simple argument

A rejoinder is an objection to a reason.  A rejoinder provides evidence that a reason is not a good reason, i.e., not good evidence for its contention.

A rebuttal is an objection to an objection.  A rebuttal provides evidence that an objection is not a good objection, i.e., not good evidence against its contention.

A chain of reasoning is a multi-layer argument.  Usually the term is applied to arguments with more than two layers.

An argument web is an argument which is both multi-reason and multi-layer.

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