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Exercise 2.2 Model Answer

Consider this simple argument map, which is based on the reasoning in paragraph 6.5 of Apollo Moon Landings:

Exercise 2.2 is to produce a full, properly structured argument map showing all co-premises.

This argument map shows all hidden premises, and every significant term or concept appears in at least two claims.  

Lets walk through how we get from the problem to the answer.

When you look at the simple argument map, your first thought should be: there is a hidden premise or premises - what are they?  What claim(s) would connect the stated premise (the astronauts travelled at about 25,000km/h) to the contention?

Clues as to what they should be come from applying the Rabbit and Holding Hands tests.  These will tell us if there are terms and concepts which are currently "dangling," and will give us clues as to what the co-premises should be.

Applying the Rabbit Test, we can see right away that there are two danglers: Van Allen Belt and 1.5 hours. This means that the co-premises are going to have to include at least one claim involving the Van Allen Belt, and at least one claim involving 1.5 hours.  These might be the same claim, but for the moment lets suppose that they will be two distinct claims.  Putting this on the map, we get:

Look at the second co-premise.  It is something about the Van Allen Belt.  The contention says it takes 1.5 hours to travel through it.  What is it about the Van Allen Belt which is relevant to the time it takes to travel through it?  Its size or width, of course.  So it seems to make sense that the second co-premise should tell us how wide the Van Allen Belt is.  Now at the moment we don't know that directly.  However we can deduce it from the other claims we already know: that the astronauts travelled at 25,000 km/h and the took 1.5 hours.  A little elementary math reveals that the Van Allen Belt must be 37,500 km (25,000 x 1.5) wide.  So lets put that in the claim box:

So far so good.  We still have to figure out what the third co-premise is.  We know that it has to involve 1.5 hours.  But what else?  To answer this, just apply the Holding Hands Test.  Are there any significant terms or concepts which appear in a premise, but not in the contention or any other premise?

Yes there are! For example, 25,000 km/h in the first premise is currently dangling.  That is some raw material for the third co-premise.  But if you look carefully, you'll see something else.  It is in the second co-premise - the one we just added.  It is 37,500 km.  We introduced that term in order to get a sensible second premise.  However it creates another violation of the Holding Hands Rule.  So we're going to have to have that appear somewhere else as well. 

So, applying the Holding Hands test gives us these two items:

• 25,000 km/h
• 37,500 km.

But these are obviously related to each other and to 1.5 hours in the third co-premise, and should go in that co-premise:

In fact, the third co-premise just tells us mathematically how these relate to each other: