But how are these statements related?
To find out, we draw a diagram. Using the numbers to rep- resent the premises and conclusion, we write down the number for the conclusion and place the num- bers for the premises above it. Then to show how the premises support the conclusion, we draw arrows from the premises to the conclusion. Each arrow indicates the logical connection between premise and conclusion, representing such expressions as “Premise 11 supports the Conclusion (14)” or “the Conclusion (14) is supported by Premise 11.” Here’s the completed diagram:
In the simplest relationship depicted here, Prem- ise 13 provides direct support to the conclusion. Premise 11 also supplies direct support to the Con- clusion (14), and this premise in turn is backed up by Premise 12. (See how an arrow goes from 11 to 14, and then from 12 to 11.) Premises 7 and 8 are linked to the conclusion in a different way, reflect- ing the fact that some premises are dependent and some are independent. An independent premise (such as Premise 13) supports a conclusion without relying on any other premises; a dependent prem- ise gives little or no support on its own and requires the assistance of at least one other premise. Prem- ises 7 and 8 are dependent premises and are joined by a plus sign to represent this fact. Together, Prem- ises 7 and 8 provide support to the conclusion; they give a reason for accepting it. But if either premise is deleted, the remaining premise can provide no substantial support.
As you work through the diagramming exer- cises at the end of this chapter, you will come to
12 7 � 8 13
11
14
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understand why diagramming arguments can be so useful. You will learn a great deal about the struc- ture of arguments—which is a prerequisite for being able to devise, deconstruct, and evaluate them.