Diagramming Arguments
Several Premises

2. Several Premises in Support of a Conclusion

Some arguments are more complex: They have more than one premise in support of a conclusion.

In some cases, the premises are dependent on one another - two or more premises work together to make a single argument for a conclusion.

In other cases, the premises are independent - they do not work together; each one offers a separate line of support for the conclusion.

These two patterns are diagrammed in different ways, so we have to decide which pattern is present in a given argument.

Arguments with Independent Premises

In an argument with independent premises, each premise offers a separate line of support for the conclusion.

The following passages are from Alexis de Tocqueville's classic work, Democracy in America:

[1] In America the principle of the sovereignty of the people is neither barren nor concealed, as it is with some other nations; it is recognized by the customs and proclaimed by the laws; it spreads freely, and arrives without impediment at its most remote consequences.
[2] In America the people appoint the legislative and the executive power and furnish the jurors who punish all infractions of the laws. The institutions are democratic, not only in their principle, but in all their consequences. . . . The people are therefore the real directing power.

This argument could be stated as follows: (1) The people choose the legislature and the president, and (2) the people serve as jurors to decide whether someone may be punished for a crime; therefore, (3) the people control the actions of the government.

Premises 1 and 2 independently support the conclusion (3) Thus the fact that we elect our government officials, taken by itself, does provide some evidence that the people control the government, regardless of whether we also use juries in criminal law.

The existence of the jury system, taken by itself, does provide some evidence for popular control (though admittedly not much), regardless of whether we elect our representatives.

In diagramming this argument, we don't use the plus sign. We use two arrows to join each premise to the conclusion separately.

Arguments With Dependent Premises

In an argument with dependent premises, two or more premises work together to make a single argument for a conclusion.


"`The truth is,' Mr. Reagan said, `politics and morality are inseparable, and as morality's foundation is religion, religion and politics are necessarily related. We need religion as a guide.'" (New York Times, August 24, 1984)

In essence, President Reagan said: (1) politics depends on morality, and (2) morality depends on religion; therefore, (3) politics depends on religion. Premises 1 and 2 must be combined in order to have an argument for the conclusion (3).

The premise that politics depends on morality, taken by itself, does not tell us anything about religion, so it doesn't give us any reason to think that politics depends on religion.

In the same way, the premise that morality depends on religion, taken by itself, does not tell us anything about politics, so again we would have no reason to think politics depends on religion.

It is only when we put the premises together that we have an argument.

We represent this fact by using a second symbol, the plus (+) sign, to join the premises.

How To Tell Whether Premises Are Dependent or Independent

To tell whether a set of premises is dependent or independent, we look at each premise separately and ask whether the kind of support it offers to the conclusion depends on the other premises. A good way to pose the question is to suppose that the other premises are unknown or even false. If that would significantly affect the logical impact of the premise in question, then the relationship among the premises is one of mutual dependence and a plus sign should be used in the diagram.

On the other hand, if the premise in question would still give us a reason for accepting the conclusion, then it is independent of the other premises and should be diagrammed with a separate arrow. The goal is to put together those premises that form a single line of thought and separate them from premises that represent distinct lines of thought.

But this is not always easy. If the relationship between premises is unclear, it is a good idea to treat them as dependent.

Single Premise | Several Premises |
Several Conclusions | Multistep Arguments

Diagramming Arguments

© Copyright 1998, W.W. Norton & Co.