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
In other cases, the premises are independent - they do not work
together; each one offers a separate line of support for the
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:
 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
 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
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
It is only when we put the premises together that we have an
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.