Logic is a very effective tool for persuading an audience about the accuracy of an argument. However, people are not always persuaded by logic. Sometimes audiences are not persuaded because they have used values or emotions instead of logic to reach conclusions. But just as often, audiences have reached a different logical conclusion by using different premises. Therefore, arguments must often spend as much time convincing audiences of the legitimacy of the premises as the legitimacy of the conclusions.

For instance, assume a writer was using the following logic to convince an audience to adopt a smaller government:

Premise 1: The government that governs least, governs best.
Premise 2: The government I am proposing does very little governing.
Conclusion: Therefore, the government I am proposing is best.

Some members of the audience may be persuaded by this logic. However, other members of the audience may follow this logic instead:

Premise 1: The government that governs best, governs most.
Premise 2: The government proposed by the speaker does very little governing.
Conclusion: Therefore, the government proposed by the speaker is bad.

Because they adhere to a different logical sequence, these members of the audience will not be persuaded to change their minds logically until they are persuaded to different values through other means besides logic. See the OWL resource here for more examples of how to integrate argument and rhetorical strategies into your writing.