Originally Posted by The Unfan

The double negative rule doesn't cancel prefixes as a prefix doesn't change the definitive phrasing of a word, it makes a new word in its place. "Disagree" isn't the "negative" of agree.

To parse his sentence another way what he said would mean "I am not convinced that you're wrong." which is in no way a double negative and doesn't necessarily mean he agrees.

Originally Posted by carnegie mellon free online uni

Okay, so when ought we to accept the conclusion of an argument as being true? Well, there are two issues, one is logical in nature, whereas the other is not. First, the premises of the argument should be true. Now, the truth of a particular statement is something that logic, in general, cannot determine. Of course, there are some statements that are true (or false) just by virtue of their logical form (don't worry, we will come back to this point later), and such statements are the notable exception to this general guideline. Second, and this is where logic comes into play, in addition to being true, the premises of the argument should actually constitute evidence in favor of the truth of the conclusion. Another way of putting this is that the steps leading from premises to conclusion should be truth-preserving—logical steps taken from true premises should lead to a true conclusion.

"Why do we need both of these criteria?" you might be wondering. Think of a table. If you have a design for a table that includes a table top and some number of legs, then any engineer could tell you by looking at the design whether the legs would be able to hold up the table top. Of course, the table legs won't do a very good job of holding up the table top if you never even get around to building all of them. A good argument is just like a good table—it has the right design, and just like a good table actually has all of its legs, the premises of a good argument are all actually true.