Over several years, many Kossacks have shown an interest in studying logical argument. The skills of clear thinking & sound reasoning remain the best counters to the otherwise persuasive power of prejudice & propaganda. (Skill in the art of active persuasion, rhetoric, helps against them as well — but it works best when well-informed by logic.)
While I myself am not a logic teacher — & learned most of what I know on a self-directed amateur basis from old books — I've collected enough notes on the basics that I may be able to get things started reasonably well.
My early attempt at a sample lesson past the Kos Wingding...
A proposition is a statement that may be either true or false.
Examples: "Daily Kos" is not a statement, but a name. "Thoughts fly far", though what it means is obscure without any context, is a proposition. On the other hand, "California is a state of the United States", while true today, would have been untrue when California was a western territory or independent republic & so it is a falsifiable proposition.
Whether a proposition is true or false depends on its inherent nature. (In the above case of California, one can determine its statehood depending on its politics at a particular point in its history.)
An argument is a group of propositions that may be either valid or invalid. An argument typically has premises & a conclusion.
Example: If this site is Daily Kos, then it was founded by Markos Moulitsas.
This site is Daily Kos.
Therefore, this site was founded by Markos Moulitsas.
An argument's validity depends on its structure. One of the best ways to prove an argument to be invalid is to show that a false statement can come from true premises.
Remember that validity is not the same thing as soundness, the situation in which all given propositions are true & the given argument that they form is valid. When studying logic, validity is more important — since the important thing in logic is learning valid argument forms — & finding out whether an argument is valid occasionally means learning how to handle propositions whether they are true or not.
...Now, a bit of a note for fellow literary types: Describing the argument which a sentence makes — or whether it makes an argument — is not always as easy as identifying sentence types! Thus, "rhetorical questions" & the many other creative ways we use language make this more of an art than a science.
(...Well, that's my fast-&-furious crash introduction. What do you think?)
Thu Apr 05, 2012 at 11:00 AM PT: Simplified definition of proposition; changed example "Thoughts fly far" to reflect that it is a statement. Thanks to ends with space for noticing these inaccuracies.