Last week I identified and demonstrated seven fallacies of irrelevant conclusion, by which a person tries to win an argument using language that has nothing to do with the point being argued. Those fallacies actually fall under the larger heading "material fallacies." A material fallacy makes an error of argument, in contrast to a formal fallacy which makes an error of logic.
Before I get into specific kinds of material fallacies, let me describe the basic principle of syllogism. A syllogism has a major premise, a minor premise, and a conclusion. Each of the premises has a common term; we call this "distribution" in that the common term is "distributed" between both premises. Without distribution, the syllogism is invalid.
Note that "invalid" means the logic is wrong; "untrue" means the conclusion is wrong.
Here's an example of a valid and true syllogism:
Major premise (MP): Men are mortal.
Minor premise (mp): David is a man.
Conclusion (C): Therefore, David is mortal.
The word "man" is distributed between the premises, making the conclusion valid. Since the major premise is true for all men, and the minor premise is true, then the conclusion is true.
So let's look at two kinds of fallacies where the logic is sound but the conclusions might be false.
Agrumentum per accidens (secundum quid)
An "argument by accident" suggests that because something applies in general, it applies in this specific case. Here, for example, is an argument you may have heard from a political leader in the past:
MP: People from Mexico have committed crimes. Generally true–but not in all cases.
mp: These people are from Mexico. Specifically true.
C: Therefore, these people have committed crimes. False.
This is a material fallacy, because it turns out while this syllogism is perfectly valid, it's just not true. That is, it's false (not to mention racist and offensive) because while there are some people from Mexico who have committed crimes, not all of them have; therefore, it overgeneralizes to say that any random group of Mexicans has committed crimes.
MP: Prosecutors charge people with obstruction of justice when they find evidence of it. Generally true.
mp: The president has not been charged with obstruction of justice. True.
C: Therefore, there is no evidence that the president obstructed justice. False.
Again, arguing from a generality to a specific case is logically valid, but in this specific case, the president has not been charged with a crime despite the evidence, not because no one found any.
Converse accident (hasty generalization)
This fallacy comes from thinking a specific case represents the general case. This time the conclusion may be true, but probably isn't, and it may also be invalid:
MP: Health care is a complicated subject. True.
mp: I didn't know that health care was a complicated subject. True.
C: Therefore, "nobody knew health care was complicated." False.
In this case, the speaker takes a specific case of ignorance (his own) and incorrectly infers that everyone else has the same lack of basic policy competence.
Another example: "Another historic trade blunder was the catastrophe known as NAFTA. I have met the men and women of Michigan, Ohio, Pennsylvania, Indiana, New Hampshire, and many other States whose dreams were shattered by NAFTA."
While NAFTA may have caused unfortunate consequences for the men and women with whom the president spoke, to say that it was generally bad for the country as a whole overgeneralizes from those few examples.
Next time: we'll go around in circles, because that's how I roll.