Basics of Argument
Inductive Reasoning: makes a generalization based on a series of specific facts:
Joe got hives thinking about his summer-reading test.
Joan suffered a heart attack thinking about her summer-reading test.
Jeanne required psychiatric intervention for a panic attack over her summer-reading test.
The summer-reading test induces stress.
Deductive Reasoning: comes to a logical conclusion based on a generalization:
All animals need food.
A dog is an animal.
A dog needs food.
A syllogism: a 3-part deductive argument:
1.) generalization, or major premise
2.) specific example, or minor premise
3.) conclusion
Logical Fallacies:
http://www.csun.edu/~dgw61315/fallacies.html#Post%20hoc%20ergo%20propter%20hoc
Argumentum ad hominem (argument directed at the person). This
is the error of attacking the character or motives of a person who has stated
an idea, rather than the idea itself. The most obvious example of this fallacy
is when one debater maligns the character of another debater (e.g, "The
members of the opposition are a couple of fascists!"), but this is
actually not that common. A more typical manifestation of argumentum ad
hominem is attacking a source of information -- for example, responding to
a quotation from Richard Nixon on the subject of free trade with
Argumentum ad ignorantiam (argument to ignorance). This is the fallacy of assuming something is true simply because it hasn't been proven false. For example, someone might argue that global warming is certainly occurring because nobody has demonstrated conclusively that it is not. But failing to prove the global warming theory false is not the same as proving it true.
Argumentum ad misericordiam (argument or appeal to pity). The English translation pretty much says it all. Example: "Think of all the poor, starving Ethiopian children! How could we be so cruel as not to help them?" The problem with such an argument is that no amount of special pleading can make the impossible possible, the false true, the expensive costless, etc.
Argumentum ad nauseam (argument to the point of disgust; i.e., by repetition). This is the fallacy of trying to prove something by saying it again and again. But no matter how many times you repeat something, it will not become any more or less true than it was in the first place. Of course, it is not a fallacy to state the truth again and again; what is fallacious is to expect the repetition alone to substitute for real arguments.
Circulus in demonstrando (circular argument). Circular argumentation occurs when someone uses what they are trying to prove as part of the proof of that thing. Here is one of my favorite examples (in pared down form): "Marijuana is illegal in every state in the nation. And we all know that you shouldn't violate the law. Since smoking pot is illegal, you shouldn't smoke pot. And since you shouldn't smoke pot, it is the duty of the government to stop people from smoking it, which is why marijuana is illegal!"
Cum hoc ergo propter hoc (with this, therefore because of this). This is the familiar fallacy of mistaking correlation for causation -- i.e., thinking that because two things occur simultaneously, one must be a cause of the other. A popular example of this fallacy is the argument that "President Clinton has great economic policies; just look at how well the economy is doing while he's in office!" The problem here is that two things may happen at the same time merely by coincidence (e.g., the President may have a negligible effect on the economy, and the real driving force is technological growth), or the causative link between one thing and another may be lagged in time (e.g., the current economy's health is determined by the actions of previous presidents), or the two things may be unconnected to each other but related to a common cause (e.g., downsizing upset a lot of voters, causing them to elect a new president just before the economy began to benefit from the downsizing).
Non Sequitur ("It does not follow"). This is the simple fallacy of stating, as a conclusion, something that does not strictly follow from the premises. For example, "Racism is wrong. Therefore, we need affirmative action." Obviously, there is at least one missing step in this argument, because the wrongness of racism does not imply a need for affirmative action without some additional support (such as, "Racism is common," "Affirmative action would reduce racism," "There are no superior alternatives to affirmative action," etc.).
Post hoc ergo propter hoc (after this, therefore because of this). This is the fallacy of assuming that A caused B simply because A happened prior to B. A favorite example: "Most rapists read pornography when they were teenagers; obviously, pornography causes violence toward women." The conclusion is invalid, because there can be a correlation between two phenomena without one causing the other. Often, this is because both phenomena may be linked to the same cause. In the example given, it is possible that some psychological factor -- say, a frustrated sex drive -- might cause both a tendency toward sexual violence and a desire for pornographic material, in which case the pornography would not be the true cause of the violence.
Slippery slope. A slippery slope argument is not always a fallacy. A slippery slope fallacy is an argument that says adopting one policy or taking one action will lead to a series of other policies or actions also being taken, without showing a causal connection between the advocated policy and the consequent policies. A popular example of the slippery slope fallacy is, "If we legalize marijuana, the next thing you know we'll legalize heroin, LSD, and crack cocaine." This slippery slope is a form of non sequitur, because no reason has been provided for why legalization of one thing leads to legalization of another. Tobacco and alcohol are currently legal, and yet other drugs have somehow remained illegal.
Straw man. This is the fallacy of refuting a caricatured or extreme version of somebody's argument, rather than the actual argument they've made. Often this fallacy involves putting words into somebody's mouth by saying they've made arguments they haven't actually made, in which case the straw man argument is a veiled version of argumentum ad logicam. One example of a straw man argument would be to say, "Mr. Jones thinks that capitalism is good because everybody earns whatever wealth they have, but this is clearly false because many people just inherit their fortunes," when in fact Mr. Jones had not made the "earnings" argument and had instead argued, say, that capitalism gives most people an incentive to work and save. The fact that some arguments made for a policy are wrong does not imply that the policy itself is wrong.
Argumentum ad numerum (argument or appeal to numbers). This fallacy is the attempt to prove something by showing how many people think that it's true. But no matter how many people believe something, that doesn't necessarily make it true or right. Example: "At least 70% of all Americans support restrictions on access to abortions." Well, maybe 70% of Americans are wrong!
This fallacy is very similar to argumentum ad populum, the appeal to the people or to popularity. When a distinction is made between the two, ad populum is construed narrowly to designate an appeal to the opinions of people in the immediate vicinity, perhaps in hope of getting others (such as judges) to jump on the bandwagon, whereas ad numerum is used to designate appeals based purely on the number of people who hold a particular belief. The distinction is a fine one, and in general the terms can be used interchangeably in debate rounds. (I've found that ad populum has better rhetorical effect.)