FALLACIES OF WEAK INDUCTION
Fallacies of weak induction are weak inductive arguments in which the premises are evidentially relevant to the conclusion (unlike fallacies of relevance), but are not strong enough to justify belief in the conclusion without being supported by additional premises. Any argument that commits a fallacy of weak induction is (unsurprisingly) a weak inductive argument. These fallacies are often related to the phenomenon of confirmation bias, which occurs when a person overestimates the strength of evidence that supports existing beliefs and underestimates the strength of evidence that goes against them.
A hasty generalization fallacy occurs when a conclusion about a group is supported by premises concerning sub-groups that are unlikely to be representative. Stereotyping often involves this fallacy. The general form is:
Form: X% of sample S have characteristic C. S is a [unrepresentative] subpopulation of P. So, X% of P have characteristic S. Example 1: A poll of 1,000 likely college students shows that a majority support gay marriage. So, a referendum in favor of gay marriage is likely to succeed. Problem: Not all voters are college students. Example 2: Mark Maguire, Sammy Sosa, and Barry Bonds only hit over 50 home runs in a season because they cheated. It must be that anyone who hits over 50 home runs in a season is cheating. O Problem: This is a small sample. Also, these players all played baseball around the same time, and it could be that steroids were more common during this era than in other times.
Hasty generalizations often occur when too much weight is given to anecdotal evidence concerning a small number of cases (often, the arguer's own personal experience or the experience of his acquaintances). For example consider the (bad) argument: "My friend had his cheese sandwich stolen by two teens wearing Green Bay Packers jerseys. So, most Green Bay Packers fans must be criminals." It's very unlikely the person would draw this conclusion if it hadn't happened to a friend. And while this example might be a silly one, these sorts of generalizations have sometimes been used to justify racist or sexist stereotypes.
FALLACIES ABOUT CAUSATION
The fallacy of false cause occurs when the premises fail to support the existence of a causal connection that the conclusion depends on. There are several forms of this fallacy.
Simple Form: X causally contributed to Y. So, X is the cause of Y. Example: The southern states' desire to have their own flag was a causal contributor to their decision to secede from the U.s. So, these states' decision to secede had nothing do with slavery. Problem: The fact that there were multiple motives at work doesn't allow you to conclude that slavery was irrelevant (or that it wasn't the major reason).
Post hoc ergo propter hoc ("after this, therefore because of this): X preceded Y. So, X caused Y.
Aunt Edna took aspirin right before she died. So, her taking aspirin must have caused her death. In general, the fact that X happen