Although there are more than two dozen types and subtypes of logical fallacies, these are the most common forms that you may encounter in writing, argument, and daily life:
Begging the question, also known as circular reasoning, is a common fallacy that occurs when part of a claim—phrased in just slightly different words—is used in support of that same claim.
Example: Special education students should not be required to take standardized tests because such tests are meant for nonspecial education students.
Notice how the author‘s claim (x should not take the exams) merely presupposes what it is supposed to be proving: that x should not take the exams. This type of fallacy shows up in dissertation prospectus problem statements in which the problem and its cause are defined to be the same.
Hasty generalization is an error of induction that occurs when a writer jumps to an inference based on limited or inadequate data. Something to pay attention to when reviewing research design (for instance, when doing a literature review or an article critique) is whether the authors of the research paper have based their conclusions on unreliable data or too small a sample size.
Example: Two out of three patients who were given green tea before bedtime reported sleeping more soundly. Therefore, green tea may be used to treat insomnia.
In this example, a sample size of three is way too small to generalize about the effectiveness of green tea—not to mention that patients‘ self-reports don‘t always make the most reliable data!
Sweeping generalizations are related to the problem of hasty generalizations. In the former, though, the error consists in assuming that a particular conclusion drawn from a particular situation and context applies to all situations and contexts. For example, if I research a particular problem at a private performing arts high school in a rural community, I need to be careful not to assume that my findings will be generalizable to all high schools, including public high schools in an inner city setting.
Non sequitur is a Latin term that means "does not follow," and the fallacy occurs when no true logical (especially cause-effect) relationship exists between two notions.
Example: Professor Berger has published numerous articles in immunology. Therefore, she is an expert in complementary medicine.
Notice, in this example, that there is no necessary relationship between knowledge of immunology on the one hand and expertise in complementary medicine on the other. It does not follow that Dr. Berger will be an expert in both areas.
Post hoc ergo propter hoc, another Latin term, means "after this; therefore, because of this." This fallacy results from assuming that because something chronologically follows something else, then the two things must be related by a cause-effect connection. Just because x follows y in time, though, does not mean that y caused x. If we look back to the very first example about the NCLB Act, we can see the claim is founded on this false assumption:
Example: Drop-out rates increased the year after NCLB was passed. Therefore, NCLB is causing kids to drop out.
Although it may be true NCLB is contributing to drop outs, this cannot be concluded by the chronology of events alone. Correlation is not causation, so the cause-effect connection would have to be proven. For all we know, some third variable may have caused both the passage of the Act and the change in drop-out rate.
False dilemma, also known as black and white fallacy, results when a writer falsely constructs an either-or situation. Claims of policy are especially prone to false dilemma errors as the following example shows:
Example: Japanese carmakers must implement green production practices, or Japan‘s carbon footprint will hit crisis proportions by 2025.
The writer of this claim of policy assumes that there are only two options—green car production on the one hand or a catastrophic carbon footprint on the other. However, it is likely that car production is only one of many, many factors contributing to Japan‘s carbon emissions problem. It is unreasonable to focus so absolutely on this one factor.
In addition to claims of policy, false dilemma seems to be common in claims of value. For example, claims about abortion‘s morality (or immorality) presuppose an either-or about when "life" begins. Our earlier example about sustainability (―Unsustainable business practices are unethical.‖) similarly presupposes an either/or: business practices are either ethical or they are not, it claims, whereas a moral continuum is likelier to exist.