[Math Lair] Material Fallacies

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A material fallacy is a type of informal fallacy relating to problems with the facts (the matter) of the argument. Material fallacies can further be classified into two subcategories: Fallacies of evidence, which refer to arguments that do not provide the required evidence for the conclusions drawn, and fallacies of relevance, which refer to arguments that have supporting statements that are irrelevant to the conclusion and so cannot establish the conclusion's truth.

Here is a list of several types of material fallacies:

Begging the Question (Petitio Principii)
This fallacy is a type of circular reasoning that is fallacious. It occurs when the proof of a statement assumes that the statement is true to begin with. This can be done subtly. For example, "Allowing people to drive at unlimited speeds on residential streets poses a threat to the community, because it is dangerous to have cars travelling at high speeds in residential areas". If you carefully read the premise (stated second in the argument above) and the conclusion (stated first), you'll notice that they're saying the exact same thing, so nothing is accomplished.
Non Causa Pro Causa
This fallacy occurs when something is identified as the cause of an event, but no such relationship has been demonstrated.
Post Hoc Ergo Propter Hoc
The Latin means "after this, therefore because of this." This fallacy occurs when something is assumed to be the cause of an event merely because it happened before an event. This is a common fallacy, as it is very easy for human brains to see causal relationships where none exist. Being able to tell a story about an occurrence is important to humans, and a story involving a causal chain is easier to accept than two unrelated events. For example, "Thousands of women got sick after getting breast implants. Therefore the implants cause illness."
Cum Hoc Ergo Propter Hoc
Similar to post hoc ergo propter hoc, this fallacy is committed when one assumes that, because two events occur together, they must be causally related. If events A and B occur together, there are in fact four possibilities:
  1. A causes B.
  2. B causes A.
  3. Another event, say C, causes both A and B.
  4. There is no causal relationship between A and B; it is just a coincidence.
So, assuming that one event causes another just because they occur together is not necessarily valid. For example: "In drug addicts, the area of the brain involved in executive control is damaged. Therefore, drug use causes damage to that area of the brain."
Slippery Slope
This argument states that, if one event occurs, other harmful events will also, without giving any proof of a causal relationship. For example, "If we legalize marijuana, then we would have to legalize heroin and crack and we'll have a nation full of drug addicts on welfare. Therefore we cannot afford to legalize marijuana".
Bifurcation, also known as the black-and-white fallacy or false dilemma, occurs when one assumes that only two alternatives are available in a situation, when in truth there are others. For example: "You aren't for us. Therefore, you are against us."
Extended Analogy
This fallacy is to assume that two different situations are analogous to one another. Typically found when arguing about a general rule that involves the two situations.
Texas Sharpshooter Fallacy
This fallacy gets its name from the story of a Texas marksman who fires his gun several times at his barn, and then paints a bulls-eye around whichever spot has the most bullet holes. This fallacy occurs when one argues that a cluster in some data must have a certain cause solely because of that clustering. Taking such a position ignores that clusters in data can be caused by chance. For example, if you were to plot locations of, say, cancer patients on a map of a city, you would likely find clumps or clusters. Arguing that some characteristic of whatever area those clusters occurred in (e.g. polluted water, high-voltage power lines, nearby industries, etc.) causes cancer, without any other evidence, would be an instance of this fallacy. See also clustering illusion.

Sources used (see bibliography page for titles corresponding to numbers): 15, 44.