7. Inductive reasoning I

Inductive errors of thought are intended to support the probability that their conclusions are true, but are in reality too weak to be able to do so. Chapter 11 will provide further information about inductive reasoning. However, this information is not necessary to be able to understand this chapter. This chapter is devoted to inductive thinking errors.

What are the fallacies when it comes to inductive generalizations?

Two thinking errors often occur with inductive generalizations are: (1) generalizing too quickly ("hasty generalizing") and (2) incorrect generalizing ("biased generalizing"). Below is an overview of the thinking errors that are made in inductive generalizations:

• Fallacy of hasty generalization: this fallacy occurs when the chance of an argument being correct is extremely overestimated because it was based on a sample that is too small. This is also called the "fallacy of Small Sample". We humans are quick to make this mistake by using a one-time personal experience for a general conclusion. Such a "small sample" can be a personal experience, or a group of friends or a neighbor, etc.
  • Fallacy of the Lonely Fact: when a conclusion is made based on a single fact. This is an alternative to the aforementioned thinking error.
  • Argument by Anecdote: this is a form of generalizing too quickly. Often an argument in this case is based on one person or event. The chance that an argument is correct is then overestimated.
• Generalizing from exceptional cases means that a statement is made based on a rare or biased sample. The latter is also called the "fallacy of biased sample". Another form of generalizing from exceptional cases is "self-selection fallacy". This is overestimating the correctness of a conclusion, which is derived from a relatively large but self-selected sample. An example is an online poll - people often forget that only a very specific group will find the poll at all.

The fallacy of "accident" is the reverse of the generalization of special cases. It happens when a speaker or writer assumes that a general statement automatically also applies to a specific case that is exceptional.

The weak analogy

The fallacy of "weak analogy" (also called false analogy) is a weak argument based on unimportant similarities between two or more things. Often these similarities are completely taken out of context in order to make the analogy. Example; "If you kill someone with a knife, it's murder, so if a surgeon kills someone on the operating table, it's murder too."

Mistaken appeal

A common mistake is the "mistaken appeal to authority". With this fallacy, a writer or speaker tries to support the content of a statement by providing the opinion of someone who has absolutely no authority in that area. Example; "My father says the president is lying about the test, so it must be that he is indeed not telling the truth."

Mistaken appeal to popularity (sometimes called "fallacious appeal to common belief"): This mistake occurs when a writer or speaker makes a statement and emphasizes that "everyone knows" or that it is "general knowledge." Often this is not the case and claiming that everyone knows something does not immediately make your statement correct or true.

Mistaken appeal to common practice: this fallacy occurs when a writer or speaker uses an argument that occurs a bit more often, or that it is tradition. If this really were a correct argument, slavery and stoning people to death would also have been justified because people had been doing that for years. I think you can see why this is a mistake.

Bandwagon fallacy: a writer or speaker uses the phrase "everyone thinks" (and other sentences similar to this). More about this can be found in chapter 1.

What are examples of unjustified cause-effect relationships?

The following two thinking errors have in common that they make an unjustified cause-effect relationship between two variables.

Post Hoc, Ergo Propter Hoc: this literally means "after this, therefore because of this". That still sounds very complicated, but it simply comes down to the fact that a writer or speaker wrongly assumes that when one event occurs after another event, then this event is caused by the other. This fallacy is often shortened to "post hoc".

There are different variants for "post hoc":

• Overlooking the possibility of coincidence: a writer overestimates the possibility that two sequential events happened by chance at the same time
• Overlooking a possible common cause: here a writer overestimates the possibility of a common cause, such as "I fell last night and this morning I had a headache," but I hereby forget to say that I had consumed way too much alcohol yesterday, which could very well be the cause of those two things.
• Overlooking the possibility of random variation: this ignores that variables fluctuate randomly. When it is wrongly decided that this random fluctuation is due to a certain explanation, this thinking error is involved. For instance; not every time you throw a stone it will be the same length away. You just don't have to immediately assign the fact that this time you drank red bull before you threw to be the cause of the fact that you threw further than ever, without taking into account that there may be some random fluctuation.
• Overlooking the possibility of regression: the chance of "regression to the average" is overestimated. Do you also occasionally have a day that doesn't go well? And if you then take a vitamin pill in the evening and it goes better the next day, then you commit the fallacy of overlooking the possibility of regression if you then put this on the vitamin pill.

Cum Hoc, Ergo Propter Hoc: this literally means "with this, therefore because of this." A speaker or writer makes this mistake when he or she assumes that the fact that two events occur at the same time is because one of these events causes the other event.

Here too there are different variants:

• Overlooking the possibility of coincidence, as mentioned earlier, where you overlook the chance of chance.
• Overlooking a possible common cause: where you overlook the existence of a common cause.
• Overlooking the possibility of reserved causation: a reverse cause-effect relationship may be drawn here. Example; successful people often drive expensive cars. Driving an expensive car makes you successful.
• Argument by anecdote: there is also a cause-related "argument by anecdote". A story is attempted to provide support for a cause and effect claim.

Slippery slope

The slippery slope error is an argument based on an unsupported warning that is controversial. It is suggested here that there will be an extremely undesirable outcome if one takes a certain, single step. Example; "No, we should not lower the alcohol limit, because once it is back to 16 next morning, it’ll be down to 11 next year and in five years, babies are already drinking beer!"

What is meanty by the non-testable explanation?

If someone gives an explanation that cannot be tested, then there is a non-testable explanation of an argument error (untestable explanation). Since this useless, vague, non-testable assertion ultimately does not provide evidence for anything, they cannot be used as arguments either.

Practice questions

1. What is the similarity and difference between generalizations and analogies?
2. What are inductive errors?
3. Which two errors of thought often occur in inductive generalizations?
4. What does the "weak analogy" fallacy mean?
5. Name two known thinking errors in which an wrong cause-effect relationship is assumed.

Answers practice questions

1. With both forms we can draw a conclusion about a certain group. However, in an analogy this is done by comparing the group with another group. For example: if group A and group B look alike at this stage, then group A and group B will look alike in the next stageWith generalization you draw a conclusion about a group by looking at a sample. If a sample from that group shows these traits to a large extent, the group will most likely also show these traits.
2. Inductive errors of thought are intended to support the likelihood of their conclusions, but are in reality too weak to be able to do so.
3. Two errors of thought that often occur with inductive generalizations are: (1) generalizing too quickly ("hasty generalizing") and (2) incorrect generalizing ("biased generalizing")
4. The fallacy of "weak analogy" (also called false analogy) is a weak argument based on unimportant similarities between two or more things.
5. Two known thinking errors are "post hoc, ergo propter hoc" and "cum hoc, ergo propter hoc".