8. What are the different types of thinking errors?

What are formal thinking errors?

The three formal errors of thinking that will be discussed are "confirmation of the consistent", "denial of the antecedent" and "the undivided middle."

Confirmation of the consequent

In this chapter examples are given for two premises and one conclusion. An incorrect example is given below:

1. If P, then Q.

2. Q.

3. Therefore P.

In this example, the first part of the premise after "if" is the antecedent of the claim (sentence 1). The part after "then" is the consequent (sentence 2). The example is the thinking error "confirmation of the consequent". A premise incorrectly confirms the consequent of the other. When P and Q are turned around in (2) and (3), the argument is valid.

Incorrect Example;

1. If a dog is pregnant, then it is a female. (If P, then Q)

2. The dog is a female. (Q)

3. So the dog is pregnant. (P)

Denial of the antecedent

A premise denies the antecedent of the other. An example of this is:

1. If P, then Q.

2. Non-P.

3. Therefore non-Q.

Example;

1. If something is a reptile then it is an animal.

2. A sheep is not a reptile.

3. So a sheep is not an animal.

The undivided middle

This fallacy occurs when the speaker or writer assumes that two things that are related to a third thing are, in result, also related to each other. An example is:

All cats are mammals.

All dogs are mammals.

That's why all cats are dogs.

An example of such a scheme is:

1. X has characteristics a, b, c, etc.

2. Y has characteristics a, b, c, etc.

3. Therefore: X is Y.

This is an incorrect reasoning.

What are equivocation and amphiboly thinking errors?

Ambiguous statements can produce a thinking error. This is the case, for example, with the equivocation thinking error. This is related to semantic ambiguity. With this fallacy, statements such as premises and / or conclusions are used that contain words or sentences that can be interpreted in more than one way, and thus a false interpretation of a premise is made.

The ambipholy error also uses semantic ambiguity. In this fallacy, statements such as premises and / or conclusions are used that contain ambiguity because of their grammatical structure.

What are composition and distribution thinking errors?

The fallacy of composition occurs when an attribute of parts of something is erroneously assigned to the whole. The opposite of this is the division of thought: assuming that something that is true for the whole is also true for parts of the whole.

Composition reasoning error vs hasty generalization reasoning error

• Composition: from part to whole. If the reasoning is that what is true of a part of something must also be true of the whole thing of which it is part ("a machine is defective because one of the parts is defective" - ​​a machine can still do well even if a part is defective).
• Hasty generalization: from specific to generic. If the reasoning is that what is true for a member of a group is also true for other members of the group ("one of the parts of the printer is defective, so all parts are defective").

Distribution reasoning error vs accident reasoning error

If something can be said of each member of the class / group, the reasoning error is called accident. If something can only be said of the class / group as a whole (and therefore it would not be useful to apply the statement to all individual members of the class), we speak of division:

• Distribution: from whole to part. The average Dutch person has 3.5 bicycles. Jan is an average Dutchman. So he has 3.5 bikes. This statement is about the group / class as a whole and does not apply to Jan as an individual, since it is difficult to cycle on half a bike.
• Accident: from generic rule to specific case. Freedom of expression is laid down in the law. So John should not be prosecuted for shouting "fire!" last night during the concert. The law applies to every individual, so it concerns the accident fallacy.

What other errors are there?

Confuse statements with apologies

With this fallacy it is thought that someone wants to justify a bad situation (for example the beginning of the Second World War) or to apologize for it, while the person in reality tries to explain something. A statement does not say what someone did or what happened was correct or justified (it is not an excuse), it simply explains why it happened.

Confuse contraries with contradictions

Contradictions are two statements that are the opposite of each other. This means that they will never have the same value. Two statements that cannot both be true, but both can be wrong, are not exact opposites of each other. They are called contraries.

When contradictions are confused with contraries, the person who makes this mistake is unable to notice that two conflicting assertions can be both contraries and contradictions.

Example; The fact that a stone does not "live" does not mean that it is immediately "dead". "Death" implies that it once lived, which is not the case with a stone.

Consistency and inconsistency

It is a necessity for rationality that there is consistency in one's beliefs. If a person abruptly changes his or her point of view or contradicts himself, then we will scratch our heads relatively quickly. However, we must take into account that when someone is inconsistent, this says nothing about being right on this particular .

Incorrect calculation of chances

People regularly overestimate or underestimate the chance of a certain event. If the probability of the occurrence of two events simultaneously has to be calculated, the probabilities of these events must be multiplied by each other (and not added together).

The gambler's mistake

A common mistake is the gambler's mistake. Someone is convinced that the earlier performance of independent events will have an effect on a subsequent independent event. An example is when someone incorrectly states that if he has thrown "head" three times at head-or-coin, the chance of throwing "coin" is greater (however, this chance remains 50% each time).

Overlooking prior probabilities

The prior probability one assumes that there is an already known chance of an event. If the a priori chance (prior probability) is overlooked, the chance of an event (where all other factors are kept constant) is incorrectly estimated. No account is taken of all the things that could change our opportunity outcome. For example: James and Alex are incredibly good at programming and drawing respectively. So it is assumed that they will score a good job within "their" field. You don't take into account that there are more jobs in programming than in art.

Incorrect induction conversion

With a false induction conversion (false positive) there is a false alarm in recognition. Missing false positives happens when a probability calculation is made of, for example, an event. Example: 50 people in the small village of Jonestead come to the doctor with stomach problems on 26 December 2016. A large part of them ate fries at Tony's snack bar he day before. Conclusion: It seems wise to stay away from Tony's snack bar.

The logic in this reasoning is not entirely correct. If all people who had stomach problems had eaten at the fries stall, it would have been a logical conclusion. But in this case it's only part. If the fries stall is the cause, then how do people who have not been to the stall get the symptoms?

In this case, let's call the people with stomach complaints A's, and the people at the fries call stall B's. With an incorrect induction conversion, information is often known about the A’s that are B’s, but the A’s that are not B’s or the B’s that are not A’s are overlooked.

Practice questions

1. Name three formal thinking errors.
2. What do the thinking errors "equivocation" and "ambipholy" have in common?
3. What is the difference between the thinking errors "composition" and "denial"?
4. What does the "gambler's mistake" mean?

Answers

1. Three formal errors of thought are "confirmation of the consistent", "denial of the antecedent" and "the undivided middle".
2. With these two errors of thinking, a mistake is made regarding the semantic ambiguity.
3. The fallacy of composition occurs when an attribute of parts of something is erroneously assigned to the whole. The opposite of this is the division of thought: assuming that something that is true for the whole is also true for parts of the whole.
4. Someone is convinced that the earlier performance of independent events will have an effect on a subsequent independent event.