Identifying and Correcting Common Logical Errors in Reasoning
Formal Fallacies: Errors in Syllogistic Structure
Formal fallacies are errors in the structure or form of a deductive argument, making the conclusion invalid regardless of the truth of the premises.
Fallacy of the Undistributed Middle
This fallacy occurs when the middle term of a syllogism is not distributed in either premise, failing to connect the major and minor terms.
Example:
- All dogs are mammals.
- All men are mammals.
- Conclusion: All men are dogs.
Affirmative Conclusion from a Negative Premise
This fallacy is committed when an affirmative conclusion is drawn from a syllogism where at least one of the premises is negative. According to the rules of syllogisms, if one premise is negative, the conclusion must also be negative.
Example:
- No criminal is an honest man.
- Some honest men are rich.
- Conclusion: Some rich people are criminals.
Informal Fallacies: Deception and Ambiguity
Informal fallacies are used with the intention of showing an apparent truth to deceive or manipulate. They rely on rhetorical tricks, often involving ambiguity, rather than structural errors. For example, in a courtroom setting, a lawyer might use ambiguity—giving double meaning to words—to mislead a witness or jury and achieve a favorable outcome.
Fallacies of Relevance and Ambiguity
These fallacies occur when the premises, though perhaps psychologically relevant, do not logically pertain to the conclusion, thus failing to establish its truth. We examine several types below:
A. The Complex Question Fallacy
This fallacy is committed when a question is posed as if it were simple, demanding a single “Yes” or “No” answer, but it actually presupposes the truth of a hidden, unproven assertion. This is a type of trick question.
Lawyers should be familiar with this fallacy as it can be used against a client. Legal Examples:
- “Tell us, where is the document hidden?” (Presupposes the person knows the location and hid the document.)
- “Tell us where the murder weapon is hidden?” (Presupposes the person knows the location of the weapon.)
B. Fallacy of False Cause (Post Hoc Ergo Propter Hoc)
This fallacy mistakenly assumes that because one event precedes another, the first event must be the cause of the second, confusing temporal priority with causation.
Example:
After the appearance of Halley’s Comet, there have been epidemics, political conflicts, economic problems, earthquakes, and floods. Therefore, these calamities are the effect of the comet’s appearance.
Note: While a cause precedes its effect, not everything that precedes an effect is necessarily its cause.
C. Fallacies of Ambiguity
These fallacies are found in arguments containing ambiguous words or phrases whose meaning shifts during the course of reasoning, rendering the argument false. These include:
1. Fallacy of Equivocation
This consists of using a single word in two different senses within the same argument.
Example:
- What is rare (uncommon) is expensive.
- A slightly expensive car is rare (uncommon).
- Conclusion: Therefore, a slightly expensive car is expensive.
2. Fallacy of Amphiboly
This is committed when an argument relies on premises whose overall grammatical construction or wording is ambiguous, allowing for two interpretations.
Example:
- Premise: This book is Amalia’s. (Ambiguous: Does it belong to her, or did she write it?)
- Conclusion: Therefore, Amalia is a writer.
3. Fallacy of Emphasis
This fallacy occurs when the meaning of an argument changes depending on which words are stressed or taken out of context, often through selective emphasis.
Example:
Consider the statement: “We should not criticize our leaders.”
If emphasis is placed on “our” (“We should not criticize our leaders”), the implication is that we are free to criticize leaders of other groups or nations.