Mastering Logical Reasoning and Identifying Common Fallacies

Fundamentals of Logic and Reasoning

What is Logic?

Logic is the philosophical discipline that studies the correctness or validity of our reasoning.

The Role of Language in Argumentation

By means of language, we perform various actions: begging someone to lend us money, asking for directions, describing our home, or even, if you have sufficient authority, issuing a command like throwing someone in jail.

Structure of Reasoning, Arguments, and Inferences

A valid argument or inference consists of two main components:

1. Premises: A set of statements expressing the input data or evidence.
2. Conclusion: The final statement expressing new information obtained directly from the premises.

Example of Deductive Reasoning

• Premise 1: The cheese thief is a cat or a mouse.
• Premise 2: The footprints show that it is not a mouse.
• Conclusion: The cheese thief is a cat.

Types of Reasoning

Deduction

Deduction consists of moving from general premises to a less general conclusion. When this type of inference is correct (valid), the conclusion necessarily follows from the premises: it is impossible that if the premises are true, the conclusion can be false.

Induction

Induction is a type of reasoning where a general conclusion is reached from less general information given in the premises. In induction, however, we can only assign a certain probability to the conclusion, even if the premises are true.

Common Logical Fallacies

A logical fallacy is an error in reasoning that renders an argument invalid or unsound.

Fallacies of Relevance

Ad Verecundiam Fallacy (Argument from Authority)

This fallacy occurs when an argument relies on the authority of a person or source that is not necessarily an expert in the relevant field, or when the authority is misused.

Example (Translated): "There are no sunspots, because Aristotle says that the stars are made of perfect and incorruptible matter."

Example (Translated): "They said it on television, so it must be true."

Ad Hominem Fallacy (Attacking the Person)

This fallacy attacks the character, motive, or other attribute of the person making the argument, rather than addressing the substance of the argument itself.

Example (Translated): "It is false that women are discriminated against in current society. It is well known that feminists are all exaggerators."

Ad Populum Fallacy (Appeal to Popularity)

Defending a conclusion without justification, solely appealing to the feelings, emotions, or prejudices of the audience.

Ad Ignorantiam Fallacy (Appeal to Ignorance)

Asserting that something is definitively true (or false) because we cannot prove the opposite.

Ad Baculum Fallacy (Appeal to Force or Threat)

This occurs when one threatens or coerces, instead of providing logical reasons.

Example (Translated): "This problem must be solved this way, because otherwise, you will fail the course."

Fallacies of Weak Induction and Ambiguity

Faulty Generalization (Hasty Generalization)

Drawing a conclusion about an entire group based on an insufficient sample size.

Example (Translated): "Hake is oviparous, the frog is oviparous, and the ostrich is oviparous. Surely all vertebrates are."

False Cause Fallacy (Post Hoc Ergo Propter Hoc)

Assuming that because one event follows another, the first event must have caused the second.

Example (Translated): "I failed the exam because a black cat crossed my path before entering the classroom."

Equivocation (Semantic Fallacy)

Using a word or phrase in two different senses within the same argument.

Example (Translated): "Many people like green. Furthermore, this year it is the fashionable color. Therefore, surely the Greens (political party) will win the elections this year."

Circular Reasoning (Begging the Question)

An argument that assumes the truth of the conclusion in the premises.

Example (Translated): "Girls are smarter than boys because they get better grades. Why do they get better grades? Well, because they are smarter than boys."