1. Idea of Fallacies
A fallacy is a mistake in reasoning that makes an argument invalid or unreliable. A fallacy may look convincing at first, but the logical connection between the premises and the conclusion is broken.
Recognising fallacies helps avoid incorrect conclusions and strengthens logical thinking.
1.1. Why fallacies occur
Fallacies often arise from misusing logical rules, misunderstanding implications, or drawing conclusions too quickly. Identifying them helps prevent faulty reasoning.
2. Affirming the Consequent
This fallacy occurs when a true implication is incorrectly reversed. The mistake is assuming that if the result happens, the original condition must have happened.
2.1. Form of the fallacy
\(P \Rightarrow Q\)
\(Q\)
Therefore, \(P\) (incorrect)
2.2. Example
Premises:
1. If it rains, the ground becomes wet.
2. The ground is wet.
Conclusion: It rained.
This is incorrect because the ground could be wet for other reasons.
3. Denying the Antecedent
This fallacy occurs when the condition of an implication is denied, and the conclusion is incorrectly denied as well.
3.1. Form of the fallacy
\(P \Rightarrow Q\)
\(\neg P\)
Therefore, \(\neg Q\) (incorrect)
3.2. Example
Premises:
1. If a number is divisible by 4, then it is even.
2. The number is not divisible by 4.
Conclusion: The number is not even.
This is incorrect because many even numbers are not multiples of 4.
4. Circular Reasoning
Circular reasoning occurs when the conclusion is simply a restatement of the premise. The argument goes in a loop instead of providing real support.
4.1. Idea of the fallacy
The argument says nothing new; the conclusion is assumed in the premises.
4.2. Example
Premise: "This method works because it is effective."
Conclusion: "It is effective because it works."
The reasoning forms a loop without explanation.
5. False Cause
This fallacy assumes a cause-and-effect relationship where none is proven. It links two events without confirming that one actually caused the other.
5.1. Idea of the mistake
Just because two events happen together does not mean one causes the other.
5.2. Example
"Whenever I use my lucky pen, I score well, so the pen brings good marks."
The connection is assumed, not logically supported.
6. Irrelevant Conclusion
This fallacy gives a conclusion that does not logically connect with the premises. The reasoning misses the actual point.
6.1. Idea of the mistake
The argument may sound related, but it does not address the true issue raised by the premises.
6.2. Example
Premise: "Regular practice improves skills."
Conclusion: "Therefore, everyone should buy the latest version of the book."
The conclusion does not logically follow from the premise.
7. Notes and Observations
Important points about fallacies:
- Fallacies make arguments unreliable even when the statements sound reasonable.
- They often come from misusing implication or ignoring logical structure.
- Identifying fallacies strengthens logical thinking and avoids incorrect conclusions.
- Careful reasoning and clear understanding of implications prevent most fallacies.