Definition:Fallacy
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Definition
A (logical) fallacy is a mistake caused by an application of an invalid argument.
Logical fallacies abound.
Most of the documented fallacies that can be found in the literature arise from linguistic imprecision or deliberately misleading statements, or both.
Frequently the commission of fallacies is as deliberate as the telling of lies.
Examples
Arbitrary Example
| \(\ds x\) | \(\ge\) | \(\ds y\) | by hypothesis | |||||||||||
| \(\ds y\) | \(\ge\) | \(\ds z\) | by hypothesis | |||||||||||
| \(\ds \leadsto \ \ \) | \(\ds x\) | \(>\) | \(\ds z\) |
is a fallacy.
Also see
- Results about logical fallacies can be found here.
Historical Note
Fallacies have been the subject of investigation, identification and classification since the time of Aristotle.
Sources
- 1964: Donald Kalish and Richard Montague: Logic: Techniques of Formal Reasoning ... (previous) ... (next): $\text{I}$: 'NOT' and 'IF': $\S 4$
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): fallacy