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In mathematics , certain kinds of mistaken proof are often exhibited, and sometimes collected, as illustrations of a concept called mathematical fallacy. There is a distinction between a simple mistake and a mathematical fallacy in a proof, in that a mistake in a proof leads to an invalid proof while in the best-known examples of mathematical fallacies there is some element of concealment or deception in the presentation of the proof. For example, the reason why validity fails may be attributed to a division by zero that is hidden by algebraic notation.

Mathematical paradoxes and fallacies have long intrigued mathematicians. A mathematical paradox is a mathematical conclusion so unexpected that it is difficult to accept even though every step in the reasoning is valid. A mathematical fallacy, on the other hand, is an instance of improper reasoning leading to an unexpected result that is patently false or absurd. The error in a fallacy generally violates some principle of logic or mathematics, often unwittingly. Such fallacies are quite puzzling to the tyro, who, unless he is aware of the principle involved, may well overlook the subtly concealed error.

At some step in proving the Liar Paradox in natural language, a sentence is derived that seems overdetermined with respect to its semantic value. I argue that proofs of the Eubulidean Liar either use a principle of truth with non-canonical names in a fallacious way or make a fallacious use of substitution of identicals. Tarski never committed the first fallacy and may have himself considered it fallacious. Nevertheless, I clarify that it is fallacious. I then argue substitution of identicals needs to be restricted within the scope of the truth predicate.

Statistical fallacies are common tricks data can play on you, which lead to mistakes in data interpretation and analysis. Explore some common fallacies, with real-life examples, and find out how you can avoid them. The worst and most harmful example of being dishonest with data.

This is a list of paradoxes , grouped thematically.

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