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In logic and mathematics, proof by example (sometimes known as inappropriate generalization) is a logical fallacy whereby the validity of a statement is illustrated through one or more examples or cases—rather than a full-fledged proof. [1] [2] The structure, argument form and formal form of a proof by example generally proceeds as follows ...
Fallacy of many questions (complex question, fallacy of presuppositions, loaded question, plurium interrogationum) – someone asks a question that presupposes something that has not been proven or accepted by all the people involved. This fallacy is often used rhetorically so that the question limits direct replies to those that serve the ...
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 ...
An example of a language dependent fallacy is given as a debate as to who in humanity are learners: the wise or the ignorant. [18]: 3 A language-independent fallacy is, for example: "Coriscus is different from Socrates." "Socrates is a man." "Therefore, Coriscus is different from a man." [18]: 4
An argument that actually contains premises that are all the same as the assertion is thus proof by assertion. This fallacy is sometimes used as a form of rhetoric by politicians, or during a debate as a filibuster. In its extreme form, it can also be a form of brainwashing. [1] Modern politics contains many examples of proofs by assertion.
An argument from authority [a] is a form of argument in which the opinion of an authority figure (or figures) is used as evidence to support an argument. [1]The argument from authority is a logical fallacy, [2] and obtaining knowledge in this way is fallible.
The above example commits the correlation-implies-causation fallacy, as it prematurely concludes that sleeping with one's shoes on causes headache. A more plausible explanation is that both are caused by a third factor, in this case going to bed drunk, which thereby gives rise to a correlation. So the conclusion is false. Example 2
These examples, one from mathematics and one from natural language, illustrate the concept of vacuous truths: "For any integer x, if x > 5 then x > 3." [11] – This statement is true non-vacuously (since some integers are indeed greater than 5), but some of its implications are only vacuously true: for example, when x is the integer 2, the statement implies the vacuous truth that "if 2 > 5 ...