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The fallacy of division [1] is an informal fallacy that occurs when one reasons that something that is true for a whole must also be true of all or some of its parts. An example: The converse of this fallacy is called fallacy of composition, which arises when one fallaciously attributes a property of some part of a thing to the thing as a whole.
Mathematical fallacy. 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 ...
A false dilemma, also referred to as false dichotomy or false binary, is an informal fallacy based on a premise that erroneously limits what options are available. The source of the fallacy lies not in an invalid form of inference but in a false premise. This premise has the form of a disjunctive claim: it asserts that one among a number of ...
Division by zero. The reciprocal function y = 1 x. As x approaches zero from the right, y tends to positive infinity. As x approaches zero from the left, y tends to negative infinity. In mathematics, division by zero, division where the divisor (denominator) is zero, is a unique and problematic special case.
Begging the question. In classical rhetoric and logic, begging the question or assuming the conclusion ( Latin: petītiō principiī) is an informal fallacy that occurs when an argument's premises assume the truth of the conclusion. Historically, begging the question refers to a fault in a dialectical argument in which the speaker assumes some ...
In this example, a valid conclusion would be: ~P or Q. The name denying the antecedent derives from the premise "not P", which denies the "if" clause (antecedent) of the conditional premise. One way to demonstrate the invalidity of this argument form is with an example that has true premises but an obviously false conclusion. For example:
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