Search results
Results From The WOW.Com Content Network
A counterargument might seek to cast doubt on facts of one or more of the first argument's premises, to show that the first argument's contention does not follow from its premises in a valid manner, or the counterargument might pay little attention to the premises and common structure of the first argument and simply attempt to demonstrate that ...
Persuasive definition – purporting to use the "true" or "commonly accepted" meaning of a term while, in reality, using an uncommon or altered definition. (cf. the if-by-whiskey fallacy) Ecological fallacy – inferring about the nature of an entity based solely upon aggregate statistics collected for the group to which that entity belongs. [27]
It is an informal antonym for pathological. For example, one might conjecture that a differential operator ought to satisfy a certain boundedness condition "for nice test functions," or one might state that some interesting topological invariant should be computable "for nice spaces X ."
Since assuming P to be false leads to a contradiction, it is concluded that P is in fact true. An important special case is the existence proof by contradiction: in order to demonstrate that an object with a given property exists, we derive a contradiction from the assumption that all objects satisfy the negation of the property.
Reductio ad absurdum, painting by John Pettie exhibited at the Royal Academy in 1884. In logic, reductio ad absurdum (Latin for "reduction to absurdity"), also known as argumentum ad absurdum (Latin for "argument to absurdity") or apagogical argument, is the form of argument that attempts to establish a claim by showing that the opposite scenario would lead to absurdity or contradiction.
However, in 1974 Perko discovered a counterexample called the Perko pair, a pair of knots listed as distinct in tables for many years that are in fact the same. Hilbert's twenty-first problem . In 1908 Plemelj claimed to have shown the existence of Fuchsian differential equations with any given monodromy group, but in 1989 Bolibruch discovered ...
Procatalepsis, also called prolepsis or prebuttal, is a figure of speech in which the speaker raises an objection to their own argument and then immediately answers it. By doing so, the speaker hopes to strengthen the argument by dealing with possible counterarguments before the audience can raise them.
In mathematics, a minimal counterexample is the smallest example which falsifies a claim, and a proof by minimal counterexample is a method of proof which combines the use of a minimal counterexample with the ideas of proof by induction and proof by contradiction.