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As an idiom, leap of faith can refer to the act of believing something that is unprovable. [1] The term can also refer to a risky thing a person does in hopes of a positive outcome. [ 2 ] Moreover, leap of faith may also refer to a mechanic in videogames in which the player is forced to jump to a platform or location that cannot be seen from ...
Some adherents of young-Earth creationism make an argument (called the Omphalos hypothesis after the Greek word for navel) that the world was created with the appearance of age; e.g., the sudden appearance of a mature chicken capable of laying eggs. This ad hoc hypothesis introduced into young-Earth creationism is unfalsifiable because it says ...
Definitional retreat – changing the meaning of a word when an objection is raised. [23] Often paired with moving the goalposts (see below), as when an argument is challenged using a common definition of a term in the argument, and the arguer presents a different definition of the term and thereby demands different evidence to debunk the argument.
The unprovable statement G F referred to by the theorem is often referred to as "the Gödel sentence" for the system F. The proof constructs a particular Gödel sentence for the system F , but there are infinitely many statements in the language of the system that share the same properties, such as the conjunction of the Gödel sentence and any ...
John Locke. Argument from ignorance (from Latin: argumentum ad ignorantiam), also known as appeal to ignorance (in which ignorance represents "a lack of contrary evidence"), is a fallacy in informal logic.
Many, if not most, undecidable problems in mathematics can be posed as word problems: determining when two distinct strings of symbols (encoding some mathematical concept or object) represent the same object or not. For undecidability in axiomatic mathematics, see List of statements undecidable in ZFC.
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Goodstein's theorem was among the earliest examples of theorems found to be unprovable in Peano arithmetic but provable in stronger logical systems (such as second-order arithmetic). He also introduced a variant of the Ackermann function that is now known as the hyperoperation sequence , together with the naming convention now used for these ...