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In logic a counterexample disproves the generalization, and does so rigorously in the fields of mathematics and philosophy. [1] For example, the fact that "student John Smith is not lazy" is a counterexample to the generalization "students are lazy", and both a counterexample to, and disproof of, the universal quantification "all students are ...
The Gettier problem, in the field of epistemology, is a landmark philosophical problem concerning the understanding of descriptive knowledge.Attributed to American philosopher Edmund Gettier, Gettier-type counterexamples (called "Gettier-cases") challenge the long-held justified true belief (JTB) account of knowledge.
Frankfurt's examples are significant because they suggest an alternative way to defend the compatibility of moral responsibility and determinism, in particular by rejecting the first premise of the argument. According to this view, responsibility is compatible with determinism because responsibility does not require the freedom to do otherwise.
Models And Counter-Examples (Mace) is a model finder. [1] Most automated theorem provers try to perform a proof by refutation on the clause normal form of the proof problem, by showing that the combination of axioms and negated conjecture can never be simultaneously true, i.e. does not have a model.
offering a modified assertion that definitionally excludes a targeted unwanted counterexample; using rhetoric to signal the modification; An appeal to purity is commonly associated with protecting a preferred group. Scottish national pride may be at stake if someone regularly considered to be Scottish commits a heinous crime.
For example, a particular statement may be shown to imply the law of the excluded middle. An example of a Brouwerian counterexample of this type is Diaconescu's theorem, which shows that the full axiom of choice is non-constructive in systems of constructive set theory, since the axiom of choice implies the law of excluded middle in such systems.
13. Evergreen Terrace is a dwelling within the meaning of 42 U.S.C. § 3602(b). RELEVANT HOUSING STATUTES 14. In 1974, Congress created the Section 8 program “[f]or the purpose of aiding low-income families in obtaining a decent place to live and of promoting economically mixed housing . . . .” 42 U.S.C. § 1437f(a).
The assumption that if there is a counterexample, there is a minimal counterexample, is based on a well-ordering of some kind. The usual ordering on the natural numbers is clearly possible, by the most usual formulation of mathematical induction; but the scope of the method can include well-ordered induction of any kind.