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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.
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.
Frankfurt cases (also known as Frankfurt counterexamples or Frankfurt-style cases) were presented by philosopher Harry Frankfurt in 1969 as counterexamples to the principle of alternate possibilities (PAP), which holds that an agent is morally responsible for an action only if that person could have done otherwise.
Counterexamples in Topology (1970, 2nd ed. 1978) is a book on mathematics by topologists Lynn Steen and J. Arthur Seebach, Jr.. In the process of working on problems like the metrization problem, topologists (including Steen and Seebach) have defined a wide variety of topological properties.
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.
Hear an expert's take on 8 common mindsets that could be holding you back from financial success — plus tips to counter them. When it comes to money, it always helps to take a step back ...
Grinberg's theorem, a necessary condition on the existence of a Hamiltonian cycle that can be used to show that a graph forms a counterexample to Tait's conjecture; Barnette's conjecture, a still-open refinement of Tait's conjecture stating that every bipartite cubic polyhedral graph is Hamiltonian. [1]