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One example of a proof that was impossible to satisfactorily verify without formal verification is the famous proof of the four color theorem. This theorem stumped mathematicians for more than a hundred years, until a proof was developed that ruled out large classes of possible counterexamples, yet still left open enough possibilities that a ...
Formal logic and mathematical rules are examples of rigorous consistency. An example would be: if all As are Bs and all Bs are Cs, then all As are Cs. While this standard is of high value, it is limited. For example, the premises are a priori (or self-apparent), requiring another test of truth to employ this criterion. Additionally, strict ...
Logical Intuition, or mathematical intuition or rational intuition, is a series of instinctive foresight, know-how, and savviness often associated with the ability to perceive logical or mathematical truth—and the ability to solve mathematical challenges efficiently. [1]
Intuition, in contrast, is a more instantaneous, immediate understanding upon first being confronted with the math problem. Intuition is also distinct from implicit knowledge and learning, which inform intuition but are separate concepts. Intuition is the mechanism by which implicit knowledge is made available during an instance of decision-making.
Distinct types of logical reasoning differ from each other concerning the norms they employ and the certainty of the conclusion they arrive at. Deductive reasoning offers the strongest support: the premises ensure the conclusion, meaning that it is impossible for the conclusion to be false if all the premises are true.
Intuition was assessed by a sample of 11 Australian business leaders as a gut feeling based on experience, which they considered useful for making judgments about people, culture, and strategy. [45] Such an example likens intuition to "gut feelings", which — when viable [clarification needed] — illustrate preconscious activity. [46]
Apodicticity or apodixis is the corresponding abstract noun, referring to logical certainty. Apodictic propositions contrast with assertoric propositions, which merely assert that something is (or is not) true, and with problematic propositions, which assert only the possibility of something's being true. Apodictic judgments are clearly ...
Truthiness is the belief or assertion that a particular statement is true based on the intuition or perceptions of some individual or individuals, without regard to evidence, logic, intellectual examination, or facts. [1] [2] Truthiness can range from ignorant assertions of falsehoods to deliberate duplicity or propaganda intended to sway ...