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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]
Mathematical logic is the study of formal logic within mathematics.Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory).
An argument is a set of premises together with a conclusion. [60] An inference is the process of reasoning from these premises to the conclusion. [43] But these terms are often used interchangeably in logic. Arguments are correct or incorrect depending on whether their premises support their conclusion.
It is part of a broad class of indispensability arguments most commonly applied in the philosophy of mathematics, but which also includes arguments in the philosophy of language and ethics. [14] In the most general sense, indispensability arguments aim to support their conclusion based on the claim that the truth of the conclusion is ...
The mathematician Paul Erdős was known for describing proofs which he found to be particularly elegant as coming from "The Book", a hypothetical tome containing the most beautiful method(s) of proving each theorem. The book Proofs from THE BOOK, published in 2003, is devoted to presenting 32 proofs its editors find particularly pleasing.
[18] [24] But the terms "argument" and "inference" are often used interchangeably in logic. The purpose of arguments is to convince a person that something is the case by providing reasons for this belief. [25] [26] Many arguments in natural language do not explicitly state all the premises.
In logic, proof by contradiction is a form of proof that establishes the truth or the validity of a proposition by showing that assuming the proposition to be false leads to a contradiction. Although it is quite freely used in mathematical proofs, not every school of mathematical thought accepts this kind of nonconstructive proof as universally ...
The logical form of this argument is known as modus ponens, [39] which is a classically valid form. [40] So, in classical logic, the argument is valid, although it may or may not be sound, depending on the meteorological facts in a given context. This example argument will be reused when explaining § Formalization.