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The argument hinges on the idea that a satisfactory naturalistic account of thought processes in terms of brain processes can be given for mathematical reasoning along with everything else. One line of defense is to maintain that this is false, so that mathematical reasoning uses some special intuition that involves contact with the Platonic realm.
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).
Many prominent researchers [a] assumed that, having (almost) solved the "hard" problems, the "easy" problems of vision and commonsense reasoning would soon fall into place. They were wrong (see also AI winter), and one reason is that these problems are not easy at all, but incredibly difficult. The fact that they had solved problems like logic ...
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]
To Create His Geometric Artwork, M.C. Escher Had to Learn Math the Hard Way. Fourier Transforms: The Math That Made Color TV Possible. The Game of Trees is a Mad Math Theory That Is Impossible to ...
Despite its name, mathematical induction is a method of deduction, not a form of inductive reasoning. In proof by mathematical induction, a single "base case" is proved, and an "induction rule" is proved that establishes that any arbitrary case implies the next case.
Introduction to Meta-Mathematics (Tenth impression 1991 ed.). Amsterdam NY: North-Holland Pub. Co. ISBN 0-7204-2103-9. In Chapter III A Critique of Mathematic Reasoning, §11. The paradoxes, Kleene discusses Intuitionism and Formalism in depth. Throughout the rest of the book he treats, and compares, both Formalist (classical) and Intuitionist ...
Presenting mathematics may be hard since the general public suffers from mathematical anxiety and mathematical objects are highly abstract. [209] However, popular mathematics writing can overcome this by using applications or cultural links. [ 210 ]