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Humans are animals, despite the fact that the word animal is colloquially used as an antonym for human. [176] [177] Ecosystems do not naturally move back towards an equilibrium using negative feedback. [178] The concept of an inherent "balance of nature" has been superseded by chaos theory. [179]
The term antonym (and the related antonymy) is commonly taken to be synonymous with opposite, but antonym also has other more restricted meanings. Graded (or gradable) antonyms are word pairs whose meanings are opposite and which lie on a continuous spectrum (hot, cold).
The general consensus of large-scale studies that compare traditional mathematics with reform mathematics is that students in both curricula learn basic skills to about the same level as measured by traditional standardized tests, but the reform mathematics students do better on tasks requiring conceptual understanding and problem solving. [3]
A priori and a posteriori knowledge – these terms are used with respect to reasoning (epistemology) to distinguish necessary conclusions from first premises.. A priori knowledge or justification – knowledge that is independent of experience, as with mathematics, tautologies ("All bachelors are unmarried"), and deduction from pure reason (e.g., ontological proofs).
Mathematics is essential in the natural sciences, engineering, medicine, finance, computer science, and the social sciences. Although mathematics is extensively used for modeling phenomena, the fundamental truths of mathematics are independent of any scientific experimentation.
In mathematics and logic, ambiguity can be considered to be an instance of the logical concept of underdetermination—for example, = leaves open what the value of is—while overdetermination, except when like =, =, =, is a self-contradiction, also called inconsistency, paradoxicalness, or oxymoron, or in mathematics an inconsistent system ...
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Kant's antinomies are four: two "mathematical" and two "dynamical". They are connected with (1) the limitation of the universe in respect of space and time, (2) the theory that the whole consists of indivisible atoms (whereas, in fact, none such exist), (3) the problem of free will in relation to universal causality, and (4) the existence of a necessary being.
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