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These paradoxes may be due to fallacious reasoning , or an unintuitive solution . The term paradox is often used to describe a counter-intuitive result. However, some of these paradoxes qualify to fit into the mainstream viewpoint of a paradox, which is a self-contradictory result gained even while properly applying accepted ways of reasoning .
According to Simplicius, Diogenes the Cynic said nothing upon hearing Zeno's arguments, but stood up and walked, in order to demonstrate the falsity of Zeno's conclusions. [25] [2] To fully solve any of the paradoxes, however, one needs to show what is wrong with the argument, not just the conclusions. Throughout history several solutions have ...
The hindrance of a quantum system by observing it is usually called the Quantum Zeno effect as it is strongly reminiscent of Zeno's arrow paradox. [ 32 ] [ 33 ] In the field of verification and design of timed and hybrid systems , the system behavior is called Zeno if it includes an infinite number of discrete steps in a finite amount of time.
For Zeno, it is not clear whether or not Anaxagoras or Empedocles influenced or were influenced by any of his ideas, although they appear to have lived at approximately the same time. [1] For Melissus, who lived one generation later, the problem of influence is further complicated by additional potential influences of Leucippus , Democritus ...
The title alludes to one of Zeno's paradoxes of motion, [2] in which Achilles could never overtake the tortoise in a race. In Carroll's dialogue, the tortoise challenges Achilles to use the force of logic to make him accept the conclusion of a simple deductive argument.
Reductio ad absurdum, painting by John Pettie exhibited at the Royal Academy in 1884. In logic, reductio ad absurdum (Latin for "reduction to absurdity"), also known as argumentum ad absurdum (Latin for "argument to absurdity") or apagogical argument, is the form of argument that attempts to establish a claim by showing that the opposite scenario would lead to absurdity or contradiction.
Men of Mathematics: The Lives and Achievements of the Great Mathematicians from Zeno to Poincaré is a book on the history of mathematics published in 1937 by Scottish-born American mathematician and science fiction writer E. T. Bell (1883–1960). After a brief chapter on three ancient mathematicians, it covers the lives of about forty ...
Zeno's paradoxes state that if one were to examine individual moments of an object moving in a given direction, (as with an arrow flying towards a target) or overtaking a second, slower object, (as with Achilles challenging a tortoise to a race) one would not actually be able to find a moment of the act of change or motion taking place, thus proving Zeno's view of motion as illusory and ...