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Paradox: Difference between revisions
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<pre>Or suppose one of us to have a portion of smallness; this is but a part of the small, and therefore the absolutely small is greater; if the absolutely small be greater, that to which the part of the small is added will be smaller and not greater than before.</pre> | <pre>Or suppose one of us to have a portion of smallness; this is but a part of the small, and therefore the absolutely small is greater; if the absolutely small be greater, that to which the part of the small is added will be smaller and not greater than before.</pre> | ||
from [https://gutenberg.org/cache/epub/1687/pg1687-images.html\ Parmenides by Plato (Project Gutenberg)] | from [https://gutenberg.org/cache/epub/1687/pg1687-images.html\ Parmenides by Plato (Project Gutenberg)] | ||
=== Achilles and the tortoise paradox === | === Achilles and the tortoise paradox === | ||
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In the paradox of Achilles and the tortoise, Achilles is in a footrace with the tortoise. Achilles allows the tortoise a head start of 100 meters, for example. Suppose that each racer starts running at some constant speed, one faster than the other. After some finite time, Achilles will have run 100 meters, bringing him to the tortoise's starting point. During this time, the tortoise has run a much shorter distance, say 2 meters. It will then take Achilles some further time to run that distance, by which time the tortoise will have advanced farther; and then more time still to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles arrives somewhere the tortoise has been, he still has some distance to go before he can even reach the tortoise. As Aristotle noted, this argument is similar to the Dichotomy.[13] It lacks, however, the apparent conclusion of motionlessness. | In the paradox of Achilles and the tortoise, Achilles is in a footrace with the tortoise. Achilles allows the tortoise a head start of 100 meters, for example. Suppose that each racer starts running at some constant speed, one faster than the other. After some finite time, Achilles will have run 100 meters, bringing him to the tortoise's starting point. During this time, the tortoise has run a much shorter distance, say 2 meters. It will then take Achilles some further time to run that distance, by which time the tortoise will have advanced farther; and then more time still to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles arrives somewhere the tortoise has been, he still has some distance to go before he can even reach the tortoise. As Aristotle noted, this argument is similar to the Dichotomy.[13] It lacks, however, the apparent conclusion of motionlessness. | ||
</div> | </div> | ||
=== Zeno's indivisibility of time === | |||
* many of his paradoxes rely on the idea that time and space are infinitely divisible and thus yield absurd conclusions | |||
* therefore, according to Zeno (and Parmenides) motion is an illusion | |||
** ironically, video or motion pictures are made up of still images that create the illusion of motion when shown in rapid succession | |||
=== Arrow paradox === | |||
* at any given instant, a flying arrow is in a certain place, so, since its entire flight is made up on such motionless instants, motion is impossible. | |||
** | |||
* a described by Aristotle in [https://archive.org/details/aristotle_physics ''Physics'' VI:9, 239b5] | |||
If everything when it occupies an equal space is at rest at that instant of time, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless at that instant of time and at the next instant of time but if both instants of time are taken as the same instant or continuous instant of time then it is in motion. | |||
=== Dichotomy paradox === | |||
* if you keep walking half-way to somewhere, you will never get there | |||
* Aristotle described it in [https://archive.org/details/aristotle_physics ''Physics'' VI:9, 239b10] as: | |||
That which is in locomotion must arrive at the half-way stage before it arrives at the goal. | |||
=== Moving rows paradox === | |||
* given three rows of four individuals (rows A, B, & C) | |||
** if row A is not moving, and rows B and C are moving in oppositive directions past row A at equal speeds | |||
** since B and C both move past A at one speed, they move past each other at double the speed they move past the stationary row A | |||
** thereby half of a time is equal to its double | |||
* | |||
=== Paradox of place === | |||
* since everything has a place, and a place is a thing, then every place has a place, ''ad infinitum'' (onward forever) | |||
=== Paradox of the grain of millet === | === Paradox of the grain of millet === | ||
* if a single grain of millet (a seed) makes no sound upon falling, yet 1,000 grains that fall do make a sound, how can 1,000 nothings create a sound? | * if a single grain of millet (a seed) makes no sound upon falling, yet 1,000 grains that fall do make a sound, how can 1,000 nothings create a sound? | ||
See | |||
* [https://iep.utm.edu/zenos-paradoxes/ Zeno’s Paradoxes | Internet Encyclopedia of Philosophy (utm.edu)] | |||
== Science & technology paradoxes == | == Science & technology paradoxes == | ||