Editing Sorites paradox (section)

==Original formulation==
The word ''sorites'' ({{langx|grc|[[wiktionary:σωρείτης|σωρείτης]]}}) derives from the Greek word for ''heap'' ({{langx|grc|[[wiktionary:σωρός|σωρός]]}}).<ref>{{Cite book|title = An Introduction to Many-Valued and Fuzzy Logic: Semantics, Algebras, and Derivation Systems|last = Bergmann|first = Merrie|publisher =[[Cambridge University Press]]|year = 2008|isbn = 978-0-521-88128-9|location = New York, NY|page = [https://books.google.com/books?id=zEwNfoAZEGoC&pg=PA3 3]}}</ref> The paradox is so named because of its original characterization, attributed to [[Eubulides|Eubulides of Miletus]].<ref>{{Harv|Barnes|1982}}, {{Harv|Burnyeat|1982}}, {{Harv|Williamson|1994}}</ref> The paradox is as follows: consider a [[wikt:heap|heap]] of sand from which [[grain]]s are removed individually. One might construct the argument from the following [[premise]]s:<ref name=Sorensen2009/>

:''{{val|1000000|fmt=commas}} grains of sand is a heap of sand'' (Premise 1)
:''A heap of sand minus one grain is still a heap.'' (Premise 2)

[[Mathematical induction|Repeated applications]] of premise 2 (each time starting with one fewer grain) eventually forces one to accept the [[logical consequence|conclusion]] that a heap may be composed of just one grain of sand.<ref>{{Cite journal| doi = 10.1111/j.1467-9205.2004.t01-1-00230.x| title = Why Induction Is No Cure For Baldness| year = 2004| last1 = Dolev | first1 = Y.| journal =[[Philosophical Investigations]]| volume = 27| issue = 4| pages = 328–344 }}</ref>
Read (1995) observes that "the argument is itself a heap, or sorites, of steps of ''[[modus ponens]]''":<ref name="Read">Read, Stephen (1995). ''Thinking About Logic'', p.174. Oxford. {{ISBN|019289238X}}.</ref>

:''{{val|1000000|fmt=commas}} grains is a heap.''
:''If {{val|1000000|fmt=commas}} grains is a heap then {{val|999999|fmt=commas}} grains is a heap.''
:''So {{val|999999|fmt=commas}} grains is a heap.''
:''If {{val|999999|fmt=commas}} grains is a heap then {{val|999998|fmt=commas}} grains is a heap.''
:''So {{val|999998|fmt=commas}} grains is a heap.''
:''If ...''
:''... So {{val|1}} grain is a heap.''
One grain of sand is not considered to be a heap of sand.<ref>{{Cite book |last=Thorsrud |first=Harald |url=https://www.google.com.br/books/edition/Ancient_Scepticism/dqnCBQAAQBAJ |title=Ancient Scepticism |date=2014-12-05 |publisher=Routledge |isbn=978-1-317-49283-2 |pages=63 |language=en}}</ref> So the argument, although seeming valid and with plausible premises, has a false conclusion, which makes it a paradox, according to a popular (though not universally accepted) academic definition of "paradox".<ref>{{Cite book |last=Sainsbury |first=R. M. |url=https://www.google.com.br/books/edition/Paradoxes/vIU2NK1WNdgC |title=Paradoxes |date=2009-02-19 |publisher=Cambridge University Press |isbn=978-0-521-89632-0 |pages=1 |language=en |quote=This is what I understand by a paradox: an apparently unacceptable conclusion derived by apparently acceptable reasoning from apparently acceptable premises.}}</ref><ref>{{Cite book |last=Bunnin |first=Nicholas |url=https://www.google.com.br/books/edition/The_Blackwell_Dictionary_of_Western_Phil/M7ZFEAAAQBAJ |title=The Blackwell Dictionary of Western Philosophy |last2=Yu |first2=Jiyuan |date=2009-01-27 |publisher=John Wiley & Sons |isbn=978-1-4051-9112-8 |pages=503 |language=en}}</ref><ref>{{Cite book |last=Cuonzo |first=Margaret |url=https://www.google.com.br/books/edition/Paradox/puXUAgAAQBAJ |title=Paradox |date=2014-02-14 |publisher=MIT Press |isbn=978-0-262-32140-2 |pages=6-7 |language=en}}</ref>