A filing cabinet on the internet by Rob Giampietro

The Paradox of the Heap

A Sorites paradox is
a key issue in the philosophy of language, with the word “Sorites”
translating in Greek to “heap.” The paradox can be stated in two
premises, 1) A heap of sand is comprised of a large collection of
grains, and 2) A heap of sand minus one grain is still a heap. The
problem is that if you continue executing premise 2, you’ll soon have
neither heap nor even one sand grain left. The many possible resolutions
to this problem suggest a cache of ways philosophers try to deal with
problems of vagueness. Some
resolutions trivialize the problem, casting “heap” as a basically
meaningless term. Others try to set limits, either fixed by number
(although what’s the difference between 9,999 grains and 10,001?) or
positional (a heap has sand grains supporting other sand grains off the
ground, multiple heaps cannot also belong to a single heap, etc.).
So-called “fuzzy” logic
allows not just for on and off positions (“heap” and “not-heap”) but
also a third position, “unsure,” which may be subdivided into
“mostly-heap,” “partly-heap,” etc. Other solutions may be as simple as
group consensus (the majority of people would call it a “heap”) or as
complex as hysteresis, which
suggests certain systems make it impossible to predict an output from a
given input and instead it must be taken into account whether the heap
in question started out as a heap, a desert, or a single grain of sand.
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