Information Technology Reference
In-Depth Information
15
A Layperson Reflection on Sorites
Enric Trillas and Itziar García-Honrado
15.1
Introduction
Concerning the so-called 'Sorites Paradox' there are dozens of papers, mainly of a
philosophical character, in which the concept of 'heap' is viewed as only depend-
ing on the number of grains in each heap, but avoiding any consideration on its
three-dimensional shape [9], [3]. Such a radical simplification can actually be sur-
prising for a layperson who, interested in Philosophy has, at least, some perceptive
experience on heaps.
In any case, heap is a word or linguistic term that refers to a particular instance
of physical objects, whose meaning is captured through its common perceptive use
in language and requires some kind of distinction between what is and what is not a
heap. That is, to understand the statement ' h is a heap' it should also be understood
when ' h is not a heap' ,to perceptually recognize if a physical object constituted
by grains of sand is, or is not, a heap. On the contrary, any set of grains could
simultaneously be a heap and a not-heap without the possibility of recognizing what
it is actually.
All that is not to mention the actual lack of any antonym or opposite of the term
heap, like it could be the non existent term 'unheap'. Only the term 'flat' referring
to some set of grains of sand could tentatively be used as an opposite of heap.
In those philosophical papers, a heap appears as a theoretical construct not actu-
ally different from the finite subset of natural numbers denoting which is the number
of grains in the heap, something that is absolutelly not in the layperson's perceptive
use of the term. Hence, philosophical papers on the Sorites type of reasoning cannot
be included in commonsense reasoning. In addition, their conclusions are reached
by repeatedly using the scheme of Modus Ponens that, as it is well known, is a
typical way of performing deductive reasoning. Consequently, Sorites deserves to
be reconsidered from the point of view of everyday or commonsense reasonig, by
distinguishing between the heap, and the set of the grains of sand in it.
The so-called paradox is often presented by saying that if a heap, denoted by
(
)
(
)
h
p
,has p grains of sand, also when removing a single grain is h
p
1
a heap, and
(
) , ...,
(
) , ...
(
)
h
p
2
h
p
n
,andafter p
1 steps is h
1
a heap, against the common
 
Search WWH ::




Custom Search