In this essay, I am going to describe the paradox of the

heap (sorites paradox). Following on from this, I am going to put forward its

reserve argument, which was associated with mainly Peter Unger, as his idea was

to reject the existence of heaps altogether. In light of Unger’s argument, I

still maintain to put forward other alternative solutions regarding the sorites

paradox in an attempt to solve the paradox from its semantic problems, as I

find it hard to accept Unger’s conclusion, although no logical problems come from

accepting his conclusion.

Envision a heap

of sand (n). You deliberately remove one grain (n – 1). Is there still a heap?

The undeniable answer is yes. Subtracting one grain doesn’t transform a heap

into no heap. That rule can be used again as you remove another grain, and

after that another. After each

subtraction, a heap still remains, as indicated by modus ponens (if p then q;

p, so q). Be that as it may, there were just limitedly many grains to begin

with, so inevitably you get down to a heap with only three grains, at that

point a heap with only two grains, a heap with only one grain. Yet, that is

strange. There must be some kind of problem with the rule. At some point,

expelling one grain turns a heap into no heap. In any case, that appears to be

strange as well. How might one grain have so much effect? This puzzle is known

as the sorites paradox, from the Greek word for ‘heap’.

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There would be no

issue in the event that we had an exact definition of ‘heap’ that disclosed to

us precisely what number of grains are required for a heap. The inconvenience

is that we don’t have such a definition. The word ‘heap’ is vague. There isn’t

an unmistakable limit amongst heap and no heap. Generally, that doesn’t make a

difference. Using the word ‘heap’ causes no problems when used generally in

non-specific cases. In any case, if the town committee, for example, accused

you of having dumped a heap of sand in an open place, and you denied that it added

up to a heap, whether you needed to pay a vast fine may rely upon the

importance of the word ‘heap’.

The most drastic

response to the paradox is offered by Peter Unger as he supports another

version of the argument. Unger’s argument is basic. To start off, think of the

concept of a heap. Obviously, one grain of sand (n) is inadequate for a heap.

Be that as it may, if there isn’t a heap before us, adding one grain (n + 1)

won’t make a heap. Thus, no finite number of grains (even 10,000 grains) is

adequate for a heap (Unger 1979, p. 118). Therefore, there are no heaps, and

the concept we have of a heap is incoherent. Unger looks at this as a direct

argument for his reasoning concerning heaps. We can look at it from another

viewpoint, that there can be heaps and that a million grains of sand, suitably

placed constitute a heap. Given that we have a heap of a million grains,

expelling one grain of sand won’t leave us with no heap, nor will expelling one

more etc, until at last we achieve the conclusion that one grain of sand is

suitable for a heap. This, Unger believes is outrageous; our unique supposition

that there exists a heap is in this manner becomes absurd.

This thinking is

viewed as an indirect argument that there are no heaps, and that the concept of

a heap is disjointed. To embrace Unger’s direct argument is to regard a

negative sorites argument as a sound argument, and a veridical paradox. The

negative sorites argument is taken to give demonstration to the non-existence

of heaps. (Olin 2003, p.172). The demonstration can be explained using Unger’s

main idea, which follows the reasoning that no physical object (he uses the

example of a table, rock or swizzle stick), can be that the subtraction of an

atom or two should make a difference as to whether it exists or not. However,

being a finite object, a point is reached where the continuous removal of an

atom or two would ultimately leave us with nothing left. A couple of atoms do

not make the object, nevertheless, a point is reached where they make something

e.g. a rock, no longer a rock. This idea leaves us with no option other than to

give up the idea we have of tables, rocks, swizzle sticks etc. altogether, as

the idea that removing one atom can change an object is incomprehensible

(Unger, 2006 p. 6-8)