Using "a new belief set" to solve Sorites paradox

[Kriminal99]

Sorites paradox involves a heap of sand which contains 1 million grains.

 

1) 1 million grains make a heap of sand.

2) The removal of a grain of sand will never make the difference between a heap and a pile.

3) Therefore 999,999 grains of sand make a heap

4) Therefore 999,998 grains of sand make a heap

...

1,000,002) Therefore 1 grain of sand makes a heap

1,000,003) 1 grain of sand does not make a heap

 

Logical contradiction.

 

However if we say that a heap is a visual idea, (ie it is defined visually) then we can simply realize that 2) is true because we can not see the difference when a single grain of sand has been removed. However we can see the difference when X grains of sand have been removed, where X depends on the precision of the vision of the observer as well as factors such as the lighting where the grains are removed etc.

 

Therefore we see that premise 2 is not the case because every xth grain removed results in a visual difference that could be the threshold between a heap and a pile.

[Qfwfq]

The weakness of 2) lies in the lack of definition of "heap" and "pile" and in the word "never". I wouldn't consider it necessary for those two definitions to be given in visual terms.

[Kriminal99]

I agree with you that the definitions were lacking, but the whole point of the paradox is to use the every day definitions.

 

You could simply define heap to mean 10,000 grains of sand, but this would be arbitrary and not related to the common definition of heap.

 

The point of my solution is that my definition of heap seems to have the same attributes as the every day definition of heap, yet is precise enough to solve the paradox. Thus indicating that the everyday definition of heap is based on a function of visual memories, thus reinforcing "a new belief set"