Sorites Paradox
Sorites paradox is attributed to the ancient Green philosopher Eubulides of Miletus. The paradox goes as follows: consider a heap of sand from which grains are individually removed. One might construct the argument, using premises, as follows:
1. 1,000,000 grains of sand is a heap of sand (Premise 1)
2. A heap of sand minus one grain is still a heap. (Premise 2)
Repeated applications of Premise 2 (each time starting with one less grain), eventually forces one to accept the conclusion that a heap may be composed of just one grain of sand (and consequently, if one grain of sand is still a heap, then removing that one grain of sand to leave no grains at all still leaves a heap of sand, and indeed a negative number of grains also form a heap).
The problem with this apparent paradox is in the definitions themselves: One assumes that 1,000,000 grains of sand is a heap of sand, however, if 1,000,000 grains of sand is spread over a large area so that it is only one grain of sand deep, it can hardly be considered a heap of any kind.
If we look at the definition of heap, we find it says: A collection of things thrown one on another.
Given this, we see that our premises are wrong and should read:
1. 1,000,000 grains of sand may be a heap of sand (Premise 1)
2. A heap of sand minus one grain may be still a heap. (Premise 2)
Again, using the proper definition of heap in this construct we see that repeated applications of premise 2 allows us to have a heap to a minimum of 2 grains of sand, provided that one grain is stacked on top of the other grain. At the point where no grain is stacked upon another grain, the sand stops being a heap. Additionally, any sand that is not stacked upon one another is no longer part of the heap. Further, by taking grains away so that we end up in multiple stacks creates multiple heaps, not a single heap created from the original.
Why this is important: How we define things is critical of how we look at and interpret things. With the wrong definitions we can make incorrect assumptions which lead to bad decisions.
1. 1,000,000 grains of sand is a heap of sand (Premise 1)
2. A heap of sand minus one grain is still a heap. (Premise 2)
Repeated applications of Premise 2 (each time starting with one less grain), eventually forces one to accept the conclusion that a heap may be composed of just one grain of sand (and consequently, if one grain of sand is still a heap, then removing that one grain of sand to leave no grains at all still leaves a heap of sand, and indeed a negative number of grains also form a heap).
The problem with this apparent paradox is in the definitions themselves: One assumes that 1,000,000 grains of sand is a heap of sand, however, if 1,000,000 grains of sand is spread over a large area so that it is only one grain of sand deep, it can hardly be considered a heap of any kind.
If we look at the definition of heap, we find it says: A collection of things thrown one on another.
Given this, we see that our premises are wrong and should read:
1. 1,000,000 grains of sand may be a heap of sand (Premise 1)
2. A heap of sand minus one grain may be still a heap. (Premise 2)
Again, using the proper definition of heap in this construct we see that repeated applications of premise 2 allows us to have a heap to a minimum of 2 grains of sand, provided that one grain is stacked on top of the other grain. At the point where no grain is stacked upon another grain, the sand stops being a heap. Additionally, any sand that is not stacked upon one another is no longer part of the heap. Further, by taking grains away so that we end up in multiple stacks creates multiple heaps, not a single heap created from the original.
Why this is important: How we define things is critical of how we look at and interpret things. With the wrong definitions we can make incorrect assumptions which lead to bad decisions.
Labels: Paradox, Philosophy
posted by Wizgang | 3:43 PM
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