Ahem, we of the sorites appreciation society are not amused :meh:
Try bald vs. hairy, black vs. white etc. — bongo fury
like imagining a heap of sand that never changes after a grain is removed or added.
— sime
... leading to the conclusion (incompatible with a premise, or there's no puzzle) that a single grain is a heap. Does that happen also with your "infinite" element, so that it can evaluate to 1? — bongo fury
Any finite number of grains of sand does not have this property. — sime
the semantics which concern the precise moment when an actual heap of sand is considered to be mere grains of sand, isn't linguistically specified a priori but is decided by speakers on a case specific basis. — sime
Any finite number of grains of sand does not have this property.
— sime
So... isn't a heap? — bongo fury
Agreed. But what is the smallest number of grains that would need considering by speakers as a particular case? Is it 1? — bongo fury
There is no a priori linguistic definition of "heap" in terms of any specific number of grains of sand, — sime
which is why "heap" must be logically represented as referring to a potentially infinite number of grains of sand. — sime
Any finite number of grains of sand does not have this property.
— sime
So... isn't a heap?
— bongo fury — sime
But what is the smallest number of grains that would need considering by speakers as a particular case? Is it 1?
— bongo fury
It is you and only you who gets to decide the answer to that question — sime
Sure. Heap is a spectrum. No puzzle.
A single grain is a minimal heap. A completely bald man is minimally hairy. Black is minimally white. — bongo fury
(like the threshold of hearing a noise) differs for people — Gregory
A single grain is a minimal heap. A completely bald man is minimally hairy. Black is minimally white.
The puzzle requires an intuition to the contrary. — bongo fury
I think you are approaching this from a subjective angle for or less, which is how I see it — Gregory
There is no a priori linguistic definition of "heap" in terms of any specific number of grains of sand,
— sime
Yes, that is the problem. — bongo fury
Why is linguistic imprecision a problem? — sime
This paradox is fun to think about. Remember though that thinking of perception (like the threshold of hearing a noise) differs for people. SO defining what is out there in discrete terms will not result in the same answer for everyone. I think you are approaching this from a subjective angle for or less, which is how I see it — Gregory
Yes, to me it is fun to think about. I believe it's a good example of how our brain works in dealing with specifics (one grain of sand), and generalities (a pile of sand).
Try this approach: Start by imagining a single grain of sand. Now, add another grain of sand. We can easily imagine two grains of sand that are close together (not far apart). Add another grain - it's also easy to imagine three grains of sand that are close together. Now - when we try to add another grain - such that we would have four grains of sand - it gets harder to imagine. Do you visualize all four grains at the same time, or do you visualize two groups of two? The brain automatically tries to regroup numbers greater than three into new "visual" groups - hence; two groups of two. Adding more grains changes the image again, A group of five, or more, grains causes the brain to sub-divide the grains again into new distinct groups with a maximum of three grains each until one gets to three groups of three - or nine grains total. However, the brain simply can't visualize nine grains of sand in a group - only three groups of three. Try it yourself.
As a result of this simple "thought experiment" one could conclude that the maximum number of grains of sand (where one can visualize the individual grains) is nine. Any number of grains greater than nine results in an "image" of a pile - not individual grains. We have knowledge (math) that we can add more grains to the pile - or take grains away - but it's the image that will not change in our minds, not the actual number.
Ancient philosophers didn't have the knowledge of brain mechanics that we do today so they didn't think in terms of how the brain actually counts. However, they did understand the mechanics (math) of adding, or subtracting, grains of sand to a pile. They were just not able to "visualize" what was happening by adding or subtracting mentally. I believe the Sorites Paradox is a mental paradox - not a physical one. — Don Wade
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