You've lost one of the two required (and puzzlingly opposed) intuitions that we are trying to reconcile. — bongo fury
We just don't have that many images of piles of sand such that we can visualize a "different" pile to account for every single grain. — Don Wade
I suppose it boils down to having multiple images for a "pile" of sand and removing grains of sand one by one simply switches between one of these images of a pile and another image of a pile, the result being the pile remains a pile despite grains of sand being taken away. — TheMadFool
The problem, as stated in the sorites paradox, is not being able to determine at what point a group of grains of sand becomes a pile. Whatever number one may choose that constitutes an image of when a group of grains becomes a pile - then one grain added, or subtracted, should "change" that image. But, it doesn't. The "image" of the pile remains the same whether a grain is added, or subtracted. It's not the math - it's the way our brain works in creating the image — Don Wade
The first question gets the sorites paradox going. The second question is nonsensical. — jkg20
Even though the pile-size may change, the visual image of the pile remains the same. — Don Wade
That generalised image must mean the smallest pile is 4 grains - three as a triangular base and one perched on top. Take that away an only have a clump or group of grains? Move the grains gradually apart and at some point they are not even a group? — apokrisis
Try bald vs. hairy — bongo fury
Slightly more formally: treating a grain as a centre of gravity with a spatial boundary, four points are required to define a three dimensional space, so four grains are required to define a three dimensional shape that constitutes a heap. — unenlightened
Yes. I'm not qualified to follow the complex logic & arcane terminology of your link : Supervaluationism ; Hysteresis ; Resolutions in utility theory ; etc. But a simple philosophical change of perspective can allow you to see the Whole instead its Parts. No abstruse math required --- not even addition (summation). Just re-focus the eye of your mind. :smile:This solution is not predicated on vagueness or fuzzy logic - it is simple recognizing the limits of how our brain creates images of objects. — Don Wade
So, the un-bound is restricted by the bound, or the un-limited is confined within limits. Sounds like, not a paradoxical koan puzzle, but a simple contradiction in terms. If anything, I would expect the opposite relationship to be true : our finite space-time world exists within the context of Eternity & Infinity. Is there a rational interpretation of that koan? :smile:the infinite is contained in the finite so there really isn't a distinction between the two — Gregory
like imagining a heap of sand that never changes after a grain is removed or added. — sime
I mean the critical point determines when a heap/pile becomes such. — DeGregePorcus
To a man-sized being a heap has more than a "few" grains arranged one upon another, — DeGregePorcus
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