3 ms·
You're right, that isn't really the best statement of the paradox. Try this: Imagine you have a heap of sand. Now, if you remove a single grain of sand from a
by dsg42 10y ago
You're right, that isn't really the best statement of the paradox. Try this:
Imagine you have a heap of sand. Now, if you remove a single grain of sand from a heap, it's still a heap, right? But if you remove every grain of sand, then eventually, you're left without any sand, which is definitely not a heap. So somewhere along the way, when removing individual grains of sand, the heap stopped being a heap. But where, exactly, did that happen?
- chongli 10y agoIt happened at the exact moment when none of the grains were supported by any of the others. A flat, single grain layer of sand on the ground is not a heap no matter how many grains are in it.
- cgio 10y agoSoros in Greek does not have the structural connotation of heap in English (which I infer from your reply, given English is not my mother tongue).
- stcredzero 10y agoFor very blocky, stackable grains of sand, it could've happened at 2. It undoubtedly happened somewhere below 9. That's as exact as this needs to be, unless you are a pedant. In which case, fuggedaboudit!
- ikeboy 10y agoJust use a different example, e.g. baldness, or the pumpkin one from http://philpapers.org/archive/FRAQTV.pdf http://philpapers.org/archive/FRAQTV.pdf
- dragonwriter 10y agoIt stopped being a heap at the moment at which there were no longer both: (1) more than one vertical layer (the requirement for it to be a pile), and (2) each grain not directly in contact with the ground being above a point on the ground within the triangle defined the points on the ground directly underneath three lower grains (distinguishing a heap from other piles). (Of course, you may have a different definition of a heap, but if once you make concrete what you mean by a "heap", the problem is resolved. If you view heap as a fuzzy concept, then there is a continuous-valued fuzzy membership function, and there is no crisp point at which the collection stops, or starts, being a heap.)
- datashovel 10y agoTo describe this concept I've always used a boat as the subject. Imagine you have a boat. Now take a piece off of it. Is it still a boat? How far can you go until it no longer holds the distinction of being a boat?
- mannykannot 10y agoI imagine 'when it sinks' would work for most people.
- EdwardCoffin 10y agoAnd if it is constructed entirely from wood that floats?
- mannykannot 10y agoThen it may still function as a boat. As in all of these examples, X-iness is context-dependent, but for some boats, unlike the other examples here, there actually is something approaching an objective decision procedure. Yes, I know that submarines are colloquially known as (and are in fact) boats.
- datashovel 10y agoSo if I understand correctly, then twigs and leaves could be boats? :) I guess if a boat was originally constructed of a bunch of twigs (some of which still had leaves on them), but caught on fire. One lucky leaf was knocked off and managed to survive the fire. Everything else sunk. The single remaining artifact of the boat was that one leaf. And it's still floating... Everyone looked at me perplexed when I told them all that we were looking at a boat! :)