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Heap big Problem
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FromMessage
 obsteve10-Jan-11, 17:52

Heap big Problem
Here's an old one-

I have a heap of sand and take away the grains one by one. Is it still a heap when only one grain remains? If not, when did it change from a heap to a non-heap?

 coopershawk15-Jan-11, 22:15

False Dichotomy?
Is this not an example of a false dichotomy? The question presumes incorrectly that the sand is either a "heap"
or "not a heap." The term "heap" is subjective so the sand may not be either, or it may be both. This particular
fallacy is a favorite of demagogues the world over.
 obsteve19-Jan-11, 16:48

Feeling argumentative...
I have a heap of sand, of that there is no doubt.

It is not a "not a heap", it is definitely a heap, made of sand, belonging to me. My heap.

If you saw my heap of sand, I have no doubt you would agree, "ok, that's a heap of sand", or "yes that's sand, and it's a heap of the stuff", or some such similar utterance.

perhaps you might call it a pile (if you preferred), or even a mound, or perhaps simply "a large quantity of sand".

I strongly refute your suggestion my heap can simultaneously be a heap and a non-heap. I am quite offended.

 darwin0919-Jan-11, 18:44

When does. . .
. . . a molehill become a mountain?

When my wife decides it's so.
 obsteve20-Jan-11, 17:02

That'll be just about the final straw then?
 shamash21-Jan-11, 14:09

from Quantitative change to Qualitative change
you're moving from quantitative change of state to qualitative change.
from a change in quantity to a change in quality.

(Karl Marx offers a good discussion of this when he considers the example of a man who loses the hairs of his head one by one until he is in a state of baldness.)
 obsteve21-Jan-11, 17:44

quantitative to qualitative
Hi Shamash, it sounds like a similar paradox-

hairy minus one hair is still hairy

But could you please explain what you mean by quantitative to qualitative change?

Steve

 shamash21-Jan-11, 18:13

when quantitative change becomes qualitative change
2 Qualitative states:
By definition,
a hairy head is a head with hair. hair grows on it.
a bald head is a head with no more hair. hair no longer grows on it.

Quantitative change:
a hairy head with a million hairs is a head with hair
a head losing hair but still with ten hairs is a head with hair
a head losing all but one hair growing is still a head with hair

When the head with hair loses its last hair, and its ability to grow hair -- it undergoes a qualitative change
from a head with hair growth to baldness.

(and there are Better examples that hair. I think atomic theory offers examples in terms of change of state, the photo-electric effect, and an electron shifting its orbital level)
 antinephilehi22-Jan-11, 09:10

sand everywhere.
What if I have two heaps with sand?
IN the first we have 4 cubic sand.and in the second we have 7cubic sand.
What do we get if we put them together?
 sonata29622-Jan-11, 11:28

a lot of sand for sure
 obsteve22-Jan-11, 12:21

Hairy v Bald, hmmm
I'd say a if a person had but one or two hairs on their head they were still bald. I think I'm with cascadejames on this one- I think it's totally subjective.

Thanks for the Q-Q lowdown Shamash, and I'm tempted to say a heap is not a quantity either, but a quality- ie the manner in which the sand is erm "heaped"

I've just had a random idea. Let's say I was an artist, and decided to craft my heap of sand into a sand sculpture (for example, a representation-of-the-temptation-of-christ-in-the-desert)

Same quantity, different quality?

Then I start removing grains of sand- at what point does it become a non-representation-of-the-temptation-of-christ-in-the-desert?

Antinephilehi- we have 11 cubic sand!
 antinephilehi22-Jan-11, 13:35

Really
Obsteve,I thought it whould give us one heap of sand.