4 ms·

It's just interesting when you have discrete entities and you can't show inductively that there is any point where the classification changes from non-heap to h

by hderms 10y ago

It's just interesting when you have discrete entities and you can't show inductively that there is any point where the classification changes from non-heap to heap, but clearly that point must exist. It's interesting from the same perspective as what makes the ship of Theseus interesting. the probability of something being viewed as a heap could only be measured statistically as the probability doesn't derive from some direct process. The issue can be viewed in both an axiomatic and a empirical way and both views lead to interesting conclusions.

empath75 10y ago
That point may not exist though, if it just gains more 'heapness' over time. Even if 99% of people agree that a collection of grains of sand is a 'heap' there might be some people who still insist that it is not.
- coldtea 10y ago
  After a point, 100% will agree (anybody not agreeing that an obvious heap of say 100kg of sand is not a heap but just grains, can be discarded as a madman). But still the exact point can't be specified, we only know when it's over-surpassed. It's like in the famous trial, when they asked someone to specify is a film is "porn" or "erotic art", and he said: "I shall not today attempt further to define the kinds of material I understand to be embraced within that shorthand description ["hard-core pornography"], and perhaps I could never succeed in intelligibly doing so. But I know it when I see it, and the motion picture involved in this case is not that."
Retra 10y ago
That point doesn't need to exist. A "heap" is not a formally defined concept, and the Sorites paradox is basically what you get when you improperly assume it must be. Think about how you learned the meaning of the word "heap." People just used it. They used it in some varying contexts, and your brain picked up on a pattern. It's like if I said "This is my dog, Blue" and someone was all hung up on the paradox of "what color is the dog, really." Blue is the name of the dog. You know this because I used it as a name. You don't need a formal definition, all you need is to know how a name-context works, and you can tell it's the dogs name. "The probability of something being viewed as a heap" is not the right way of looking at it. What's important is the probability of it being correct to be called a heap, which is derived from the correlations in usage patterns of the word "heap" around various things.
mcphage 10y ago
> but clearly that point must exist Rather, it's very clear no such point exists, and the assumption that it does is both nonsensical and leads to foolish conclusions.

by hderms 10y ago

empath75 10y ago

That point may not exist though, if it just gains more 'heapness' over time. Even if 99% of people agree that a collection of grains of sand is a 'heap' there might be some people who still insist that it is not.

coldtea 10y ago
After a point, 100% will agree (anybody not agreeing that an obvious heap of say 100kg of sand is not a heap but just grains, can be discarded as a madman). But still the exact point can't be specified, we only know when it's over-surpassed. It's like in the famous trial, when they asked someone to specify is a film is "porn" or "erotic art", and he said: "I shall not today attempt further to define the kinds of material I understand to be embraced within that shorthand description ["hard-core pornography"], and perhaps I could never succeed in intelligibly doing so. But I know it when I see it, and the motion picture involved in this case is not that."

Retra 10y ago

That point doesn't need to exist. A "heap" is not a formally defined concept, and the Sorites paradox is basically what you get when you improperly assume it must be. Think about how you learned the meaning of the word "heap." People just used it. They used it in some varying contexts, and your brain picked up on a pattern. It's like if I said "This is my dog, Blue" and someone was all hung up on the paradox of "what color is the dog, really." Blue is the name of the dog. You know this because I used it as a name. You don't need a formal definition, all you need is to know how a name-context works, and you can tell it's the dogs name. "The probability of something being viewed as a heap" is not the right way of looking at it. What's important is the probability of it being correct to be called a heap, which is derived from the correlations in usage patterns of the word "heap" around various things.

mcphage 10y ago

> but clearly that point must exist Rather, it's very clear no such point exists, and the assumption that it does is both nonsensical and leads to foolish conclusions.