The term ''heap'' in common usage doesn't actually mean a ''certain'' number of grains. — TheMadFool
More accurately a ''heap'' includes in its definition the size of the components, the shape of the collection, in addition to the number of objects in the collection. — TheMadFool
Therefore, to isolate one variable, the number of objects in the collection, may be a mistake. — TheMadFool
doesn't detract from the problem of vagueness, the central message of the paradox. — TheMadFool
If you are against either of these reductions, then hooray. If your talk of "incommensurability" isn't, after all, about trying to separate usage of heap from the naturals, then even better. — bongo fury
two or more quantities having no common measure.
Therefore, to isolate one variable, the number of objects in the collection, may be a mistake. Nonetheless this is an issue for the heap paradox specifically and doesn't detract from the problem of vagueness, the central message of the paradox. — TheMadFool
In the case of the heap, the WD may say: "We shall consider any haphazardly thrown together comparatively identical objects a HEAP if hit has 100 or more elements, and a NON-HEAP if it has fewer than 100 elements." — god must be atheist
But what about the big picture, a poll of judgements, or of individual thresholds? What if the tail end of such a distribution (of thresholds) reaches back to a single grain? From your observations about means, we guess that it will.
Then, for some enthusiasts at least, this play of the game is over. From their point of view, you won't play. You decline to agree that a single grain is absolutely not a heap. You admit that this grain is, in the current idiom, "on the spectrum" of (usage of) heap. Albeit at one far end of that spectrum. You've lost one of the two required (and puzzlingly opposed) intuitions that we are trying to reconcile. — bongo fury
When we look at paradoxes, the usual reason for them is that we have the premises wrong. Just as here, where we make the totally incorrect and false presumption that everything could be reduced to being measured by a common measure, notably with natural numbers. — ssu
When does a beautiful girl stop being beautiful and become 'OK looking' or 'ordinary' or even be outright 'ugly'? If you cannot draw a specific line, then is the notion of being beautiful in peril?What other method would you choose to describe how a heap of sand stops being a heap? Isn't it the number of sand grains in a collection that determines the heap-ness? — TheMadFool
No.Isn't it the number of sand grains in a collection that determines the heap-ness? — TheMadFool
That's how you just get to the paradox: you are insisting that an exact number of sand grains determines what a heap of sand is. — ssu
You aren't getting the point. The measurement system of heap of x < mountain of x isn't straight forward calculus as you cannot answer exactly how much bigger is a mountain of sand compared to a heap of sand. Hence you cannot add them up together and divide them into two, because you are using the number system. In order to talk about mathematical functions, you do need the number system and arithmetic to calculate functions. With heaps it isn't so!Well, to insist we must. - . If there are two points on a function... — god must be atheist
In order to talk about mathematical functions, you do need the number system and arithmetic to calculate functions. With heaps it isn't so! — ssu
So your correlation 2 goes totally against the definition — ssu
And very often (any slippery slope ethical dilemma, any artistic play with discrete perceptual categories, e.g. musical pitches), you want to work with the usage as it is, not precisified — bongo fury
And for this you need arithmetic to apply and there needs to be a number system.That's the beauty in Calculus. You can describe incredibly complex relationships without using numbers, or many numbers. — god must be atheist
Actually, it really doesn't genuinely apply.IN this case, the fundamental law of Calculus applies, but it yields a (possibly) different value of number of sand from human to human. — god must be atheist
This again is a fallacy here, because you simply deny the existence of incommensurability. Think about it: if you have a heap of sand and a mountain of sand, what then is the middle, really? It would be something like "an amount more than a heap and less than a mountain". Is that useful? Likely not, and still you don't have any idea when a heap turns into 'more than a heap and less than a mountain'. The laws you refer to don't really solve the issue at all.In fact, the first fundamental law of Calculus only uses 2 to find the midpoint between two values. But it does not go beyond that in any more ways of using numbers. — god must be atheist
Not sure I understand. — bongo fury
correlation 2: an arbitrary individual threshold... a policy with some good PR (e.g. "you have to draw the line somewhere, and that's that"), but which will inevitably deprive the usage of its useful fuzziness / tolerance — bongo fury
) Hooray if, for example, you want to resist this correlation because you have a sense of clarity or absolutism about certain cases of heap and of non-heap, and a sense that the same clarity will transmit from these cases to certain others. — bongo fury
If you [ssu] are against either (I meant both) of these reductions, then hooray. If your talk of "incommensurability" isn't, after all, about trying to separate usage of heap from the naturals, then even better. — bongo fury
"You have to draw the line somewhere" is itself the problem. — ssu
Hooray if, for example, you want to resist this correlation because you have a sense of clarity or absolutism about certain cases of heap and of non-heap, and a sense that the same clarity will transmit from these cases to certain others.
— bongo fury
The issue won't transmit so easily, because notice the definition of incommensurability: two or more quantities having no common measure. — ssu
4) So in which natural number are you in the end...exactly? — ssu
Yet "somewhat large" or "a small number" is quite practical sometimes — ssu
assuming there is an universal agreement just what the range is. — ssu
If people get puzzled with the Sorites paradox, then yes.you think usage of heap should be kept separate from the naturals. — bongo fury
Oh it's not me, it's the logic in mathematics. You see a crude counting system, like "nothing, 1,2,3, many" is logical in it's own way, if one hasn't the need to count things more than up to three. For some animal it can be a splendid counting system: why would they need to count to several thousands? And so is with "heap of x" versus "mountain of x" as a simple scale system.You are so appalled by inappropriate reductions of systems to arithmetic that you won't hear of any such intermingling. — bongo fury
Tacit agreement is the word.The challenge of the heap game is to describe the fuzzy/tolerant bounds of this tacitly agreed range. — bongo fury
This again is a fallacy here, because you simply deny the existence of incommensurability. — ssu
This again is a fallacy here, because you simply deny the existence of incommensurability. Think about it: if you have a heap of sand and a mountain of sand, what then is the middle, really? It would be something like "an amount more than a heap and less than a mountain". Is that useful? Likely not, and still you don't have any idea when a heap turns into 'more than a heap and less than a mountain'. The laws you refer to don't really solve the issue at all. — ssu
It's as wrong as to try to put infinity, as a number, or an infinitesimal, as a number, on the number line. You simply cannot do it. And thus people don't regard either as numbers. Yet both are extremely useful in mathematics, so there isn't anything wrong with them. — ssu
The issue won't transmit so easily, because notice the definition of incommensurability: two or more quantities having no common measure. — ssu
"You have to draw the line somewhere" is itself the problem. When you don't have a common measure, just how are you going to draw the line somewhere? You simply need that common measure to draw the line somewhere. This is similar to ↪god must be atheist where just assumes Calculus, but forgets what it means not having a common measure — ssu
I think we're approaching some kind of agreement. — ssu
Isn't it the number of sand grains in a collection that determines the heap-ness?
— TheMadFool
No. That's how you just get to the paradox: you are insisting that an exact number of sand grains determines what a heap of sand is. — ssu
The problem is simply to assume that you can do it, and that you get an exact answer. — ssu
So basically your argument is the vagueness of the language.What we (I, and TheMadFool if I'm not wrong) are admitting is that usage of many vague labels like heap relates to numbers without difficulty in some cases, e.g. a single grain, and the problem is to describe the fuzzy border further along. — bongo fury
Ok, it's seems you didn't get my point, because I don't find anything close to my reasoning in this.Your passion against settling for an arbitrary sharp border, which we applaud, stops you from admitting this, and from appreciating that a vague category usually correlates in this puzzling way with some or other more fine-grained (often continuous) series. — bongo fury
Ok, it's seems you didn't get my point — ssu
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