But why shouldn't we use terms that are imprecise? — Banno
The interesting (and paradoxical) thing is that the clarity is so easily achieved, — bongo fury
I do indeed venture that there are no natural boundaries; that like simples, boundaries are not found but inflicted on the world. The point being that no matter how we divide stuff up, we might have done otherwise. I'd be more than happy to consider counter instances, should you have any at hand. — Banno
A heap denotes a number of things. — Cheshire
Perhaps, but I was thinking the time sensitive value they had to each person that might need one. Like the phrase "Guard this heap with your life"; seems silly and I'm suggesting for a reason that reflects a universal subtext. I've been wrong before though.Out of respect for the victims of some disaster? Ok. But not for any reason relevant to the puzzle. — bongo fury
People are instructed on how to define something they intuitively understand?It has distinguishable senses, like all sorts of words. The puzzle as usually conducted inspires (often) recognition of a sense agreed for the game. With clear examples and counter-examples, and an implication of some kind of boundary. What kind being the puzzle. — bongo fury
I already replied to this. — bongo fury
...what gives me pause is that some divisions do seem more "natural" than others. — T Clark
I'm thinking we use it in a more exact way than we realize. The assumption the exactness is a number seems like the mistake. A heap is usually a large enough amount that having it gathered together is the plausible driving force behind its accumulation in an area. It implies a supply that will be broken down.If it is the use of the term that gives it its applicability, where its use has no perfect standard, neither will its applicability. — Snakes Alive
I think it must be just an artefact of familiarity. That is, we've been treating the apple and the tree as distinct for so long that it doesn't seem we could do otherwise. — Banno
I'm not trying to look at this through a lens of preciseness only. I think, it also seems to me to be an issue about inherent vagueness in language — Shawn
"Guard this heap with your life"; seems silly — Cheshire
People are instructed on how to define something they intuitively understand? — Cheshire
Yes... and the collective pronoun is a paucity of donor kidneys. — Tom Storm
Bald and hairy, black and white, on and off, heap and whatever its potential antonym (pittance?)... they all operate perfectly well as alphabets (or conceptual schemes) of two characters (concepts) separated by a comfortable no-mans-land. The puzzle is how to look closely at that without it reverting [...] to a mere spectrum. — bongo fury
The demand that there be an exact criterion determining what is or is not a heap comes from a mistaken metasemantics – the assumption is that ... — Snakes Alive
Yes, but the premises, that we are obliged to reject or reform at least one of, are, rather:
P1. a single grain is clearly not a heap
P2. adding a single grain can never turn a non-heap into a heap
P3. heaps exist
Please clarify which, or how. — bongo fury
As to the Sorities Paradox, it is Premise 2 that is false – one is often at liberty to say that the addition of a single grain creates a heap where there was none before. — Snakes Alive
The delightful thing about the sorites is that it can spring up again from the rubble... — Bongo Fury
sorites reasoning, [...] like a virus, will tend to evolve a resistant strain. — R.M. Sainsbury, Concepts without boundaries
the semantics which concern the precise moment when an actual heap of sand is considered to be mere grains of sand, isn't linguistically specified a priori but is decided by speakers on a case specific basis.
— sime
Agreed. But what is the smallest number of grains that would need considering by speakers as a particular case? Is it 1? — bongo fury
P2. adding a single grain can never turn a non-heap into a heap — bongo fury
Ok. And does assuming a rate of flow perhaps render the tipping point unknowable, as per url=https://thephilosophyforum.com/discussion/comment/559805]epistemicism[/url]? — bongo fury
The question doesn't ask for a tipping point, — Cheshire
but rather the method of transformation. — Cheshire
P3. heaps existWhich question asks such a thing? — bongo fury
It's asking how not when. — Cheshire
[2] Well, certainly, a single grain is simply the least in a series of cases ordered according to the acceptability of 'heap' as an English descriptor. — bongo fury
If premise 3 is true it implies criteria for a heap exists. The same criteria could produce a lower and upper bound. But, none of this addresses a paradox.[1] Tell me, do you think that a single grain of wheat ever amounts to a heap, for any rate of flow? — bongo fury
If premise 3 is true it implies criteria for a heap exists. — Cheshire
P3. heaps exist — bongo fury
But, none of this addresses a paradox. — Cheshire
Ok, I didn't realize this was the format. I'll keep it in mind.The puzzle, it should be clear, is how to reach P3, or avoid denying it, while accepting both P1 and P2. — bongo fury
If you tell me heaps exist then you can prove the existence of a heap through some criteria. Once I have this criteria I can tell you which grain completes the min. heap.You lost me. What exactly do we need to agree is implied by P3. heaps exist — bongo fury — bongo fury
Alright, then grain 1,000,000,000 makes a heap. Where do I send the invoice?Not that we need to straight away consider examples, but I'd offer, say, any billion-grain collection. Premise 1, on the other hand, does refer to an alleged counter-example. — bongo fury
Ok, I didn't realize this was the format. — Cheshire
If you tell me heaps exist then you can prove the existence of a heap through some criteria. — Cheshire
Where do I send the invoice? — Cheshire
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