But why shouldn't we use terms that are imprecise? — Banno

I already replied to this.

The interesting (and paradoxical) thing is that the clarity is so easily achieved, — bongo fury

It's obvious you only skim, all the time. Never mind.

A heap denotes a number of things. It reflects the import of the resource in question. You never have a heap of donor kidneys.

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

You and I agree on this, but what gives me pause is that some divisions do seem more "natural" than others. A bunch of sand may or may not be a heap, but that spherical object hanging on that apple tree over there is definitely an apple. A tree is pretty much a tree even if a bunch of trees may or may not be a forest, copse, woodlot, woods, grove, or stand.

Out of respect for the victims of some disaster? Ok. But not for any reason relevant to the puzzle.

A heap denotes a number of things. — Cheshire

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.

Out of respect for the victims of some disaster? Ok. But not for any reason relevant to the puzzle. — bongo fury

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.

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

People are instructed on how to define something they intuitively understand?

I already replied to this. — bongo fury

But not in an interesting way. To do that, you would have to give a reason for preferring exactitude, where no such reason is needed.

...what gives me pause is that some divisions do seem more "natural" than others. — T Clark

I agree; that is, I agree as to the seeming. But 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.

But what is stopping us?

A heap denotes a number of things. It reflects the import of the resource in question. You never have a heap of donor kidneys. — Cheshire

Yes... and the collective pronoun is a paucity of donor kidneys.

Would you want one offered out of a heap?

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 words have their criteria of application like an element might have an atomic number. We look at it closely enough, and we determine exactly what it is.

But what determines whether a word is applicable in a certain case? There is no fact about this independent to its being used to apply to various cases. Therefore we do not first have the word with a well-defined applicability criterion, and then people using it correctly or incorrectly according to that criterion. Rather, we have people using the word for certain cases, and in virtue of this, we say that its use is correct or incorrect insofar as it conforms with those prior cases (subject to semantic drift over time).

If it is the use of the term that gives it its applicability, where its use has no perfect standard, neither will its applicability. You've got it backwards – that we don't use heap in an exact way is the datum, the 'fact of life,' not that which emerges as a problem from the assumption that all terms have an exact application (false).

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.

Now maybe this strikes you as puzzling because it seems that one would not be able to find a great criterion for which grain ought to cause the shift. But that's the point – where we have to make a decision about how to apply the term (and often we will not, and just shrug instead), and we're free to do so at arbitrary levels of precision if we so please. Of course, as we get away from the borderline cases, our arbitrary decision will become less and less defensible in the linguistic community, as we move farther and farther away from standard usage. But in the gray area, people will be tolerant with us, and allow us a fairly large range of such decisions, if there ever is the need to make them.

Of course, we seldom have to decide a boundary of one grain at which a heap becomes not a heap. Where we do have to decide (let's say, for some reason, we're buying a quantity of sand, and a 'heap' costs so much), then we actually are free to agree on arbitrary levels of precision down to the grain in the use of the term, if we want to. Hence, Premise 2 fails.

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'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.

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 agree, but I don't think "familiarity" is the right word. I think it's something more deep-seated. I think that's the reason it's a tougher argument to make - seeing reality as a collection of objects is natural for us. Seeing it as a continuum with fluid boundary distinctions isn't.

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

This is the killer though. @Banno waves this off as a problem with a philosopher's psychology, but it is so tied to how we think I take the resolution as an analytical problem. The desire you are trying to see with is creating your picture of the concept. Emerson and Heidegger both have the image of closing our (human) hand and everything spilling out. We grasp with the criteria of certainty, specificity, universality, and we end up without the essence of what a heap is, its gist--this is not ontological or correlative or definitional--it is what matters to us about heaps and the judgments we make about them, etc., our lives with heaps. This need is crystallized with Logical Positivism, which excluded everything vague and uncertain. So Wittgenstein's Philosophical Investigations is the obvious guide out of these woods. His term Concept, like, say, "game", is pulled and pushed to show how our lives are measured in more ways than a simple theory would like. He discusses "vague" at #71, starting "One might say that the concept 'game' is a concept with blurred edges." and to ask "Isn't the indistinct [picture] often exactly what we need?" and also "is it senseless to say: 'Stand roughly there?'" Or at #98 "Where there is sense there must be perfect order--so there must be perfect order even in the vaguest sentence." Now this isn't to say there aren't mistakes, misuses, laziness, etc. but the point is laid out in #101 "We want to say there can't be any vagueness in logic. The idea absorbs us, that the ideal must be found in reality." The cart is before the horse; the game is rigged before the thought problem, say, of criterion, is even set up. But this is a classic philosophical hand-wringer. There is confusion, miscommunication, and lack of agreement, and philosophy blames common language and sets out to correct it or clarify or qualify, but our ordinary criteria (for heaps, games, vagueness) is the most connected to our actual lives.

"Guard this heap with your life"; seems silly — Cheshire

Really? A heap of diamonds? Or (in bad taste but logical enough) of donor kidneys? Are they not suitable for the order?

People are instructed on how to define something they intuitively understand? — Cheshire

Challenged at least to either reject or reform at least one of three intuitively acceptable but evidently incompatible premises, or else the standard logic by which they may be combined.

Yes... and the collective pronoun is a paucity of donor kidneys. — Tom Storm

Thank you, with your permission I'll use 'paucity' along with 'pittance' to expound my antonym-based constructive solution.

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

Proposed solution here.

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, yes.

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

I.e. can you play the game, or is it beneath you? Ah good:

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

Absolutely. However,

The delightful thing about the sorites is that it can spring up again from the rubble... — Bongo Fury

Or

sorites reasoning, [...] like a virus, will tend to evolve a resistant strain. — R.M. Sainsbury, Concepts without boundaries

E.g.

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

I.e.

[1] Tell me, do you think that a competent speaker of English can ever call a particular case of a single grain a heap?

Which might or might not get traction. I for one am inclined to reply,

[2] No, I think that any single grain is far enough away from being a heap in ordinary language as to make it an obvious case of a non-heap, for any competent speaker.

But if you, on the other hand, prefer

[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.

... then of course, game over.

We might agree, in passing, that your rejection of P2 has not, as an epistemicist's might well have done, survived into the new round of the game. You have ditched P1, after all. A single grain is a minimal heap. Black is minimally white. Etc.

P2. adding a single grain can never turn a non-heap into a heap — bongo fury

Adding a single grain at a rate of grains/time is the only thing that can turn a non-heap into a heap.

Ok. And does assuming a rate of flow perhaps render the tipping point unknowable, as per epistemicism?

Or does it imply a range of possible tipping points, and hence a restart of the game as just described?

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, but rather the method of transformation. Which is clearly the addition of material at some rate if the material is accounted for by single units. The philosopher is asking for an answer to a question that isn't being asked.

The question doesn't ask for a tipping point, — Cheshire

Which question? Player 1's second line here?

[1] Tell me, do you think that a single grain of wheat is a heap?
[2] No, absolutely not.
[1] And tell me, do you think that adding a single grain could ever turn a non-heap into a heap?

This question clearly enough signals that the next one may be "which grain?", although a popular version of the game proceeds grain by grain, with the same result, i.e. that you need to be able to answer the question of which grain.

but rather the method of transformation. — Cheshire

Which question asks such a thing?

Which question asks such a thing? — bongo fury

P3. heaps exist

It concludes heaps exist. I accounted for the existence of heaps by showing the second premise is false. It's only the addition of a single grain at some rate that turns a non-heap into a heap. It's asking how not when.

It's asking how not when. — Cheshire

Well, if by 'it' you mean player 1's second line, then yes, ok, the 'signal' of a subsequent question perhaps isn't as strong as all that.

You can say that you think it must happen at some point (some grain) but you aren't prepared to say which.

(P3, though?? It hasn't even been put as a question as yet.)

In that case, are you with the epistemicist in supposing an unknowable answer to the numerical question?

I suspect not, and that you imagine it happening at different points (grain numbers) on different occasions of flow. But then you can't blame me for wondering,

[1] Tell me, do you think that a single grain of wheat ever amounts to a heap, for any rate of flow?

I.e. whether you have any respect for P1. Or are, like many people, of the opinion that black is minimally white, off is minimally on, etc.

Interesting.

[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

Definition of "heap" - a disorderly collection of objects placed haphazardly on top of each other.

Definition of "collection" - a group of things or people.

Definition of "group" - a number of people or things that are located close together or are considered or classed together.

Definition of "number" - several.

Definition of "several" - ....

I guess it's turtles all the way down.

[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. The same criteria could produce a lower and upper bound. But, none of this addresses a paradox.

If premise 3 is true it implies criteria for a heap exists. — Cheshire

You lost me. What exactly do we need to agree is implied by

P3. heaps exist — bongo fury

?

I take it to mean, simply, that there are some heaps.

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.

But, none of this addresses a paradox. — Cheshire

The puzzle, it should be clear, is how to reach P3, or avoid denying it, while accepting both P1 and P2.

The puzzle, it should be clear, is how to reach P3, or avoid denying it, while accepting both P1 and P2. — bongo fury

Ok, I didn't realize this was the format. I'll keep it in mind.

You lost me. What exactly do we need to agree is implied by P3. heaps exist — bongo fury — 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.

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

Alright, then grain 1,000,000,000 makes a heap. Where do I send the invoice?

Ok, I didn't realize this was the format. — Cheshire

Of course it could just as easily start from P2 and P3, asking how you can possibly go bald one hair at a time, etc.

If you tell me heaps exist then you can prove the existence of a heap through some criteria. — Cheshire

I wasn't trying to prove anything. Only to look for examples we can agree on. I don't see the relevance of criteria. Unless you want to say, being a billion grain collection is a criterion, or a sufficient condition. Fine. Bring it on board. How does it help?

Where do I send the invoice? — Cheshire

Reminds me of when my bank operated a no-charge policy for "small" overdrafts...

Absolutely. — bongo fury

Then we're done, aren't we?

Behind you!!