Cheers. Jenny and John in the example are not in a disagreement about what is the case, but as to how to appropriately use the word "heap". As was said...

It's a choice we've made based on the kinds of things we want to say. It doesn't necessarily correspond to some natural boundary. — T Clark

Well, no, there is no paradox. — Banno

If only.

An excess of precision impairs our actions.

And precision is available, as required. — Banno

Likewise,

Why is linguistic imprecision a problem? "Heap" trades referential precision for flexibility, whilst retaining the necessary semantics for useful, albeit less precise communication. — sime

However,

obviously it's a puzzle if we accept also the premise that calling a single grain a heap is absurd. If calling it a heap is tolerable then, as I keep saying, no puzzle.

[1] Tell me, do you think that a single grain of wheat is a heap?
[2] Well, certainly, it's the very smallest size of heap.

Game over. — bongo fury

But,

The interesting (and paradoxical) thing is that the clarity is so easily achieved, by choosing obvious counter-examples. Which is what the sorites puzzle reminds us of. Occasionally. When it pumps absolutist zeal, so that the game gets started:

[1] Tell me, do you think that a single grain of wheat is a heap?
[2] No of course not, and I know I'm a long way from the smallest number of grains that could possibly be the smallest heap! Far enough that a single grain is an obvious case of a non-heap!

Of course, later on, the same player may feel differently...

[1] Tell me, do you think that a single grain of wheat is a heap?
[2] Well, certainly, it's the very smallest size of heap.

Game over. People often finish up claiming 2 had been their position all along. Perhaps it should have been, and the puzzle is a fraud. — bongo fury

The puzzle is how to avoid arriving at that position [assuming we are indeed determined not to], without denying the validity of any one step along the way. — bongo fury

what can one say about this problem of the valence of what a "heap" actually is. — Shawn

According to me, and contra epistemicism, that it's a voting matter: but not a free vote. So there are three cases: unanimously and obviously a non-heap (e.g. a single grain, otherwise you aren't a semantically competent speaker), controversially a heap, and unanimously a heap (e.g. a million grains). Of course, you may want to throw that back at me, and restart the puzzle:

[1] Tell me, do you think that a single grain of wheat is even vote-ably a heap?

I would hope so.

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

It's fallible, because it needs two opposing intuitions.

Where it leads me is here, if you're interested.

Well, yes; but, the paradox is still pertinent. — Shawn

There's only a "paradox" if you insist on the truth of contradictory premises, such as:

P1. objects have a set of attributes that are necessary to their identity (essentialism)
P2. no specific number of items is necessary for a collection of items to be a heap
P3. heaps exist

The "solution" is to reject one of the premises. I reject the first. Essentialism isn't the case.

There's only a "paradox" if you insist on the truth of contradictory premises — Michael

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.

But of course you are able to use the word "heap" effectively, not despite it's imprecision, but in virtue of its imprecision.

Compare "throw yours on the heap" to "add your twenty-seven to that four thousand, two hundred and seventy three".

An excess of precision impairs our actions.

And precision is available, as required. — Banno

:up:

But...

Is it possible that vagueness is an illusion?

Take the heap/sorites paradox. The heap-ness has nothing at all to do with the sand grains individually but what it actually is is the shape (roughly conical). So when you remove grains of sand but the shape doesn't change, you can't claim the word "heap" is vague. The shape of a sand heap is at best, an imperfect function of the number of sand grains or at worst, has no correlation with the number of sand grains. Even when sand grains are removed the shape is maintained, the word "heap" applies to the shape and not the number of sand grains.

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

There's no contradiction or paradox there. There is, however, perhaps implicit in the argument that to become a heap there must be a point at which adding a single grain "turns it into" a heap, but that would be essentialism which ought be rejected.

There are good piano players and bad piano players, but you can't look at someone's progress from bad piano player to good piano player and point to a specific instant where they "became" good.

And there's no specific generation where a proto-human gave birth to a human. Would you say that there's a paradox of speciation?

I wonder why the focus is on grains of sand anyway. Four grains of sand might not make a heap, but four pillows might, depending on how they're arranged. Perhaps it's more about topology than number of parts.

There's no contradiction or paradox there. — Michael

I don't understand. Are you saying they are, all 3, compatible, as they stand and appear to signify?

There is, however, perhaps implicit in the argument that to become a heap there must be a point at which adding a single grain "turns it into" a heap, but that would be essentialism which ought be rejected. — Michael

Garbled? What are you saying might perhaps be implicit in what?

There are good piano players and bad piano players, but you can't look at someone's progress from bad piano player to good piano player and point to a specific instant where they "became" good. — Michael

Yes, this is the paradox? If parsed into a plausible set of premises, and subjected to logical iteration? You are familiar with how this is generally done?

I don't understand. Are you saying they are, all 3, compatible, as they stand and appear to signify? — bongo fury

Yes.

Garbled? What are you saying might perhaps be implicit in what?

The implicit premise is "if P1) a single grain is clearly not a heap and P2) adding a single grain can never turn a non-heap into a heap then C) heaps can't exist". Only then does the premise "P3) heaps exist" create a contradiction.

However this implicit (essentialist) premise is false. The existence of heaps does do not depend on there being a specific number of grains that qualifies a collection as a heap.

Yes, this is the paradox? If parsed into a plausible set of premises, and subjected to logical iteration? You are familiar with how this is generally done?

It's not a paradox because one of the premises is false, namely the essentialist premise that there is a set of (mutually exclusive) necessary and sufficient conditions that qualifies a player as either good or bad.

The implicit premise is "if P1) a single grain is clearly not a heap and P2) adding a single grain can never turn a non-heap into a heap then C) heaps can't exist". — Michael

No, that's implicit logic. Requiring iteration of the usual, implied, kind. "Step by step". Grain by grain. Or recursion. But not another premise.

However this implicit (essentialist) premise is false. The existence of heaps does not depend on there being a specific number of grains that qualifies a collection as a heap. — Michael

That's not what you just called an implicit premise. And all it amounts to is incredulity at the conjunction of the premises with C. (= P3.) Fine. That's what people are generally content to call paradox. A worthy game. A demonstration that apparently innocuous premises are incompatible and need reform.

You have a hunch that my P2 hides essentialist dogma. Fine. Perhaps that enables you to suggest a suitable reform? "Nothing to see here folks" is less interesting.

And there's no specific generation where a proto-human gave birth to a human. Would you say that there's a paradox of speciation? — Michael

Another good example.

And another.

"Nothing to see here folks" is less interesting. — bongo fury

Less interesting, but correct. Essentialism is false. There isn't a set of (mutually exclusive) necessary and sufficient conditions that qualifies a piano player as either good or bad. Words don't always capture some clearly defined feature of the world. Language is messy. It's often vague and ambiguous. This doesn't show some paradox about the metaphysics of identity or whatever it is things like the Sorites paradox try to show. A language that doesn't have a word comparable to "heap" doesn't fail to refer to some "real" identity inherent in a number of grains of sand in close proximity.

The Sorites paradox is a paradox, because one can reason from some prima-facie plausible premises to a contradiction. It's just a not a very stubborn paradox, and, correctly understood (and here I agree with Banno), leads to the important idea of vague predicates. And these resolve the paradox. Some paradoxes are tougher than others.

Where I don't agree with Banno is that all predicates are like this. Nor do I agree all philosophical problems can be solved this way. Some putative examples of non-vague terms (there aren't many, at least outside maths perhaps): less than seven, spatial, conscious.

Requests for definitional clarity are sometimes unreasonable, but sometimes they are reasonable. It depends on the context. Banno's position is extreme and dogmatic. Definitions are not all essentialist - Banno himself showed this.

Less interesting, but correct. — Michael

Yes. Lazy. Assuming straw men.

This doesn't show some paradox about the metaphysics of identity or whatever — Michael

What, like essentialism? Who brought that up?

A language that doesn't have a word comparable to "heap" doesn't "fail" to refer to some "real" identity inherent in — Michael

Enough metaphysics! Solve the puzzle.

Enough metaphysics! Solve the puzzle. — bongo fury

There is no puzzle. There are times when we call a collection of sand grains a heap and there are times when we don't, but there is no clearly defined rule that prescribes exactly when we should call a collection of sand grains a heap and when we shouldn't, determined by how many grains of sand there are. And "being a heap" isn't some independent identity that a collection of sand grains has, determined by how many grains of sand there are, that we either succeed or fail to refer to in using or not using the word "heap" to talk about it. This essentialist interpretation of language is wrong.

There is no puzzle. — Michael

obviously it's a puzzle if we accept also the premise that calling a single grain a heap is absurd. If calling it a heap is tolerable then, as I keep saying, no puzzle.

[1] Tell me, do you think that a single grain of wheat is a heap?
[2] Well, certainly, it's the very smallest size of heap.

Game over. — bongo fury

Take the heap/sorites paradox. The heap-ness has nothing at all to do with the sand grains individually but what it actually is is the shape (roughly conical). — TheMadFool

I don't think there is any good reason to fiddle around with "heap" to make it more precise, but if there were, this would be a good way of going about it.

There's no contradiction or paradox there. There is, however, perhaps implicit in the argument that to become a heap there must be a point at which adding a single grain "turns it into" a heap, but that would be essentialism which ought be rejected. — Michael

If we cared enough, which we don't, we could set up a method for determining the meaning of "heap" the same way they measure the toxicity of a substance. LD(lethal dose)50 is the amount of the substance that will kill a rat in 50% of cases. So we could have HD("heap" definition)50, the point at which 50% of a group of people would define a bunch of sand as a heap. Or we could spend our time polishing the silver, which would be more productive.

adding a single grain can never turn a non-heap into a heap then — Michael

Following the Clark method, developed by philosopher T Clark in 2021, there would be a way to determine when a single grain turns a non-heap into a heap.

Definitions are not all essentialist - Banno himself showed this. — bert1

This is what Wikipedia says about "essentialism."

Essentialism is the view that objects have a set of attributes that are necessary to their identity.[1] In early Western thought, Plato's idealism held that all things have such an "essence"—an "idea" or "form". In Categories, Aristotle similarly proposed that all objects have a substance that, as George Lakoff put it, "make the thing what it is, and without which it would be not that kind of thing".[2] The contrary view—non-essentialism—denies the need to posit such an "essence'".

When you identify a definition as "essentialist," do you mean that the definition corresponds to a natural boundary inherent in the phenomenon and not established by human consensus? If so, I, and I think @Banno and @Michael, don't believe any phenomenon has an essentialist definition.

Banno's position is extreme and dogmatic. — bert1

I don't agree.

unanimously a heap (e.g. a million grains). — bongo fury

A bunch of sand with a million grains, or a trillion or a quadrillion, would not be a heap if they were spread out on a surface a single grain thick. It's not just number, the configuration is also important.

When you identify a definition as "essentialist," do you mean that the definition corresponds to a natural boundary inherent in the phenomenon and not established by human consensus? — T Clark

I was trying to follow the usage in this thread, esp. from Michael. So I guess I'm thinking of something like the definition of 'bachelor' as that of an unmarried man. These are severally necessary and jointly sufficient for object X to be a bachelor. Is that a form of essentialism? Have I got this wrong? The essence of a bachelor is that it is unmarried and a man. Heaps, on the other hand, don't seem to have an essence. And if they do, it's a vague one.

I think this is different from the concept of vagueness though, although the two ideas probably track each other somewhat, I'm not sure. Have to think about it. So even 'bachelor' could be vague, as at precisely what point does someone go from being unmarried to married? "I pronounce you man and wife", but then exactly when did the word 'wife' finish being uttered? When the registrar's lungs stopped contracting? Or when the sound wave battered the eardrums of the couple? Or what? So vagueness/non vague is a different concept pair from essentialist/non-essentialist. But I've only just started thinking about it so I may have misunderstood something.

Have I got this wrong? — bert1

I wasn't questioning your usage, I just wanted to make sure I understood.

So even 'bachelor' could be vague, as at precisely what point does someone go from being unmarried to married? — bert1

In the good old days, it was after the marriage had been "consummated." Wink, wink, nudge, nudge, say no more, say no more.

Banno's position is extreme and dogmatic.
— bert1

I don't agree. — T Clark

The reason I'm having a somewhat random whack at Banno is because his views on language and definitions prevent him talking about things that I and many others want to talk about, for example, my philosophical interest, consciousness. However it doesn't stop him writing posts anyway and messing up threads. I've tried to get him to talk about consciousness, but he insists on talking about consciousness. I tell him to shut the fuck up and stay on topic. And he says he is on topic.

I don't think there is any good reason to fiddle around with "heap" to make it more precise, but if there were, this would be a good way of going about it. — T Clark

Another issue with the heap paradox, taking the example fat, seems to hinge on the distinction subjectivity-objectivity.

At one end (thin) - grey zone (thin/fat aka borderline cases) - at the other end (fat)

Thin and fat, at opposite ends pose no issue but the grey zone is a logical nightmare. Imagine I see Mr. P and to me he's fat. You see Mr. P and he's thin to you. Now, vagueness treats both yours and my judgment as legit. That means P is both fat AND P is thin. This is a contradiction which only rears its ugly head when we consider vagueness as factual, a part of reality as it were.

One way out of it is to ask the obvious question, "is P really thin/fat?" The question immediately makes vagueness subjective - disagreement (contradiction) tolerated - and thin/fat objective concepts - disagreement (contradiction) prohibited.

As you can see, vagueness is now subjective. There's another kind of phenomenon that's subjective, hallucinations. Vagueness is an illusion.

obviously it's a puzzle if we accept also the premise that calling a single grain a heap is absurd. If calling it a heap is tolerable then, as I keep saying, no puzzle.

[1] Tell me, do you think that a single grain of wheat is a heap?
[2] Well, certainly, it's the very smallest size of heap.

Game over. — bongo fury

The latter way of avoiding play is to reject

P1. a single grain is clearly not a heap — bongo fury

For better or worse. No reform, just bite the bullet of the contrary premise, "everything is a spectrum".

From this point of view, the converse way of avoiding play is to baldly reject, and bite the bullet which is contrary to,

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

Obviously there is a puzzle if we accept P2 (in addition to P1). Whereas, if such a sudden transition is not absurd but tolerable, then, as I would in that case very likely keep saying, no puzzle.

[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?
[2] Well, certainly it could, it's just that, for somewhat technical reasons, we can probably never discover which grain that is.

This second way of spoiling the game at the outset is what the OP is (I expect) referring to as 'epistemicism'. Just thought I'd sketch (or caricature) it out.

Although language is a human construct, — Nigel Warburton, aeon article

So far so reasonable...

that does not make it transparent to us. — Nigel Warburton, aeon article

Well yeah but that surely doesn't mean there's anything definite there, for us to see or fail to see, does it?

Like the children we make, the meanings we make can have secrets from us. — Nigel Warburton, aeon article

Woah. What just happened. Provocation? Fair enough then. Nice.

You are misusing bivalence. — Banno

This is clearly defined in the SEP entry to be an issue of bivalence for epistemic criteria for what constitutes a heap.

https://plato.stanford.edu/entries/sorites-paradox/#EpisTheo

Here's from the SEP entry, which I've been concerned about as to what a heap constitutes:

Another possible route to knowledge of the boundary locations is blocked by the fact that our knowledge of the application of a vague term is inexact. Inexact knowledge is governed by margin for error principles, viz., principles of the form ‘If x and y differ incrementally on a decisive dimension and x is known to be Φ (old, blue, etc.), then y is Φ’.[2] For example, where knowledge is inexact, we can know of a blue object that it is blue only if objects whose colors are incrementally different are blue as well—hence, only in clear cases. In contrast, in the borderline or “penumbral” region of a sorites series for ‘blue’, where the boundary lives, some shade of blue is only incrementally different from, indeed may look the same as, a shade that is not blue; and we cannot know where this difference lies. Consequently, if we classify the former shade as blue, that classification is correct by luck, and so does not constitute knowledge. (On the plausible assumption that seeing that something x is blue is sufficient for knowing that x is blue, it follows that some blue things are such that we cannot see that they are blue, even under ideal viewing conditions.)

The virtues and the appeal of the epistemic theory are significant, and it has earned its share of supporters. At the same time, the view may be hard to accept. Even its proponents grant that epistemicism is intuitively implausible; and it seems to multiply mysteries. As a first approximation, the epistemicist says that

vague terms have unknowable sharp boundaries that are fixed by an unknown function of their unknowable (i.e., not fully knowable) patterns of use. — SEP

There's only a "paradox" if you insist on the truth of contradictory premises, such as:

P1. objects have a set of attributes that are necessary to their identity (essentialism)
P2. no specific number of items is necessary for a collection of items to be a heap
P3. heaps exist

The "solution" is to reject one of the premises. I reject the first. Essentialism isn't the case. — Michael

It isn't so much a attribute, but, an issue of vagueness. I'm not sure if you follow that line of reasoning or care to.

And, anticipating Banno, I don't think language itself solves the issue. It seems corollary to saying that tall isn't vague because we can use it a certain way to precise its meaning.

The reason I'm having a somewhat random whack at Banno is because his views on language and definitions prevent him talking about things that I and many others want to talk about, — bert1

Yes, our friend Banno can be a pain in the ass. I have no objections to you giving him a hard time, it's certainly something he likes to do to others. I think it comes from eating all those didgeridoos and billabongs.

Be that as it may, I don't think his position in this matter is dogmatic.

It seems appropriate to reply to several folk with the one post...


But why shouldn't we use terms that are imprecise? Indeed, demonstrably, we do, and unproblematically, except for a few folk who contrive problems for themselves and others...

It's not difficult to think up situations in which it make sense to talk of piles of one or even zero things. Despite this the notion of a pile remains useful. Indeed, that usefulness comes in part because of, not despite, that inherent vagueness.

[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?
[2] Well, certainly it could, it's just that, for somewhat technical reasons, we can probably never discover which grain that is. — bongo fury

Again, the problem here is in your misusing the notion of a pile, of treating it as if it were precise when it isn't. This is an important example, showing how misuse of a term - taking it into places for which it was never meant - brings about philosophical bedazzlement. This isn't the only philosophical quandary that has its source in misuse.

Where I don't agree with Banno is that all predicates are like this. Nor do I agree all philosophical problems can be solved this way. Some putative examples of non-vague terms (there aren't many, at least outside maths perhaps): less than seven, spatial, conscious. — bert1

Well, perhaps not all; very many are, though. Identifying the ones that aren't - now that's an interesting task.

When you identify a definition as "essentialist," do you mean that the definition corresponds to a natural boundary inherent in the phenomenon and not established by human consensus? If so, I, and I think Banno and @Michael, don't believe any phenomenon has an essentialist definition. — T Clark

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.

The reason I'm having a somewhat random whack at Banno is because his views on language and definitions prevent him talking about things that I and many others want to talk about, for example, my philosophical interest, consciousness. However it doesn't stop him writing posts anyway and messing up threads. I've tried to get him to talk about consciousness, but he insists on talking about consciousness. I tell him to shut the fuck up and stay on topic. And he says he is on topic. — bert1

I'm flattered. Thank you.

Yes, our friend Banno can be a pain in the ass. I have no objections to you giving him a hard time, it's certainly something he likes to do to others. — T Clark

It's arse, you donkey. And I have no objection to folk giving me a hard time, either - it happens all to rarely. There should be more of it.

But neat that you relate this to the Problem of the Criterion; there's a similar unjustified expectation of exactitude in what one counts as knowledge, or as true. We don't need a definitive understanding of knowledge in order to establish that we know this thread is in English. — Banno

I would agree that a rigorous definition or rejection of one has no bearing on the use of know in this context. I'd also note that people don't tell each other they know obvious things. So, using the language "in use" as representing knowledge is at least as obtuse as expecting the term true to hold a binary meaning.