Sorry, I don't get the joke you're making. If P2 is false, we're done, presumably? I looked through the rest of your post but couldn't make sense of how it was making a rebuttal (if that's what it was doing).

one is often at liberty to say that the addition of a single grain creates a heap where there was none before. — Snakes Alive

And do I take it that you disagree with the epistemicist position, that if we each recognise said threshold at different places then fewer than two of us will be correct?

Yep. A better way of putting the point I made.

it is Premise 2 that is false — Snakes Alive

Here I disagree, but only in that it is not any one of the premises that is false, but the formulation of the argument. As you wrote in your previous comment:

we don't use heap in an exact way is the datum — Snakes Alive

Hence an argument in which it is assumed there is an exact way of using "heap" is grammatically inept.

Perhaps wants to play the bivalence card again, but again, if John and Jenny disagree as to whether that is a heap, they are not disagreeing as to the truth of a proposition or as to the state of things in the world, but on the use of the word "heap".

Emerson and Heidegger both have the image of closing our (human) hand and everything spilling out. — Antony Nickles

Even as you seem to be closing your hand around an argument only to have it slip out. I don't see in your post anything specific enough to disagree with.

Who is correct is a matter of arbitrary decision in this case, since it is a matter of arbitrary decision wether we choose to apply the word 'heap' or not, and so construe it as correctly applied or not (and something is a heap iff the word 'heap' is correctly applied to it, 'iff' being read as material equivalence).

We might disagree over something's being a heap, even if we know very well what sort of thing it is – but this will not be a disagreement over anything involving, say, the nature of the pile of sand, but rather a disagreement over whether, given that we know what the pile of sand is like, whether the word 'heap' is rightly applicable to it. Who is 'right' or wrong' in these scenarios? It's a matter of adjudicating how to use the words, which may or may not be important.

The epistemicist has the 'atomic number' model of metasemantics, which as I said, is in my view mistaken.

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? — bongo fury

Ok, I didn't realize heaps were an understood matter of consensus. You asked me if a single grain can change a heap to non-heap; rather insisted it couldn't. If your defining heaps by grain number; the only possible context in which your question becomes answerable and therefore implied to be the case, then yes. I can identify that transitional grain. I'm a little lost to what I was supposed to be believing, but it's been a pleasure. Thanks for the feedback.

And do I take it that you disagree with the epistemicist position, that if we each recognise said threshold at different places then fewer than two of us will be correct? — bongo fury

The epistemicist has the 'atomic number' model of metasemantics, — Snakes Alive

Agreed. It's partly because they insist on a distinction between

whether we choose to apply the word 'heap' or not, and so construe it as correctly applied or not — Snakes Alive

and whether the word is correctly applied or not.

The first question suggests a possible poll of personal thresholds likely to exhibit a bell curve when plotting popularity of threshold against grain-number:



Or, roughly equivalently, an 'ogive' or half bell curve rising from next to nothing at a single grain and levelling out to a plateau at about, maybe, who knows, a few thousand. This might represent the distribution of actual applications of the word in ordinary discourse.



Whereas, the second question is envisaged by epistemicism as an underlying fact of the matter, albeit the linguistic matter, such that an appropriate graph would extend horizontally at a height of zero, then step suddenly up to 1 at the correct threshold, and continue horizontally.






Which I think we both reject, but is what is being defended here:

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

Happily, probably everyone agrees with

something is a heap iff the word 'heap' is correctly applied to it, 'iff' being read as material equivalence). — Snakes Alive

The controversy is over whether to distinguish between 'applied' (and so construed as correctly applying) and 'correctly applied'. Whether there are any incorrect applications (and construals).

Now, I wonder if you will approve of any of these suggested clarifications? I should have thought you might have reservations.

I certainly do. Ridiculous as I find the 'hidden step', I think that ordinary usage deserves some kind of recognition of its ability to distinguish between correct and incorrect, in some way that doesn't fizzle out to 'relatively correct'. Usage can sometimes be a matter for negotiation, and adjudication, but sometimes not. We know that anything black is an obvious counter-example to white, and is therefore anything but minimally white, and similarly for off and on, bald and hairy, etc.

Hence my readiness to restart, and invite you to consider an absolutist position on a single grain. E.g.,

[1] Tell me, do you think that whether a single grain can be correctly called a heap in common English is a matter for negotiation or adjudication in context?

I appreciate fully that you may well see no need at all to deny that proposition. (I'll have to bluster that you don't speak English, but never mind!) But if that's because you have embraced anything like the half bell curve as a picture of usage (or of fuzzy truth), then notice that you are, after all, ditching P1 and not P2.

The grain doesn't transform a non-heap into a heap. An assertion without negation does.

Why do you think this vagueness of the predicates such as a "heap" or a "hole" arise in language? — Shawn

They are indefinite quantifiers. They seem to arise because the level of precision they express suffices for certain purposes.

"Tom is so popular, he has a heap of Facebook friends! Wait, let me check and give you the exact number ... yes, he has 23,456 friends on Facebok!"



As for transforming a non-heap into a heap: this has got to depend on what is being counted and what the standards are as to what counts for "a lot" of said thing.

If you need four of your teeth repaired, then you have a heap of teeth to repair.
If you have four FB friends, then you do not have a heap of friends. By some people's standards, even a 100 FB friends isn't a lot.

I certainly do. Ridiculous as I find the 'hidden step', I think that ordinary usage deserves some kind of recognition of its ability to distinguish between correct and incorrect, in some way that doesn't fizzle out to 'relatively correct'. Usage can sometimes be a matter for negotiation, and adjudication, but sometimes not. We know that anything black is an obvious counter-example to white, and is therefore anything but minimally white, and similarly for off and on, bald and hairy, etc.

Hence my readiness to restart, and invite you to consider an absolutist position on a single grain. E.g.,

[1] Tell me, do you think that whether a single grain can be correctly called a heap in common English is a matter for negotiation or adjudication in context?

I appreciate fully that you may well see no need at all to deny that proposition. (I'll have to bluster that you don't speak English, but never mind!) But if that's because you have embraced anything like the half bell curve as a picture of usage (or of fuzzy truth), then notice that you are, after all, ditching P1 and not P2. — bongo fury

All these things are a matter of adjudication. You could choose to use a word in a highly nonstandard way, and people could go along with it – but they often won't, and they'll be more unwilling to, the farther you move away from an established usage. But if you decide to use 'heap' to refer to a single grain too, then sure, go ahead, that's also a pattern of usage that could be established. It would be 'incorrect' in virtue of some prior pattern of established usage, but so what? Patterns of usage can be re-negotiated as well. This is a matter of how to apply the word, not an interesting inquiry either into the nature of language, or the nature of sand and piles of it.

The epistemicist, in appealing to a strict notion of 'correct usage,' is invoking a kind of magical view of language. That is, in addition to facts about how speakers coordinate their thoughts and behaviors using words, epistemicists seem to think there is some extra fact about words, unknowable in principle, that determines what intrinsic property they have, in addition to or maybe even independent of, all these facts. But there is no reason to believe such a thing exists – again, it is like thinking words 'have' meanings the way elements 'have' atomic numbers. But this is a fundamental misunderstanding – to say a word has a meaning is no more and no less than to say the word has certain causal powers in virtue of a community of speakers coordinating to use it in a certain way. There are no other semantic properties hiding behind this, as if words had magnetic properties attracted to some physical objects and not others.

In terms of the history of semantics, I think of what many of the analytic philosophers of language do as a kind of return to a magical or pre-modern view of language, whereby people tend to think that words have quasi-magical powers in their own right to attach to or 'get at' objects – hence the metaphors of magnetism in reference, and so on. But semanticists have known forever that this isn't so – words relate to things by having causal effects on interpreters, who then causally interact with those things (this is Ogden & Richards, from the 1920s, who take this insight to be the start of modern semantics). Analytic philosophers are sort of like the magicians who want to know something's true name, in other words – yes, we can call Johnny any number of things, but which thing really refers to him? There is a very, very basic confusion happening here. Johnny is the referent of 'Johnny' because of how people are disposed to refer to him – the name 'Johnny' doesn't have other special properties that designate that man is its intrinsic proper referent, over and above all facts of usage!

When someone says a certain usage is correct, they might either mean: (i) as a descriptive matter, this is how people tend to use the term, as summed up by some statistical measure (based on prior usage or an inference about disposition to future usage, or whatever), or (ii) as a normative matter, that some use is to be singled out as to how the word is to be used. But neither of these are descriptive facts about words having meaning as if that were something else beside how people use a word. This, as I said above, is the return to the kind of magical, pre-modern view of meaning.

Of course, I would not reject P1, because I think using 'heap' is such a non-standard way is pointless and confusing.

The grain doesn't transform a non-heap into a heap. An assertion without negation does. — Cheshire

I kind of agree. Does it matter who asserts and who negates? Are you equating 'heap' with 'allegedly a heap' or with 'unanimously a heap'? (Or both or neither, or something else.)

Of course, I would not reject P1, because I think using 'heap' in such a non-standard way is pointless and confusing. — Snakes Alive

Well of course, I would not reject a statement to the effect that a bishop can't move directly forwards, because I think using it in such a non-standard way is pointless and confusing. However...

All these things are a matter of adjudication. You could choose to use a word in a highly nonstandard way, and people could go along with it – but they often won't, and they'll be more unwilling to, the farther you move away from an established usage. But if you decide to use 'heap' to refer to a single grain too, then sure, go ahead, that's also a pattern of usage that could be established. It would be 'incorrect' in virtue of some prior pattern of established usage, but so what? Patterns of usage can be re-negotiated as well. — Snakes Alive

But I'm guessing you don't offer the same advice in regards to the chess move? Because it wouldn't be chess? Well I, like any dictionary compiler or competent speaker, take the same view of the single grain, that it's well outside of the range of correct application of 'heap', in ordinary English as spoken literally. (As opposed to metaphorically.)

This is a matter of how to apply the word, not an interesting inquiry either into the nature of language, or the nature of sand and piles of it. — Snakes Alive

But how to apply the word is interesting and puzzling and inquires into the nature of language because, unlike in chess, the rules are flexible at the same time as they are strict. They can be bent, but not too far, and obviously how far is the puzzle.

So, you do reject P1 with respect to general usage, in English, of the word 'heap'. I accept that you accept P1 with respect to your own usage. Your personal threshold is perhaps much further along than one. But you appear happy to acknowledge that usage as a whole allows for literal application of the term to a single grain. A linguist or dictionary compiler may beg to differ. They would offer a single grain as an obvious example of incorrect usage, or opposite meaning.

The epistemicist, in appealing to a strict notion of 'correct usage,' is invoking a kind of magical view of language. — Snakes Alive

Wasn't it clear we agree about this?

to say a word has a meaning is no more and no less than to say the word has certain causal powers in virtue of a community of speakers coordinating to use it in a certain way. — Snakes Alive

But isn't that verging on a kind of magical thinking? You'll never cash out those causal powers at the level of linguistic analysis. (Chomsky's famous ridicule of "the probability of a sentence".) Better to describe the (pretended, sure) relations and rules and moves of the game.

When someone says a certain usage is correct, they might either mean: (i) as a descriptive matter, this is how people tend to use the term, as summed up by some statistical measure (based on prior usage or an inference about disposition to future usage, or whatever), — Snakes Alive

Graphs 1 and 2.

or (ii) as a normative matter, that some use is to be singled out as to how the word is to be used. — Snakes Alive

Graphs 3 and 4.

But neither of these are descriptive facts about words having meaning as if that were something else beside how people use a word. — Snakes Alive

Yes, and we don't want them to be, but, we do want the first (1&2) to better acknowledge where a line of acceptable usage (however blurred) has been crossed, and the second (3&4) to better show how the line is both created and blurred by use.

I.e., we want P1, and we want P2.

They can be bent, but not too far, and obviously how far is the puzzle. — bongo fury

The problem is this is not true. You seem to be hung up on the false idea that a magical barrier exists preventing people from using words in certain ways. It doesn't – of course people tend not to bend too far, but it's not like they can't, as some philosophically interesting matter. Of course they can (and they can even move the bishop non-diagonally – try it yourself...).

So, you do reject P1 with respect to general usage, in English, of the word 'heap'. I accept that you accept P1 with respect to your own usage. Your personal threshold is perhaps much further along than one. But you appear happy to acknowledge that usage as a whole allows for literal application of the term to a single grain. A linguist or dictionary compiler may beg to differ. They would offer a single grain as an obvious example of incorrect usage, or opposite meaning. — bongo fury

I accept P1 because I wouldn't apply 'heap' to a single grain.

You seem to think that because 'heap' has some property preventing it from being applied to a single grain, therefore P1 is true because people 'can't' apply it to a single grain.

But you've got it backwards. It's because people don't use 'heap' for a single grain that P1 is true. We could turn around and decide to start applying it to a single grain, if we wanted to, and declare P1 false as a result. I just wouldn't want to, because changing around the application of words is confusing and sometimes pointless. And so I take P1 to be true.

I kind of agree. Does it matter who asserts and who negates? Are you equating 'heap' with 'allegedly a heap' or with 'unanimously a heap'? (Or both or neither, or something else.) — bongo fury

As a little check and balance I'm trying to use answers that would hold for heap making or hole(non-specified dimensions) digging at the same time.

Well, the agent with the shovel would have to believe the heap or hole was sufficient to the context. In example, the hole big enough to contain X or grain amount by estimated volume X. The agent may or may not be working to a 2nd parties expectations. So, for the simplest heap or hole it is who controls the dimensions of the heap or hole.

When you add a second party it becomes a matter of wanting a heap or hole of relative size. I don't think it still remains a non-heap/hole if within reason. Otherwise we could debate whether it was a golf shoe should some one insist upon it; which isn't useful discourse.

The problem is this is not true. — Snakes Alive

Oh well, if you put it as emphatically as that, with italics and all...

You seem to be hung up on the false idea that a magical barrier exists preventing people from using words in certain ways. — Snakes Alive

I honestly don't know how it seems like that, when I keep mentioning how reference is a game of pretend.

they can even move the bishop non-diagonally – try it yourself... — Snakes Alive

I have. People say, "ok, if you like, but you know it won't be chess?" And this is me, "what makes you think there's any fact of the matter whether what we do is chess?". And they're like, "sorry mate, we only play chess not philosophy."

I accept P1 because I wouldn't apply 'heap' to a single grain. — Snakes Alive

Ok, I'm grateful if someone at least avows P1. We might have a game. Now, bearing in mind,

it is a matter of arbitrary decision whether we choose to apply the word 'heap' or not, and so construe it as correctly applied or not — Snakes Alive

... Let's try.

[1] Tell me, do you construe the word 'heap' as being correctly applied to a single grain?

You seem to think that because 'heap' has some property preventing it from being applied to a single grain, therefore P1 is true because people 'can't' apply it to a single grain. — Snakes Alive

Well, whether or not I ever lapse into magical thinking, and I'm only human after all, I would indeed tend to offer scare quotes around can't, and be ready to clarify, as I keep doing, that either of us doing what they 'can't' merely prevents us from agreeing that the game is indeed 'chess', or 'spoken English' or whatever. Which is usually a game-stopper. (Which may or may not be good for the quality of the game as generally played.)

But you've got it backwards. — Snakes Alive

Surely there's no back or front? If we're not thinking magically or essentially?

It's because people don't use 'heap' for a single grain that P1 is true. — Snakes Alive

Ok, if you prefer. Although I preferred your more symmetrical "material equivalence", earlier. What I really like here is "people"...

We could turn around and decide to start applying it to a single grain, if we wanted to, and declare P1 false as a result. — Snakes Alive

My emphasis, for the same reason, that you are on the verge of recognising a general rather than personal proscription against the application, such that reversing it in a collective endeavour might create a new and different game with the same word. (Where P1 was indeed false.)

I just wouldn't want to, — Snakes Alive

Ah, rats.

Still...

[1] Tell me, do you construe the word 'heap' as being correctly applied to a single grain?

Ah, OK. I think I didn't pick up sufficiently on the 'pretend' part.

Surely, though, pretended things aren't so? Is your position that we ought to pretend there is a single correct use of a term, and in the case of vague language, pretend to be epistemicists?

But here, as we discuss this now, we presumably aren't pretending – so shouldn't we say epistemicism is false?

Epistemicism as a 'noble lie' would be a funny position to take! Or maybe it's a mutual pretense we're all in on? But then, I have to admit I fail to see the value in acting like vague language determines precise boundaries. Sometimes it's useful to be more precise, sometimes not.

Surely, though, pretended things aren't so? — Snakes Alive

Is this suddenly a problem?

we all know precisely well what we mean by saying they do or don't exist, and no one is confused. — Snakes Alive

Is your position that we ought to pretend there is a single correct use of a term, — Snakes Alive

No, but in playing or describing the game we ought to respect the cases of correct and incorrect that are clear. We ought not pretend that we are playing chess by moving the bishop non-diagonally, nor that we are speaking English literally by construing the word 'heap' as being correctly applied to a single grain. We ought to pretend instead that the word 'non-heap' applies to or points to or is otherwise connected to a single grain.

, and in the case of vague language, pretend to be epistemicists? — Snakes Alive

No, I think vague language can be described as a game of pretend that tolerates disagreement about what is pretended. The puzzle is how to square the tolerance in some places (P2) with the clarity in others (P1). Epistemicism (a minority view, as its proponents admit) thinks all disagreement is a symptom of error. It says that a proper description of a vague game, if it were possible, would weed out the errors and leave a precise and perfectly consistent game.

But here, as we discuss this now, we presumably aren't pretending — Snakes Alive

We're doing our best to agree enough (pretended) reference to have viable discourse about our actual linguistic behaviour.

so shouldn't we say epistemicism is false? — Snakes Alive

Sure. Not because we aren't pretending (we are) but because the game is better described as tolerating dissent.

But then, I have to admit I fail to see the value in acting like vague language determines precise boundaries. — Snakes Alive

Quite, but the puzzle is to explain how it can have blurred boundaries. How to get from P1 and P2 to P3.

Sure. Not because we aren't pretending (we are) but because the game is better described as tolerating dissent. — bongo fury

The issue is also that insofar as epistemicism purports to be a description of this game, it is a false one – vague language isn't somehow secretly precise, and players of the game are to some extent metasemantically aware of this. An untutored person pretty much invariably (in my experience) finds epistemicism absurd upon first hearing of it. No only that, it takes quite some time to even get them to understand what epistemicism is, because the very notion is so far from what they take for granted about the way language works that it takes a while even to explain it.

So if epistemicism neither captures people's metasemantic awareness of their own language, nor does it seem to describe anything 'objective' in the practice itself, what is its utility as a hypothesis? Are you defending it in any capacity, or just using it as a springboard to talk about the difficulties with vagueness? I could see the proposal to act like it's true, as a recommendation that we ought to treat language as arbitrarily precise, as a coherent opinion, though still not a good one. What you seem to be saying now, however, is that epistemicism isn't really true in any sense – it just helps us highlight some features about vague language that are puzzling to us (though even here I disagree – I think vague language is vague, and so can cause concrete problems of indecision in everyday life, but that doesn't make it puzzling, as if we were fundamentally confused about what's going on).

So if epistemicism neither captures people's metasemantic awareness of their own language, — Snakes Alive

because it fails to endorse P2 or offer a substitute...

nor does it seem to describe anything 'objective' in the practice itself, — Snakes Alive

hence the faint mystical glow of the Warburton quote, which I've probably unfairly represented, I must check...

what is its utility as a hypothesis? Are you defending it in any capacity, — Snakes Alive

No.

or just using it as a springboard to talk about the difficulties with vagueness? — Snakes Alive

Yes, which it is good for from my point of view, because it at least endorses P1. It doesn't offer the kind of argument for P1 that would stop people from so carelessly abandoning it, is the shame. On the other hand, we are at least talking in terms of trying to draw a suitable graph of usage.

I could see the proposal to act like it's true, — Snakes Alive

No no no, I never proposed anything of the kind, and I absolutely propose that you carry on doing the opposite :up:

What you seem to be saying now, however, is that epistemicism isn't really true in any sense — Snakes Alive

Except in its support of P1.

it just helps us highlight some features about vague language that are puzzling to us — Snakes Alive

Yes, how to draw a convincing graph of usage.

I think vague language is vague, [...] but that doesn't make it puzzling, — Snakes Alive

It does if you accept any responsibility for the care of P1 as well as P2, and try to apply logic.

Now then...

[1] Tell me, do you construe the word 'heap' as being correctly applied to a single grain?

It does if you accept any responsibility for the care of P1 as well as P2, and try to apply logic. — bongo fury

I've already answered this a couple times. I'm not sure what you're hung up on.

Even as you seem to be closing your hand around an argument only to have it slip out. I don't see in your post anything specific enough to disagree with. — Banno

I enjoy the irony of a comment about vagueness being unspecific. I wanted to point towards how and why the preoccupation here is philosophically important.

this vagueness that irritates philosophers.
— Shawn

That's a psychological problem for philosophers, not a philosophical problem. — Banno

Okydoke.

It seems that another interesting topic related to the heap issue is one of whether the truth or falsehood of applying the bivalence principle to the heap issue is de facto an issue if one professes a correspondence theory of truth toward realism?

In my opinion this is at face value false to say that the correspondence theory of truth in fact adheres towards the use of the word "heap", otherwise, what does "heap" correspond to?

Instead, I think, that the heap issue presents a novel representation of coherentism in language.

Thoughts?

It's a novelty of a self-referential measuring tolerance. We'd all produce a different cubit if measured to the micron. We'd all be right relative to our arms and wrong relative to the others. So, people don't use tight tolerances for measures with unbounded variances. I wouldn't buy lumber from a short armed man 3000 years ago.

It's a novelty — Cheshire

Sure. A 3000 year old novelty.

We'd all produce a different cubit if measured to the micron. — Cheshire

And then the puzzle is to specify the smallest (or largest) number of microns that is no longer a cubit.

We'd all be right relative to our arms and wrong relative to the others. — Cheshire

No, some of us would be obviously right relative to the cubit system, some of us obviously wrong, and some of us neither.

So, people don't use tight tolerances — Cheshire

Narrow tolerances or precise tolerances?

for measures with unbounded variances. — Cheshire

Unbounded precisely, i.e. not graph 4; or unbounded ever i.e. graph 2? Or unbounded how?

No, some of us would be obviously right relative to the cubit system, some of us obviously wrong, and some of us neither. — bongo fury

Using a cubit instead of visual verification highlights the issue in a physical way. The cubit system is based on the measure of one's own arm. As long as everyone measured with their arm they are technically right as I understand it.

And then the puzzle is to specify the smallest (or largest) number of microns that is no longer a cubit. — bongo fury

You don't add or subtract length to your arm to meet a standard, so this is incoherent.

Narrow tolerances or precise tolerances? — bongo fury

Industry term for a small margin of error. The narrower the tolerance, the higher degree of measuring precision.

Unbounded precisely, i.e. not graph 4; or unbounded ever i.e. graph 2? Or unbounded how? — bongo fury

It's the length of your forearm to middle finger. If your working with multiple people then I imagine the "foreman's cubit" is fabricated and used as a local standard.

The next step I believe was the use of barley corns to measure an inch. You had to have 3 of them. It's a more precise measure that assumed the variance in barley corn lengths averaged out well enough to be useful. Now we use like the planck length against some measure of gravity or something.

As long as everyone measured with their arm they are technically right as I understand it. — Cheshire

Well, I do hope neither of us is about to reach for Wikipedia. My point is that any such primitive measuring system is as good an example as any of the potential quandary. Line up the population of the village in order of height. Now, whose arm is the first valid cubit stick? Hence,

And then the puzzle is to specify the smallest (or largest) number of microns that is no longer a cubit. — bongo fury

Which is merely to envisage a radically longer line-up. Because you said microns. Which is fine in principle.

You don't add or subtract length to your arm to meet a standard, so this is incoherent. — Cheshire

How about now, any clearer?

It's the length of your forearm to middle finger. — Cheshire

What is? Presumably not the variance, whose unboundedness I was inquiring into.

So, people don't use tight tolerances for measures with unbounded variances. — Cheshire

Unbounded precisely, i.e. not graph 4; or unbounded ever i.e. graph 2? Or unbounded how? — bongo fury

Did you just mean, people don't use narrow tolerances to measure wide tolerances? But of course engineers do just that, as you seem aware.

How about now, any clearer? — bongo fury

I think you might have removed some context to create the appearance of inconsistency. In present day measurement 'a standard' is a fixed value. In this context a standard is a definition. So, we do not in fact change the length of a thing to meet a physical value in the cubit system. It's simply a comparative measurement to one's arm. There is no micron equivalent that holds true across cases. I imagine there's a distribution of arm lengths and as a result a very, nearly exact distribution of cubits.

In a sense the arm "asserts" the length of a cubit.