No epistemic criteria to determine a heap?
When one thinks about language, there are many phrases that are inexact or vague and ambiguous. For example, when one thinks about the Sorites paradox, one encounters inexactness in language as to what constitutes a "heap" or more precisely a vague predicate.
The way I see it, I don't think there's anything that can be said about how to measure a "heap". Indeed, this is another example of a vague predicate that cannot seemingly be precise.
Apart from the perception of a "heap" to be determined just by seeing, I am concerned about why can't terms like a "hole" or a "heap" cannot be precise, as the only thing left to talk about is the size of the heap to, in a sense, measure it and make it a quantifiable measure?
Why do you think this vagueness of the predicates such as a "heap" or a "hole" arise in language?
The way I see it, I don't think there's anything that can be said about how to measure a "heap". Indeed, this is another example of a vague predicate that cannot seemingly be precise.
Apart from the perception of a "heap" to be determined just by seeing, I am concerned about why can't terms like a "hole" or a "heap" cannot be precise, as the only thing left to talk about is the size of the heap to, in a sense, measure it and make it a quantifiable measure?
Why do you think this vagueness of the predicates such as a "heap" or a "hole" arise in language?
Comments (124)
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.
Well, yes; but, the paradox is still pertinent.
Asides from that, I understand that "heaps" or "holes" have this vagueness that irritates philosophers. I'm not necessarily asking for a more precise meaning as much as asking why do these words make philosophers talk about them at length?
And, even counterfactually, what does this reveal about language and human perception in language games?
Unsure if you might find this more interesting than the other thread, @I like sushi?
Well, no, there is no paradox. The supposed question" how many items make a pile?" simply misunderstands the use of "pile"; there is no precision, and yet it functions adequately.
Quoting Shawn
That's a psychological problem for philosophers, not a philosophical problem. What it reveals is that language functions despite an excessive expectation of precision on the part of certain individuals.
There isn't a conceptual problem here, only the misplaced discomfort of a few odd folk.
That is the case with most supposed philosophical issues.
Contrary to what you are implying, that the use of pile is adequate perhaps by the latter Wittgenstein, I think there's reason for doubt or concern by other philosophers. These vague predicates are very heavily loaded with human perception and often cause confusion in language.
Or another way I just thought is that for the case of the heap of sand is where phenomenological issues manifest in language.
Have you heard of the Problem of the Criterion?
My own instinct is that language has usage, not meaning and for everyday functioning such words have been more than adequate. I have more concerns with words like democracy and truth.
SO give an example of that confusion.
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.
SO again, there isn't a conceptual problem here, only the misplaced discomfort of a few odd folk.
Well, it's a prime example in philosophy, and with my concern over epistemic discursions over criteria I think, it's a really interesting case example to argue for a more formal way of using language.
I would even argue that cognitively a "heap" is what can be called a phenomenological expression if its so inexact.
It might seem trivial; but, once you see the vague predicate and assume doubt it instantly becomes a problem rather than not.
Such as,
'What is a "heap"?'
An untidy collection of objects, place on top of each other.
But you understood that, and as a competent speaker of English you use the word correctly, as well as in jest.
SO what is the confusion?
Quoting Banno
An epistemist might ask you a question such as,
"Does the Sorites paradox entail a too strict principle of bivalence by (what you call) a prejudice of the arising doubt or is there any need to maintain the principle of bivalence towards what constitutes a "heap"?"
I can state this more eloquently, as,
"Why does epistemicism cause confusions around what constitutes a "heap"?
It's always seemed to me that the real issue with the so-called "Sorites paradox" isn't that the idea of a heap is vague so it's hard to know what is and what isn't. As others have noted, we don't generally have any trouble using the word "heap" without confusing people. I see the real issue being the arbitrariness of the distinctions we make for everything we talk about. A heap is just an easily understood example.
The world is the world. There are no paradoxes in the world. We starting confusing ourselves when we lose track of the difference between the world and the words we use to describe it. That's what we're talking about when we talk about paradoxes.
There's a way of understanding what a heap is, that is not dependent on an explicit formulation of what constitutes a heap in each and every case. Instead, it is demonstrated in actually using "heap" in real situations.
Set the task of discovering if someone knew what "heap" meant, should you be satisfied with their providing the dictionary definition? Or should you note their use of the word "heap" in comparison and contrast to "pile", "stack", "mound" and so on?
It's not that the use of "heap" is arbitrary; Capricious, whimsical, random.
And yes, this goes for everything we talk about. It's the upshot of use in the place of meaning.
Well, I beg to differ.
Let's assume that vagueness arises where the law of bivalence is not clearly defined or sharp, for a heap. Therefore, what can one say about this problem of the valence of what a "heap" actually is.
I understand your point but my version for the world doesn't have straight lines or precise definitions (except by explicit agreement) so it is a problem which doesn't impact. It's context. If someone says to me; 'I'll give you heaps of money." I might ask, "How much is heaps?" But if someone says, "There's a heap of wood in the back yard for the fire", I probably will be satisfied by this.
Have at it:
https://aeon.co/ideas/on-vagueness-when-is-a-heap-of-sand-not-a-heap-of-sand
How is it context? I'm no specialist in language theory; but, to me this is such a phenomenon widespread in informal languages, that I don't really see this as a way of meaning as use. More akin to treating 'tall' as a relative term, a 'heap' or a 'hole' seem to be associated with the problem of the principle of bivalence not being able to suffice for the way that term is used by philosophers.
Which, is puzzling and interesting as to why the principle of bivalence or even fuzzy logic might not even help.
How is it not context?
Can you show me a specific example of how this language imprecision cause harm or an insurmountable problem?
So, what kind of world does the ontology of a 'heap' inhabit? Purely, "worldly" or phenomenological; because the law of excluded middle wont let both be satisfied at the same time, no? I might be wrong; but, a heap comes off as a epistemological problem, as specified by philosophers and their criteria for other terms such as 'holes' or heaps upon heaps.
On a face value reading, it might seem as a context issue. But, 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 for not only 'heaps'; but, something of the sort of, 'the worn out sole of my shoe', 'the smelly bathroom', or 'the tall man'. If it's so apparent, then doesn't this warrant what's going on language that this is so easy for it to arise?
Quoting Tom Storm
In determining valency or affect in language as a general measure? I think there's the issue of realism in language or whether it's really all a correspondence theory that's on shaky grounds?
What does "heap" correspond to?
The expression 'hard work' always stuck me as delightfully fecund.
I said the distinction between what is considered a heap and what isn't is arbitrary. Maybe I used the wrong word. The line we draw between heap and not-heap is one we've drawn. 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. And, as we've both noted, we make that choice with all the words we use.
I don't think I understand what you mean by "worldly" or "phenomenological" in this situation. "Heap" is a label we put on a phenomenon we observe in the world. The word is artificial, human-made. Is that what you mean by phenomenological?
No, I think that it makes sense to state that it is phenomenological; but, don't think that's what I'm trying to say.
Mainly, when we say that a 'heap' exists, what does that mean about how we perceive reality? In a direct-1-1-correspondence of the word to a pile of sand? Then how does that make sense when the pile of sand cannot be specified precisely?
Other interesting questions could be, "can a heap be specified more precisely"?
When you say
"We starting confusing ourselves when we lose track of the difference between the world and the words we use to describe it. That's what we're talking about when we talk about paradoxes."
this is exactly right and well put. The example I like to use to illustrate this is the question "Why is there something rather than nothing?". Most people seem to mix up "nothing" itself and the mind's conception of "nothing". In "nothing" itself, no minds, including that of the person thinking about it, are there.
In applying what you say to a "heap", a heap is just a term that everyone has their own definition of about how big a collection of items is. The real point to me is what causes a heap, or any collection of items, to exist as a separate entity from the items considered individually. My view is that a grouping of items is an existent entity wherever that grouping exists, whether that's in a person's mind or outside the mind. In other words, there's one existent heap outside the mind, but another existent entity is a person's mental image of that heap. Anyways, that's my view.
I feel differently. I don't think things exist as phenomena separate from the undifferentiated world until someone like us brings them into existence by naming them. That is the essence of what Lao Tzu wrote in the Tao Te Ching.
Quoting Shawn
The Law of Bivalence: A statement is either true or it is false; no middle value is available.
Hence, "This is a heap of sand" is either true, or it is false.
Nothing here is "not clearly defined or sharp".
If there are ten grains piled up, is that a heap? A hundred? a thousand? The idea is that we must specify a number, such that more than that number is a heap, less is not a heap. But that's not how heaps work.
Suppose John says it is a heap, but Jenny says it isn't. Is one of them right, as a matter of fact, and the other wrong? We don't say things such as this, except in unusual situations. We say "Heap that stuff up for me", "Use that heap of sand in your concrete", or "make those two heaps into one big heap".
We can contrive a situation in which we do talk of this being a heap, but no that. Jenny has a heap of coins, a hundred in all. John shows his, which contains a thousand, saying "that's not a heap, this is a heap!"
Does it follow that when Jenny says "This is a heap of a hundred coins", she is uttering a falsehood?
Nothing here is a breach of bivalence. To do that we would need Jenny to assert something like "This is a heap, and it is also not a heap".
Jenny says it is a heap, John says it isn't. This is not a disagreement as to the facts, but as to the use of the word "heap".
Quoting T Clark
If only.
Quoting Banno
Likewise,
Quoting sime
However,
Quoting bongo fury
But,
Quoting bongo fury
Quoting bongo fury
Quoting 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:
I would hope so.
Quoting Don Wade
It's fallible, because it needs two opposing intuitions.
Where it leads me is here, if you're interested.
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.
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.
: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.
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.
I don't understand. Are you saying they are, all 3, compatible, as they stand and appear to signify?
Quoting Michael
Garbled? What are you saying might perhaps be implicit in what?
Quoting 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?
Yes.
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.
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.
No, that's implicit logic. Requiring iteration of the usual, implied, kind. "Step by step". Grain by grain. Or recursion. But not another premise.
Quoting 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.
Quoting Michael
Another good example.
And another.
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.
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.
Yes. Lazy. Assuming straw men.
Quoting Michael
What, like essentialism? Who brought that up?
Quoting Michael
Enough metaphysics! Solve the puzzle.
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.
Quoting bongo fury
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.
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.
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.
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.
Quoting bert1
I don't agree.
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.
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.
I wasn't questioning your usage, I just wanted to make sure I understood.
Quoting bert1
In the good old days, it was after the marriage had been "consummated." Wink, wink, nudge, nudge, say no more, say no more.
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.
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.
The latter way of avoiding play is to reject
Quoting 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,
Quoting 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.
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.
Quoting Nigel Warburton, aeon article
So far so reasonable...
Quoting 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?
Quoting Nigel Warburton, aeon article
Woah. What just happened. Provocation? Fair enough then. Nice.
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
Quoting SEP
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.
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.
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.
Quoting 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.
Quoting bert1
Well, perhaps not all; very many are, though. Identifying the ones that aren't - now that's an interesting task.
Quoting 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.
Quoting bert1
I'm flattered. Thank you.
Quoting 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.
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.
I already replied to this.
Quoting bongo fury
It's obvious you only skim, all the time. Never mind.
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.
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.
Quoting bongo fury
People are instructed on how to define something they intuitively understand?
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.
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?
Yes... and the collective pronoun is a paucity of donor kidneys.
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).
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.
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 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.
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.
Really? A heap of diamonds? Or (in bad taste but logical enough) of donor kidneys? Are they not suitable for the order?
Quoting 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.
Quoting Tom Storm
Thank you, with your permission I'll use 'paucity' along with 'pittance' to expound my antonym-based constructive solution.
Quoting bongo fury
Proposed solution here.
Quoting Snakes Alive
Yes, yes.
Quoting bongo fury
I.e. can you play the game, or is it beneath you? Ah good:
Quoting Snakes Alive
Absolutely. However,
Quoting Bongo Fury
Or
Quoting R.M. Sainsbury, Concepts without boundaries
E.g.
Quoting bongo fury
I.e.
Which might or might not get traction. I for one am inclined to reply,
But if you, on the other hand, prefer
... 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.
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?
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.
Which question? Player 1's second line here?
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.
Quoting Cheshire
Which question asks such a thing?
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.
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,
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.
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.
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.
You lost me. What exactly do we need to agree is implied by Quoting 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.
Quoting Cheshire
The puzzle, it should be clear, is how to reach P3, or avoid denying it, while accepting both P1 and P2.
Ok, I didn't realize this was the format. I'll keep it in mind.Quoting 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.Quoting bongo fury Alright, then grain 1,000,000,000 makes a heap. Where do I send the invoice?
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.
Quoting 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?
Quoting Cheshire
Reminds me of when my bank operated a no-charge policy for "small" overdrafts...
Then we're done, aren't we?
Behind you!!
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?
Quoting 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:Quoting 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".
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.
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.
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.
Quoting Snakes Alive
Agreed. It's partly because they insist on a distinction between
Quoting 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:
Quoting Nigel Warburton, aeon article
Happily, probably everyone agrees with
Quoting 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.,
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.
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.
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.
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.)
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...
Quoting 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.)
Quoting 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.
Quoting Snakes Alive
Wasn't it clear we agree about this?
Quoting 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.
Quoting Snakes Alive
Graphs 1 and 2.
Quoting Snakes Alive
Graphs 3 and 4.
Quoting 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.
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...).
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.
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.
Oh well, if you put it as emphatically as that, with italics and all...
Quoting Snakes Alive
I honestly don't know how it seems like that, when I keep mentioning how reference is a game of pretend.
Quoting 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."
Quoting Snakes Alive
Ok, I'm grateful if someone at least avows P1. We might have a game. Now, bearing in mind,
Quoting Snakes Alive
... Let's try.
Quoting 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.)
Quoting Snakes Alive
Surely there's no back or front? If we're not thinking magically or essentially?
Quoting Snakes Alive
Ok, if you prefer. Although I preferred your more symmetrical "material equivalence", earlier. What I really like here is "people"...
Quoting 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.)
Quoting Snakes Alive
Ah, rats.
Still...
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.
Is this suddenly a problem?
Quoting Snakes Alive
Quoting 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.
Quoting 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.
Quoting Snakes Alive
We're doing our best to agree enough (pretended) reference to have viable discourse about our actual linguistic behaviour.
Quoting Snakes Alive
Sure. Not because we aren't pretending (we are) but because the game is better described as tolerating dissent.
Quoting Snakes Alive
Quite, but the puzzle is to explain how it can have blurred boundaries. How to get from P1 and P2 to P3.
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).
because it fails to endorse P2 or offer a substitute...
Quoting Snakes Alive
hence the faint mystical glow of the Warburton quote, which I've probably unfairly represented, I must check...
Quoting Snakes Alive
No.
Quoting 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.
Quoting Snakes Alive
No no no, I never proposed anything of the kind, and I absolutely propose that you carry on doing the opposite :up:
Quoting Snakes Alive
Except in its support of P1.
Quoting Snakes Alive
Yes, how to draw a convincing graph of usage.
Quoting 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...
I've already answered this a couple times. I'm not sure what you're hung up on.
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.
Quoting Banno
Okydoke.
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?
Sure. A 3000 year old novelty.
Quoting Cheshire
And then the puzzle is to specify the smallest (or largest) number of microns that is no longer a cubit.
Quoting Cheshire
No, some of us would be obviously right relative to the cubit system, some of us obviously wrong, and some of us neither.
Quoting Cheshire
Narrow tolerances or precise tolerances?
Quoting Cheshire
Unbounded precisely, i.e. not graph 4; or unbounded ever i.e. graph 2? Or unbounded how?
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.
Quoting bongo fury You don't add or subtract length to your arm to meet a standard, so this is incoherent.
Quoting bongo fury
Industry term for a small margin of error. The narrower the tolerance, the higher degree of measuring precision. Quoting 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.
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,
Quoting bongo fury
Which is merely to envisage a radically longer line-up. Because you said microns. Which is fine in principle.
Quoting Cheshire
How about now, any clearer?
Quoting Cheshire
What is? Presumably not the variance, whose unboundedness I was inquiring into.
Quoting Cheshire
Quoting 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.
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.
Quoting Cheshire
I don't quite get the 'very nearly exact' but never mind that. The puzzle (for an enthusiast of the heap puzzle who recognises here a classic case) is: exactly where (along a reasonably long line of arms positioned in ascending or descending order of length) does the distribution of cubits end, and the distribution of non-cubits begin?
Quoting bongo fury "very nearly exact" sounded funny, but I see injecting subjective satire is probably not the best strategy for navigating this puzzle.
Quoting bongo fury According to non-Bayesian statistics if the value is continuous there isn't one. There are some very unlikely cubits and the limit of observed cubits, but by definition both extend to infinity. Or said another way, the 1 micron cubit is very unlikely, but not excluded by the definition on an impractical yet technically accurate level.
But unnecessary presuppositions aside...
Quoting Cheshire
So, finally,
Quoting bongo fury
So graph 2, i.e. ditch P1, because after all, "everything's relative", or "on a spectrum".
Quoting bongo fury
Which is cool, if you find [2] an acceptable description of usage, and would say that black is minimally white, bald is minimally hairy, off is minimally on etc.
Quoting Cheshire
... is a questionable notion, but key to my
Quoting bongo fury
Which of course is of no interest if there is no problem.
A problem remains if the question/puzzle is subject to context. If the heap amount has any future purpose or supposed representation of value. You can't sell 1 grain heaps and expect to keep a good business rating. So, the conclusion is true in a vacuum, in reality we rely on what is reasonable. Pretending irrational things are true for the sake of pretending objectivity isn't doing philosophy any credit. Or maybe it is; I never owned the gate keys. Fun though, well played sir.