Your response didn't make a lot of sense to me, unfortunately. — Terrapin Station

That's ok! Thanks for trying.

Also, you seem to be writing as if you think that I'm a representationalist or idealist? I'm not. I'm a direct (aka "naive") realist. — Terrapin Station

No, I get that!

I'm one too, I think... as long as I'm allowed to see plenty of the knowledge we get about the things out there as got via inference? You're not against that? It isn't about some notion of direct acquaintance that rules out intermediate steps?

Anyway, I was assuming that that (agreement on that point) was the case. But I wasn't joining battle. I thought I was invited to explain my skepticism about mental pictures? And the alternative. Which is where I might have implied a "third way": only in the arrogant claim that both sides should put their phones down and listen to my more important business!

Perhaps it was off topic anyway. No worries.

In my opinion the questions were kind of a mess in context and every term there would have to be sorted out, which would be a ridiculous amount of work that's not necessary — Terrapin Station

I was just curious to know whether you wanted mental pictures in the picture, at all. Evidently you did.

But if you don't think that either some form of idealism or representationalism OR something like direct realism is how things work, — Terrapin Station

It would be great not to get pigeonholed... for a few more milliseconds. But I guess you'll see where I'm getting it all from.

... then what would you say is going on/how would you say that perception (or whatever you figure it is) works? — Terrapin Station

That slash is significant? On one hand what's going on... what perception actually looks like and what's generally happening, i.e. the psychology / and on the other hand how it works... affords knowledge of the outside i.e. the epistemology. I didn't want to do any of the latter, just point out that IMO it was hopeless carried out against the background of a largely mythical psychology. But I bet a lot of the disputes in this thread could benefit from a separation according to this slash. I notice that a lot of it could be conducted well away from any brains. That is, I'd like to know what the two sides do claim about the forensic / evidential / epistemic reach of actual photos, paintings etc.

However, what's going on in perception if not mental pictures? Fair question. Thanks for asking. We should say instead that we get skillful in responding appropriately to stimuli, or on a more attenuated level, refining our readiness to select (appropriately) from repertoires of responses. For humans in particular, that involves playing with sub-vocal and sub-visual reactions that refine our readiness to select appropriate (real) words and pictures to point at things, and to establish agreement with each other regarding which words and pictures are pointing at which things.

Our excellence in this area outstrips, not surprisingly, our intellectual understanding of the skill, and it was natural to spread the myth of inner words and pictures, even before camera and early (pre-connectionist) computer technology showed us examples of actual inner words and pictures (in the form of retrievable film and text files), and tended to reinforce the myth. Maybe the myth helps us master the skill, in ways that make it even harder to unpick, objectively. But what's really going on is playing of a complex social game with symbols that are outside not in.

You may disagree. Stick an electrode in someone's cortex (or a madeleine under their nose), you say, and chances are the person accesses just the stored files, the pictures or other sensory images, that I presume to deny. Not necessarily. Think of the brain as a complex coil of coiled springs or elastic bands, disposed (by innate constitution and its history of environmental tweaking and prodding) to respond to stimulation (not least an electrode) with symbolic behavior. We can see in this way that recall isn't access to a more or less corrupted file, but a more or less convincing symbolic reaction. Perception likewise... kinda.

Anyway, why worry about the straw man of some literal inner woodland, which the opposition will rightly deny they ever implied, and will put down to misunderstanding and rhetoric, when we have this more urgent matter of, er, an iron man of error?? If you see what I mean. A man to whom all sides seem in thrall.

No. There's no reason to believe that it's perceiving a mental picture of the tree
— Terrapin Station

Having / hosting / receiving / making / storing / processing / being a mental picture of the tree?

Any of those? — bongo fury

All of those, then? But, like a photograph, it (the perception/mental picture) is a more or less direct trace of physical events, and the opposition are claiming otherwise? They are claiming it's less realistic, like a painting?

If so, then I have to be quite annoyingly arrogant and say "you're both wrong!" (like Homer Simpson, tragic I know.)

But yes. I say: "none of those". Mental pictures are a myth. One as old as real pictures, and probably responsible for all the mutual incomprehension in this kind of discussion. (I did warn you.)

No. There's no reason to believe that it's perceiving a mental picture of the tree — Terrapin Station

Having / hosting / receiving / making / storing / processing / being a mental picture of the tree?

Any of those?

Perceiving the tree is seeing the tree as it is, from a particular point of reference, via the mechanisms of perception--receiving sensory data via light or sound or touch, etc. where nerve signals are sent to your brain, etc. — Terrapin Station

Is it (is perceiving the tree) experiencing a mental picture of the tree?

Just wondering. Not planning any traps. Not that I could possibly hope to catch you in one. (Noble testudine.) Just curious where you stand on that question.

To be fair, if your Inuit says "delicious" while throwing up, you will object along the same lines as when he calls "blue" what we call "green". So you can treat (1) and (2) merely as sorting different domains (psychological responses to foods vs foods, respectively) in much the same way, which is good old classification.
— bongo fury

This is true, — StreetlightX

Hooray!

and it reinforces what I was getting at re: variables of meaning. — StreetlightX

Boo!

In the case of the Inuit who throws up or scrunches up his face while calling the food delicious... — StreetlightX

But bear in mind I was suggesting (first, in the bit you quoted, an alternative coming the paragraph after) that we interpret his "delicious" as sorting the domain of subjective reactions to foods, not the foods. He is calling his reaction a "finding-it-delicious"; describing a reaction not a food.

... we know that those reactions are relevant to his use of the word in a way they are not when it comes to the word 'green'. — StreetlightX

Bearing in mind the choice of domain, you wouldn't be saying that, would you? A reaction's being a throwing-up would be relevant to his use and our use of "finding-it-delicious" in exactly the clear and obvious way that an object's being (reflecting) a certain physical shade is relevant to his use and our use of the word "green".

On this basis, and with the mastery of langauge that we have, we would question whether he knew what the word meant. — StreetlightX

Well, yes. But now you've flipped and are (with me) assuming a sorting of subjective reactions. Which is great, but you think you have implicated the "relevance" business into the scenario. I don't agree. Allow that "relevance" into the idiolectic sorting of foods, sure.

On the other hand, the Inuit who throws up at the mention of the word Green likely doesn't have an issue with the meaning of the word green, but some kind of pathology. — StreetlightX

Ha ha, but seriously, and notwithstanding that this is based on the foregoing misunderstanding, I disagree. Your (Pitkin's) theory seems to me founded on an easy but unhelpful distinction between negotiable and non-negotiable systems. Your use of green might well turn me a funny colour, and, far from being pathological, this could obviously matter to future usage.

To be fair, if your Inuit says "delicious" while throwing up, you will object along the same lines as when he calls "blue" what we call "green". So you can treat (1) and (2) merely as sorting different domains (psychological responses to foods vs foods, respectively) in much the same way, which is good old classification.

Or you can treat them as sorting the same domain (foods) in systems maintained on different social scales: standard usage vs idiolect. (Or dialect, somewhere in between.) Both classifying, once again, just with different criteria, if any, and at any rate effecting different divisions of the domain. I.e. disagreeing, as people do.

Also, why any need to distinguish type (3), as though classifications of colour, psychological responses and anything else aren't all subject to social agreement, dispute and negotiation?

Ok, it's seems you didn't get my point — ssu

Well I was definitely talking about usage, and aware that you weren't, directly.

Nonetheless I thought our views might be commensurable :wink:

Maybe not.

I think we're approaching some kind of agreement. — ssu

So near, and yet so far.

With your admirable aversion to correlation 2 (reforming a perfectly good vague predicate according to an arbitrary bi-partition of the naturals), and your interesting insights about natural development of more complex vague systems (your few-grains... heap... mountain, etc., and by the way I suggest smidgen for the first), you really should be an enthusiast for the heap puzzle, not one of its detractors!

But you repeatedly misapprehend my meaning and TheMadFool's too, if they don't mind me speaking for them.

Isn't it the number of sand grains in a collection that determines the heap-ness?
— TheMadFool
No. That's how you just get to the paradox: you are insisting that an exact number of sand grains determines what a heap of sand is. — ssu

The problem is simply to assume that you can do it, and that you get an exact answer. — ssu

No! You think we are committing correlation 2, but all 3 of us are opposed to that, I assure you. Others are more or less cool with it, their doubts (if any) assuaged by gestures towards allowing a distribution of different sharp thresholds. Which process, as I was saying previously, hopefully draws them back into the game at some point.

What we (I, and TheMadFool if I'm not wrong) are admitting is that usage of many vague labels like heap relates to numbers without difficulty in some cases, e.g. a single grain, and the problem is to describe the fuzzy border further along. Your passion against settling for an arbitrary sharp border, which we applaud, stops you from admitting this, and from appreciating that a vague category usually correlates in this puzzling way with some or other more fine-grained (often continuous) series.

Rude and unwelcome, as you say, to contrive such a background series in some cases. But consider musical scales. Twelve equal ("well tempered") divisions of the octave is some people's sole map of the terrain. Diatonic keys/scales all defined, for them, as subsets of these divisions. But plenty of alternatives persist, some with more wiggle room at each step, some with less, all of them dividing the octave differently (but nearly all into fewer than 12 steps). Potentially, all of them are independently viable, so that correlation or commensuration is unnecessary - and to some tastes undesirable. And the practitioner of any one system has no need to refer her judgements to any physical measure of the pitch continuum. But in practice plenty of mixing happens (blues scale theories anyone?) and it would seem a bizarre privation not to refer any good description of the result (how it divides the octave) to the scales that are being mixed and to the background continuum (or a discrete approximation of it). No?

No reason to fear the interrelating.

If you [ssu] are against either (I meant both) of these reductions, then hooray. If your talk of "incommensurability" isn't, after all, about trying to separate usage of heap from the naturals, then even better. — bongo fury

No second hooray, then: you think usage of heap should be kept separate from the naturals. But still hooray!

"You have to draw the line somewhere" is itself the problem. — ssu

Yes, I said that too. I'm saying it's an inappropriately crude reform of actual usage, and that radical reform may be unnecessary anyway. We both recommend following actual usage instead. But I'm happy to follow usage with reference to numerical comparisons, despite the challenges of the heap puzzle. I'm against unnecessary reform, but enamoured of careful correlation, or "commensuration" with number talk. Partly because ordinary usage of heap seems pretty deeply soaked into ordinary usage of number words. You are so appalled by inappropriate reductions of systems to arithmetic that you won't hear of any such intermingling.

Hooray if, for example, you want to resist this correlation because you have a sense of clarity or absolutism about certain cases of heap and of non-heap, and a sense that the same clarity will transmit from these cases to certain others.
— bongo fury

The issue won't transmit so easily, because notice the definition of incommensurability: two or more quantities having no common measure. — ssu

Yes! I do notice that, and I'm grateful you followed my reasoning, poorly expressed. Yes, I was talking about a sense of likely transmission from case to case, a sense fueled by having started the game well away from the fuzzy border in question. I agree that we have to be careful how we formulate this intuition. We have to deny the transitivity of the transmission in some acceptable way. No need to assume this is not feasible, though.

4) So in which natural number are you in the end...exactly? — ssu

Who said exactly? We are interested in tracing vague discourse. Such as,

Yet "somewhat large" or "a small number" is quite practical sometimes — ssu

... Well, quite! And here you aren't going to deny that our usage of "small" and of "large" map in some interesting way onto the naturals, are you?? No, apparently not...

assuming there is an universal agreement just what the range is. — ssu

The challenge of the heap game is to describe the fuzzy/tolerant bounds of this tacitly agreed range. Although I'm not sure I read that last quote right.

So your correlation 2 goes totally against the definition — ssu

Not sure I understand. I'm correlating two systems (both apparently in working order) of grain-collection labels: one is the system of two labels, heap and non-heap; the other system is the naturals, with respect to grain-collections in particular... a single grain, a pair of grains, 3 grains, etc.

The apparent behavior of the first does seem to correlate in some way with the second. The game is to try and discuss the correlation without paradox. But we can map certain of one system onto certain of the other, and get the feeling that some "commensuration" or correlation is there to be described adequately, somehow.

Correlation 1 is the common policy of settling for a different grade of heap for each natural, which is tantamount to giving up on heap vs non-heap. (So game over in that kind of play.)

Does this help?

In the case of the heap, the WD may say: "We shall consider any haphazardly thrown together comparatively identical objects a HEAP if hit has 100 or more elements, and a NON-HEAP if it has fewer than 100 elements." — god must be atheist

Yes, the arbitrary threshold solution: correlation 2, above.

I'm glad you chose so as to give some breathing space to non-heap, this time! Going for 4-grains-or-more seemed a bit extreme, but fair enough, you wanted to think outside the box of entrenched usage? Anyway, this way (100) you get more of a sense of "absolutely not!" at a single grain.

We lose, of course, any sense of give, or tolerance. You make a good case for not caring: the scientific context may be about nothing to do with usage of "heap"... nor of "hunger", etc.

If we can interest you in trying to characterise either of these usages (or of some more emotive predicate... poverty? ... where your threshold is liable to dispute), then you may want to examine a possible distribution of thresholds, to accommodate some fuzziness. And it begins again...

But what about the big picture, a poll of judgements, or of individual thresholds? What if the tail end of such a distribution (of thresholds) reaches back to a single grain? From your observations about means, we guess that it will.

Then, for some enthusiasts at least, this play of the game is over. From their point of view, you won't play. You decline to agree that a single grain is absolutely not a heap. You admit that this grain is, in the current idiom, "on the spectrum" of (usage of) heap. Albeit at one far end of that spectrum. You've lost one of the two required (and puzzlingly opposed) intuitions that we are trying to reconcile. — bongo fury

The term ''heap'' in common usage doesn't actually mean a ''certain'' number of grains. — TheMadFool

Agreed.

More accurately a ''heap'' includes in its definition the size of the components, the shape of the collection, in addition to the number of objects in the collection. — TheMadFool

(Assuming that by "its definition" you mean any reasonable characterisation of its usage...) Yes, there is a range of related aspects that help us decide.

Therefore, to isolate one variable, the number of objects in the collection, may be a mistake. — TheMadFool

Happy, myself, to make that mistake.

doesn't detract from the problem of vagueness, the central message of the paradox. — TheMadFool

Yes, and we can always play the bald man or other versions, for variety.

Based on that, I'm willing to state that a single grain is not a heap. Absolutely? Nothing in language, or anything else, is absolute. — T Clark

No, but I think when people are inspired to declare that a single grain is absolutely not a heap, they mean it is a safe distance outside the range of potential application of the label "heap".

This sense of distance is destroyed by one of the usual suggested reforms of usage (correlation 1, above), which is to have a grade of heap for each natural number.

Are you comfortable with that reform, for some or all vague predicates?

Wasn't there some point or utility in dividing the domain into relatively few zones? (A slightly different point, I know, but connected with the sense of distance.)

Basically you have incommensurability between a heap and an exact number of grains. The paradox rises when we don't take into account the incommensurability between the two. — ssu

Which will be all the time, then, because our usage of heap quite clearly appeals to numerical comparisons to decide cases, and withholds the term from, well, small numbers of grains. It relates in an obvious though not necessarily exact way to usage of large number and, like that sibling concept (which provides its own popular variant on the game), it (heap) inevitably involves some sort of commensuration with the series of natural numbers. Some kind of imperfect correlation, deserving of adequate formulation, why not.

So that's what's wrong. Simply that we think every logical system can be reduced to a simple system of arithmetic. — ssu

(Leaving aside the politics of reducing or not reducing formal systems to arithmetic).
Hooray if that means you want to accord respect to usage of heap, in some way that resists correlating it perfectly with the naturals, in either of the two common but unsatisfactory perfect correlations:

• correlation 1: having a different grade of heap for each natural. (Which is, effectively, some people's solution. Boo to that.) Hooray if, for example, you want to resist this correlation because you have a sense of clarity or absolutism about certain cases of heap and of non-heap, and a sense that the same clarity will transmit from these cases to certain others. I.e. a sense that a single grain is far from being any kind of a heap.
• correlation 2: an arbitrary individual threshold... a policy with some good PR (e.g. "you have to draw the line somewhere, and that's that"), but which will inevitably deprive the usage of its useful fuzziness / tolerance (boo).

If you are against either of these reductions, then hooray. If your talk of "incommensurability" isn't, after all, about trying to separate usage of heap from the naturals, then even better.

If "incommensurability" means settling for both reductions, to be used according to context, then boo, and the game isn't pumping intuitions as it ought, or at any rate sometimes can.

What this illustrates is that some concepts are simply vague and didn't require precise definitions because despite their vagueness conversation/discourse wasn't hampered. — TheMadFool

Except that you do want your conversation/discourse to withstand the pressure of logical clarification. The puzzle suggests that any clarification renders the clarity at one point (e.g. a single grain) incompatible with vagueness/tolerance further along. E.g.,

what is unambiguous to ALL is the starting point itself - one single grain of sand is definitely not a heap. — TheMadFool

I agree, but try setting a limit (higher than zero grains) on your projection of larger and larger samples of usage. E.g. on your statistical "support" for projected possible usage. It doesn't look very scientific to say no one could ever call a single grain a heap, after all. The intuition of clarity is lost rather easily. The heap game usually pumps it, though, which is fun, and gratifying if (like me) you think the intuition of clarity at some point is important.

I can't think of a situation where vagueness is a crucial aspect. Do you have an example? — TheMadFool

• When does an abortion become unacceptably late?
• How big an overdraft deserves a charge? My bank boasts that it doesn't charge for trifling amounts. Presumably it knows if it sets an exact limit for a free overdraft I will use that as my new zero credit. (Too right.)
• Musical intonation, and timing. You want a performance to push the envelopes (preferably in a good way), but not play wrong notes.

Yes. I think the vagueness of the word matches the vagueness of what it describes. — T Clark

Not sure about that. If it at least means we agree that vague words are useful in all their vagueness, then cool.

But does your conception of vagueness allow you to deny absolutely that a single grain is a heap?

Well, or if you want to know what people like (their preferences), or what their opinions about something are, etc., sure. — Terrapin Station

And very often (any slippery slope ethical dilemma, any artistic play with discrete perceptual categories, e.g. musical pitches), you want to work with the usage as it is, not precisified. So you need both intuitions, clarity and fuzziness. The heap game, and other natural incursions by logical thought, can make you doubt this is possible, so you abandon one or the other. Then you come to, and realise you are in a mess without both. E.g. IMO fuzzy logic: analog-digital interfacing in wolf's clothing. Or e.g. Brexit.

If we wanted to be more specific, we could tighten it up. — T Clark

But otherwise, we can use it as it is. With certain embarrassing difficulties on slippery slopes, admittedly.

What lots of people say only tells you what lots of people say. — Terrapin Station

Which, when you want to know about usage, is what you want to know.

And, otherwise of course, not. But I am interested in usage, so I am.

a situation where the idea of 'a heap of sand' has been an issue ! — fresco

Any "slippery slope" issue.

... is where, at any rate, 'a heap of sand' has seemed a pertinent analogy.

What if the tail end of such a distribution (of thresholds) reaches back to a single grain?
— bongo fury

Can you expand on that? — TheMadFool

By "threshold" I hoped to refer to what you were calling a "private definition of heap".

E.g., GMBA's 4-grains-or-more. From their observations about taking mean averages I guessed they were interested in a larger pattern or distribution of different individual thresholds, in order to reconcile their own sharp threshold with their own intuition of fuzziness. And I wondered whether this was likely to end up compromising their intuition of clarity, in the case of a single grain (your starting point).

Ok so far?

Sorry for not relating my comments directly to the OP. I was interested in that particular exchange between you, as an instance of the heap game, considered as a challenge to reconcile clarity with fuzziness. For which I am an enthusiast.

That makes sense but the definition of "heap" in this case would be private and others will probably disagree with you.
— TheMadFool

You're absolutely right. That's why I made no bones about it, and did not declare that my proposition is the ultimate answer. I came out straight away and said under what circumstances my opinion holds. — god must be atheist

But what about the big picture, a poll of judgements, or of individual thresholds? What if the tail end of such a distribution (of thresholds) reaches back to a single grain? From your observations about means, we guess that it will.

Then, for some enthusiasts at least, this play of the game is over. From their point of view, you won't play. You decline to agree that a single grain is absolutely not a heap. You admit that this grain is, in the current idiom, "on the spectrum" of (usage of) heap. Albeit at one far end of that spectrum. You've lost one of the two required (and puzzlingly opposed) intuitions that we are trying to reconcile.