I agree that induction can't be justified using deduction, — Purple Pond

And that is the only kind of justification which Hume is seeking to deny to induction. He isn't trying to discredit induction as an enterprise, he is only asking how, in general, it might get done. Rather than inventing some infallible method, he quite sensibly looks at how animals generalise beyond their experience. You can question the flow of sources backing up his biological and psychological claims about the role of habit, but you can't say he is inconsistent. Quite the opposite. He is probably reaching these claims through the exercise of precisely those habits of mind that he ends up claiming are efficacious (though fallible) for such a purpose.

What I find odd is that right after Hume talks about how induction is unjustified — Purple Pond

Nope! He approves of it.

From what I see, it's not only that Hume uses induction when he argues that induction is unjustified, — Purple Pond

Nope! He loves it.

Hume is using induction as if it were a perfectly fine method to show that, after all, it's a rather arbitrary method (habit, custom). — Purple Pond

Nope! Not arbitrary, depends on experience.

Whereas, I see it as a game of 'pretend', on which we must collaborate.
— bongo fury

Yes, I understand this, but where does the "we must collaborate" come from? — Metaphysician Undercover

So... you do understand how I might see your example (of how you use the words to point at different things) as a game of 'pretend', but it surprises you that I might see this as likely to involve collaboration?

You wouldn't expect a game of 'pretend' to involve agreement about what is to be pretended? (If it is to amount to a game between or among players, and not just a set of one-person games?)

Do you recognize a difference between loving a person and using a person? — Metaphysician Undercover

Rather, you are saying you oppose dignifying a narrower, technical sense of "use" whereby it means, more specifically, "using a word to refer to something" (https://en.wikipedia.org/wiki/Use–mention_distinction)? You want instead to emphasise and keep in play the very general sense of "using something in some way"? Resist reducing linguistic "use" to the mere pointing of words at things?

Such a disagreement between us (where you resist what I embrace) is what I said I expected to be the case, yes. Do you agree this is the disagreement? — bongo fury

Agreement (about just where it is we disagree) looming in sight? No, I don't kid myself, but anyway...

You say,

When I say something to someone, and the person understands what I have said (understanding is demonstrated by the person's actions), I do not think that it is the case that the person agrees with how I use the words to point at different things. I think it is simply the case that the person understands how I use the words to point at different things. — Metaphysician Undercover

Exactly! As though there were some fact of the matter (to be understood) of how you use the words to point at different things.

Whereas, I see it as a game of 'pretend', on which we must collaborate.

You say,

So for example, when a person speaks to me using a lot of jargon which I do not think is warranted in the situation, I might understand what that person is saying, but I wouldn't agree with that person's use of words. — Metaphysician Undercover

Whereas I reject the jargon for the reason that it is not conducive to the necessary collaboration. We won't be able to agree (enough) what things (we should pretend) the words are pointed at.

Hence the gulf between our agendas, explaining why you answer this,

Do you associate meaning with use? (Or were you just interrogating T Clark on the point?) I certainly do associate the two. Equate them, even. But probably I see it/them quite differently to you. I see it as definitely not a matter of fact, but one we can reliably find agreement on in many cases (the clear ones). Like the case of a single grain of wheat not being a heap, snow not being black etc. I deny that you can (within the language) succeed in pointing the word heap at a single grain. Whereas, from what you say, I'm guessing you will accept any such attempt at use as inevitably counting as an instance of use of the word, however anomalous? — bongo fury

... with this,

I do associate "use" with meaning, but I would not equate the two. I believe that meaning extends beyond use. We could consider the metaphysical distinction between "good" and "beauty". "Good" is associated with use, but "beauty" is something desired for no purpose, just for the sake of itself. So "a good" is desired, and called "good" for some purpose, use, and it is meaningful because it is useful for that purpose. But things of beauty are desired and are apprehended as meaningful, though not because they are useful for a purpose. That brings meaning more toward the desire, rather than the act which is intended to fulfill the desire (use). This is why I believe that "use" accounts for some aspects of meaning, but it doesn't account for the entirety of meaning. — Metaphysician Undercover

Which is fine, I'm not complaining. We have different agendas, different half-baked theories of discourse. I speak for mine when I say half-baked - yours can be done if you like.

As expected, very different views on "use", the difference resting, if I'm not mistaken, on whether we see reference as a matter of fact.

Bongo had said that we strive for agreement, — Metaphysician Undercover

... about, specifically, which words (or pictures or sunsets) are pointed (already or eventually) at which things.

I was aware that as a description of human discourse this calls for plenty of clarification, and I was trying to begin it by alluding to the "inscrutability of reference": the (alleged) fact that any actual connection between symbol and object is in our imagination or diagram. (Straw man version: no bolt of energy passes between symbol and object.) MU thought this irrelevant, so I wasn't surprised to find it difficult to know how best to engage with their subsequent critique, or whether it really engaged with mine.

But I fancy that their evident fear and loathing of equivocation might be related to my own fascination with what I see as a kind of equivocation at the heart of the social game (of agreeing what is pointed at what). As when, for example, we equivocate between implying that a particular token is (or isn't) pointed at a thing and implying rather that every single token "of the word" is (or isn't) pointed at the thing. Not to mention the equivocation dual with this, between referring to a single thing and referring to each of a whole class of ("same") things.

Not that I would think that all of this equivocating is necessarily a problem, if properly understood. Nor that I'm assuming anyone else would think it necessarily a problem, or that they don't already understand it better than I do. Hard to know what people's assumptions are in a discussion of this sort. Well, obvs.

Being smothered to death by a blanket though does not seem like a good way to go. — Fooloso4

You're drunk, aren't you?

... reposting... below

Sure, why not. — Fooloso4

No reason at all. We're all gonna die. Etc.

Let's compromise: snooty joke.

In my opinion Witty [...] was a genius who stopped his thinking at a premature insight, whereas he ought to have proceeded further in his thinking.

"A conclusion is a place where you stop when you got tired of thinking." -- traditional, origin unknown. — god must be atheist

Well! With these kinds of views, I'm surprised you dare to show your face here in church.

I think our poor little three year old has suffocated under her blanket. It seems that no one has been paying attention to her. — Fooloso4

Fair, if snooty, point. If my last post above is in any way to blame for your sense of dislocation then I should admit that I didn't explain how I might have expected MU, or anyone, to appreciate the relevance of "inscrutability" to the girl's efforts. In fact, I didn't even link back to here,

But if you think of "meaning" in this way, as something which is attributed to words, you would have to accept that we can use words without knowing the meaning of the words. How would we characterize this type of use then? The child gets some sort of message across to the parents, but we cannot call it "meaning", because the child doesn't know the meaning. What is the child doing?
— Metaphysician Undercover

She is doing what we all have to do all the time, to a greater or lesser extent. Play the game of pointing the words (or pictures or sunsets) at what they (already, or are destined eventually to) point at. About which there obviously can be (as famously noted) "no fact of the matter". But about which we are nonetheless happy to strive to agree. — bongo fury

... which might have helped - since neither of us, here, is badly neglecting the child. I generalising unashamedly, yes.

Do you, also, find there being or not being a fact of the matter of meaning to be irrelevant to the girl's concerns?

Bongo had said that we strive for agreement, — Metaphysician Undercover

... about, specifically, which words (or pictures or sunsets) are pointed (already or eventually) at which things.

I was aware that as a description of human discourse this calls for plenty of clarification, and I was trying to begin it by alluding to the "inscrutability of reference": the (alleged) fact that any actual connection between symbol and object is in our imagination or diagram. (Straw man version: no bolt of energy passes between symbol and object.) MU thought this irrelevant, so I wasn't surprised to find it difficult to know how best to engage with their subsequent critique, or whether it really engaged with mine.

But I fancy that their evident fear and loathing of equivocation might be related to my own fascination with what I see as a kind of equivocation at the heart of the social game (of agreeing what is pointed at what). As when, for example, we equivocate between implying that a particular token is (or isn't) pointed at a thing and implying rather that every single token "of the word" is (or isn't) pointed at the thing. Not to mention the equivocation dual with this, between referring to a single thing and referring to each of a whole class of ("same") things.

Not that I would think that all of this equivocating is necessarily a problem, if properly understood. Nor that I'm assuming anyone else would think it necessarily a problem, or that they don't already understand it better than I do. Hard to know what people's assumptions are in a discussion of this sort. Well, obvs.

If we say that there is a "way of using" a word, then the generalization is intrinsic to this concept, "way of using". What would validate a "way of using", if not some faulty assumption that X (a particular instance of use) is the same as Y (a particular instance of use)? — Metaphysician Undercover

Nominalist, heal thyself!

- Does unconscious processing = unconscious awareness ? (e.g. in a thermostat)
- Does unconscious processing = unconscious attention ? (e.g. in a CCTV camera)
— bongo fury

What your definition of Awareness and Attention ? And of unconscious processing too — Basko

What my examples suggest is that, by any definitions plausibly grounded in common usage, Awareness and Attention fail, by themselves, to distinguish conscious from unconscious processing, because they pervade both.

But that shouldn't discourage the defining and the modelling. We (or they) will get there in the end!

My hobby horse is, we need to improve our descriptions of consciousness by questioning the folk-psychology of inner words and pictures. AI (still a few years at least from creating consciousness) appears to have moved on from the time when it assumed a basis in image files and other internal symbols, located in and retrievable from memory stores. And so ought psychology. And philosophy.

But I agree that defining and recognising consciousness - what kinds of processing are to qualify - is key. My hunch (if you asked me? perhaps not!) is that the difference coincides very roughly with the gap between us and chimps... or human new-borns... or (so far, as yet) robots. What we can do that they largely can't. Which is play the social game of pointing actual symbols (words and pictures) at things in the world.

As expected, very different views on "use". Thanks for going over yours once more.

Anyway, I remain a fan of your previous diatribe against (other people's) unnecessary multiplication of types or categories of meaning.

My questions are simple :

- Does consciousness = Awareness ?
- Does consciousness = Attention ?
- Does consciousness = Both ? or Something else ? — Basko

... and helpful, I think. How about the following refinement?

- Does consciousness = conscious awareness ?
- Does consciousness = conscious attention ?
- Does consciousness = Both ? or Something else ?

To which we could add,

- Does unconscious processing = unconscious awareness ? (e.g. in a thermostat)
- Does unconscious processing = unconscious attention ? (e.g. in a CCTV camera)
- Does unconscious processing = Both ? or Something else ?

Answering (any or all of these) is taking a punt on picking the best way to discover and explain the difference between conscious and unconscious processing.

Thanks for the further clarification.

I'm guessing you can't mean "there is no such thing as 'using something' in a general sense because each instance of using something is unique and particular"?

Rather, you are saying you oppose dignifying a narrower, technical sense of "use" whereby it means, more specifically, "using a word to refer to something" (https://en.wikipedia.org/wiki/Use–mention_distinction)? You want instead to emphasise and keep in play the very general sense of "using something in some way"? Resist reducing linguistic "use" to the mere pointing of words at things?

Such a disagreement between us (where you resist what I embrace) is what I said I expected to be the case, yes. Do you agree this is the disagreement?

As expected, very different views on "use". Thanks for the clarification.

What other way would it be? Figurative pain? Metaphorical pleasure? Abstract taste? Well, maybe that one for some people. Non-literal feelings?

I dream of platonic reds and functional sounds. — Marchesk

Ok... I mean, SUPPOSING all that were ok... how do you answer the inevitable, literal-minded question, "where are they, then?"

Are they in a brain?

What's this --- we are happy to strive to agree? In some instances we co-operate and truly do strive to agree, happily. But in other instances, like in the philosophy forum, we happily disagree. — Metaphysician Undercover

Happily? Only, I would say, in those lucky cases where we can agree about what we are disagreeing about (in my book, agree about what each of us were pointing the words at). Only then can we say: either, ok, it's a matter of opinion, we'll agree to disagree; or else, oh dear, one version must be wrong, but we'll allow both accounts to co-exist for now. But, in that case, only for now. I'm surprised you can't see the strife as striving for agreement? No one need assume that any eventual settlement must be congenial for all parties.

Hope you and T Clark don't mind if I butt in here, because it's relevant to the above...

Do you see a difference between knowing how a word was used, and the act of using a word? If you associate meaning with use, then I would say that knowing the meaning of a word is knowing how the word was used. This accounts for the fact that the same word has different meaning in different instances of use. Meaning is specific to the instance of use, and knowing its meaning is knowing how it was used in that particular instance. — Metaphysician Undercover

Do you associate meaning with use? (Or were you just interrogating T Clark on the point?) I certainly do associate the two. Equate them, even. But probably I see it/them quite differently to you. I see it as definitely not a matter of fact, but one we can reliably find agreement on in many cases (the clear ones). Like the case of a single grain of wheat not being a heap, snow not being black etc. I deny that you can (within the language) succeed in pointing the word heap at a single grain. Whereas, from what you say, I'm guessing you will accept any such attempt at use as inevitably counting as an instance of use of the word, however anomalous?

So these people are trying to create a division between this type of meaning and that type of meaning, without any supportive principles to show that one supposed "type" is actually different from the other. In reality, the meaning which a defined word has is no different from the meaning which a piece of art has, which is no different from the meaning which a beautiful sunset has. — Metaphysician Undercover

:up: :up: :up:

But if you think of "meaning" in this way, as something which is attributed to words, you would have to accept that we can use words without knowing the meaning of the words. How would we characterize this type of use then? The child gets some sort of message across to the parents, but we cannot call it "meaning", because the child doesn't know the meaning. What is the child doing? — Metaphysician Undercover

She is doing what we all have to do all the time, to a greater or lesser extent. Play the game of pointing the words (or pictures or sunsets) at what they (already, or are destined eventually to) point at. About which there obviously can be (as famously noted) "no fact of the matter". But about which we are nonetheless happy to strive to agree.

Spartan enough and general enough?

I just have them along with pains, sounds, tastes, thoughts, etc. — Marchesk

I meant literally?

Are you a philosophical zombie? Because you argue as if you have no conscious experiences. If I ask whether you experience pain, are you going to give me some functional/physiological response? — Marchesk

Ha ha, I have wondered if I am transitioning into a consciousness-denier! I don't think so. I think I'm learning to recognise some wrong descriptions.

Is it the skepticism about mental pictures / symbols in the brain? Do you need them in your intuition of consciousness or perception? You can have pictures and other symbols in a camera or a computer, obviously. Presumably they aren't sufficient for consciousness or perception. Are they necessary?

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.