Because.

Mornington Crescent.

:100:

And when I read your post I "imagine your voice", or so shiver my brain as to invite that modern rationalisation. Any rationalising is potentially disturbing. I can easily "hear" a chorus of competing drafts (more or less deranged) of each new sub-vocal thought. The more vivid the more deprived of sleep, I have to say.

What you demonstrate by giving a sensible answer, is that you do not on this occasion doubt the meaning at all. — unenlightened

Nah, only rather that when in Rome (i.e. ordinarily) I can play their language games, regardless their philosophy of games and rules. Not sure why you would say, or think that Witty would say, that in making a play I can't entertain competing hypotheses as to the Romans' hypotheses and dogmas about the game and the rules.

If I start to doubt that these words mean what I think they mean, what can I say about that? — unenlightened

That you have realised that there is no fact about that kind of matter?

The hand proposition is the big fat fact.

Yep. Zeno’s paradoxes also hinge on this logical issue — apokrisis

But do you see the difference I just pointed out?

Is reality discrete or continuous at base? — apokrisis

No, the sorites doesn't directly address that.

The sorites starts from the happy reality of being able to order a sequence of objects (grain collections, heads, photos) in correspondence with the natural numbers and to discuss choices of how to superimpose a dramatically smaller ordering on the same objects. — bongo fury

My argument is that predication is vague. But that is not a problem because we can sharpen it to the degree that pragmatically matters by adding constraints. — apokrisis

I'm willing to learn more about Peirce's and/or your theory of vagueness, sharpening and pragmatic constraints, within the limit of my low tolerance for abstract nouns. (This nominalism from which I do suffer.) Meanwhile, you may or may not be interested that Goodman has a detailed theory of those phenomena, which examines how sharpening of an important kind (replicability) is facilitated by vagueness at the edges of syntactic (and potentially also semantic) elements. Which thus explains the fortunate starting point mentioned above. And, I believe (as detailed here), the puzzle itself.

Create a quote in the normal way from the post in the other thread. Copy or cut it from the text box in that thread, return to your thread and paste.

It both might and usually does.... — apokrisis

Yes, but as I say, a nice feature of the sorites is how it shows that the vague and non-technical usage "everything is on a spectrum" can be interrogated, with interesting results, even on the discrete interpretation, "everything is on a scale of tiny steps", or "there is only (some large number of) shades of grey".

And it's not clear that a non-discrete interrogation could look anything like the sorites, where a problematic place is reached worryingly soon: it would probably have to be more like one of Zeno's puzzles, where you can't get anywhere.

:up:

A spectrum suggests unbroken continuity. — apokrisis

I suppose "spectrum" ought to have come with a health warning: it alludes only to the vague non-technical attitude of mind that "everything is on a spectrum". Which nicely describes the attitude of this play-stopping first reply:

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

Yes of course "spectrum" might suggest unbroken continuity. The fact that the sorites doesn't have to is for me one of its most attractive features. So, warning not too late, I hope.

That's why I said that doubting that a single grain is a single grain is playing a different game... An interesting variant, quite possibly. And I admit that black vs. white (or red vs. yellow) does raise the question of continuity (or at least density... with terminology potentially confusing there also), and that that question is deeply relevant to the issues that concern us. But the classic heap version, as well as bald vs. hairy, and "small" vs. "large" number, show that the question is removable.

Equally so with the colours. We can simply use a sequence of different (discernibly or indiscernibly, it doesn't really matter) shades and - with or without presenting actual samples of the shades, it doesn't really matter either - ask the same questions about those as about the numbers of grains or hairs.

Note that @Don Wade's version is essentially that one. His sequence of photographs may be either discernibly or indiscernibly different, and need not correspond to each cardinal size of grain-collection. (Except for the first few.) Each step in the sequence might represent a fairly large addition. Just as the actual change in luminance from shade to shade is arbitrary.

The sorites starts from the happy reality of being able to order a sequence of objects (grain collections, heads, photos) in correspondence with the natural numbers and to discuss choices of how to superimpose a dramatically smaller ordering on the same objects.

But the sorites paradox demands discrete acts of addition or subtraction. — apokrisis

Yes, and these create enough of a puzzle.

So we have the two poles of a metaphysical spectrum right there. The discrete~continuous. And the confusion arises in trying to satisfy these two formally antithetical constraints at the same time. — apokrisis

No, not at all, the discrete version is enough.

All of your strenuous metaphysics might be missing the point.

But the meaning of bits (the signified) seems to remain somewhat vague. — T H E

Yes, with the interesting exception of systems of notation, as investigated by Goodman (along with the varieties of vagueness) in Languages of Art.

is pure sensation or physiology — javi2541997

So not real enough?

True purple, for which there seems to be no place in the physical spectrum, — javi2541997

... You mean, no corresponding light beam with a clear, single spectral peak? Each point (or strip) along the length of a rainbow produced by a glass prism, say, is reflecting such a beam. So the rainbow display is roughly analogous to a pure sine tone sweeping up in pitch through time. Stop the sweep at any moment and have a stable pitch, and that stable tone is roughly like a point (or strip) along the length of the rainbow.

On this analogy, purple is like a musical chord (or an ordinary non-pure tone from a violin, say). A light beam with more than one spectral peak in frequency. Real enough, then?

So as Don says, — apokrisis

... and then, spectrum, spectrum, spectrum.

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

You might at least now see how that is your position.

Sure, a spectrum has extremes. What the puzzle often reminds us, though, is that, pervading language, there is a subtly (puzzlingly) different way of looking at it. Bald and hairy, black and white, on and off, heap and whatever its potential antonym (pittance?)... they all operate perfectly well as alphabets (or conceptual schemes) of two characters (concepts) separated by a comfortable no-mans-land. The puzzle is how to look closely at that without it reverting (under however much cover of mystical pazazz) to a mere spectrum.

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

Or rather, the right predicate value is "vague". — apokrisis

Ah, so maybe we have a new game?

[1] Tell me, do you think that a single grain of wheat is vaguely a heap?

Granted, we may not. You may not be inclined, as I am, to respond,

[2] No of course not, and I know I'm a long way from the smallest number of grains that could possibly be even vaguely the smallest heap! Far enough that a single grain is an obvious and non-vague case of a non-heap!

... leading in turn to the intrigue of,

[3] And would you agree that adding a single grain could never turn a definite case of non-heap into a vague case?

... and so on.

No communication of one person to another can be entirely definite i.e. non-vague… — C S P

But yes it can in the sense that we can reproduce digital or alphabet-based text or speech or music indefinitely. Puzzling, certainly, when we look closer at the fuzzy boundaries of the characters, phonemes, notes and tones.

And now, my spam: How to look closer.

I thought I was clear that fruitful oppositions are what it is always about. So you can be too vague, and also too pernickety, in your language. — apokrisis

But is it too pernickety to insist that a single grain is absolutely and obviously not a heap? That's what I was trying to get at.

How is that my position? — apokrisis

Well,

And we can be looser or more precise about the matter to the degree we might agree that a less vague, or even more vague, definition is useful. — apokrisis

So if push comes to shove, just specify the precise (possibly unitary) size of heap. Everything is on a spectrum.

Language would seize up if it had to be exact beyond the point that exactitude is useful. — apokrisis

Still, if push comes to shove, give the exact point on the spectrum.

"Is that man bald?" "Is that a heap of wheat?" Given a logic of vagueness, more or less becomes the best possible answer. — apokrisis

Ditto.

And this larger view can change its mind. It can insist on a sharper dividing line as to a definition of baldness, or relax it as well. — apokrisis

Ditto. These all suggest,

[1] Tell me, do you think that a single grain of wheat is a heap?
[2] Well, certainly, [when pressed for details we must admit] it's the very smallest size of heap. — bongo fury

My own response would be to question your claims of being certain that a single grain is a single grain. — apokrisis

Well, that's a different game.

Language would seize up if it had to be exact beyond the point that exactitude is useful. — apokrisis

Don't you think it would seize up for the opposite reason, too? If it didn't have a syntax, and in many cases a semantics, based on clarity and the consequent possibility of potentially endless digital reproduction based on sameness of "spelling" (in the widest sense)?

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

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

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

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

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

Which seems to be your position. Oh well.

Predicament (G): The spontaneous correction reported in (F) has, pleasingly, become voluntary; or has, at least, coincided with a marked improvement in the efficacy of (B), so that I can expect to recalibrate and regain certainty about my location sometimes as readily as by tooting or plucking on a nearby instrument... but more usually demonstrating the continued necessity of "going into a bit of a trance". Anyway, generally, a much quicker trance.

(H) Another pleasant surprise: although the trance still requires silence in order that the image should land without being thrown off course, landing in occupied territory is easier than expected. Quite probably off target, but with the feasibility of assessing the matter. Off target probably as a result of achieving a musical fit of the core/standard image (usually the Ravel) with the occupied territory. Identifying the g4 itself to a diatonic step in the occupied territory (the sounding music), for example. Probably also not just any diatonic step, but one that allows further agreement between other steps. But, as I say, the degree (or at least the fact) of deviation from the correct target feels (and seems upon verifying to be) discernible, despite all the noise. So I'm able to have a go at guessing the key of music on the radio, say. I should report on this more systematically, or more often, now that I'm not filing reports on (because rarely verifying) the acts of silent calibration.

(I) The faintest glimmer of hope of being able (in silent mode) to recalibrate (i.e. B) without losing entirely the previous image: being able therefore to re-land that previous image (at the same pitch) in the recalibrated context so that I can see what pitch it really (according to the new context) was. Then I may be able to monitor the (non-relative kind of) accuracy of random earworms (D).

Vagueness is often illustrated by the sorites paradox, or "problem of the heap". — Don Wade

Yeppity.

There seems to be a problem with our (human) ability to think in terms of exactness (focus) - as in a grain of sand, and in terms of generalities - such as a pile of sand - (at the same time). — Don Wade

So you say. But this is more about your proposed solution of the puzzle than about the problems actually created or revealed by the puzzle. Fair enough, you have a theory. But several people in your other thread pointed out that ability may be less relevant than need or inclination. So it's not clear (ha) that you are really answering the puzzle.

So, is vagueness itself a philosophy? — Don Wade

It's a feature of natural language.

So, not surprisingly there are philosophies of vagueness, yes.

Or do you mean, has anyone thought of basing their philosophy on vagueness? Yes, all the time, because it's a feature of language.

... Apparently not.

Conceiving of philosophical zombies appears to require it being obvious that we are each two things instead of one.

I'm sorry you're upset.

I don't suppose you could clarify whether you hold this notion,

that everything that exists is actual. — Banno

to be itself mistaken? Maybe I jumped to the conclusion that you do.

I wondered if you had a better argument against it than the fact that we make up fictions?

related...
— bongo fury
Always leave the quantifier hanging. Then you make no commitment. — Banno

That, er, needs developing. I suppose I can understand if you would rather not.

"Pegasus flies" is true in the domain of winged horses.

is no kind of an argument that winged horses exist in some related sense of the word.

:roll:

You are using the word "literally" to mark a domain of discourse. — Banno

You are using the phrase "domain of discourse" to confuse use and mention. (See above.) Which is a bad habit.

Moreover, there are innumerable true modal statements ranging over things that are not actual. — Banno

Which is hooking it to your veins.

Dictionaries are definition porn. You'll have seen plenty of that?

We all talk to ourselves from time to time — jgill

Might the comic possibilities of that line maybe explain our willingness to indulge such a brilliantly bonkers theory?

Language gave us imagination, but a deep confusion about it, too. Witness our precarious and probably dangerous modern pathologising of "hearing voices".

I'd buy (and for a long while tried to) the hypothesis of "godlike instructions", if only I could believe that humans haven't always and ever been inwardly rehearsing clever things to say to each other. (And the likely replies.)

"A hobbit walked into Mordor" is true in the domain of Lord of the Rings. — Banno

But is there, in all of Heaven and Earth, a domain of Lord of the Rings, containing hobbits?

I don't generate any internal humming when I sing with others, so I have no idea what you're talking about. — frank

Fine...

You are authorised to verify the match between your internal image of you humming and a similar real sound event, by your proven competence in verifying the match between two sound events, such that your judgement agreed with others'. I.e. by singing together.

I don't know how to get a third party verification, the first two parties being me silently humming and me listening to it. — frank

You are authorised to verify the match between the two internal images, one perceptual and one not, by your proven competence in verifying the match between two perceptual images, such that your judgement agreed with others'. I.e. by singing together. (Not using an app! :vomit: )

It's not a private language of private sensations, it's a public language of private sensations and/or their corresponding public stimuli.

Yes. I understand what numerical identity is. — frank

My bad.

I don't understand the nature of qualia in general. What's happening? How does it work? — frank

Yeah, me too. Or, at any rate, how does the myth work. :lol:

I can check the frequency I'm humming. Only I know the sound of internal humming. — frank

But of course you probably wouldn't ever check the frequency of an external sound, as such. You would check that it matched in pitch with another sound, such as that of a tuning fork. Likewise you can check the pitch of an internal humming against another image or an external sound or both.

The physics is a kind of back-story. Indeed, if we are partisan internalists, we might even aspire to "divide through and cancel it out", leaving only the internals (the images both perceptual and merely imagined or recalled); just as Witty suggests we might in certain conditions eliminate the internals, and their questionable solipsistic back-story (the private language).

Numerical identity? — frank

the relation that holds between two relata when they are the selfsame entity, that is, when the terms designating them have the same reference — Collins

As opposed to identity in a particular (known or unknown) respect.

I really don't understand the nature of an internal humming. — frank

Is it different to qualia in general?

Existential quantification can range over things that are not actual — Banno

Only by being (or making the clause) literally false.

They get confused, because they think this implies hobbits must be actual. — Banno

Only if they think the story is literally true.

Uncanny...

There's a genetic anomaly that's associated with perfect pitch. — frank

Interesting theory.

On the other hand, some people are tone deaf. — frank

Likewise. (But a rather antiquated theory.)

So if there is a classification system in play, we each learn it from whom? Ourselves? — frank

Each other.

The social divide is between those who can and those who can't reliably compare tones (whether internal or external) that are in entirely separate musical contexts, so that there is no feasible chain of local and easier intermediate comparisons reaching between them.

Obviously there is huge variation in the skill of relative pitch: of maintaining a chain.

The can't beat them so might as well join them [the absolute pitchers] comes partly from knowing (or failing to remedy) my limitations. Which are, mainly, losing track around modulations, some more than others obviously. — bongo fury

How do you know the early and later internals are the same [pitch]? — frank

In the kind of imagery talk that I think the PLA isn't designed to attack: by comparing them for pitch just like a pair of externals, or like an internal and a corresponding external.

Internals and externals are all part of the same game or classification system.

The internals might (if you like) be memory traces, like computer records. They don't literally match in frequency, but they match in pitch exactly as do all and only (or mostly) sounds that also match in frequency. So they are like a mental image of a time-table that can be tested for correctness. (cf PI 264)

Does Witty elsewhere critique this notion of a public sensation language? (Grateful for leads.) But it clearly isn't the private one.

The private language argument misleads us into thinking that we must recognize two things as being the same thing in order for such a recognition to be useful. But this is not the case, because we only need to recognize similarities, and hence types. — Metaphysician Undercover

I don't see that. I think it attacks the British empiricist psychology of ideas and impressions: the narrative of a private construction of mind from sense-data. His argument seems to be that identity and similarity of the internals has no basis when asserted in private. I don't see any conflating of numerical identity with similarity.

The problem inherent in the private-language scenario is (I think I gather from Witty) the lack of criteria for identifying and classifying internal entities (sensations, qualia, images), should these be (as folk-psychology often leads them to be) conceived as the sole and sufficient basis for their own classification. Where, on the other hand, such criteria are available, because the entities are conceived instead as part of a larger, pre-existing game (e.g. there is meaningful comparison with blood pressure, or actual train times), no immediate critique is offered.

So I don't think that your returning

back to the same starting frequency — frank

is a problem for Witty, because you are judging the pitch-identity (vs. difference) of the earlier and later 'internals' according to a pre-existing system that (if it recognises them as internal) maps them to externals that are identified or distinguished according to frequency. So he wouldn't see that judgement as a problem. He would doubt that the imagery-talk is true literally, but he wouldn't be sceptical about the viability of pitch comparisons among internal images...

I found I had to practice to even duplicate it with my voice, — frank

...nor between images and actual sounds. And neither would I. So I'm still curious as to the nature of the difficulty you describe.

Far as I can tell, no... or, not so as the ear beetles would matter, or cause an unacceptable philosophical scene, by refusing to 'drop out of the equation', at least in principle, and give way to corresponding external stimulus types.

To be fair, the creatures haven't exactly been (as Witty's figure has it) 'cancelled out' from my 'arithmetic', here. I'm certainly talking the talk of internal sensations (phenomenal qualia, mental images). I guess this is largely because I'm talking about non-perceptual imagery. But Witty doesn't seem to regard either the presence or absence of an external stimulus as characteristic of the problematic scenario critiqued as "private language". The problem inherent in that scenario is (I think I gather) the lack of criteria for identifying and classifying the internal entities, should these be (as folk-psychology often leads them to be) conceived as the sole and sufficient basis for their own classification. Where such criteria are available, because the entities are conceived instead as part of a larger, pre-existing game (e.g. there is meaningful comparison with blood pressure, or actual train times), no immediate critique is offered.

So I don't think that your returning

back to the same starting frequency. — frank

is a problem for Witty, because you are judging the pitch-identity (vs. difference) of the earlier and later 'internals' according to a pre-existing system that (if it recognises them as internal) maps them to externals that are identified or distinguished according to (an ordering correlating roughly with) frequency. So he wouldn't see that judgement as a problem. He would doubt that the imagery-talk is true literally, but he wouldn't be sceptical about the viability of pitch comparisons among internal images...

I found I had to practice to even duplicate it with my voice, — frank

...nor between images and actual sounds. And neither would I. So I'm still curious as to the nature of the difficulty you describe.

@frank's thread.

No worries.

Haha. No? Not a plausible reading of "the whole of math"?

Consistency and provability are always relative to a given axiom system. — fishfry

Sure. I was assuming that by "the whole of math" Boolos meant simply the maximal (consistent) extension or union of all the systems you mention. Thereby saving himself the bother of translating "any system strong enough to satisfy the Hilbert-Bernays provability conditions" into words of one syllable.

By omitting the fact that we are always working in a particular axiomatic system, the essence of the matter is ignored. — fishfry

But on my assumption,

First of all, when I say "proved", what I will mean is "proved with the aid of the whole of math".

is hardly omitting the fact (of the relativity of proof to system).

what he wrote was wrong. — fishfry

How?

My guess is that he means ZFC, — TonesInDeepFreeze

Cool, although it didn't matter what he meant, so long as it was bigger than e.g. Robinson arithmetic, was my point.

Isn't he just ensuring that what 2 + 2 is equal to is being discussed with respect to a system big enough for the second theorem to apply?

https://en.wikipedia.org/wiki/Hilbert%E2%80%93Bernays_provability_conditions?wprov=sfla1