That's not an argument, it is an opinion. — A Raybould

You're really missing the point. "Evolution is conservative therefore we all experience redness the same way" is also an opinion. Opinion dismissal is no justification for another opinion; all opinions should be held to the same standard, even if you happen to hold one of them.

Furthermore, it is an opinion of an argument, not an opinion about how minds work. — A Raybould

Not... exactly. This is a guideline to applying relevant standards. You're arguing about differences and similarities of experiences between humans, under the presumption of a physicalist interpretation. So let's start here... is there reason for you to disagree that the key factor to look at here is the neural correlates to experiences?

You are entitled to your opinions, but don't expect anything like this, doubly removed as it is from any substantive issue, to be persuasive. — A Raybould

But convincing you isn't supposed to be the goal. The goal is supposed to be applying a valid truth criteria. In this case, the criteria of truth should have something to do with neural correlates to experience... would you agree?

ETA:

What does 'binding' mean? How are 'interesting' categories determined? — A Raybould

Binding in this case simply means creating some sort of stable state at some layer in the network; "interesting categories" can be self-discovered by features of the net analogous to how deep neural networks work. I'm not too interested in fleshing out this theory since I don't particularly subscribe to it... I'm more interested in gating the justifications to the things that they're supposed to be including (here is an ancient video including presentation of self-discovered categories using deep neural nets; but here is a link to a paper discussing the kinds of things I think should be included in any speculation).

At this point, my working hypothesis is that you do not have any plausible arguments for that proposition. — A Raybould

Your working hypothesis doesn't work.

Your next sentence reinforced that view, and your final paragraph did not lead me to change my mind.

Did you bother to try? At the highest level of abstraction this seems incredibly simple to me. We just postulate that there's a large number of potential experiences and that the brain, while learning to see colors, simply picks any of these to bind to the interesting categories. Synesthesia demonstrates that there are different kinds of experiences to pick from, and that they can at least be useful in some people as category tags even cross-sensually. My natural response to this is, if there are this many kinds of experiences, how many can there be? Incidentally, what made you make up your mind in the first place such that it would need to be changed?

but plausibility itself does not come out of nothing; it needs an argument in support. — A Raybould

But the argument here is, at least IMO, trivially made. The arguments given for same-experience to me sound like classic textbook hasty generalization. It seems you're describing an approach that is particularly vulnerable to argument from personal incredulity, and is way too quick on the belief button for my tastes.

(FYI, there's a lot of other stuff you're saying I've no problems with; it's just that I'm only going to pick on where we conflict).

Biologists tell us about the color experiences of cats and dogs, why not humans? — Harry Hindu

So? We can talk about color experiences of humans too... we agree on color categories in those 95% of individuals I described earlier. But that says nothing about the experience being the same... only that the categories are.

it is a plausible hypothesis. — A Raybould

...and so is its null hypothesis.

For example, I am not a synaesthete, and so will clearly experience some things differently than those who are. — A Raybould

...color grapheme synesthetes (for example) still see color... they're just able to associate graphemes with color. Plausible explanations for color-grapheme synesthesia are here. The existence of conditions like synesthesia only seem to beef up the plausibility of the null hypothesis.

What arguments are there for the proposition that everyone experiences things differently? — A Raybould

I could think of arguments, but that's irrelevant. The only argument necessary for my strong defense of a non-position is that the null hypothesis is plausible (see below).

Or do the three of us just have diffferent intuitions about how different they are?

You misunderstand. I don't have a theory of similarity, differentness, or even commensurability of experiences of color. What I have, instead, is a standard... an expectation of what kinds of things I need to see before I start doing silly things like believing a thing, that no random guy with some strong opinion and bad arguments is going to get me to lower. And as unfair as it may seem to be, I expect others to meet this standard before I can grant them my approval of their conjectures.

So far the arguments I've heard for same experience is, we're the same species, and evolution selects for fitness. Okay, sure, we are, and it does, and yet I can't use that argument to prove we all have green eyes, so how are you going to use it to demonstrate that we experience red the same way? It's simply not good enough... you need an argument that actually argues for what you're arguing for.

Then we can know about color experiences — Harry Hindu

Well, no... but we can work out what a metamer is and a theory of protanopia and deuteranopia. I'm pretty sure the things you're looking for are somewhere in the visual cortex.

Sure, thanks to differences in genes. — Harry Hindu

Or differences in development.

What differences in genes would we point to that makes us experience different colors when looking at the same thing?

You have this backwards. Both alleles and environmental differences exist in the human genome and human development; both in general, and in relation to known traits involving the visual system (e.g., there are alleles of genes that express the precise chemistry of your cone opsins; and vast differences in the distribution of cones between eyeballs); so it's dubious to just a priori speculate that there's no variance in the visual system elsewhere (in this particular case, in factors related to how color winds up getting experienced).

You have a same-experiences conjecture based on us all being the same species. That translates to a hypothesis that the development of color experiences in humans is largely independent of alleles and environmental variations in brain development.

And that is the thing you need to demonstrate in order to able to say that you have an adequately justified conjecture.

Then we aren't talking about knowing red, rather we are talking about knowing what it is like for Harry to see red — Harry Hindu

Correct.

I should say that I don't believe that we each experience different colors when looking at the same thing. We are related - members of the same species that evolved from prior species with eyes and brains, therefore we should experience things similarly. — Harry Hindu

That argument isn't compelling. Being of the same species suggests tons of similarities, and we do have those... we generally tend to have opposable thumbs, walk upright, sweat, etc. But there are also a lot of differences that we have; different eye colors, body types, hair types, etc. Simply being of the same species is not enough to suggest we have the same color experiences; I would be more compelled if the argument specifically invoked studies of how the process of learning color works, and supported the thesis that there's a common representation (under the presumption that the nature of experience is built by the nature of the representation, and various other caveats)... but to simply conclude that the color experiences are the same because we're all human sounds to me more like guesswork.

you have billions of children all getting what is said and learn the words for the colors — Harry Hindu

Agreed.

So, what exactly is the problem? — Harry Hindu

Well, it's this:

(A) Red only exists as an experience, and not outside of an experience. — Harry Hindu

(B) Your inverted spectrum would still be consistent, where your blue equals my red, — Harry Hindu

A and B conflict. If we define h-red to be the experience you have when you look at a red crayon, then this category would be completely useless... only Harry Hindu could relate to it. If instead, we define c-red to be the "same color" as the crayon with "red" written on it (as we do in the kindergarten), then we could talk about said things, so long as we demonstrate the capability of recognizing what "same color" means, which we can establish with your kindergarten exercises for about 95% of individuals.

but that isn't saying anything about the object rather it is saying something about us as different individuals with different eyes and brains that interpret the wavelength that enters our eyes. — Harry Hindu

That's closer to being right, but note that this isn't an "experience" versus "wavelength" argument at this point, given we've introduced new entities with properties to consider (like "eyes").

The same way your kindergarden teacher showed you - by showing an object or picture that is red. In showing a variety of different objects, none of which have anything in commom except their color, you should be able to realize what I'm referring to when I use the same sound when showing you ask the different objects. — Harry Hindu

But that's conveying an "equivalence class" of objects and associating it with an "equivalence class" of sounds. This exercise requires me to recognize what "same sound" means, but let's grant that as a detail (and also, btw, we need to recognize objects as "not red"). I am then expected to have a capability of seeing that some of these objects have a "same-ness" to them and some a "different-ness"... if say I'm a protanope, I would have some difficulties here. If hypothetically I were a tetrachromat, it might be a bit confusing at first but I'd be able to pull it off.

But none of these are requiring me to match my experience to the teacher's experience. Quite the contrary; I'm being asked to recognize common and distinct properties "of" objects... the exercise is treating color as-if it's a property of objects. The entire exercise is ignoring experience... except insofar as it is used for me to measure this property "of" objects. E.g., if I had an "inverted spectrum", nobody would be the wiser, or even care.

Red only exists as an experience, and not outside of an experience. — Harry Hindu

I don't think it's even possible to define red in terms of an experience. How are you going to tell me which experience the color red is?

From the SEP entry on the topic:
...
Why do you think is the philosophical significance of the argument against physicalism? — Wayfarer

I think you've misread something. You quoted me as objecting to the meaningfulness of saying that science's ambition is "of course" to extend the level of prediction and control over all of nature. Following that anthropomorphic attribution of motive to science, you start quoting SEP's entry on the knowledge argument.

Why[sic-What?] do you think is the philosophical significance of the argument against physicalism? — Wayfarer

I think generalizing the motive behind objecting to physicalism has the same flaw as generalizing the motive of science; people have motives, ideas do not. I could speculate about what people's motives generally are, but I'm not sure I'm well informed enough in statistics of what's going on in peoples' minds to realistically apply any truth criteria to the matter.

As for what KA is about, we experience things, and there's some disagreement over whether or not to call that experiencing a physical process. I'm not sure at the lowest level if anything even is at stake; if it boils down to two different views of what "physical" means, then the stakes may very well be illusory.

The ambition of science is, of course, to extend this level of prediction and control over the whole of nature. — Wayfarer

I'm not sure this actually describes a physical system well, or that saying that this is "the ambition of science" says anything meaningful. Maxwell's Demon vs the 2LT, for example, seems to suggest that even in the most deterministic of worlds predictability may not be allowed.

But the problem is, subjects are not fully determined by physical laws - you can't predict what a subject will do or say.

...and I'm not sure you can say that either.

because the brain-state of knowing what brain-state corresponds to actually seeing red and the brain-state of actually seeing red are themselves two different brain-states and being different they can't have the same effect. To clarify further, suppose x is the brain-state of seeing the color red and y the brain-state of knowing x. — TheMadFool

Just as an additional point of clarification... once Mary sees red for the first time (fast forward through all of the "learning how to see" red to this point), Mary is experiencing red, and that is a brain state.

Now, let's have Mary do nothing but walk back into the room... no red objects allowed. There is likely, presumably, another new brain state... that of Mary knowing that she saw red.

I'm not objecting to anything here... but oft in these discussions the treatment of experience is equated to treatment of remembering having an experience, and I wish to point out that these two things are also separate. The former is where the "what-it's-likes" apply... but the latter is really a form of a self-model (knowledge-that one has experienced x is a model that there's such a thing as an experience of x, that you had it, that you are capable of having it under certain kinds of situations, and possibly that you are capable of recognizing the experience and comparing it to the particular past one).

You say that in that case the result isn't necessarily chaotic. That's what I'd like more information on, because it seems intuitively like it must be chaotic, — Pfhorrest

It's a bit tough to talk about since in my mind the specs are a bit fuzzy.

These tournaments I describe are often playing with some game theoretical situation... in these situations there could be an ideal strategy such as "pick at random A 30% of the time, B 5% of the time, C 0% of the time, and D 65% of the time, regardless of any past behaviors of the entity you play against". A simple program playing this strategy could do no better; suppose we had a pragmatic ideal... call it the MTS, which uses a Mersenne Twister to approximate this strategy in a straightforward way (it just generates large numbers uniformly, and uses partitioned ranges according to the above percentages to drive its selection directly). We might then have another candidate in the pool that also employs a Mersenne Twister, but this program runs an incredibly deep Monte Carlo Simulation (so call this the MCS), and it turns out this program would play very close to the ideal strategy as a result. In practice in such a tournament MTS could consistently rank first followed by MCS. Generally in this situation, your top ranking programs would be stable regardless of whether the programs predict (MCS) or not (MTS). But I get the feeling that you're reasoning that MCS would somehow be unstable because it predicts; to which I reply, if in at least some situations, you have a predictor program whose behaviors are not-chaotic, then your reasoning underspecifies what's required for a system to be chaotic, and in this sense your reasoning is flawed.

Intuitively (from my end), there's a bit of fuzziness as to what you're describing. You seem to be comparing (a) what an entity would "ordinarily" do, to (b) what an entity would do "if" it had a predictor. But what are (a) and (b) actually describing? In the above scenario the MTS is a type of "(a)", but how would you apply "(b)" to it? And the MCS is a type of "(b)", but what is the "(a)" that the MCS would do? Or is (a) vs (b) comparing the MTS to the MCS? If that's the case, the actual behaviors of the MCS in this tournament are really more approximations of a stable strategy, not a factor generating chaotic behavior (at least in and of itself).

if you could send information back in time (backward causation) to show someone their future, their foreknowledge of that future would then change their behavior and so also change what their future ends up actually being. — Pfhorrest

If information simply went back in time at all, it would be a "resulting" physical state that is also a "prior" physical state, but being a physical state in at least a Newtonian sort of sense, it should have some effect on the resulting physical state which could lead to a different result. You wouldn't need an intelligence to cause the conflict. Something akin to this is behind the Chronology Protection Conjecture.

Likewise, if that person merely predicts their own future in an ordinary way (or just hears such a prediction), those expectations about the future will change their behavior and so make their actual future vary from the predictions. — Pfhorrest

Suppose instead of a person, it's just a computer program competing in a "tournament" of sorts. A program may be coded, say, to run Monte Carlo simulations of other programs to affect its odds of winning the tournament. In such a way we can abstract out the intelligence and the person. (Incidentally I've competed in such tourneys before... it's fun). But this isn't changing any program's behavior; it's simply coding what the behavior is. And the result isn't necessarily chaotic just because your program is playing by these rules. Does that make sense?

Either we are the atoms, or we are some magical observer that only experiences the information that the atoms produce — Kev

...or, we're implemented by the atoms.

That is that if causality is constant, and we truly are observers of a mind that is determined by external forces, we would not have self-awareness. — Kev

There seems to be some suspect "I am not part of the universe" kind of thing going on in this reasoning.

There is no such thing as a "scientific" psychological study. — Gregory

If scientific is the standard and this is the rationale, I would think you should be skeptical of both Napoleon Hill's and Dunning-and-Kruger's studies. So I'm particularly interested in the fact that you're only skeptical of the latter.

See the WIki article. — Banno

Oh I'm not so interested in the actual Napoleon Hill, as I am in the epistemic standard being employed (though I would like to imagine Napoleon Hill playing a nice game of chess against DrDrunkenstein).

Same as every psychological study that has ever been done: observation — Gregory

Were they scientific, though? You know, as opposed to those unscientific Dunning-Kruger studies?

Napoleon Hill had perfectly legit reasons to believe that if people tell themselves they are good at something they become good at it through the use of their subconscious. — Gregory

...

So I reject their conclusion as unscientific. — Gregory

What scientific methods did Napoleon Hill employ?

there are only three options when providing further proof in response to further questioning: — Münchhausen trilemma (wiki)

• The circular argument, in which the proof of some proposition is supported only by that proposition
• The regressive argument, in which each proof requires a further proof, ad infinitum
• The axiomatic argument, which rests on accepted precepts which are merely asserted rather than defended

...but I'm not sure I get the point of playing the Münchhausen trilemma as a game.

I don't think that theorem has much, if anything, to do with compatibilism. — Gregory

It's a fine point in the mechanics you describe. Suppose we're mulling over three options; A, B, and C. In terms of "effort" they may rank B, A, C; in terms of "fun" they may rank C, B, A; and so on. Under compatibilism there must be some sort of actual process resolving these desires into a selection. Whatever that process is, you can view it analogously to the desires being voters, and the options being what's voted on. The analogy dissolves when you consider that the math doesn't change just because these desires aren't literally voters. All I'm saying is that "strongest" desire doesn't necessarily fit the mechanics... it's simply some sort of messier resolution.

Things seemed already planned for me, but I seem most certainly free at the same time. Is the pre-established harmony choices of my own soul that come to the surface for me to see? — Gregory

Well if there are deterministic rules, then for all practical purposes our soul is physical and made of meat... but said meat would still cause things.

I tend to be skeptical about the subconscious or unconscious or pre-conscious making chooses for my ego — Gregory

That seems to presume that your ego is limited to what you're conscious of. I'm not quite sure I buy that; it violates specific observations involving self reflection. To me, it appears that anything meaningful that I call "me" is more than what I'm aware of... it's just that the stuff I am aware of happens to be that part that I'm aware of. The "me" is bigger, consisting of all of the stuff I mean, all of the stuff I know, all of the stuff I know how to do, and so on, whether I'm currently thinking about such things or not (and furthermore, the factual knowledge about my "me" seems to be a constructed model of myself). Furthermore, I don't think I can be conscious of a thing before there's a thing to be conscious of, so unless things loop from consciousness to mulling and back (or something to that effect), they generally start unconsciously.

You're mistaken in where your unwarranted assumption lies.

The one and only assertion I made in my original post was: "there are quite a few... hazy assertions in the preceding deluge." — Key

This presumes that there are hazy assertions. Under a charitable interpretation, you misread the assertions.

I beg you to find any understanding of Laplace's demon that would remotely agree with you. Laplace's demon is a concept of causal determinism. — Key

In my second post (replying to you) I stated that the probability of an actor existing in a universe of potentially limitless realities and being bound to a maximum of two conscious choices is less than a snowman's chance in hell. — Key

Okay, so Laplace's demon is a concept of causal determinism. But under causal determinism, there is only one possible sequence of events. If there's only one possible sequence of events, there is only one reality. So what are these limitless realities you're talking about? I only count one of them.

Your unwarranted assumption is that @Gregory is talking about potential realities. Getting back to my original statement, options being considered in a choice are considerations, not realities. Considerations are just mental states. You don't need two potential realities to consider two options; you just need two mental states.

Here's a few questions you should consider answering: why does your actor only possess a greater and lesser choice? — Key

Because you quoted Gregory, and Gregory's model is that we always choose the "strongest" desire. This implies a well ordering of desires that specifies the choice, such that there's a well defined maximum. I've already critiqued this using Arrow's Impossibility Theorem, but it works just fine for two choices. But aside from there technically not being a clean concept of "strongest desire", the number really doesn't matter, so long as it's more than one.

Sorry; let me rephrase this more simply... you're making an unwarranted assumption.

If you look rather briefly at the entirety of my post and the references I made to the original post... you may note the thick, goopy sarcasm. The question mark might also help you. — Key

Okay.

Your footnote for 1 was here:

But I think we are free none the less to choose the lesser one and although we never will choose it, we will always consider it¹. — Gregory

"Free ... to choose the lesser one" admits to a potential interpretation that the lesser is part of the consideration and that the actor is the cause of the choice. The particular phrasing of this sentence supports this interpretation.

If Laplace's demon indicates the possibility for a good number of realities, the likelihood that only two of those are ever available to be chosen from isn't too hot. — Key

Laplace's demon would indicate that the greater happens. This is consistent with the fact that there was a consideration of the lesser and that the actor was the cause of the choice; that is, all three of the following can be true:

• The actor considered the lesser and the greater option
• The actor selected the greater option
• Laplace's demon specifies that selecting the greater option would happen

I can see a conflict if we add the presumption that "free to choose the lesser" must require that the actor be capable of violating his own nature. But you would have to specifically add that presumption to get the conflict.

we always follow our strongest desire, but we are free in our choices. — Gregory

Out of interest, I offer the view that this is a bit too "easy" of a theory, and there's reason to suspect it can't quite work this way (this is quite nit picky, but I'm actually particularly interested in the weeds). In particular, when we choose something, we choose options, not desires; the desires we have sort of rank the options, and somehow choices come out. If you view this like voting, then Arrow's Impossibility Theorem comes into play... this suggests that at least when more than 2 options are presented, then there's simply some sort of messy conflict resolution between the options, and AIT kind of proves that it has to be messy.

assuming there are only two possible choices is completely ignoring Laplace's demon? — Key

Options being considered in a choice are considerations, not "realities". (I have no qualms how you map this to "free will" one way or the other, but having a single outcome does not entail a choice was not made... all it entails is that if a choice was made, that outcome was what was chosen).

Could they be the same? — Banno

They're distinct... Laplace's demon has free omniscience... Maxwell's demon's knowledge has costs.

Of course; but which one: Maxwell's or Laplace's? — Banno

Depends on the discussion... the conversation about epistemic limits reminded me a lot about Maxwell's demon.

The standard philosophical prejudice is that given an accurate enough account of the position of the box and a given ball, a competent physicist will be able to tell us which of the bins across the bottom the ball will land in. — Banno

That's absurd... no competent physicist would even attempt such a thing. They would use a demon.

The idea that one is a product of zero. — Metaphysician Undercover

Oh you silly confused soul, seeing liars behind your eyelids. I suppose you also see lies in the fact that 3*3=9, given we're multiplying two threes and getting an odd number? Maybe this whole math thing isn't going to work for you.

You mean, I am here to learn, and not to be deceived, don't you? — Metaphysician Undercover

Alright I'll play. What is the nature of this deception?

First class example of deception. — Metaphysician Undercover

Yes, but it's quite ineffective... we already knew you weren't here to learn. Along the same lines, I never heard that paragraph after the one you quoted about the history of primes (gee, I wonder why, wink wink... o/c I know why and everyone with a browser can find out why in 30 seconds). Also along the same lines, that wiki page on mathematical objects that you could just as easily have looked up as the primes is still there.

And what about 1? — Metaphysician Undercover

Good question. 1 is the product of zero primes: https://en.wikipedia.org/wiki/Empty_product

I have yet to see a definition of "mathematical object" which allows for the application of the law of identity. — Metaphysician Undercover

Where have you looked? Or am I your personal search engine now?

Sure, leaving the definition — Metaphysician Undercover

We have the terms rational and real, so, you're just whining.

I do not understand numbers well enough to create such a theory. — Metaphysician Undercover

I beg your pardon:

I'm still waiting for someone to explain to me how the so-called "object", or "number" which is represent by "1" and is by definition not a multitude, and therefore not composed of parts, can be divided into nine parts. — Metaphysician Undercover

I note here that you're not just asking for a definition of number. You're asking for a definition of number that has these properties.

Also:

I'm a metaphysician, and some mathematical axioms are derived from metaphysical concepts such as the concepts of unity and continuity, which are features of "being", a subject of metaphysics. So I'm not exactly a layman on these issues. — Metaphysician Undercover

Something tells me that it's partly solipsism, partly an expression of aggression against the imposition of an external control over his thinking. — dex

MU has a metaphysical theory of numbers, he's a believer in them in the full b-word sense (it's part of his identity... almost literally), and modern math is kind of a heresy wrt it. That's my take. I personally envision his theories as being roughly of both the form and value of Eric the half a bee.

It was only in relatively modern times that mathematicians wanted 1 to be a number, and this created the problem which required an exception to be added into the rule of primality. — Metaphysician Undercover

What are you talking about, "problem" and "required"? The fundamental theorem of arithmetic states, in the modern reading, that all positive integers can be represented as a unique product of primes (barring order). That's perfectly phraseable with prime including 1, it's just clumsy: "All positive integers can be represented as a unique products of primes, barring order, excluding from said product the number 1". Both phrases describe the same fact. One is just clumsier.

I provided a... — Metaphysician Undercover

Pretty much.

This is the point I've argued from the beginning of the thread. To know whether the op offers an acceptable representation of numbers, we need a working definition of "number", — Metaphysician Undercover

Sort of, but not really. "Number" applies to a lot of things. But that's not a problem; it's actually a benefit. The definition of number should not merely not be nailed down; it should be open. But part of the point of categorizing these numbers is so that we can give particular kinds of numbers names.

Clearly "2+2", and "4" do not refer to the same "object" by any conventional definition of "object". — Metaphysician Undercover

This is jargon... they refer to the same mathematical object.

Any system of interpretation which ignores the role of "+" within an equation, to claim that "2+2" says the same thing as "4", cannot really be taken seriously. — Metaphysician Undercover

Anyone who uses the decimal system to count above 9 shouldn't take your pronouncement seriously.

Your so-called history of prime numbers is backward compared to what Wikipedia has to say: — Metaphysician Undercover

...

So, according to Wikipedia — Metaphysician Undercover

...while we're on the subject, what does the very next paragraph say?

Then, in more modern times mathematicians wanted to treat 1 as a number, so they had to include it in the prime numbers and this created a problem. Now they've excluded 1 from the prime numbers, by definition. — Metaphysician Undercover

Welcome to the year 2020. So what's the problem?

What is a problem is conceited people making the universal, uncategorized statements like "we already know what numbers are", when it's very evident that they haven't the foggiest idea of what a number is. — Metaphysician Undercover

...so where does that leave you? Do you have the foggiest idea what a number is? Do you make universal, uncategorized statements about numbers?

It is not logical to refer to a property of a special type of number (real number) to demonstrate what a number is in general. — Metaphysician Undercover

I think you're lost, MU. This is supposed to be a thread about 0.(9)=1.

I apologize for not joining your little game, but I see no reason to restrict our discussion of "numbers" to real numbers. — Metaphysician Undercover

Well that's really easy MU. Here's the primary motivation, in your words:

I'm trying to learn the language, and I don't like inconsistency or contradictions within the language I use. Such things lead to misunderstanding and even deception. — Metaphysician Undercover

The way to avoid inconsistencies and contradictions that lead to misunderstandings and deceptions (aka, amphibolies/equivocations) where languages have homonyms is to restrict the conversation to applicable shades of meaning. When in a pool hall and someone talks about how to sink the 7 without sinking the 8, English should be regarded as a pool-technique, so it simply means to invoke a spin on the ball... countering a discussion invoking the use of English with debates about how some hypothetical guy from England might sink the 7 is a meaningless distraction. In this context, we're supposed to be talking about 0.(9)=1. 0.(9) is a repeated decimal. Repeated decimals are special cases of fractions, suggesting a treatment of at a minimal Q, though decimals just commonly invoke R. So to avoid misunderstandings and deceptions, to meaningfully talk about Q and R, we should be employing the context of one of these two things.

Incidentally MU, even if we don't restrict our discussions to the reals, 2+2 and 4 refer to the same object in the reals, and you claim they don't refer to the same object (again, in case you missed it, "Do you make universal, uncategorized statements about numbers?"). This implies you're flat wrong in at least one context. According to your pretended concerns about the inconsistency or contradictions with language leading to misunderstandings or deceptions... according to your pretense of avoiding smoke and mirrors, just having this single context in which you are wrong is challenge enough to warrant a clarification of your claims anyway... you know... to... avoid misunderstandings and deceptions?

TL;DR, we should restrict our discussion to the reals because that's the context within which 0.(9)=1 and 0.(1)=1/9 are meant to be discussed; i.e., it is this context from which the meaning of such things derives. Ranting and raving about what some guy in 300BCE would have called 1 is a meaningless distraction.

Denial is one of many possible responses. — Metaphysician Undercover

And you're immune to it?

What kind of nonsense is this? — Metaphysician Undercover

It was meant to be an analogy... primes are numbers, but not all numbers are prime, was the point. But apparently you're even more messed up than this:

They are called "prime numbers". And "one" fulfills all the conditions of "being called a prime", except that it is not a number. — Metaphysician Undercover

Utterly wrong. There is a history to the concept of prime numbers... after some time in the development of number theory, it was quite apparent that it would be more useful to exclude one from the definition of primes in particular to avoid having to keep making exceptions for it, especially in the fundamental theory of arithmetic which is heralded as being an especially important theorem. That has nothing to do with considering one as a number though... that ship has long since sailed:

1 (one, also called unit, and unity) is a number, and a numerical digit used to represent that number in numerals. It represents a single entity, the unit of counting or measurement. For example, a line segment of unit length is a line segment of length 1. — one

...but ultimately it's just a loss of religion. There's no actual deep reason to not consider 1 (and 0) a number, except a bunch of meaningless mumbo jumbo.

TL;DR version: That one is not considered prime has nothing to do with the consideration of one being a number. It's just yet another confusion of yours.

This is very clearly not true, as I think everyone else on this thread has admitted, except you. — Metaphysician Undercover

You still have no idea what you're talking about... consistent with everything I've been saying for 11 pages, this is a language barrier and you're still confused.

There is no clear definition of what a number is, and there are supposed to be different sorts, natural numbers, rational numbers, real numbers.

You're referring to the fact that @Michael listed some categories of numbers here; namely, N (the whole numbers), Z (the integers), Q (the rationals), R (the reals), and C (complex numbers). Those are indeed categories, but there are more; beyond C, there are quaternions and octonions. In contrast to R, there are surreals and hyperreals. Take just Z into the complex plan and you get Gaussian Integers. This is not an exhaustive inventory. All of these things have their own kinds of numbers, and we can even make up new kinds of numbers on the fly.

I'm far from unaware of this MU... in fact, we've both gone through this. Here is the post where you said you were "trying to learn the language". And here is the reply I gave you seven days ago. Numbers defined differently is not a problem for math; it's just homonyms... just a feature of languages. To avoid the issues a language speaker just applies context.

What the other participants in this thread have indicated is that "number" is just a vague term with no real defining features. — Metaphysician Undercover

Vagueness is not transitive. An animal can be anything. My pet is an animal. But my pet cannot be anything; my pet is a cat. A number in general likewise could be just about anything. But 1/9 is a fraction, and 0.(1) is a repeated decimal. Generally discussions of such things are in R, though Q suffices.

Sorry, but I have no idea what your little diagram is supposed to be showing. — Metaphysician Undercover

That doesn't surprise me, but I gave you a link to it. So I guess a bit more spoon feeding you is in order:

In basic mathematics, a number line is a picture of a graduated straight line that serves as abstraction for real numbers, denoted by $\displaystyle \mathbb {R}$. Every point of a number line is assumed to correspond to a real number, and every real number to a point. — number line (wikipedia)

On the same page:

Two numbers can be added by "picking up" the length from 0 to one of the numbers, and putting it down again with the end that was 0 placed on top of the other number. — number line (wikipedia)

Compare to here.

It's obviously not providing a definition, or any sort of indication as to what a number is. — Metaphysician Undercover

The diagram tells you how you're supposed to play the language game with real numbers. 0.(1) is a real number.

If you actually knew what your nonsense babblings were trying to whine about, then you should recognize that in this picture:

...we have a number line (top), whereby we add 2 (purple) to 2 (blue) by applying the addition rules (see links) to get 2+2 (green), and that refers to the same number (point on a number line, black, circled) as 4 (same point, literally). This counters your idea that 2+2 and 4 don't refer to the same number.

So how is that diagram supposed to argue your case?

Silly MU, there is no case. You have no jurisdiction, the defendant is a non-entity (language), there is no standing, and there is nothing actionable.

You're objecting to the rules of a language game by playing different language games, and pretending you've said something meaningful. That's all there is, except for the fact that there are 11 pages of it.

Sorry, but we haven't resolved the question — Metaphysician Undercover

Sorry, but we haven't resolved that there's an actual problem here (not to me, or to anyone else here that I've seen).

If you think it represents a number, then why is this number not a prime number? — Metaphysician Undercover

If turtles are animals, why do they lay eggs? Since when does being called a prime have anything to do with being a number? The very fact that you even asked this question and actually think it's relevant shows that something is majorly wrong with your "problems".

The point is that 1/9 is not a name for anything. — Metaphysician Undercover

the question of whether "1" is the representation of a number or not. — Metaphysician Undercover

1/9 and 1 sure look like they name points on the number line to me. So where's the actual problem again?

Your notion that a mathematical expression names a thing, is the problem you need to deal with. — Metaphysician Undercover

We already know what numbers are and what expressions mean. The only problem here is you, and we don't even have to deal with that problem. But you've diverted 11 pages on this thread so far on your ego tripping delusions of having a problem. That's the problem.

This idea allows people like fishfry to argue that "2+2" refers to the same object as "4". — Metaphysician Undercover

Looks like the same point on the number line to me. So where's the actual problem again?

In the eleven pages of your rantings, I have yet to see an actual problem.

Take a look at the divisibility of "1" in base two, and compare it with the divisibility of "1" in base ten, for a good example — Metaphysician Undercover

Lousy example. The number's representation is no more the number than you are a white M in a pink rectangle.

You keep telling people to take a look at binary. Okay. 1/9 = 0.(000111)₂. And? That's just another name for 1/9. Do you have a real point or a confused one? What do you think 1/9 being 0.(000111)₂ proves? Five bucks it only proves you're confused.

ETA: If you really want to learn what the fuss is about, try this.

^^-- here's a picture using the number line abstraction.

If 1 is divisible, its divisibility is different in base nine from what it is in base ten. — Metaphysician Undercover

Call me crazy, but why isn't a base 9 and a base 10 representation of the same number a base 9 and base 10 representation of the same number?