Is that what you're objecting to? That the area under 1/x from 1 to infinity is infinite? Or what mathematical fact are you objecting to? — fishfry

I'm objecting to the method employed by the person in the YouTube clip, which replaces the stated infinite limit, (approaches zero) with zero, as I referenced above. By that method, the equation for the volume of the horn resolves to pi, as stated in the op. If you have a method to figure out the volume of the horn without that substitution, then you might present it. If not, then we probably don't disagree, and we're just wasting our time talking past each other.

I suggest that the proper representation is that the volume is necessarily indefinite, rather than finite, and there is no paradox. This means that the amount of paint required to fill the horn cannot be determined. Therefore no act of pouring a determined amount of paint into the horn will fill it

The extended reals serve as a shorthand so that we don't have to use cumbersome limits to talk about expressions involving infinity. — fishfry

I think the real issue is that it's cumbersome to talk about limits when the subject is infinite, because it's contradictory. Is the horn closed (limited), or is it infinite (unlimited). Clearly the premise is that it is unlimited, infinite, and any mathematical axioms which deal with it by imposing a limit, are not truthfully adhering to the premise. And that's why the appearance of a paradox arises.

Let me change that to: "a result of a past act of thinking" — Ken Edwards

OK, so we have identified two features, the act called thinking, and the results of that act, thoughts.

If so how has that thinking been provoked? Might it not have been provoked by something exterior like a tree or a traffic cop. Or provoked by an earlier thought coming from either of the two minds or from the newly discovered default mind?

How does "directed" come into it? — Ken Edwards

What I tried to explain in the last post, is that i do not think that thinking is provoked, it just goes on and on, somewhat automatically. However, it is directed, guided. This is why it is not totally random like dreams can be, though dreams are generally guided to an extent anyway, and so are not completely random. We can know that it is guided rather than provoked, because we sense many different things at the very same time, and we only direct our thinking toward particular things. You would say that these are the things which provoke us, but if we ask why did this provoke, rather than that, we must turn to an internal reason and explain it by saying that the thought was directed toward this rather than that, for whatever reason.

So, consider your example, "a tree or a cop". What makes you think about the tree rather than the cop, or the cop rather than the tree? Think of all the visual stimulus around you, the aural stimulus, and things like smells. Of all those things, why do you direct your attention to this or that thing instead of the many other things? You would say that these are the things which provoke you, but it's not the thing which is responsible here, it is you who is seeing the thing as interesting. The thing is doing something, which for some reason interests you, so I turn to you, and ask why does this thing interest you. Why are you directing your thought toward this thing and not something else?

The sense of touch provides a very good example because it is very high in the hierarchy of capacity to attract one's attention. If something, or someone touches you physically, it's almost impossible not to direct your attention, and therefore think about that thing which touches you. Now if you think about the sense of sight, there is at any time many things within your field of sight, which you see, but you will not think about. So I think I can conclude that something touching me physically is much more important to me than something simply being in my field of vision. That's why when something touches me I direct my attention to it.

Banno thinks that if two distinct numbers are made compatible through an equation, then they become one — Banno

You expect me to believe that? Two distinct things become one and the same thing, if they are assumed to be equal. No, equal things are not the same thing. Doesn't anyone have any respect for the law of identity anymore?

Philosophers are trying to save the human race from their greatest enemy, themselves. They haven't been able to do it, therefore philosophy is a failure. Wait a minute, human beings haven't annihilated themselves yet, so on what basis is "failure" claimed.

The point being that we judge a process as a success or failure in relation to whether it achieves a stated goal. Snakes states the goal of philosophy as to "unlock general features of the universe", and concludes that since features remain locked, philosophy has failed. But Snakes seems completely ignorant of the role which philosophy has played in unlocking those features which have already been unlocked.

Banno thinks that if two distinct frames of reference are made compatible through a transformation theory, then they become one. What Banno doesn't recognize is that this is just a matter of using theory to reconcile the differences between two distinct perspectives. And so it is just a matter of Banno saying that they are one, when they are treated by the theory as two, and that's hypocrisy.

Ok to be fair, as I've mentioned, I've seen Gabriel's horn before but didn't watch the video, so I don't know if perhaps he said something misleading. But it's true that as x gets arbitrarily large, y gets arbitrarily close to zero. That's what's meant by "going to zero." It's a technical phrase meaning that as x increases without bound, y gets as close as you like to zero. But x never "becomes infinite" nor does y ever become zero. The mathematical phrasing is a clever and subtle way of talking about these things WITHOUT saying that x becomes infinite or that y becomes zero. It's your mathematical ignorance of this terminology that's leading you into error. And since you repeatedly do this, when Wikipedia and other online sources could easily explain these things to you, I must assume at some point you choose not to learn the math, but rather to flail at strawmen of your own creation. I don't mean to sound uncharitable but if you have a better explanation I'm open to hearing it. — fishfry

It's not a matter of what is "meant by 'going to zero'", it's a question of what value is given in the calculation. Look at 6:25 in the video where he's doing the calculation, plugging the values into the formula. He says "well one over infinity that's zero, so you get nothing from that".

Absolutely correct. Also absolutely irrelevant, since nothing in this problem involves dividing one by infinity. — fishfry

Clearly you are using a different calculation than the one in the video then. If you know of a method to figure out the volume of that horn, which avoids rounding off the infinitely small dimeter to zero, then maybe you should present it for us.

Do you happen to understand that there is no "closure at the bottom" of the cone? — fishfry

One divided by infinity is not zero, it is indefinite. If you assume that one divided by infinity equals zero, you assume that the value for y reaches zero, therefore closure. It's very clearly stated in the YouTube video, he says we're taking the value of y to zero. However, this clearly contradicts the premise that the horn continues infinitely. The real issue is that integrals are approximations, and infinity has no place in an approximation. So that method of integration is simply not applicable to an infinitely long cylinder.

-I am not sure what you mean by the word "directing". That is a verb and it requires a subject and a complement to make sense, "He directed me to his mother's house". So, could not the over-mind direct parts of itself to other parts of itself? I think much more probable, the over-mind directing the conscious min and visa-versa. — Ken Edwards

I use "direct" here in the sense you suggest, as to guide something. The issue I indicated, is that if the mind was directing itself, there would be no need to assume an "over-mind". And if we need to assume an over-mind as the director, it is because the direction is coming from somewhere outside the mind, somewhere the conscious mind does not have control over. But if we see that the nature of the mind is such that it is being directed by something outside it, then why wouldn't the over-mind, being itself a type of mind, have the same characteristics? So if we find that it is necessary to assume that the mind is being directed by an over-mind, I see no reason to stop there and conclude that the over-mind is not being directed by something outside of it.

The conscious mind cannot direct thoughts towards me because the conscious mind IS me. (I think) — Ken Edwards

So do you not find that you are capable of directing your own thoughts? If so then why do we need to assume a over-mind?

Remember that I assume that Thinking is not an abstraction anymore than belching is an abstraction. Thinking is the actual movement of a living piece of matter inside of the skull. — Ken Edwards

The question is what directs that "actual movement"? I'm sure you must have noticed that your thinking is generally guided toward specific goals, ends, purposes. It's what we call intentional. What is it which does that guiding? Is it the purpose itself which guides the thinking toward it? If so, what would choose which specific purposes to be guided by? But if this is a form of thinking which makes those decisions, as to what will guide the thinking, then we're just going around in a vicious circle. The thinking guides itself, and now there is no need to assume a mind, or an over-mind.

-I think thinking is the creation of thoughts that may or not lead to more thoughts ie questions and answers, and are things in themselves. The act of thinking can be precipitated by many kinds of stuff. A pretty sunset, an angry face, a question, a kick in the ass an erotic picture etc. — Ken Edwards

Here, I think we need to distinguish between what you call "precipitated by", and what I call directed. I think that thinking is going on all the time in my head, I cannot stop it. It goes on even while I'm sleeping, as dreams. So I think that the thinking gets directed toward these things which you mention, the pretty sunset etc., not precipitated by them. And, it seems to me like the more focused and directed the thinking is, the more productive it turns out to be. This is due to that relationship between goals, or purpose, and thinking. I might direct my thinking to the sunset for a short period of time, but this would just be a brief distraction, before I got back to thinking about more important things. Therefore the issue here seems to be a matter of determining what is important, and therefore ought to be thought about.

<So we ought to allow that thinking is an activity which can occur without any content, no thoughts, an activity without anything moving.

-I don't think that is a true statement. — Ken Edwards

But you just said:

I think thinking is the creation of thoughts... — Ken Edwards

If thinking creates thoughts, then the existence of thinking is prior to the existence of thoughts, so there is necessarily thinking without thoughts. Thinking without thoughts would be an activity without content.

Thinking is movement, (actually the movement of electrons in an electric circuit which can be detected). — Ken Edwards

If you check the physics on this, I think you'll find that the current moves through the electric field, rather than as a movement of electrons.

If you would have listened to me in those other threads, where I explained the deficiencies in mathematical axioms, especially those which make what is mathematically indefinite into some thing definite, like the closure at the end of the infinitely long horn, you would have no problem with this issue.

It's quite obvious that the contradiction is in "infinitely long horn". If you pour paint in the top, and it is infinitely long, the paint never reaches the bottom. But if you assume the horn has a closure, a bottom, just like you might assume that .999... is 1, then the horn gets filled.

The film clip just demonstrates the inconsistencies in how "infinite" is dealt with by mathematical axioms. In one group of axioms, "infinite" is allowed to be a real mathematical object, so the infinite sutface requires an infinite amount of paint. But in cases like .999... and the volume of the horn, the infinite is rounded off and given closure.

What did Jesus say? I am son of God, or, son of Man?

If you have a better word than my word "Over-mind" please tell me. — Ken Edwards

OK, I'll go with that term. We could almost just call it "mind", but that would imply that we were limiting ourselves to the conscious aspect. I think, that when we talk about "thinking" we are talking about a directing of the mind. So if we use the limited conscious "mind" as an example, we assume some sort of conscious directing of thoughts, when we say "thinking".

Notice here that "thought" is a noun, so there is assumed things, thoughts, and "thought" also represents a past act of thinking. I think we can characterize a "thought" as the product of a past act of thinking. It's like an object which has been created, like a memory, and is now employed in the act of thinking. That object might be a word, or some other symbol (mathematical for example), or an image, or something like that. Now, we have this representation of conscious "thinking", the limited type of thinking, as an activity which is directing, or some sort of ordering, of products (thoughts) previously acquired from this activity.

If we extend this now, to the "over-mind", then we are forced to forfeit from the conscious mind, the principal capacity, which is the capacity to direct, or order this activity. But this is contrary to our experience, which demonstrates that the conscious mind does have the capacity to do this directing of thoughts. To maintain consistency with this empirical observation therefore, we must deny any relationship of supervenience. There is not a relationship of necessity between the over-mind and the conscious mind. It also proves expedient to deny supervenience because if we pass this capacity to direct on to the over-mind, we have no means for locating what sort of thing actually does the directing, Then we're faced with an infinite regress, or determinism, or else some sort of homunculus.

So we have a little problem here which is that thinking is an activity of directing thoughts, and thoughts are the product of such directed activity, but we cannot locate what is actually doing the directing. To assign the capacity for directing to the over-mind is not the answer, because it is contrary to what we experience, that the conscious mind has some capacity to direct itself, free from the direction of the over-mind. But if the conscious mind, as a higher, more free power, emerges from the over-mind, as the base of that power, then we have to allow that the over-mind has the capacity to create within itself, a limited realm of autonomous activity, free from the causal necessity of that base.

We are at this moment using our 2 vastly limited semantic minds with occasional flashes of intuition from the overmind and trying to do the impossible. — Ken Edwards

What I think, is that if we can determine precisely what the over-mind actually does contribute, in the form of direction, to the conscious mind, this will give us a great advantage toward understanding the mode of directing. And that's what thinking is, right? It's a simple act of directing. If thinking requires thoughts (remembered content from previous thinking), we're looking at an infinite regress. So we ought to allow that thinking is an activity which can occur without any content, no thoughts, an activity without anything moving. Then as thoughts come into being, the activity may be free from the influence of prior thoughts, to direct these thoughts as required. In reality then, the over-mind must contribute nothing to the act of thinking, no content, just the capacity for this activity, the capacity to think.

I think that there are, indeed, many other ways of thinking. My problem is that I don't have good names for these. Intuitve thinking, thinking by the overmind, aesthetic thinking, musculer control calculations, sight, hearing and feeling acivities etc are commonly used much more often, perhaps a million times more often than Conscious mind thinking. — Ken Edwards

I don't think it is particularly useful to attempt at distinguishing specific types of thinking, like this. I believe that if true boundaries between this or that type of thinking, cannot be found, then such imposed divisions may be more misleading than not. And, I believe that the tendency to make such distinctions emanates from psychology, then it compounds itself in neurology where theorists will attempt to prove certain parts of the brain are responsible for certain types of thinking, and things like that. But I believe there is far too much crossover, back and forth of neurological activity to allow such proposed divisions to provide a meaningful representation of thinking.

But, the coscious mind is not negligable. Consider. You might pause in your days activities to add up a grocery list with a pencil. That would be Conscious mind thinking. You might pause to make a telephone call. That would be Conscious mind thinking. You might pause to write a letter. That would be Conscious mind thinking. Your sister might come for a visit. You might hug each other. That would Not be Conscious mind thinking. Then you might converse. That would be Conscious mind thinking. — Ken Edwards

So I believe that even this fundamental division of conscious mind thinking, and non-conscious mind thinking, is a misleading division to make, fraught with problems. I believe that all thinking which you propose as "conscious mind thinking" has a huge component of non-conscious activity mixed throughout it. But since the non-conscious is not evident to the conscious mind, it gives the impression that we can make such a division. However, I think the conscious activity is just like the tip of the iceberg, and there is a vast amount of non-conscious activity going on, which is supporting a tiny amount of conscious activity. We could represented it like a pyramid, the base being non-conscious, with the point at the top being conscious. Since it is activity we are talking about, represented as a thing (the pyramid), there is continuous back and forth throughout this proposed "thing".

As conscious beings, we look from the top down, but the base is all hidden from us. So we propose a division. However, the division makes understanding the causality of the situation impossible. We want to understand the consciousness as being in control over the thinking, because this is how it seems intuitively, but the imposed division prevents the possibility of top down causation. We cannot consciously control the non-conscious, because we can't apprehend it. Then if we allow that causation is bottom up, from the non-conscious into the consciousness, we have no way to account for the reality of the influence of conscious decisions, and freely willed activity. Therefore it seems like the only representation which could be consistent with reality is a continuous back and forth between the two. But this renders the representation of such a division as misleading.

It's not clear why one would think that the methods of philosophy can unlock general features of the universe – on reflection the idea seems somewhat insane. — Snakes Alive

Why portray philosophy in the way you do? Take Socrates for example. Socrates used philosophy to show that what people commonly believed about the general features of the universe, was wrong. That developed into the method of skepticism. When commonly held beliefs are false, do you not see a value in proving them as such?

Thinking is usually considered to be thinking with words and that there is no other way to think except by using words. — Ken Edwards

I tend to think that actual thinking does not really involve words, and this is a sort of misunderstanding that people hold. You describe relating pieces of clay together. I find most of my thinking involves relating activities. That is how I organize my day, This has to be done before that, and something else has to been done afterwards, etc.. None of this involves words, just some sort of images of the activities in question, so that I know what it is and I can related it to the other activities. In the end, I might assign words to help me remember what I figured out.

So in this type of thinking, which I think is quite common, there is what is needed, or wanted, and the means for getting it is determined. There really isn't any use of words. But if I proceed in thinking out a process, there is no need to refer back to images of activities already determined. There is a situation where activities A and B have been determined, and this has gotten me to activity C, yet I still have to get to H. Now there's a sort of hole in my thought, where A and B are, because I don't need to think about them anymore, I just take them for granted as having been determined. So I need to call them something, label them, "A" and "B" in this example, to make sure that I don't forget them.

This is what I think thinking with words is like. It's not actually a big part of real thinking. The words signify something which is known, taken for granted, so this doesn't need to be brought into the thinking. So the words are not really part of the thought, they're just there to prevent the existence of a hole in the thought, which is what has already been thought, therefore taken for granted.. The actual thinking occurs in going beyond these words, thinking in some sort of images or ideas. Then there is some actual thinking with words which involves deciding which words to use to properly represent what has been concluded by the thinking, so as not to forget it.

I think that what has happened is that we have allowed spoken language to supersede the more animalistic communications. This means that we look for meaning in the words and sentences of others rather than in the actions of others. So we ignore a whole world full of acts which actually have the most important meaning, thinking that anything important is spoken. Because of this we don't even seek the meaning of virtuous acts like loving, caring, and sharing, nor the opposing vicious acts.

What is it that is subjective in our observations of the cradle? — Banno

When I see that clip of Newton's Cradle, my first thought is "that looks fake". The accelerations and decelerations are not right, so the whole thing looks "off" to me, it's jerky, not smooth, fluid, as I think it ought to be.

If you think that there is nothing which is not public, then without a doubt you will be deceived.

However, if you can admit that Biden did receive more votes, but they were misinformed votes, based on the unchecked character assassination of Trump over 4 years, that hadn't happen when he ran against Hillary, then we can probably agree on something. — Harry Hindu

That "unchecked character assassination" was acts of informing, not disinforming.

He's a slippery character, McConnell, but at least he said it. — Wayfarer

Hopefully this is the first step to the Republicans disassociating themselves from Trump. If that happens who knows what will become of all the disenfranchised Trump supporters, maybe a third party? That's what ought to happen.

There is a need to distinguish between intersubjective and objective, in order to allow for the truly objective aspect of reality which is beyond the intersubjective, what we might call the independent world. As philosophers we seek to find ways of understanding the independent world rather than designating this as impossible. If epistemology deals with the intersubjective, then we need to allow for the two distinct aspects which are outside the realm of knowledge, the subject itself, and the object itself.

My supposition, following Wittgenstein, is that what we call "concepts" are not things in the mind to which we attach words, but learned ways of manipulating the world, including using words. — Banno

This exposes very well the need to assume two distinct aspects of reality beyond the realm of epistemology (the epistemological being the intersubjective). There is implied in your statement, three distinct aspects of reality. There is a subject (individual person) who manipulates the world, as well as an object ( the world which is being manipulated). What lies between, as the medium, is the learned ways, and this is what epistemology deals with, as the intersubjective.

We could look at the subject/predicate grammar of the sentence, "Banno manipulates the world", and see that the predicate needs to be broken down analytically, into the action which is proper to the subject, and the object which is a passive recipient of the action, but is nevertheless changed.. Therefore there is a need for metaphysics to consider the existence of those two distinct aspects of reality, the active and the passive, as distinct from understanding the nature of activities which already presumes the existence of both.,

I would add that looking and describing the grammar of a concept is only the first step; that creating examples to make claims about our ordinary criteria provides the discussion point for our philosophical issues (Cavell will call the examples "philosophical data"). — Antony Nickles

You still have not justified the validity of. or done anything to disambiguated, this proposed concept "ordinary criteria". If "ordinary criteria" refers to the criteria which an individual person applies in ordinary situations, in one's day to day life, and in use of natural language, then it refers to something which is specific and particular to the individual. But if "ordinary criteria" refers to rules of logic which are taught to us, like the rules of mathematics and geometry, then it refers to what Wittgenstein calls the "normal" picture at PI 141.

The problem is the inconsistency between these two, what is taught, and what is actually applied in the circumstances. And, as Wittgenstein indicates at PI 140, in natural language use the context of the particular application takes precedent as what is important to the meaning, thereby rendering the normal (what has been taught) as not necessarily relevant. This means that if "ordinary criteria" refers to what Wittgenstein calls "normal" (the concept as taught), we cannot rely on ordinary criteria for determining meaning.

But if you insist that "ordinary criteria" is the means by which we determine meaning, then you must allow that it refers to criteria which is specific to the particular individual, being applied according to the circumstances present. That is because what is normal (the concept as taught) is unreliable in common situations of natural language use, due to the presence of the abnormal.

If I understand correctly, "frontrunning" means receiving orders, and buying for yourself prior to filling the orders, even if just a fraction of a second before. In the case of Robinhood, since they offer free trading, they would process significant volume in a short time period, allowing for substantial frontrunning without having to hold things up, slowing things down to build up reliable volume, producing noticeable time delays. This could produce significant profit.

In essence, the logical conditional is chronologically ambiguous and cuts both ways - backward into the past and forward into the future - and which is meant needs to be made explicit using words like "was", "will", and verb-tenses. — TheMadFool

That's right, which is the cause, and which is the effect must be stipulated to avoid ambiguity.

That's like saying economic policies affect the nation but not the people. — TheMadFool

Within that conceptual framework which produces these forms, "the dips and dimples" are in the fabric of spacetime, not space. Suppose we have two objects, and assume a straight line between them in a classical 3d representation. It's impossible to measure that distance all at the same time, because measuring takes a period of time. This amount of time is determined by the speed of light, the fastest known way of measuring. But the light, in travelling from the one object to the other will really take a non-straight path due to the influence of gravity. Since light is the fastest thing to travel from the one object to the other, the shortest path between the two, is represented as this non-straight path. That is called the curvature of spacetime.

There is a standard for creating this curvature in models, which is based in the presence of mass, and assumed gravitation. However, some activities will affect the applicability of the standard, so exceptions to the standard curvature must be allowed for. These are things like gravitational waves. What this implies is that light doesn't actually take the shortest route between two objects. We think that it does, because classical representations of 3d space will show light travelling in a straight line. And, since physicists know light as the fastest thing to travel that distance, they equate the 4d fastest route with the 3d shortest route, hence the 3d straight line is equivalent to the 4d curved line. However, since other things are known to alter the shape of this "fastest" route, so there are proven wrinkles in spacetime, we can conclude that it is not really the shortest route.

As to your second I am not sure that thinking and talking and understanding are not three different aspects of the same thing but no, understandig is more extensive and includes intuitive and possibly aesthetic understanding as well as logical understanding. — Ken Edwards

Let's say that understanding is not the same as thinking. Doesn't understanding require thinking? And wouldn't some thinking not produce understanding, resulting in misunderstanding for example? So it seems to me that thinking is more extensive than understanding. Or do you think there can be understanding without thinking?

And oh, she gave that interview LAST YEAR, btw. — ssu

Right, there is very clear evidence, and a formal inquiry, which came to the conclusion that there was illegal foreign interference in the 2016 election. Therefore what Clinton said in that interview that the election "was not on the level" is well justified.

However, no one formally contested the results of the 2016 election. That's the difference. Trump did formally contest the results of the 2020 election, with about 60 or more court applications. Do you see the difference? If you beat me in an election, and I go to the media and say look, there was such and such going on behind the scenes, there were people assisting ssu using illegal practices, and I work at the effort of bringing those involved to be held accountable, that's one thing. But if I go to the authorities charged with overseeing the election, and request that the election be annulled, that's a completely different thing. The two are not comparable as if they are the same thing.

Unless stated as rules, the boundaries of conventions only exist as ideas. This is what is meant when people say agreement is "implicit", they mean that the existence of the agreement spoken about is implied only. That means that there is an act of thought required to draw the conclusion that there is such an agreement. The assumed agreement is not something which can be observed as if it were stated on a piece of paper. It is theoretical only, its claimed existence relies on that act of thought. It is not something which can be empirically observed, which it could be if it were written down.

The Dems were incessantly claiming that Trump stole the 2016 election. The Dems DID steal the 2016 Primary from Bernie and did it again in 2020. The Dems failed to call back their violent constituents and even encouraged them and people died and property was destroyed. — Harry Hindu

This is nonsense Harry. The Dems never contested the results of the 2016 election, nor were there accusations of theft. There was accusations of illegal foreign interference, which were investigated and proven as true accusations.

The Dems did not steal the primary from Bernie. What could that even mean? It's the primary of the Democrats, how could they steal it from themselves?

And I don't see how the third point is even remotely relevant.

So please don't try to pass yourself and the Dems off as holier-then-thou because they pull the same shit as the Reps. — Harry Hindu

I didn't and I won't.

Only according to your own self-imposed stipulation for how the word "rule" should be used. — Luke

As I said, you can use "rule" however you please, there's no rule which dictates how you must use the word. However, if you are trying to remain consistent with Wittgenstein, I already quoted PI 202. This is a pivotal point of PI, where the "rule" is stipulated as being outside of the private mind, to be defined as necessarily public.

So, if the boundary of a convention is implicit instead of explicit, we cannot get beyond "I think I am following a rule", because the boundary is only thought of. That is what "implicit" means, it's only produced by thinking. Therefore conventions with implicit boundaries do not qualify as "rules" by Wittgenstein's demonstration of how "rule" ought to be defined, at PI 202.

It really does not bother me if you simply want to define "rule" in a way which is inconsistent with Wittgenstein. I am often inclined to use it that way myself. What bothers me is that you pretend to adhere strictly to Wittgenstein's philosophy, while not adhering to this very important point, how we must define "rule". That's hypocrisy. But I believe this hypocrisy is not intended by you, it's the product of a simple misunderstanding. So I feel the need to bring it to your attention because I think if you developed an appropriate understanding, you would be inclined to change your ways.

I think that the "puzzling" issue of the op is explained quite easily by the fact that we learn to talk before we learn to read, or think in words. Because of this, talking is our foundation for use of words. Then, reading and thinking with words develops afterward as a reproduction of talking, which is intended to be silent. However, reading, and thinking with words, remain the same basic activity as talking, without the making of noise.

As you yourself have recognized though, thinking goes much deeper than simply using words, there is also, for instance, the matter of understanding the words. So this representation of thinking, as talking to oneself, is not a very good representation of thinking, because it's just a very shallow and small part of thinking which is being represented.

Where's the "other" option? I would say that they definitely have a different meaning, as "is" and "ought" have different meanings. But it's one philosophy, metaphysics, which deals with them both, so they are of the same domain.

If staying within the boundaries of a convention is the same thing as staying within the boundaries of a rule, then obviously a convention is the same thing as a rule. — Metaphysician Undercover

"If" it were the same... but it's not. A rule consists of a stated principle of conformity, therefore defined boundaries. A convention, by your own admission does not. Therefore staying within the boundaries of a convention is an oxymoron. A convention has no boundaries. You just think it does. And thinking that you're following a rule is not a case of following a rule.

How many times can you go around the same circle Luke?

Premise #1.

Same answer, that convention would not be a rule.

I asked you how do we determine that going outside the boundaries of a convention does not fulfil the criteria of staying within the boundaries of a rule. — Luke

We don't need to make that determination, because if this were the case, the conclusion would be the very same, that a convention is necessarily not a rule.

Where did you ever get that idea from?

This must be what you did in your argument, then? You know, since you ended up agreeing that a convention is the same thing as a rule. — Luke

Sorry Luke, you misunderstood again, as usual. I didn't agree that a convention is the same thing as a rule. I agree that for you it is. But I believe that's a misunderstanding you have, which I don't share.

You can make them that way if you want, it's just a matter of definition. You can simply define "rule" in a very ambiguous way, allowing all sorts of things to pass as rules without differentiating distinct types under the one name "rule". But if you do define them like that you cannot take advantage of the analytical benefits obtained from separating the distinct types of things.

Despite the fact that we break rules, we can make a conscious effort to follow rules. But to do this, the rule must exist, in some form which we have access to, such that the conscious mind can consult it and determine how to follow it. This is, as expressed in language. In other words, to adequately judge correct and incorrect the rule must exist in a form which we can consult, i.e. in language.

Those other things, which you are inclined to call rules, such as customs, traditions, and habits of language use, do not exist in any form which we might consult in order to make a decisive determination of correct or incorrect. In fact, we cannot say that there is necessarily even a principle (rule) being followed, if it's just a matter of copying or imitating, so there's no way to say that one person's display is the correct one while another's is incorrect when there are differences.. Sure imitation requires some sort of effort, but it is not at all the same thing as interpreting a rule and adhering to it,. And, in the case of imitation there is no written rule or principle to refer to in order to judge correctness, when different people are carrying on in slightly different ways.

Yes, we could make that judgement. But we don't stay within those boundaries, that's P2. I know you disagree with P2, and you could have saved days of back and forth just by refusing to accept it, rather than all the other shenanigans.

Now you're going to say that we don't stay within the boundaries of rules either. And I'll say, I know, that's the nature of free will, and we ought not describe human beings as rule following creatures. We've been through this all already.