I taught at the college level for many years and never thought of the subject or my teaching strategies as racist, but I know only a little of how math is taught K-9. — jgill

Your reference to "teaching strategies" indicates that you recognize that math itself is not the basic problem, but the way that it is taught may be a problem. That's what StreetlightX indicates as well. The issue is the clearest at the most basic, elementary levels. There appears to be a need to employ examples at the elementary level, and the examples are chosen, or created, with various intentions of being relevant, interesting, insightful, inciteful, or whatever. You can see that relative to different people, of different backgrounds, different examples will have different effects. If the desired effect is to encourage the student to participate and continue in the learning process, there will be discrepancies in successfulness, depending on the significance of the examples.

If we proceed toward higher levels, the issue (problem, when you see it that way) goes much deeper, and it gets much more complex and difficult to identify. The often cited issue of marking, and designating correct and incorrect is just the tip of the iceberg. I'm sure you understand that in the education of a subject like mathematics there is a very real need for direction in the form of the judgement of correct and incorrect. But we can ask what is this judgement based in, where is it grounded, and we see that "correct" means consistent with the currently accepted axioms.

Now, you'll know from my discussions in this forum, that mathematical axioms are not based in empirical truth, and I do not even believe that they are logically consistent. The mathematical axioms which are accepted into the community of those who apply mathematics, are the ones which are useful within their fields of operation, so the judgements of "correct" and "incorrect", in the teaching of mathematics are very pragmatically based. This is why the different courses of mathematical education in high school are now sometimes geared toward specific career goals, what is required for that specific field of education. It used to be that math was divided by categories like "basic" and "advanced", etc., but this was sort of degrading to the person in "basic" math, so I think the trend today is to offer the math which is designated as what is required for a specific discipline..

Consider if you will, the relationship between what mathematics is, and the way mathematics is taught. We can say that mathematics consists of tools, and the tools are accepted into use, therefore designed to an extent, for the various uses. Teaching, on the other hand is a way of manipulating minds to accept specific things as correct and incorrect. The two seem very distinct, but imagine if there is a reciprocating relationship between the two. Then the tool might be designed toward manipulating minds toward accepting specific things as correct. Historically such a tool would be known as "rhetoric". But when it infiltrates into logic and mathematics it's better known as "sophistry".

I believe that this is where the issue becomes a problem. The issue is the reality of what mathematics is. The problem is that since it's a tool to be used, it can also be used abusively. In relation to the op, the problems of the teaching strategies become a problem of the mathematics itself, when the teaching strategies become implanted into the mathematical principles themselves. That would be when the principles, or axioms are designed to manipulate minds in a specific way.

I asked you way back, weeks ago, if you minded me using "non-natural" instead of "supernatural". And you never objected to that.

Ok, rather than call what is outside of natural "supernatural", would you prefer "non-natural"? I don't really care about the terminology. If you dislike the term "supernatural" let's just call it "non-natural". — Metaphysician Undercover

Now you've just confirmed what I thought at the outset, and what I stated way back 17 days ago, when I first engaged you. You very clearly have a preconceived notion of "supernatural", and a bias and prejudice towards this notion. This prejudice disables your capacity to approach the subject logically, with an open mind.

This is clearly a biased statement.. Whenever evidence and logic indicate the reality of that which is beyond the natural, then the appropriate conclusion is the supernatural. To deny the reality of what the evidence and logic lead you toward, because it's contrary to what you already believe, is simple prejudice. — Metaphysician Undercover

I think you're misunderstanding. I'm not saying that understanding events in terms of (some kind of) causation is somehow "invalid"; in fact it is the only way we can understand events. Any explanation of the connections between events must posit some hidden forces or powers; whether those are gods, animating spirits or mechanical causes — Janus

Then how do you justify your other statement, that causation is not logically necessary?

I agree that causality is, like freedom or truth, irreducible, insofar as it cannot be explained in terms of anything else. But It is not logically necessary. There is no logical contradiction involved in thinking that events might simply happen without cause or reason. — Janus

If causation is "the only way we can understand events", how can causation be "not logically necessary"? Is there a way that we understand things (events in this case), in which we do not employ logical necessity? And how does "causation" fit into this mode of understanding?

At first glance, it would appear like if there was any sort of "understanding" which could not be demonstrated and justified through logical necessity, it ought to be dismissed as misunderstanding. What type of "understanding" is valid "understanding", yet it is not given by the means of logical necessity? We'd have to say it's not a "valid" type of understanding, yet it is still a type of understanding. How can we classify this as "understanding" when it's just as easily classified as "misunderstanding"? Or do you base "understanding" in something completely different from logical necessity? What constitutes "understanding" to you?

Well if you understand logic you would understand WHY we don't use "negations" to define things — Nickolasgaspar

You don't seem to understand that when the term being defined is the negation of another, i.e. "non...", then we refer to the other to derive our definition of the negation. For example, to define "non-drinker", we refer to what "drinker" means. To define "non-contagious", we refer to what "contagious" means, to define what "non-partisan" means we refer to what "partisan" means, and to define what 'non-natural" means we would refer to what "natural" means.

Supposed the limited capabilities as an observer do not allow you to classify something. — Nickolasgaspar

I explained that this is not the case in this instance. We know, through logic that the processes must exist. We also know from the definition of "natural" that these processes cannot ever be placed in the category of "natural" without changing that definition.

Suppose we we found out a new natural mechanism and we need to adjust the definition to include it. — Nickolasgaspar

This is contradiction. If the new mechanism is excluded from the existing definition of "natural", it cannot be called a "natural" mechanism. So finding a process which cannot be classed as "natural" by the definition, does not justify changing the definition just because you want to call it a "natural process".

Why don't you just define "natural" right now, to say that every actual thing, and every possible thing, or process is natural? I've given you that option. But I am doubtful as to how accurate it is to call a possible thing "natural".

You can not claim that there are non natural things necessary to explain our universe, while you are unable to define and show which "exotic" properties those things have that make them necessary. — Nickolasgaspar

I don't see how "exotic" has anything to do with this. If it is true that there are things in the universe, processes or whatever, which cannot be called "natural" then we can call then "non-natural". Whether or not they are "exotic" or whatever, is irrelevant.

I agree that causality is, like freedom or truth, irreducible, insofar as it cannot be explained in terms of anything else. But It is not logically necessary. There is no logical contradiction involved in thinking that events might simply happen without cause or reason — Janus

This all depends on the way you would define your terms. You have three principal terms here, "event", "happen", and "cause". When we define "event" we might allow a distinction between an actual event, and a possible event, such that "happen" is not a necessary, or essential aspect of "event". This means that any described event may have either happened, or not happened. An event might be fact or fiction. Further, we could allow that "event" is not an attribute or property of anything, so that it does not function as a predication of a subject, and assume that "an event" is a type of general, ill-defined, and vague object. Then, "an event" would be an object without a proper identity and we could find that the law of excluded middle, or the law of non-contradiction, would not apply to anything we said about "an event".

As you can see, there are numerous possibilities to how "event" might be defined. And when we position "happen" in relation with our definition of "event", it is possible to define the two such that "happen" is a necessary, or essential aspect of "event". This would mean that we can't call something an "event" unless it has already "happened", i.e., we assume factuality with "event". If we take this step, then we need justification that whatever we want to call "an event", has actually occurred. So we would refer to the present situation, and explain how the present situation is the effect of, or was "caused" by the thing which we want to call "an event" (where it is necessary that the "event" has actually happened to be able to call it "an event").

Therefore, if "event" is defined such that it is necessary that the activity called "an event" has actually already occurred, so that occurrence is an essential aspect of being "an event", then we need to allow that "causation" is also an essential, or necessary, aspect of events. This is because we have no direct access through sensation, to events which have already occurred in the past, therefore no way to identify "an event" (being necessarily in the past by this definition) through sensation, as "an event". The only sensual evidence we have, is what is occurring now, at the present time, but to necessitate, validate, or justify, the claim that a specific event has actually occurred, (therefore fulfills the criteria of "event" under this definition), we have only a relationship of causation to rely on.

Because we need to assume this relationship of causation, to have confidence concerning truth about the past (memory being insufficient), we must approach your proposal, that an event might just happen without a cause, very cautiously, and with healthy skepticism. If we decide that we want to define "event" such that an event might be occurring right now, as we speak, at the present time, and we allow "that events might simply happen without cause or reason", then we deny the necessity of the causal relationship between the present and the past. Then our method for determining the truth about the past, is designated as invalid (by your proposition), and such claims about truth are unjustifiable.

I said that scientific laws (or principles) are where 'logical necessity meets physical causation'. — Wayfarer

I believe it is important to understand that logical necessity is a form of need. It is derived from the need to understand. From the need to understand comes the "discovery" of all the principles, or rules of logic, and form this, the judgements of valid and invalid.

The judgement that one described situation is the cause of another, which is the effect of the prior, is based in principles of logic. What is required for that judgement is a definition of what constitutes a "cause".

Again, physical causation is not a necessary relation; and logical necessity sets out the way things might be spoken about, not the way things are. — Banno

I don't understand how you might propose to remove necessity from physical causation, and still retain prediction as a valuable tool in science. If, in the discipline of physics, we can say that one described situation causes another (in general), or that one described situation caused another ( in particular), and we remove "necessity" from this relation, then how do we validate the usefulness of prediction?

Here's an example of what I'm asking. Suppose that described situation A is proposed as the cause of described situation B. If there is necessity between A and B, I can say "if A occurs then B will occur", and when I create the situation of A, I can make a valid prediction of B. The "necessity" between A and B is what validates my prediction that A will result in B, which I can express with the relation of necessity, "if A then B"..

Now, let's remove "necessity" from this relationship. I create A, and predict that B will be the result. The prediction is true, but B did not necessarily come from A, because we've removed the necessity. We now allow that B could have been the result of something other than A. Nor will B necessarily be the consequence of A, because that necessity has been removed as well. What validates my rule of prediction, "if A then B" now? And, if I'm a scientist, and I want to support a hypothesis with a prediction, through experimentation, how could that hypothesis be supported, if the relation is understood to be one of coincidence rather than necessity?

It might appear, that a reasonable thing to do would be to allow probabilities instead. We could say that if the prediction is good ninety percent of the time, we'll accept the hypothesis. Or, we might say that if the description of the consequent is ninety per cent accurate, ninety per cent of the time, in ninety per cent of the situations, we'll accept the hypothesis. But what happens if in some cases, we allow eighty five per cent as the rule of thumb? If we adhere to one hundred percent, all the time, we support "necessity", and probability is excluded. But if we slip into probabilities, what standards will produce rigidity in the rules, when we allow the probabilities of practise to have supremacy over the necessity of logic?

I made that conclusion a long time ago. I don't know why I continue.

You will need to define the qualities of the non natural. — Nickolasgaspar

As I said, the meaning of "non-natural" is derived from the definition of the root, "natural". Whatever demonstrates to us, that it cannot be classified as "natural", must be classed as non-natural. That's why we cannot proceed without a working definition of "natural". You provided a definition, and I demonstrated the logical necessity of concluding that there is also non-natural things.

-No I haven't. I described you what known Natural Processes are...read my definition once more.
Just because there is a process with different characteristic but with the same natural properties that doesn't make it "non natural" . Again you need to define "non natural" or you end up with an Argument from ignorance fallacy. — Nickolasgaspar

If "natural" is defined as the process which produces things from the building blocks, then the process which produces the building blocks is necessarily non-natural. "Different characteristics" means a different process. And to say "different characteristics but with the same ... properties" is basic contradiction.

Natural Processes, as I told you are caused by fundamental building blocks of the Cosmos, which give rise to the building blocks of our Universe — Nickolasgaspar

Again, there is clear contradiction here. You are talking about processes "caused by fundamental building blocks", then you say that these processes "give rise to the building blocks". The first is necessarily posterior to the existence of the building blocks, and therefore cannot be the cause of the blocks, as the second "give rise to..." implies.

Are you satisfied with my definition on the "non natural" concept? — Nickolasgaspar

No, you use far too many contradictions. One contradiction is too many, you have at least double that amount.

I hope these definitions will help this discussion go further from arbitrarily declaring things we don't know "non natural". — Nickolasgaspar

It's not arbitrary, it's a conclusion of logical necessity. If we define a specific class of processes as "natural", then all the processes which we know must exist through the application of logic, yet which cannot be placed in that category of "natural", must by logical necessity, be classed as non-natural. It's not a case of not knowing whether the processes are natural or not, its a case of having a defined category of "natural", and knowing that these processes cannot qualify for that category.

No it doesn't. A contingent object is an object that 'can' not exist (as opposed to a necessary object, which is an object that can't not exist). — Bartricks

As you misunderstand philosophical use of "cause", you also misunderstand philosophical use of "contingent object".

Once more: if an object exists at a particular time, what's to stop it existing at all times? — Bartricks

I provided the argument for this, its based in the law of identity. You haven't adequately addressed it.

Note, if self creation is coherent,.../quote]

Obviously "self-creation" is not coherent, but you refuse to accept the principles which demonstrate its incoherency. That is not my problem.
— Bartricks

That's called an 'argument'. Address it. — Bartricks

The argument has been addressed, "self-creation" has been thoroughly demonstrated as incoherent.

There are extrinsic and intrinsic properties, and intrinsic properties are those properties that are essential to an object's identity. Temporal properties are extrinsic, not intrinsic. I am clearly the same person I was a second ago. And my mug is the same mug it was a second ago. — Bartricks

Extrinsic properties are not essential to a subject, they are accidental to the subject, that's why all human beings can be said to be "human beings". However, all accidentals, including extrinsic properties, are essential to the identity of an object, that is what makes any particular object, the unique object which it is. That objects are unique is what makes the law of identity a valid principle, and why the same thing cannot have two distinct times of existence. If your time of existence is from 1992 until the present day, you cannot also have a time of existence of 1888-1946. That's why your principle, that if an object can exist at one specified time, it can also exist at another, is false.

My conclusion is that scientific law is where logical necessity meets physical causation. I haven't seen an argument to dissuade me of that original idea, although I keep an open mind. — Wayfarer

I agree with this, but I would go further to say that "physical causation", as conceptual, is a form of the broader category, "logical necessity". From here, if we go further in the direction of the wider category, we see that "logical necessity" can be described as a form of "necessary" in the sense of what is required, or needed for a purpose. So it is related directly to intention and free will, as means to an end. In the other direction, if we look at an assumed object which "physical causation" as a subject, is supposed to represent (in the physical world), we find something which is directly opposed to our conceptions of intention and free will.

This I would say, is why there appears to be a problem in reconciling the two. "Logical necessity" is grounded in free will, while the concept of "physical causation" produces ideas of necessity which are directly opposed to concept of free will . And, like I explained earlier, the classical way to resolve the problem, is to make the thing represented by "physical causation" the result of God's Will.

This despite being shown in both the Anscombe article and Del Santo's work that physical causation is not a necessary relation; — Banno

I would argue that this proposed resolution of the problem renders "physical causation" as a completely impotent concept, and ultimately useless. To remove the necessity, commonly thought to be implied by the cause/effect relationship, removes the required logical rigour of the rules for application of the concept. Then we do not have adequate rules for applying the term "cause". And, we end up with things like what Bartricks demonstrates in his thread on self-creation: sloppy use of "cause", such that a cause and effect might be coincidental. And that is just one example of how "cause" may be misused, when logical restrictions on definition are removed. Aristotle demonstrate six distinct uses for "cause" current in his time, the four commonly cited, along with luck and chance. Luck and chance he excluded as inappropriate use of the term.

So justice contains some guarantee of education geared towards civic duty in your view? — Tobias

Such an education is unavoidable. It's part of growing up, as the difference between a baby and an adult. The younger the baby, the more real is the difference between the authority of the adult, and the open mind of the child. As I said above, it's a big feature of being a mammal, being taught by the parent or parents. The baby's dependence on the adult makes the bay naturally geared toward accepting civic duty into one's mental disposition.

Not everyone will do so and with what methods and means may the state create a role for you. — Tobias

I don't think it's a matter of the state creating a role for you, it's more like you create a role for yourself (free will), knowing from your learning experience what type of role will give you a satisfactory sort of living. And you know from your learning experience that to step outside the bounds of authority will likely cause hardship to you.

It must on the other hand also create some exit option, there should be a choice, wise or unwise, otherwise we have no real choice. I think this is meant by modern notions of autonony. — Tobias

Yes, of course "exit" is always an option, I think I sort of explained it above. I believe it's a key aspect of evolution. For the baby, to exit is certain death, and this cannot be called a wise choice. At a later age, exit and continued life, is a real possibility, like the hermit. But by that time the person has already been educated, and there is some wisdom in that choice, depending on one's societal conditions. But it's impossible to erase what one has already learned, so that exit is not a complete, or an absolute exit, like the baby's exit would be. Through meditation, reflection, introspection, skepticism, and other such practises, one might strive to erase what one has already learned, and substitute.

No, you defined "nature" that way, as what manifests from fundamental building blocks. It was your definition. — Nickolasgaspar

You produced the definition. Let me remind you:

In Science Natural is every process or phenomenon that manifest in reality through verified building blocks of the physical would and or their advanced properties. — Nickolasgaspar

-You don't know how they came in to existence. Maybe they existed all along...and this is most probably the case since none existence is not a state being on its own. — Nickolasgaspar

So, since "natural" is the things built with the building blocks, then this kind of thing which "existed all along" the building blocks themselves, are non-natural.

Well we need to be more precise. We have a cosmic quantum field where we can observe quantum fluctuations affecting the fundamental particles of our universe. We understand that there is a sub-level underlying the building blocks of our universe and they are totally natural in their behavior (A Nobel Prize was awarded for the modeling of those fluctuations). — Nickolasgaspar

Now you have gone outside the the constraints of your definition of "natural". You'll have to produce a new definition for me. We'll start all over with a new definition, and then I'll see if there are things outside your definition which are necessarily non-natural.

You now say that there is a "cosmic quantum field" whose activities to create the building blocks, are natural activities. What about that field itself, it must have been created by some other activity which is non-natural. Or maybe it "existed all along"? Then, as above, that kind of thing would be unnatural as well. Maybe you want to try for a better definition of "natural", one which might include every possible thing? Do you think a "possible thing" is something natural?

How on earth can you conclude to that claim? — Nickolasgaspar

It was your definition of "natural", manifestations of the activities of the fundamental building blocks.

The burden is on you who makes a claim for something that can't be demonstrated to be possible. — Nickolasgaspar

I made that demonstration. I proceeded from your definition of "natural", to demonstrate that there is necessarily something non-natural. Can you produce a better definition of "natural", one which would make any such demonstration impossible?

In short, we have no data to feed in our metaphysics. You can't do Philosophy Without foundational data. You assume way to many things that you know nothing about.
We don't know if this cosmic fluctuation field is eternal or not, we don't know if the emergence of processes like our Universe is a one time or constantly occurring phenomenon...we know nothing.
So assuming the ontology of the cause for a phenomenon that possibly never happened (nature came in to being) is an irrational intellectual practice.

Most importantly even if there was a cause responsible of what we identify as Nature, that wouldn't quality as "non natural"...because "Nature" is a limited label we put on what we currently know about the cosmos. — Nickolasgaspar

If you don't even know what "natural" means, why are you so vehemently opposed to "supernatural". I don't understand this. Do you give "supernatural" a meaning which is not based in the root "natural"?

It's good that even despite the inconclusive discussion about the actual topic that we've at least been able to sort out the fate of the Universe. Makes you think your day hasn't been entirely wasted. — Wayfarer

What happened to the topic? I'd conclude that there is substantial disagreement with respect to the meaning of the principal terms "necessity" and "causation".

If the two sides of the equation remain in balance, then the whole shebang can coast along forever - continuously spreading and cooling - to reach its heat death at the end of time. — apokrisis

As I said, fiction. But regardless of whether it's fiction or not, your explanation is very clearly inconsistent with your referenced article. The article explicitly says "but only after an infinite time". Therefore the article's explanation of "critical density" implies no end of time, yet your explanation states "at the end of time". A very clear contradiction in the two fictions, yet you give yours the same name, "critical density", as the other.

Note that in the updated picture - the current Lamda-CDM concordance model - the end of time (as the effective end of all discernible change) now arrives at a finite future date. — apokrisis

So, can I conclude 'end of time at a finite future', means no "critical density", which also means no flat universe? The "flat" is just an unrealistic ideal, like I've been trying to tell you. Therefore "flat universe", and "critical density", are simply fictions. How long do you think before the "updated picture" is also recognized as unreliable, is changed, and is also seen as a fiction?

Tell us again how Einstein got it so wrong and MU gets it so right. :rofl: — apokrisis

Since all cosmology produced by Einsteinian theory ends up needing to be "updated" because it's wrong, and the updates involve making further exceptions for the failings of general relativity, I think it's very clear that Einstein got it wrong.

Look at the problem with the concept of "mass" which I mentioned. By Newton's principles, an object's 'resistance to change' is attributed to its momentum, which is a product of mass and velocity. Change to velocity requires acceleration, and this is offset by the mass of the object, so "mass" here represents the resistance to change. But kinetic energy, as the capacity to change an object's momentum, represented as one half the product of the mass with the square of the velocity, already has acceleration factored within it.

The problem with the concept of kinetic energy is that acceleration is not well understood, so any representation of it is just an approximation. Now in relativistic physics we have kinetic energy with no mass, in the form of electromagnetism, light, or photons. If you look, you can see a very clear problem with the concept of 'resistance to change'. In Newtonian physics 'resistance to change' was a property of mass. In the concept of "kinetic energy" an approximation is used to account for this property of mass, such that "resistance to change" is offset by the approximation of "acceleration". An approximation is used because acceleration is not well understood.

That approximation allows that inertia (resistance to change) can be attributed to kinetic energy. But there is an inversion which is not accounted for. Kinetic energy is the capacity to effect change, to cause change, and inertia is the capacity to resist change. The two could be thought to balance each other in a static situation. However, in any act of change, some energy is lost to the system (friction for example), or whatever it is which is supposed to contain the system (it can be expressed as entropy). So there must necessarily be a discrepancy between the "inertia" attributed to kinetic energy, as a potential cause, and the "inertia" attributed to mass, as resistance, because of the reality of entropy. More "inertia" as kinetic energy is required than the amount of "inertia" of mass, to have a balance. And, attempting to produce an equivalence between these two is a mistake, because the equations used to represent acceleration are only approximations, and they cannot account for the reality of the lost energy in real acceleration. The relativity theory does not give the tools to determine how the energy is lost, because equivalence is assumed, under the one name "inertia". Hence the glaring problem in modern physics, that many processes are understood as reversible.

You're just confused. You think that contingent things have always 'come into being'. That's just false. There's nothing in the idea of an object existing contingently that implies it has come into being. — Bartricks

"Contingent" in the case of a contingent object means dependent on something else. I don't see the point in your denial. We can name thus type of thing however we want, instead of "contingent", "material thing", "physical object", "temporal object", whatever. The point is that the inductive reasoning tells us that all such things come into being in time, therefore there is necessarily time prior to them. You can deny the inductive principle if you want, but unless you give me a real example of such a thing, a thing which has always been, I'll never listen to you.

You have no argument. All you're doing is insisting that what I am saying is incoherent, even though it demonstrably isn't. — Bartricks

If it's demonstrable, demonstrate it then. Show me the reality of a thing, like a ball, which has always been. It's actually very demonstrable that balls are all produced, and there is time before each one of them, so you're really just talking nonsense in your insistence of demonstrability.

For instance, you seem blithely unaware of the fact you've been refuted. If an object exists at a time, then what's to stop it from existing at all times? You have no argument. — Bartricks

I gave you the argument. Since you didn't understand, it I'll be more clear this time. The time at which an object exists, is a property of the object, just like the space, or location where it is. And each individual object has its own unique set of properties, which makes it one and the same with itself only, by the law of identity. Therefore by the law of identity, if an object exists at one particular time, it cannot exist at another particular time without being a different object.

Why? If an object exists at a time, what prevents it from existing at all times? Explain. — Bartricks

It's an inductive conclusion, we've seen that things change as time passes, and things come into existence, and pass out of existence. You can deny this if you want, but to me, that's irrational, and that's what makes your proposition incoherent to me. I mean come on, we know that pool balls are produced from the factory, they cannot exist at all times. That's nonsensical

You are committing a fallacy known as the fallacy of affirming the consequent. If an object exists necessarily, then it always exists. But it does not follow that if an object always exists, it exists of necessity. YOu think it does which is why you think that contingent objects can't always exist. That's just fallacious reasoning on your part. Contingent objects can always exist. They will be existing contingently, but anything that exists at a time can exist at any other time, and thus can exist for all time. — Bartricks

That's not the reasoning I use at all. Like I said above, the reasoning is based in an inductive principle. Contingent objects cannot always exist because we know that each and every one of them came into existence in time, so there is necessarily time before them. We know by inductive reasoning that this is the case for all such objects

And your principle " anything that exists at a time can exist at any other time" is clearly false. Each and every thing has a time period unique to itself, and cannot exist at a different time period, because this would be a different thing.

Tell me then, how do you make sense of the quote I took from your referenced page? How is "critical density" supposed to make a universe halt its expansion after an infinite amount of time?

Perhaps, I am also not arguing for more thorough criminalization. However, is cultivating the right disposition just? It might be, but are we not crowding out a virtue that we like to cultivate, namely autonomy? I agree that this may well be a way forward and is a fundamentally different approach from a rights based approach, but leads to further questions of justice, who does the cultivating, to what end and is there or should there be a way for the individual to escape cultivation or at least object to it? — Tobias

I don't know if "autonomy" is the appropriate word here. Each and every one of us depends on others in some way or another. We were born into some sort of family, and as children we were dependent on adults. That's why there is fundamentally no escape from cultivation. We are mammals, and mammals exist in such a way that the young are dependent on the mothers, and the young learn from the adults. We cannot escape from cultivation, but it appears natural that children object to authority in one way or another, from time to time, and that might be part of the evolutionary process.

Maybe as we grow up, we earn our independence, and we could have proper "autonomy" as a loner, or a hermit or something, but I really don't think this to be a virtue which we would seek to cultivate.

Consider the way Socrates described "just" in Plato's Republic. It's a situation where everyone tends to mind one's own business without interfering with others. It's a just State, which allows that each person has a place, one's own unique role to play, and the person is capable of doing this without interfering with the role of another. Notice that there is a sort of personal autonomy here, in the sense that one is free to do one's own thing, but at the same time, "one's own thing" is defined, or constrained by the stipulations of the State, which ensures that "one's own thing" doesn't interfere with others, who are equally free to do one's own thing. What defines "one's own thing" in this way, is that the person is playing a productive role, as a part of a larger whole, the State. When the person is playing a productive role, then by definition, the person is not interfering with others.

From this perspective, cultivating the right disposition is what defines "just". It's not a matter of telling a person you must do this, or you cannot do that, it's just a matter of letting the person know that everyone is free to do whatever anyone wants to do, so long as everyone chooses wisely. So cultivation is geared toward directing the person as to how to consistently make wise decisions in such matters.

Everyone must admit that it is possible for something always to have been the case. — Bartricks

Not when the things involved are contingent objects. Balls and cushions are contingent objects. A contingent object requires a cause for its existence. Therefore it is impossible that a description of something which is said to have always been the case, could involve contingent objects.

Now, perhaps you think there is something incoherent in the notion of eternity. That's all I can think. But that's confused - eternity just means 'for all time'. That, anyway, is the notion of eternity that the example needs. And whether one believes time has a beginning or that it stretches back infinitely, there is nothing incoherent in the idea of something existing 'for all time' and thus for two things to have been in a certain relationship for 'all time'. — Bartricks

What I've explained to you a number of times now, is that there is incoherency in the idea of a contingent object (like a ball), which has always been there. A contingent object requires a cause for its existence, and the cause of its existence is prior in time to its actual existence. That means that there is time before the existence of the contingent object (the ball). Therefore to say that the ball was always there is incoherent.

What, you have never heard this before? Standard cosmology. — apokrisis

There's a lot of standard cosmology which to anyone who takes any amount of time to think about, will be apprehended as fictional. Look at Haglund's explanation of mass for example:

In the standard model this is done by making massless matter interact with a fictitious matter field, with unbelievable properties (a non-zero value of the vacuum expectation value, for which no reason is given; it's just posited). But the mass can also emerge if massless particles interact amongst themselves. Pure kinetic energy turned massive. — Haglund

Your referenced page on critical density offers another very good example:

The ‘critical density’ is the average density of matter required for the Universe to just halt its expansion, but only after an infinite time. A Universe with the critical density is said to be flat. — https://astronomy.swin.edu.au/cosmos/c/Critical+Density

Notice, critical density is the density required to make the universe halt its expansion, after an infinite time. Does that not seem strange to you? Think about it. They've managed to figure out how much density is required such that the universe will actually halt its expansion, but the actual halting of expansion will only occur after an infinite amount of time has passed.

Suppose someone laid the ball on the cushion. And suppose also that the ball is causing the depression in the cushion. I'm supposing both those things. The ball got there somehow. And now that it's got there, it's making a dip in the cushion. The ball is the cause of the dip. Of course the ball wasn't always there. There's no reason to imagine that it must have been. But now that it is there, it's causing a dip and continuing to cause that dip until it's removed - which will probably also happen. — Cuthbert

I don't think that's a proper description. When the ball got placed on the cushion, this act caused the dip in the cushion. Once the ball is there, and the dip is in the cushion, the ball is not continuing to cause the dip. The dip was caused by coming into contact with the ball, and once it has been caused, it becomes a continuous feature of the cushion, just like every other property of the cushion, until someone takes the ball away, and this act may cause the dip to go away.

I think Kant's example gives us difficulty only if we have a prior theory - namely (1) Causes must precede effects. (2) Only events can be causes. My suggestion is that the example is straightforward and well chosen. The problem is not the example but the prior theory. — Cuthbert

"Cause" is a temporal concept. If you take away the temporality from the concept, then you are just talking about something else. Your suggestion that there is a problem with the prior theory, is like saying that there is a problem with the theory which makes 2+2 equal to 4. You might say "I want 2+2 to equal 6, so I think there is a problem with the "prior theory" which makes 2+2 equal to 4. Your request to change the meaning of "cause" (reject the prior theory), is just the same as the request to change the meaning of "2" (reject the prior theory.

Sure you can claim that there's a problem with the theory, and request a change, but unless you can demonstrate an actual problem with the theory, the request is just random nonsense.

This shows that causes and effects can coherently be supposed to be simultaneous and that objects can be supposed to be causes. Of course, he might be wrong. But to show that he's wrong we need more than the stipulations that causes must precede effects and that objects cannot be causes. — Cuthbert

I would say he is wrong. He shows a misunderstanding of causation. Causation is always represented by an act. A static situation, a state, such as the ball being in a certain static relation with the cushion, is not causation. Consider the relation between the earth and the sun, or the earth and the moon, for example. The sun causes many things on the earth, in the relation between these two objects, the sun and the earth, but each is described in terms of activities. There is no static relation between the sun and the earth. Likewise with the relation with the earth and moon.

So what the real problem which Kant demonstrates with the example, is that describing two distinct objects in such a "causal" relation with each other, as having a static relation, is not a proper description. Objects are always changing, moving, and being moved, so two distinct objects in contact with each other, ball and cushion, never really have a static relation with each other. So if we want to describe such a situation as the ball causing the dent in the cushion, we must go beyond what is immediately evident to our senses, and look at the interaction between the particle of the ball, and the particles of the cushion. This is where the activity is happening (which we do not see), and this is what validates the designation of "cause".

The ball does not come to be on the cushion. It is on the cushion from the beginning. — Bartricks

This is Bartricks' insistence on incoherency. Bartricks claims that this proposition, which I claim is incoherent, just appears as incoherent to me. Now I see it's incoherent to you as well. So we can say that it is incoherent to us.

And I've had quite enough of your misrepresentations. — apokrisis

My direct quote is a misrepresentation? "The Cosmos is deemed to be flat because it has the critical mass..."


The problem is that the concept of "mass" which is principally a temporal concept, is fundamentally unintelligible under the principles employed in modern physics, relativity theory. The concept of time dilation makes the incoherency of "mass" in modern physics glaringly obvious.

Actually, there is continuing debate among physicists concerning this concept of relativistic mass. The debate is largely semantic: no-one doubts that the correct expression for the momentum of a particle having a rest mass m moving with velocity v→ is p→=m1−v2/c2√v→. But particle physicists especially, many of whom spend their lives measuring particle rest masses to great precision, are not keen on writing this as p→=mrelv→. They don’t like the idea of a variable mass. For one thing, it might give the impression that as it speeds up a particle balloons in size, or at least its internal structure somehow alters. In fact, a relativistic particle just undergoes Lorentz contraction along the direction of motion, like anything else. It goes from a spherical shape towards a disc like shape having the same transverse radius.

So how can this “mass increase” be understood? As usual, Einstein had it right: he remarked that every form of energy possesses inertia. The kinetic energy itself has inertia. Now “inertia” is a defining property of mass. The other fundamental property of mass is that it attracts gravitationally. Does this kinetic energy do that? To see the answer, consider a sphere filled with gas. It will generate a spherically symmetric gravitational field outside itself, of strength proportional to the total mass. If we now heat up the gas, the gas particles will have this increased (relativistic) mass, corresponding to their increased kinetic energy, and the external gravitational field will have increased proportionally. (No-one doubts this either.)

So the “relativistic mass” indeed has the two basic properties of mass: inertia and gravitational attraction. (As will become clear in the following lectures, this relativistic mass is nothing but the total energy, with the rest mass itself now seen as energy.)

On a more trivial level, some teachers object to introducing relativistic mass because they fear students will assume the kinetic energy of a relativistically moving particle is just 12mv→2 using the relativistic mass — it isn’t, as we shall see shortly.

Footnote: For anyone who might go on sometime to a more mathematically sophisticated treatment, it should be added that the rest mass plays an important role as an invariant on going from one frame of reference to another, but the "relativistic mass" used here is really just the first component (the energy) of the four dimensional energy-momentum vector of a particle, and so is not an invariant. — https://galileoandeinstein.phys.virginia.edu/lectures/mass_increase.html

Notice where the article says "As usual, Einstein had it right". This is really a mistake. Attributing mass to kinetic energy, instead of providing a true representation of the referred phenomenon, is what leaves "mass" as incoherent. At issue is the relation between gravity and inertia.

You're an idiot. — apokrisis

As you can see, I don't much appreciate your fiction.

I actually think we are moving in the opposite direction to what you suggest. It's much more productive to cultivate a good disposition and attitude in a person, and encourage one to behave virtuously, then to try and name, and outlaw, all the things which are apprehended as bad. This is because the person who is inclined to do bad things will continue to find more, no matter how many things you name and outlaw, while culturing one toward a good disposition only requires a general idea of what constitutes a good attitude, and the will to cultivate this.

Some evidence that this is the way that we as human beings are moving, can be found in the difference between The Old Testament's ten commandments of what not to do, and The New Testament's one commandment of what ought to be done, love your neighbour.

Did you really ever ask this question? Or are you just papering over your knee jerk misunderstandings? — apokrisis

Way back, when I first engaged you, and accused you of contradiction, in saying that space was both curved and uncurved, I gave you the option of explaining how it might change from one to the other.

And as I said, to attribute both curved and uncurved to space, is contradiction, unless you can show how space changes from being curved to being uncurved or vise versa. — Metaphysician Undercover

But you went off on a tangent of sophistry, instead of addressing the issue. You said space is curved to the degree that it's not flat, and flat to the degree that it's not curved. So I explained why this is very wrong. All the degrees are within curvature, and flat has no degrees of curvature.

Anyway, I’ve once more outlined the standard story and added the physical motivation. — apokrisis

"The standard story"? You mean your standard story. It's a good bit of fiction, ("The Cosmos is deemed to be flat because it has the critical mass..."), but I'm not too interested in fiction.

The question still remains who created matter and the laws it obeys to. — Haglund

We can't even begin on this question, until we first figure out what is matter.

Until the Greek Revival / Enlightenment gave scientists the courage to abandon the age-old all-purpose explanation --- that the omniscient-omnipotent-god-concept explains all philosophical mysteries --- most sages & scientists were forced by their ignorance of ultimate causes to postulate a hypothetical First Cause, as a catch-all non-explanation. — Gnomon

It's not really a "non-explanation". The vast majority of human beings never apprehend the logical need for a "First Cause". So there is a massive explanation required, just to get to the point of recognizing the reality behind the philosophical mysteries, and the reasons for assuming the First Cause. It's not a non-explanation at all, it only appears like such to those who don't spend the time and effort to understand the explanation, and think of it as an assumption rather than a logical conclusion..

Quantum weirdness goes deeper: It implies that the logical foundations of classical science are violated in the quantum realm; and it opens up a glimpse of an unfamiliar and perhaps older aspect of nature that some call the implicate universe.
https://web.stanford.edu/dept/HPS/WritingScience/Ferris.htm
Note -- "Implicate" means implicit or inferred intentional meaning — Gnomon

This is similar to what I said above. Understanding produces specific implications. When one does not understand, then the implications are not apprehended.

Stop making shit up. I said space would be flat to the degree it ain’t curved and curved to the degree it ain’t flat. — apokrisis

That was your attempt to justify your earlier claim that space is both curved and flat. Here's a reminder:

The flatness of space is defined by the constancy of the ratio between a radius and a circumference. Only in flat space is this ratio a constant - pi. In curved space, it ranges from the 2pi of the sphere to the infinite pi of a hyperbolic geometry.

So only in flat space does some particular angle retain that value over all its scales of extension. And should you choose, instead of degrees, you can talk about angles using a more fundamental pi-based unit like radians. — apokrisis

The issue was how to measure the kind of space you might be embedded in. — apokrisis

So I'll ask you again, the question I asked back then. If space changes from being flat to being curved, which is the only way that this sort of "kinds of space" idea you propose makes sense, by what principles do you say that this is X type of space, and that is Y type of space? What you have described is just two different ways of measuring one type of space. That's why the one transposes to the other, by making pi variable.

-lol......no those building blocks "obey" all the laws of nature. There is nothing non natural about them! — Nickolasgaspar

Look, lets say there is a bunch of building blocks, and what these building blocks do is obey the laws of nature, so that whatever they produce is said to be natural. Now, lets move along and consider how the building blocks came into existence. Clearly, the activity which caused the existence of the blocks is not an activity of the blocks themselves, because it is an activity which is prior to the existence of the blocks, causing the existence of the blocks. And only the activity of the blocks is defined as "natural". So whatever activity it was, which caused the existence of the blocks, this must be other than natural. Agree?

Come on...lets no tap dance around concepts. — Nickolasgaspar

If we're not going to "dance around concepts", then what is the point of this discussion?

You need to demonstrate that building blocks in nature NEED a supernatural agent to exist before assuming their supernatural origins. — Nickolasgaspar

No, you defined "nature" that way, as what manifests from fundamental building blocks. It was your definition. All I need to do is show that there is necessarily something outside of what is "natural", by your definition, and this is, by valid logic, non-natural. That I've done.

Substance causation is causation by an object - a thing - rather than an event. So, not causation by a thing changing, but a change caused by a thing. It's not that the thing causes the event by undergoing some change - for a change is an event. The thing causes the event directly.

The first event or events are going to have been caused this way (some argue that all events are caused this way - that events are just manifestations of substance causation). — Bartricks

Your phrase "substance causation" is still incoherent to me. (I'll be clear to add "to me" if that satisfies you). You are saying that a "substance" can cause an event without that substance undergoing any change itself. This is not consistent with any sense of "substance" which I know of. Substance never creates an event without itself changing. That's the nature of how we use "substance". Maybe you are using a definition of "substance" which I am unfamiliar with. Can you provide your definition for me?

The first event or events are going to have been caused this way (some argue that all events are caused this way - that events are just manifestations of substance causation). — Bartricks

No, the first acts are the ones which cause the existence of substance. When you claim that the first events are cause by substance, without the substance itself changing, you place "substance" outside of time, because the passing of time coincides with events. So by saying that substance causes the first event, you place substance outside of time. Then substance is necessarily inert, passive, and cannot cause anything because it cannot be active as an agent. And since substances are what are active in events, you have a distinction between an active substance and a passive substance, and no way to show how a passive substance magically creates an active substance, as the first "event".

Many in the free will debate think that free will requires substance causation, where the substance in qusetion is ourselves (that's called 'agent causation'). And an apparent example of substance causation would be our own decisions, which we seem to make directly. — Bartricks

This is incoherent to me because you have said that the substance causes an event without itself changing. If it does not change, then we cannot say that it is "active". And if it is not active we cannot say it is an "agent". A substance which does not change cannot be an agent. In your example, "ourselves", human beings, it is very clear that the substance, which is the human being actively changes when causing a freely willed event. So it is very clear that your definition of "substance causation", in which the substance causes an event without itself changing, is not applicable to the "agent causation" of freely willed acts, in which the agent, as a human being, changes.

Physicists just take Laws & Constants for granted, without further explanation. — Gnomon

It hasn't always been like this. Newton for example indicated that the reality, or truth of his first law of motion, what we call inertia, is dependent on the Will of God. Apparently, God might pull out his support for this law at any moment, and perhaps put something else in place which could be quite different, or leave no temporal continuity at all. Since God doesn't seem inclined to change His mind though, and His Will appears to be very stable, and trustworthy, human beings are inclined to take laws like this for granted. God's trustworthiness provides very good reason to take such laws for granted. When these laws are taken for granted however, there is no need to assume God anymore, because the assumption of God is only required for the purpose of accounting for the stability in these laws. And we have very good reason to take these laws for granted, because God is extremely trustworthy. So we can all become atheist.

I see what you mean, I think. But what if your space changes it's metric? Your shapes would change. If you draw lines and shapes on a thin piece of stretchable rubber, don't the shapes change form? If they keep their shape, the distances between the shapes will change, like the distance between static galaxies in the universe grows. — Haglund

That's exactly the issue, a changing space. Apokrisis claimed space was both flat and curved, which I pointed out is contradictory unless this is a temporal change. If we assume that space actually changes, then we need a relation between space and time which allows for such changes, physical "change" being an attribute of time. This would force us, by logical necessity, to assign logical priority to time rather than space. The conventional conception makes time the fourth dimension, as an attribute of space, rather than making it the zeroth dimension, as prior to space. As the fourth dimension, the properties of time are determined based on observation and analysis of changes to spatial objects. Under this conception, space is not allowed to be a changing thing (aether for example). When time is understood as prior to space, then non-spatial activity (being allowed for by non-spatial time) can be causal in the spatial world.

When the relation between space and time is understood in this way, we can give the non-dimensional point real status, as an active non-spatial point, which has location without occupying space, and is also causal in the surrounding space. The space surrounding the point can be mapped in the way I described, and changes to the physical things in this space observed. The points may be arbitrarily located for the observation purpose, but upon numerous observations of numerous points, a system can be developed to determine the real location of real non-spatial, active causal points, from the way that the surrounding spatial world is affected.

The issue with "expanding space", is that if it expands in all directions from a given point, then the point, around which the space is expanding, must have real existence, and it is most likely causal in the act of expansion.

It's only you who insists on seeing the embedding dimension that the intrinsic curvature of differential geometry has long done away with. — apokrisis

You speak of things in terms of "flat" and "curved" which implies necessarily a distinction of dimensions. What you don't seem to grasp is that the "curve" is fundamentally unintelligible in relation to a straight line or flat surface, as demonstrated by the irrational nature of pi. We always fall back on the ideals of straight lines or flat planes in any attempt to understand curves, as your example of Gaussian curvature, and the reference of zero curvature, demonstrates.

If you understood the construct which I described you'll see that there is no curvature whatsoever within the model. There are points related to each other by lines, no flat planes. However, there is always, necessarily, "space" between the points which exist in straight line relations to each other. and curvature is allowed to be a real property of this space, as waves or something like that. Representing the transmission of wave energy with straight lines is, as we know, a faulty representation. Representing the curves of waves as existing relative to flat planes is what I say is a faulty representation, despite the usefulness of this representation. The exact properties of the curves (as waves) will remain unintelligible to us until we determine the nature of the medium (space) which exists between the points.

Heat is lost into the space that gets made. — apokrisis

What exactly do you propose is the mechanism which creates space? Is that lost heat like a friction to this system, this space creating mechanism? If so, then the heat isn't lost into the space, it is lost into whatever it is which is outside of space. The space creating mechanism implies the real existence of whatever this is, which is outside of space, and is actively creating space.

I think what is required, is to first remove all reference to dimensions. It is this idea of distinct dimensions which causes the problem. Suppose we start with a non-dimensional point. From that one point, we could make lines, with angular relations to each other, and specified lengths. Connecting all the ends of the lines, would produce the outline of a spatial object (what we now know as a 3d object). The more lines one makes (theoretically an infinity of such lines is possible), the more accurately the spatial object is defined, if the specifications are made correctly.

To transpose a construction like this, into the physical world, to actually represent a real physical object, would require determining the spatial relations between any internal point of an object, and the boundaries of its perimeter. But from this perspective there is no need to assume any dimensions, (you might understand it as infinite dimensions). There is just a relationship between a non-spatial point of reference (point of location), which is somewhat arbitrarily placed in the spatial world, but only arbitrary to the extent that the required relations may be determined.

Apokrisis, I believe prefers vague boundaries, and this assumption would confound any such geometry. And that is a very difficult issue, because as we know, various objects interfere with the boundaries of each other, overlapping, and existing in the same space, at the same time. I believe the idea of "infinitesimals" is what validates vague boundaries, and I think this idea is very counter-productive toward a true understanding of physical reality.

You clearly don't really understand what substance causation is. — Bartricks

That's because I have never come across "substance causation" before, it seems to be your idiosyncrasy, and you haven't yet explained it in a coherent way.

Substance causation involves a substance - an object - causing an event. Not - not - by means of some other event. That's event causation. But directly. — Bartricks

But a substance must act to in order to cause an event. This is how we can say that the substance is an "agent".

You can put whatever label you like on the instantiation of that causal relationship - you can call it an 'act' or a teapot, it won't make a difference. The simple fact is that substance causation involves the instantiation of a causal relation between a substance and an event. And when does that occur? At the time of the event. Thus, substance causation 'is' simultaneous causation. — Bartricks

An "act", like a "teapot", is something which is describable. So, when the substance "acts" (or "teapots", whichever you prefer), to cause an event, we can describe that "act" (or "teapot"). Are you prepared to describe the proposed "simultaneous" act involved with the ball and the cushion?

I've seen some descriptions, where the cushion would push up on the ball, while the ball would push down on the cushion, the two pushings are obviously not equivalent. This is like the way that the gravity of the earth interacts with the gravity of the moon, both have an effect on the other. But this is not "substance causation" according to how you've used the phrase, because each of the two distinct substances act as causes, and each have an effect on the other. The "simultaneous causation" involved here, is two distinct causal acts acting at the same time. Is this what you mean? If so, since there is a requirement of two distinct substances acting as causes, it doesn't seem like it could support self-creation.

Gaussian curvature is an intrinsic property, which can be measured inside the curved space. For example, on a 2d sphere, initial parallel lines, after parsllel transporting them, can cross. Or triangles have different angle sums. — Haglund

For the reasons I explained, "2d sphere" is incoherent.

Bear in mind that the Cosmos exists to serve the second law and thus its aim is to maximise entropy. So even without the inherent quantum uncertainty, the Cosmos is committed to the production of uncertainty at every turn. — apokrisis

Come on apokrisis. This statement says that the cosmos was created with the purpose of maximizing entropy. That means that it was created intentionally, with that goal. But if God wanted a universe with maximum entropy, He would have just created it that way. Wouldn't that have been much easier for Him anyway?

As Haglund correctly points out, the second law of thermodynamics is simply a way that we describe things. And, I might add that it is fundamentally mistaken to apply the laws of thermodynamics to the universe (as a whole). This is because these laws are designed to be applicable only to systems, and we have no principles whereby we can conceptualize the universe as a system. Within any system, there is a quantity of energy which is lost to that system, over time. Much of that energy actually escapes the system, as heat loss from friction for example. How would we account for energy which escapes the system, if the universe was a system?

↪Haglund All elementary particles are composite in some sense even in the Standard Model view. Quarks mix like neutrinos. — apokrisis

This issue is due to the fundamental design of how we conceive of a physical object. The problem is a feature of the mathematical definition, one might say. An object is divisible. Because of that it is impossible to get to the bottom of "particles", because they will be divisible. So it is required that we choose something other than "particles" to be at the bottom, if we want a true understanding, and this is where fields are pertinent. The problem though is that fields are only understood through the appearance of "particles", and this is due to the limited observational capacities of the human being. As a result, the only real access we have toward understanding the true fundamentals, is through establishing the correct relationship between the particle and the field. But the field must be constructed on principles other than the appearance of particles, because that construction already presupposes a specific relationship.

If you call the mainstream trend of thought a fantasy, then they are right to treat you like a crackpot. — apokrisis

Well, how would we ever find out when the mainstream trend of thought was wrong, if everyone had that attitude? We'd be stuck in the ancient "mainstream" of thousands of years ago, thinking that the sun "comes up", in the morning, and "goes down" in the evening.

I think the proper limits to curvature are the infinitely small radius, and the infinitely large radius. The infinitely large radius cannot appear as a two dimensional line because a radius is the property of a circle. Therefore both the maximum curve and the minimum curve, maintain their status as 2 dimensional, and neither gets reduced to a one dimensional figure.

A 2d torus has negative Gaussian curvature on the inside, positive on the outside, and zero in between. Because its embedding in 3d. But in 4d it has zero curvature, like a 2d cylinder. — Haglund

As I explained to apokrisis, you cannot add another dimension without adding another feature. If you add another feature, then the figure is not the same figure. For example, a one dimensional line is not the same as a two dimensional plane, and a two dimensional circle is not the same as a three dimensional sphere. So it doesn't make any sense to talk about the same object in 2d, 3d, and 4d, that's a fundamental category mistake.

Or did I say the larger picture sees flatness as poised between the opposing extremes of hyperbolic and hyperspheric curvature? And that is why the value of pi might vary between 2 and infinity, with 3.14… being the special case where the Gaussian world would intersect the Euclidean one? — apokrisis

Do you not see the unintelligible (incoherent) result of your category mistake? By giving the the one dimensional plane a presence as a two dimensional figure (or two dimensional plane a presence as a three dimensional object), you produce the possibility that pi could be anything. But pi, by definition, is essentially a statement of the relationship between a one dimensional object, (the diameter), and a two dimensional object, (the circumference). Notice that this is said to be an irrational ratio, and it is irrational because the two distinct dimensions are fundamentally incommensurable. This is verified by taking two lines supposedly equidistant in two distinct dimensions, and attempting to establish a relation between them, the result is a similar irrational ratio, the square root of two.

So when you you take the two dimensional flat plane, and try to give it a presence in a three dimensional geometrical construct (or bring a one dimensional line, into a two dimensional geometry), you incorporate that fundamental incommensurability into your geometrical system. The result is that pi itself, which is by its definition, a mathematical description of the relationship between a one dimensional figure and a two dimensional figure, becomes meaningless, as you describe. So you do not actually get rid of the boundary between the distinct dimensions, which you cannot do because of the basic incommensurability, you simply incorporate that element of unintelligibility deeper into your geometry, by hiding it.

So I think what's been lost sight of is precisely the intuition of the domain of unconditional, the realm of necessary truths (arguably, the noumenal realm). — Wayfarer

As I said in my earlier post, the only sense of "necessary" which can be validated is the sense of "needed for...", as a good, for whatever purpose. The sense of "necessary" which many people propose, a necessity which is independent of the wants and needs of human beings, and supports common determinism cannot be validated. The closest we can get to such a "necessity" is the Will of God.
https://thephilosophyforum.com/discussion/comment/682932

I believe the position apokrisis is arguing is contrary to the principles of Gaussian curvature. But apokrisis refers to Gaussian curvature in an attempt to support the argued position. Apokrisis is claiming that flat and curved are two limits, so that all real shapes are somewhere between, being to some degree flat, and to some degree curved. But clearly, anything flat has zero degrees of curvature, and other shapes have varying degrees of curvature, and no degrees of flat. So it is wrong to assert that the same shape is to some degree flat, and to some degree curved. That's just apokrisis attempting to avoid the earlier contradiction in the statements that space is both curved and flat, at the same time.

Substance causation is causation by a substance. When the substance is an agent it is called 'agent causation'. You are simply referring to agent causation when you maintain that an act of will is not an event but causes an event. — Bartricks

Yes, I am referring to "agent causation". But I went through this already. A substance does not cause anything on its own, it is the act of the substance which is the cause. That's what makes the substance an "agent", it is acting. Your description, 'the ball is always on the cushion', contains no act, so there is no agent, and no causation. There is no event described, only a static situation.

But anyway, as you clearly accept the coherence of substance causation, then you should also accept that there can be simultaneous causation, for that's what one has with substance causation. When a substance causes an event, the causation and the event are simultaneous. To maintain otherwise would be to have to posit some earlier 'event' that caused the later event - but then that's event causation, not substance causation. — Bartricks

But there is no "event" in your description, only a static situation. Do you understand the difference between a static unchanging situation, a state, and an event, which is an occurrence, something which happens? You need to show me an event before you can claim that the substance and the event are simultaneous. You have given me two substances, the ball and the cushion, and a static relation between the two. Now describe the event (what occurs, or happens), the act, so that we can determine the agent, and what type of causation is involved in that event.

That is where it all comes back to defining a reciprocal relation between bounding extremes. — apokrisis

This is where you are wrong, because you are not distinguishing between the ideal and the real. I explained this already. You said a thing is flat to the degree that it's not curved, and a thing is curved to the degree that it's not flat. Clearly this is incorrect, because "flat" accepts no degrees of curvature. You said so yourself, it is zero curvature. And all degrees predicated in this subject are degrees of curvature. There is no such thing as degrees of flatness. There is no reciprocal relation between zero and many.

Therefore this is not a matter of a "reciprocal relation between bounding extremes", it is a categorical separation between two distinct types of things. A two dimensional flat plane is categorically different from a three dimensional curved surface, and it is incorrect to represent the two dimensional as a bounding limit to the three dimensional, or the three dimensional as a bounding limit to the two dimensional. We can see this difference between all levels of dimension, between zero and one, one and two, two and three, as well as between three and four. Each dimension adds a new feature, a new kind of property, that's what a "dimension" is. To describe one dimension as the "bounding extreme" of another dimension, is simply incorrect.

In simpler terms, we can represent a real spatial object, at a supposed moment in time, with three dimensions, but we cannot represent a real spatial object with two dimensions. So the two dimensional figure clearly represents nothing real in the world, there is nothing in the world which occupies space in a two dimensional way. Therefore there is a very substantial difference between what can be done with a two dimensional representation and what can be done with a three dimensional representation. The limitations of the two dimensional figure are completely different from the limitations of the three dimensional figure. They are not bounding restrictions of each other.

So quit digging and start climbing. The view is better. — apokrisis

Sorry, but when one's goal is to dispel illusion, digging down is much more productive than climbing higher. I'd rather be digging in the hole of truth, pointing at the extremely unstable grounding of your ladder, than to be at the top of that ladder which is about to fall, enjoying the excellent illusion.