You can plainly see that one ball has caused the other ball to move. What can you possibly gain by trying to deny what everyone can see with their own eyes? — Ron Cram

That's an odd description. I've never seen a cause, and the way I understand "cause" it would be impossible to see a cause, so I reject that claim as false, just like I would reject as false, the claim that someone saw God. You are obviously using "cause" in a different way from me, and are unable to make your use appear coherent to me.

In relation to Newton's laws, the question is whether you saw the force, which acted on the ball, because according to Newton, force is what causes acceleration. Until you convince me that you can see a force, you will not convince me that you saw the "cause" of motion, using "cause" in a way which is applicable to Newton's laws. Any other argument is useless equivocation.

Every pool shark with $20 riding on the outcome of a game of 8 ball knows that cause and effect is in play. — Ron Cram

Do you not understand the difference between knowing that cause and effect is in play, and seeing cause and effect? One can know something without seeing it.

This next lesson explains that kinetic energy can do work directly as mechanical energy. — Ron Cram

What your lesson actually says is that a "force" does the work. You are leaving out an essential part of the equation, the means by which one form of energy is converted to another, and that is "force". As Newton explained, the billiard ball does not directly cause the other ball to move, it does this through the means (medium) of force. There is activity which occurs in that very short time between one ball moving and the other ball moving, and this activity is represented as "force" which is understood through deceleration and acceleration. The ball applies a force to the other ball, and the force is what causes the ball to move. The fact that the so-called transfer of energy is not one hundred per cent, and some is lost to inefficiencies, is evidence of this activity in the time between. And as I explained to you, in modern physics forces are understood in terms of fields, which represent potential energy, not kinetic energy.

Correct. This is why we call it a transfer of kinetic energy. — Ron Cram

That one ball stops having kinetic energy, and the other one starts, does not mean that kinetic energy was transferred.

Because of the conservation of energy. — Ron Cram

It could only be a transfer if the very same kinetic energy was in the second ball as in the first. But some kinetic energy is lost due to inefficiencies, therefore the second ball does not have the same kinetic energy as the first, and there is no transfer.

No, we observe one slow or stop and the other begin to move. — Ron Cram

Right, we do not see any kinetic energy being transferred from one ball to the other.

Because two solid objects cannot occupy the same space, when one moves into that space, the second ball has to move out of the space. This is the physical necessity I've explained. — Ron Cram

This is nonsense. The one object could resist being moved, and just absorb the impact. There is no necessity that the object give up its place to give it to the other object. Again, you are just making up this idea of "physical necessity". It's pure nonsense.

No, what we see is a transfer of kinetic energy. The first ball was moving, now the second ball is moving. It was knocked out of its space because two solid objects cannot occupy the same space. — Ron Cram

Asserting nonsense doesn't get you anywhere. You need an argument to justify your assertions. As I explained, there is no necessity that the object gets "knocked out of its space", it might absorb the impact, and the other object might bounce of, or explode into bits. Your so-called "physical necessity" is nonsense.

False. Kinetic energy does not need to be transformed into potential energy before doing any work. Kinetic energy directly does work. — Ron Cram

Back this up with a mathematical demonstration then.

False, but let's say this weird theory were true. In that case, we would still be observing cause and effect. — Ron Cram

That's not true, and this is the whole point, which I explained to you earlier. We do not observe energy. We apply the principles and deduce that the object has energy. We do not see energy with any of our senses, we use our minds to figure out that the object has energy, through application of the principles. The same is the case with cause and effect. Which senses do you believe that we use to observe cause and effect?

What I consider the most common, a person is an individual human being.

1. One billiard ball moves, strikes a second ball and causes it to move. This is cause and effect. What you are observing is a transfer of kinetic energy. The first billiard ball "has" or "is" kinetic energy. Either term is acceptable because kinetic energy exists because the ball is moving. The kinetic energy and the moving ball are inextricable. Because two solid objects cannot occupy the same space, when the first ball strikes the second, it causes the second ball to move. The first ball has slowed or stopped and the second ball which was stopped is now moving. That you are observing a transfer of kinetic energy is plainly obvious. — Ron Cram

I'll take a look at this for you. First, we cannot say that the ball "is" kinetic energy, because a ball is more than just that, and the fact that it stops moving and has no more kinetic energy, in your example indicates that it is more than just kinetic energy. So let's assume that it "has" kinetic energy, as a property. After the first ball strikes the second ball, the first ball no longer has kinetic energy, and the second ball has kinetic energy. So one ball looses kinetic energy, and another ball gains kinetic energy.

By what principle do you say that this is a "transfer"? One object looses a property and another gains a similar property, why would this be a transfer of property? Do you observe the property coming off of the one and going into the other? If it is true that two solid objects cannot occupy the same space, how does this premise validate your claim that one object transfers a property to another? What we observe is that one object ceases to be in motion, and the other starts to be in motion. We do not see any transfer of motion.

When you understand a ball as consisting of many parts, molecules, rather than as a mass with a centre of gravity, you'll see that all the kinetic energy of the one ball must be transformed into potential energy before that potential energy can act as a force to accelerate the second ball. So there is no transferral of kinetic energy, there is a deceleration of the first ball, as its kinetic energy is transformed to potential energy, and an acceleration of the second ball, as that potential energy acts to create kinetic energy in the second ball. Potential energy acts as a medium between the two instances of kinetic energy, therefore there is no transferral of kinetic energy, only two instances of kinetic energy, with potential energy separating the two.

Why do we have a word 'designed' as a categorising term to distinguish from other apparently ordered matter? — Isaac

Actually I wouldn't be inclined to make such a distinction, it appears like if it is ordered, it must have been designed, so there is no need for that distinction.

It means put together with intent. But intent is a property of persons not objects. So we cannot see in an object the intent of the person. — Isaac

I believe it is a mistake to restrict "intent" to persons, claiming that only persons have intent. As in my earlier examples, things like beehives, beaver dams, and birds nests, exhibit intent, and we would not call the authors of these things persons. Yes, persons have intent , but they are not the only things with intent. So I think that we must widen the category of things which have intent, beyond just persons. That's what I was getting at in my discussion with terrapin, the use of "person" is generally restricted to refer to human beings only, but evidence indicates that beings other than human beings definitely have intent.

A sentence incidentally written by a random process iterated a million times is indistinguishable in every way from a sentence written that way with intent apart from by its history. Same for any object. It is only by its history which we can distinguish objects ordered by intent from objects ordered by chance. — Isaac

I don't believe this at all. Any "random process" which produces a sentence would necessarily have been created with that intention. Likewise, it is contradictory to say that objects could be ordered by chance, because then they would not be ordered. So all you are doing here is reciting contradictory nonsense.

No. I specifically did not say that. I said that any of the common definitions of personhood would do. — Terrapin Station

As I've been trying to explain to you, beings other than persons create and do things with intent. So I find your assertions to be unacceptable. One does not have to be a person to create by design.

Objects in motion possess (or are) kinetic energy. Gravity is not a kinetic energy. Gravity is one of the four fundamental forces in nature. The other three are electromagnetism, strong nuclear force and weak nuclear force. Kinetic energy is not a fundamental force but a force that is bound to objects. — Ron Cram

You seem to understand the difference between "force" and "kinetic energy", so why insist that kinetic energy is a force? Do you not recognize that forces are understood as potential energy, not as kinetic energy?

That's a good question. One element Newton and others look for is physical necessity. — Ron Cram

You are making this up. Newton discusses no such thing as "physical necessity", he simply states his "laws" of motion. Whether or not these laws are meant to represent an observed "physical necessity" is never mentioned, and such a conclusion (by you) is an absurdity.

What might sometimes be referred to as a "physical necessity" is the necessity derived from an inductive conclusion. But as Hume demonstrated, this is not truly a necessity at all, because it is probability based. There is no such thing as "physical necessity" in the way that you use it

Math can show that a physical necessity is at work, even if the physical necessity is not clearly understood. — Ron Cram

If you truly believe this, then show me an instance where math demonstrates a physical necessity which is not based in statistics and probability.

No. Leibniz did not invent the term "kinetic energy." — Ron Cram

Did I say that? It seems you do not know how to read.

Newton clearly understood that an object in motion is a force, — Ron Cram

Either you haven't read Newton's laws, or you're just demonstrating further, that you do not know how to read. A body in motion will exert a force on another. The body in motion is not the force itself. This is very clear in Newton's writing. A body in motion moves uniformly, according to the first law, and it has momentum according to its mass and velocity. If a force acts on a body, its motion changes. So "force" is understood through change in motion, not as the property of an object in motion. This is clear from the fact that gravity is a force, and it is not an object in motion.

No, a law is not declared based on frequentism. — Ron Cram

OK, then when someone like Newton declares a law, what is it based on?

Everyone knows that Newton uses the term "force" to mean "kinetic energy" and "impulse" to mean "transfer of kinetic energy." — Ron Cram

No, there's a very big difference here. Force is equal to mass times acceleration. And momentum is equal to mass times velocity. "Kinetic energy" was developed from Leibniz' "vis viva" (living force), which was expressed as mass time velocity squared. This was later modified in the concept of "kinetic energy" such that kinetic energy is half of the vis viva

You can see that "force", as mass time acceleration is quite different from "kinetic energy" as half of mass times velocity squared. Kinetic energy refers to a simple property of a body in motion, the capacity to do work. "Force" was meant by Newton to refer to the means by which a body's motion is altered; this is quite clear in Newton's first law. The capacity to do work (kinetic energy), as a potential which a moving body has, is quite distinct from a 'force" which is actively doing work, changing a body's motion. This is why the "force" of gravity, as something actively doing work, must be expressed as potential energy, the capacity to create motion (kinetic energy) in a body, rather than as kinetic energy. So you'll find that in field physics, forces which are actively doing work, are expressed as potential energy.

You are thinking about this wrong. We observe cause and effect directly. We come to understand the physical necessity involves. This leads us to understand the natural law at work. The physical law then allows us to make inductive inferences. This is how science works. Modern philosophers of science understand this, but Hume and his followers are still living in the Middle Ages. — Ron Cram

Despite your claim that I am thinking wrong, you clearly have this backward. The "physical law" is an inductive conclusion, produced from descriptions of natural occurrences. Any "necessity" which is apprehended is a logical necessity dependent on acceptance of the inductive law. This is the necessity which Hume questions. The physical law does not necessarily represent any "natural law" at work, as the physical law is merely inductive conclusion produced from our observations. So the validity of the physical law is supported by the probability of correctness of the inductive conclusion, and has the possibility of being inaccurate, due to the role of probability in inductive reasoning. Therefore your claim that we observe the natural law at work is false. There is no necessary relationship between the physical law and any "natural law".

Observe: Newton's first law, a body will remain at rest, or in uniform motion unless acted upon by a force.

Therefore, when we observe that a body's motion changes, we can conclude that it was acted upon by a force. Notice that we conclude deductively that a force acted, by applying Newton's first law as a premise. We do not observe that a force acted.

There is a third thing or quality which explains how one ball causes the other to move. It is the transfer of kinetic energy. Whenever you see an object in motion, you are looking at kinetic energy. — Ron Cram

Actually, in Newton's terms we would call this third thing a "force". But "force" is arguably entirely imaginary. Just like Hume said, its a concept devised to account for changes in momentum.

There's no 'force of gravity' or "masses attracting eachother"... gravity is the curvature of space. — ChatteringMonkey

This is what happens when you take Newton by his words. We have to account for the real existence of what he calls "force". Ron Cram refuses to do this. The modern trend in physics seems to be to relocate "force". Instead of being completely conceptual and therefore independent from the thing (as per Newton), the trend is to make force a natural property of an object. This is somewhat problematic, making Einstein's gravity a natural property of space, rather than a "force". So space must be a real substance to have this property.

False. Cause and effect are directly observable. I've given a number of examples. — Ron Cram

What you have done is substitute Newton's term "force", with the concept of "cause and effect". But force is not directly observable, it is deduced through the application of principles like Newton's laws.
Are you ready to discuss Newton's laws without substituting "force", and address directly what Newton meant by this term?

Yeah, there's not one universal defintion. That's why I said to use whatever common definition you prefer. My comments didn't hinge on a particular definition. It's just that I don't want to argue about definitions of personhood. — Terrapin Station

The question of the thread is how to tell the difference between design and no design. You refer to personhood; something can only have been designed if it was created by a person. Now you say that one is free to define "person" however one pleases. So you have made absolutely no progress toward answering the question. The distinction between design and no design is made according to whether or not there was a "person" involved, but an individual is free to use whatever definition of "person" that one might dream up. How is that useful?

I do believe you are headed toward a circle, and you would define "person" as an agent which is capable of creating by design. Is this what you were thinking of? If not, then elucidate, tell me what you believe constitutes being a person, as this is what you have mentioned as the criteria for making the distinction between design and no design.

If you'd prefer not to argue about what constitutes personhood, then why partake in this thread, where you have already stated that personhood is the criteria for distinguishing between design and no design?

For example, if you think back on something that has already happened, then you are in the past and since it already happened you kinda cant undo what ever the thought or thing was except for a few notable exceptions(some artificially produced). but thats only because the event already took place & within our reality and programming something that has already happened is in the past. — akiing585

The problem is that when you think about the past, you are not really in the past, just imagining the past. So your claims about changing the past are all based in such imaginations, and not real, because they are based in this imaginary, and false, premise.

It wasn't left undefined. There are common definitions of personhood. I directed you towards some of them via the articles in question. — Terrapin Station

For example:
"The most common answer is that to be a person at a time is to have certain special mental properties..." Said properties are left undisclosed.

Wikipedia: "Personhood is the status of being a person. Defining personhood is a controversial topic in philosophy and law..."

"Personhood continues to be a topic of international debate and has been questioned critically..."

These are quotes from your own post. "Common definitions" (notice your use of the plural) indicates that there is no universal convention, therefore no accepted definition. Clearly, "person" was left undefined, by you.

I appreciate it's your belief, and against belief I have no logical argument — god must be atheist

If the belief is illogical, it is easy to produce logical argument against it. That's why I can produce endless logical arguments against the belief that order can arise from disorder.

It is none of my business why you are incapable to see equivalence in English expressions. — god must be atheist

There is no such thing as equivalence in English expressions. Each expression is unique. I don't see imaginary things, and that's why I don't see equivalence in English expressions.

That is actually a reasonable interpretation. I can live with that. It is just that the people involved in working on that theory have developed their own lingo and views. — alcontali

I'm glad that you see this in a way similar to me.

It is just that the people involved in working on that theory have developed their own lingo and views. I don't feel like arguing with them over this, really. — alcontali

I' don't mind arguing over this. When I see people barking up the wrong tree, I feel morally obliged to point it out to others, that these people are barking up the wrong tree. The ones actually barking up the wrong tree are usually beyond hope of emancipation, so it might be a waste of time to point it out to them.

That really depends on how you define "order" versus "chaos" or "disorder". The following definition for self-organization does not seem to use your definition:

Self-organization, also called (in the social sciences) spontaneous order, is a process where some form of overall order arises from local interactions between parts of an initially disordered system. — alcontali

The problem is that in self-organization theory, "disorder" is not defined in any rigorous way. For something to be a "system" requires some form of order. Order is inherent within a "system", by definition. So the "initially disordered system" is really a contradiction because "system" requires order. What is really described by this theory is some form of order arising from another form of order, not order arising from disorder.

As I already pointed out, this "self-organization" view in exact sciences has an important foundation in John Nash's Nobel-prize winning (1994) publication (1950), "Equilibrium points in n-player strategy games", which predicts the existence of highly improbably but very stable structure-creating equilibrium-seeking processes. You can find a copy of this theorem-cum-proof in the official database of the "Proceedings of the National Academy of Sciences of the United States of America" (PNAS). — alcontali

There may be some Nobel prize winning work here, but the work does not show order arising from disorder. And if it refers to a "disordered system", which is of course contradictory, it is Nobel prize winning deception. Maybe you didn't know that Nobel prizes might be given to deceivers.

There is no hidden deception in mathematics. — alcontali

I take that as a joke.

For example, I am quite happy with Platonism, structuralism, logicism, and formalism, which each of them emphasize one aspect of mathematics, which is clearly there to me. I may not agree with all ontological views, for example, by decisively rejecting constructivism, but I also do not reject all of them. — alcontali

Platonism itself is a falsity, disproven by Aristotle. But it is essential to some modern day mathematical axioms, which require that mathematical symbols refer to mathematical objects. So right here we find deception hidden within mathematical axioms, when a mathematician claims that a symbol refers to a non-existent Platonic object.

So let me see if I understand you. You are saying that we know whether or not something was produced by design, by knowing whether or not it was produced by a "person". But what it takes to be a "person" is left undefined, and extremely vague. Doesn't that leave whether or not a thing was created by design as undeterminable?

You wrote: "So you could say that ... both of them are possible, but it is incorrect to say that they are "both possible" Why is one correct and the other incorrect? I think the two say the same thing. — god must be atheist

English is probably not your first language, because you seem to be missing out in some nuances. The way I use "both possible" implies the two together, collectively. So to say it more clearly, it is impossible to have both. This uses "both" to refer to the two collectively, and we agree that they are mutually exclusive, so it is impossible to have both, together. But when I said they are "both possible" it refers to each of the two individually, and individually each is possible. Therefore I can say that both are possible, but to have both is impossible. "Both" is used in two distinct ways, one time referring to each of the two individually, and the other referring to the two together, collectively. Sorry no confusion or equivocation was intended.

Again, congratulations for catching me on this mistake. Please reconsider my stance as corrected in this post. Thanks. — god must be atheist

OK, but as I explained in my last post, directed at alcontali, I believe that it is impossible for order to come from disorder, in any absolute sense (meaning order cannot come from absolute disorder).

I don't think that Aristotle was particularly familiar with self-organizing systems or the concept of spontaneous order: — alcontali

"Spontaneous order", is nothing but a rehash of the old concept "spontaneous generation", which was long ago disproven. It's pie in the sky.

You seem to be unfamiliar with the concepts of "spontaneous order" and "emergent behaviour" which are quite modern, only a few decades old, actually. — alcontali

As I said, your example of game theory starts with the existence of things, which itself implies order. So the theories you refer to do not describe order coming from disorder, only one form of order coming from another form of order. If you believe that these theories describe order coming from disorder, you have been misled.

Unlike metaphysics, mathematics has made incredible progress in the 20th century. — alcontali

Yes, I've noticed that mathematics has made incredible progress in misleading people. Luckily I'm not one of them. You ought to learn how to read these theories more critically and free yourself from the binds of such deception.

Yes one can certainly use the above rule in applications like in adding an apple to another to get two apples, but the properties of Apple like it having a seed for example, a DNA, etc.. all those are particulars that are not inferred from 1+1=2, so we need to abstract away those properties. Moreover if we speak in the strict formal sense then 1+1=2 can stand by itself as a syntactical game prior to any application, and so the abstract model of it would indeed provide nearer semantics to the formal essence of 1+1=2. — Zuhair

OK, now the question here is why does "2" represent one object, and not two objects. Intuitively I would say that the first "1" in "1+1=2" represents an object, and the other "1" represents an object, and "2" represents two objects. By what principle do mathematicians assume that "2" represents a single object, which might be called the number two?

Platonism is the easiest way to go about mathematics. — Zuhair

Perhaps Platonism is the "easiest way", but it is really nothing more than a cheat. Instead of recognizing, and understanding that a phrase like "1+1=2" is completely useless, and therefore meaningless, unless it is applied towards some real objects, in a real situation, the mathematician wants to say that it is implied within the phrase itself, that real objects are referred to. But this is contrary to the nature of language itself. In no instance of language use, is it inherent within the particular instance of usage, that there is necessarily objects being referred to. That this is the case, that no word necessarily refers to an object, is what allows for the existence of deception. So, claiming, or asserting that there is necessarily objects referred to, with a phrase like "1+1=2", is itself an act of deception, because there is really no language which can necessitate that if the word is spoken there is necessarily a corresponding object.

Now, the key to understanding, I believe, is to recognize that using "2" is an act which makes two objects into one object. We refer to the pair as if they are one object, using the numeral "2", but we have to remember that what is really referred to is two distinct objects, which are only made into one object through this artificial process, this synthesis, which is accomplished by someone uniting them, putting them together as one object, simply by calling them "2". So if we assert that "2" stands for one object, the true essence of this object which it stands for, is that it is really two objects which is only one object because we say that it is, and we have made it thus (one object), simply by saying that it is.

From the philosophical point of view this applicative reduction might look more prudent, but from the pure mathematical point of view, definitely platonic models would be preferable, since they are more direct engagements of what those mathematical statements are saying. — Zuhair

This is what I dispute though. The platonic model does not really engage with what the mathematical statements are truly saying. It is simply a cheat, an easier way for the mathematician, a way to avoid analyzing and understanding what the statements are really saying. Look, "2" really says two objects, and the mathematician just says consider those two objects as one object. It doesn't matter to the mathematician that there are no real principles whereby the two are considered as one, we'll just take it for granted that the two are one, and this will allow me to make all sorts of neat axioms. So the mathematician might assert that "2" says one object, and this is "what those mathematical statements are saying" but in reality we all know that the meaning of "2" is two distinct objects. So what the mathematical statement is really saying is that there are two objects here. But what the mathematician is saying is just bear with me, and consider that these two are one, so that I can perform my magic.

Not by a human being. What I wrote is "I'm using the sense of 'natural' where it's distinct from 'made by a person.'" I chose those words carefully. "Person" is broader than "human." There can be persons of different species, or even "supernatural" types of persons, if there were to be such things. — Terrapin Station

OK, what defines "a person"? Is a beaver a person, or a bird a person? Is a rock a person?

We learn that we're wrong, when we are, via an investigation into the object in question. Again, we're not simply in the dark when it comes to scientific, forensic, etc. investigations. We can formulate hypotheses and then discover that our assumptions were wrong. The butler didn't kill Mr. Jones, the cook did, for example. We can discover such things via systematic investigations. — Terrapin Station

Now I understand why we might find ourselves to be wrong. We might assume that a beaver is not a person, or that a rock is not a person, and then find out at a later date that these things really acted as persons. Aren't you really just appealing to a division in the classes of "agency"? There is a type of agent which acts with intention (person) and a type of agent which acts from a simple chemical process (like a cleaning agent).

Suppose x is defined as not spatial, "outside of space". Well, then obviously x is nowhere to be found. And x cannot have any extent, volume, area, length, or the likes, not even zero-dimensional (like a mathematical singularity). — jorndoe

This is somewhat incorrect, "outside of space" can be found with the appropriate conceptions. The problem here is that "mathematical singularity" is really a faulty (self-contradictory) concept. And if mathematicians would recognize this, and remove such conceptions from their lexicon we could represent true zero-dimensional existence as outside of space. The glaring problem is that mathematicians have occupied the category of non-spatial existence with their "mathematical objects" (Platonic realism), thereby leaving it impossible to let any other type of existence into this category.

Mathematicians treat numbers and other mathematical concepts as real objects, which of course have no spatial existence. This creates an artificial division between the spatial world (physical world which numbers are applied toward understanding) and the non-spatial world (the world of mathematical objects, the existence of which the mathematicians have assumed to support their axioms, and have incorporated into those axioms). This division does not properly represent the real categories of spatial and non-spatial existence, found in the real world, and thereby restricts our capacity to understand the real world.

Spacetime is an aspect of the universe, and "before time" is incoherent. — jorndoe

Suppose x is defined as atemporal, "outside of time". Well, then there can be no time at which x exists. And there can be no duration involved, x cannot change, or be subject to causation, cannot interact, and would be inert and lifeless. — jorndoe

"Outside of time", as well as "before time" can easily be understood when one considers the true nature of time. Time passes at the present. It is this process, of passing at the present, which gives reality to time. So to be within time means to have been present, and this is past. Therefore anything in the future is "before time", or "outside of time".

They are mutually exclusive, yes. But they are both possible.

Much like it is possible that god exists, and possible that god does not exist. One excludes the other, but both are possible.

You have to see that. If you don't see that, then you can't see how your criticism isn't right. — god must be atheist

There is nothing wrong with the criticism, because the one (if it is correct) excludes the possibility of the other. So you could say that each of them, or both of them are possible, but it is incorrect to say that they are "both possible", as this implies the two of them collectively.

And you state at #8 "it does not exclude the chain of events...", when actually 1 - 5 does exclude that chain of events. By saying this you imply that the two possibilities are not mutually exclusive, when actually each one excludes the possibility of the other.

The fact that order appears out of chaos, however, does not strike me as particularly special, or even as being such hint. — alcontali

It is actually impossible for order to appear out of pure chaos, this was demonstrated logically by Aristotle. To state the opposite is to misunderstand, or change what is meant by "pure chaos".

Say that a thing maximizes its own integrity. If it can enter a situation in which other things contribute to its own integrity, it may favour to stay in that situation. If these other things can also maximize their own integrity by maintaining that situation, then none of the things involved, is willing to change the situation. Such situation may be highly improbable, but once it exists, it will refuse to disappear. So, that creates a new, stable thing consisting of a game-theoretical equilibrium between sub-things. — alcontali

The problem with this analogy is that you already assume the existence of "a thing", and this implies order. "A thing" is an ordered existence. Lack of order would actually mean a lack of things. In Aristotelian terms a lack of order would simply be the "potential" for existence of a thing. So if you are describing how order comes out of non-order, you cannot start with the existence of a thing, because this is to presume the existence of order already.

So, incredibly complex and orderly situations tend to arise pretty much spontaneously from chaos. As far as I am concerned, they do not necessarily point to an underlying design. They could just arbitrarily be satisfying the conditions of particular game equilibria. — alcontali

Maybe you do believe this, but you seem to misunderstand what "chaos", or complete lack of order really entails.

As tim points out, #1 is the correct form. But this simple argument is rather pointless without including the difficult part, which is to demonstrate how a god is necessary for the existence of order.

When we get info that we're wrong, then we make the adjustment that we need to make. — Terrapin Station

How could you ever get info that you're wrong though? If, being created by design required , by definition, that the thing be created by a human being, and this principle is really wrong because something else like another form of creature or something, actually creates by design as well, how could you ever get information that you're wrong? It's impossible that something other than a human being could create through design, by your very definition, so it's impossible that you could ever get information that something which was created in some way other than by a human being, was actually created by design.

You're left with judging whether the thing was created by a human being in order to determine whether the thing was created by design. And accepting this false principle, that human beings are the only possible type of being capable of creating by design, closes you mind to the reality that other things like beehives, birds nests, and beaver dams are created by design as well.

Here's the proof:

1. Order can only be achieved by an orderer.

2. Only intelligent planners can be orderers.

3. Planners and orderers have order inside of themselves. They are ordered.

4. Nobody can order himself from scratch.

5. Therefore orderers must be ordered by a previous orderer.

6. This leads to infinite regress of orderers.

7. This is possible.

8. But it does not exclude the chain of events, that an orderer can be created by chance in a chaotic system. — god must be atheist

To introduce #8, you must reject the conclusion stated as #5. These two contradict each other. But #5 is produced as a conclusion from #1, #3, and #4. So, the order which an orderer has, can only have been produced by a previous orderer, And #8, that an orderer could be produced by chance is excluded by these premises.

We can make a distinction between things that people make and things that aren't made by people. — Terrapin Station

The point though, is that there is a number of problems with your approach. The first problem is that if it requires that we see a person making the thing, or that particular type of thing, in order to say that the thing is artificial, then when we find something which has already been made, and we haven't seen a person making that type of thing, we have no way to make any judgement as to whether or not it's artificial.

So TheMadFool has a different approach, claiming that there are certain characteristics which demonstrate that an object has been 'made', or designed, and we can make a judgement based on that criteria. This approach is much more useful, and widely applicable than yours, allowing us to judge a thing by its properties, rather than requiring that we observe the creation of the thing. In many cases, (such as with ancient artifacts) observing the creation of the thing is not possible.

The second problem is even more substantial. This is the fact that you are making an arbitrary division between what is "designed", and what is not designed, based on the assumption that only human beings are capable of designing things. And again, archeological evidence poses a problem here because the humanoid beings, which are not properly "human beings" were designing things. Furthermore, when we see things like a beehive, a bird's nest, and a beaver dam, applying your principles we would have to say that these things are not "designed", because they are not built by human beings. But in reality, "design" is determined by intention, and these things are just as much intentional as anything produced by human beings. All you have done is created an arbitrary division between human beings and the rest of the natural world, one which is not at all supported by the science of biology. Biology gives no such special status to the human species.

I just thought of something and would like your opinion on it.

Consider the universe as the universal set U. Now the design argument works by picking a subset D consisting of human-designed objects and then generalizes it to the set U.

Now, someone may reject the design argument by referring to another subset of U, call it R, which consists of objects that have order e.g. a flower but obviously isn't human-designed.

As you can see both arguments are on an equal footing, referencing a subset of U and then generalizing to U itself. — TheMadFool

What I see as the issue, is how we define what constitutes a "designed" object. Terrapin's approach is to limit "designed" to things made by human beings. But as you can see there are numerous problems with this approach. It is not a useful, or helpful approach, and may lead to misunderstanding in numerous different ways. The more realistic approach is to determine the characteristics of "design", and judge things accordingly. I propose that "intention" is what defines design, such that anytime there is evidence of intention, design is implied, regardless of whether the thing was produced by human beings.

Thanks for the reference Zuhair, but I really can't read the symbols used. It's like learning a new language for me, and it's a type of language which is even more difficult than a normal language, which I can't learn a new one anyway because that itself is very difficult for me. I have enough trouble with English.

Having said that, I see that the paper takes the premise of Platonic realism, assuming that symbols like "2" represent a thing called a number. This is the premise which I've been explaining to fishfry is incorrect. I believe that to adequately understand the use of mathematics it is necessary to apprehend that each time these symbols are used, in different circumstances, they represent different things, dependent on the circumstances of the application. What the symbol represents is not "a number", but a specific and unique object determined by the application of the mathematics.

So for example, when we count something, there is necessarily something which is being counted. One might just count, and claim to be counting "the numbers", having no tangible objects being counted, but as I explained, this is not a valid count. If nothing is being counted except "the numbers", then the start and finish are arbitrarily chosen, and the conclusion of "how many", which is what is determined by a count, is also arbitrary. Therefore any such count (how many), cannot be properly justified, it is just a function determined by the rules of the count, which are arbitrarily chosen. This is just an exercise, a practise, to demonstrate an understanding of the rules, like practising logic (as we discussed), where the symbols do not represent anything. If one were really going to count "the numbers", the count would never be finished. Therefore a count of "the numbers" can never be a valid count.

In reality then, the symbols in such a practise do not represent anything. Logicians recognize this when they practise the laws of logic using symbols which do not stand for anything. They know that using such symbols is just an exercise to help them learn the laws of the system. But for some reason, mathematicians like to say that such symbols actually stand for objects (Platonic), things that they call numbers, and such. But we all know that such objects are just imaginary, and have no real existence whatsoever. So we ought to recognize that these mathematicians are just fooling themselves, claiming the real existence of non-existent imaginary objects, immersing themselves into this fantasy world which the paper calls "model theory".

It's the natural/artificial distinction — Terrapin Station

As I said, there is no scientific validity to such a distinction. Human beings are natural and so are the things created by human beings. The "artificial" is just a specific type of natural thing.

No one makes a universe. It's a natural occurrence. — Terrapin Station

Yeah, just like a watch is a natural occurrence. You know, the principles employed by modern scientists tend to break down the division between artificial and natural. Human beings are considered to be a "natural occurrence", so all things which human beings create are also natural occurrences. So it's really meaningless to say that the universe is "a natural occurrence", because this doesn't distinguish it from anything else; all things are natural occurrences, even watches.

You'd need knowledge that universes are the sorts of things that are usually made by universe-makers. — Terrapin Station

Who else would make a universe?

ps -- I should add this so you understand why you are wrong. It's a basic principle of math that the same symbol means exactly the same thing each time it's used in an argument or equation. For example when we say that for all even natural numbers n, 2 divides n, then even though n ranges over all possible even numbers, in each particular instance n means the same thing each of the two times it's used.

Likewise when we say 4 + 4 = 8, it's basic to all rational enterprise that the symbol '4' refers to the exact same thing each time it's used. Without that, there could be no rational communication at all. Natural language is symbolic. If I say that today it's raining and today it's Thursday, and you claim I can't assume that "today" refers to the same day each time I use it, then we'd all still be in caves. You couldn't say "pass the salt" without someone saying, "What do you mean pass, what do you mean salt, what do you mean "the"? You are denying the foundation of all symbolic systems from natural language to computer programming to math. — fishfry

Try looking at it this way fishfry. There is a difference between what a symbol "means" (as said in your fist paragraph above), and what a symbol "refers to", (as said in your second paragraph above). So we can say that a symbol must always have "the same meaning" in order that it be useful, but the symbol doesn't necessarily refer to the same thing each time it's used. I use the word "house", for instance, and we say that it has the same meaning each time I use it, but I use it to refer to many different things which are all houses, so it doesn't always refer to the same thing.

What is important to understand here is that the phrase "the same meaning" does not use "same" in a way which is consistent with the law of identity. "Meaning" is the type of thing which varies according to circumstances, matters of context and interpretation. So in reality, even though we think "that the same symbol means exactly the same thing each time it's used", and this is necessary for a symbolic system to work, the very opposite of this is what is actually true. There must be nuanced differences in the meaning of "house", each time that I use it to refer to a different house, or else people would always think that I am referring to the exact same house each time I use the word. So "same" here really means "similar", and this is a qualitative identity, which is not what is described by the law of identity.

Qualitative identity is used to say that two things are equal, or "the same" according to some principle, or inferred criteria of judgement, but it does not mean that they are "the same" in the sense dictated by the law of identity, which would require that they are not two distinct things, but one and the same thing.

The way that we reach an abductive conclusion of there being a watchmaker from a watch is simply via knowledge that watches are artifacts that are intentionally made by people. We know (there are) watchmakers, we can observe them work, etc. If we didn't have such knowledge, the notion of a watchmaker wouldn't be justified. — Terrapin Station

That's actually a straight inductive conclusion. We see that watches are made by watch-makers, and conclude that all watches are made by watch-makers. So when we find something which looks like a watch, and acts like a watch, and we say that it is a watch, then we apply the inductive conclusion as a deductive premise, to make the further conclusion that the watch we have found was made by a watch-maker.

But other people believe that they are correct. What are you going to do, shout at each other until one gives up? — Isaac

No, reasonable people discuss things. Sometimes it takes a long time, many years of discussion, but there's no rush, and no need to shout, that's impatience.

You talk about ensuring things are in line with our experience, yet you maintain this bizarre notion that what is 'correct' can be ascertained by thought alone in complete contradiction to our overwhelming failure to do so. — Isaac

Actually, success in "doing so" requires motivation, the desire to determine what is "correct". And we can only proceed towards determining what is correct if we have a good understanding of the difference between right and wrong, and this is obviously based in an understanding of morality. Morality is the knowledge which deals with the difference between good and bad, right and wrong.

People still disagree now about exactly the same matters they disagreed about thousands of years ago. If a thousand years of discussion hasn't yielded a sufficiently convincing answer, where does that leave your 'belief' when measured by your own standards of correspondence with experience? — Isaac

This is because we've had a regression, the resurgence of monism. The philosophical problems discussed by the ancient Greeks were mostly resolved through the application of dualism. This lead to many centuries of advancement. It is false to say that the knowledge of today hasn't advanced from the knowledge of thousands of years ago. But with that advancement has come a turning away from the very principles which allowed for the advancement, and a return to the monist arguments of those ancient societies.

But perhaps you could give me a reference that supports your view. — fishfry

It's not a matter of giving you a reference, it's just a matter of whether you understand the reason or not. Do you know how to count? Say you have "1", and that 1 signifies something. And, you have another "1", and that 1 signifies something. In order that these two 1s, when they are put together (1+1), can add up to two, they must each signify something distinct from the other. If each of the two 1s signified the very same thing, there would not be two things, only one. Do you understand the reasoning here?

When we count objects, each object is counted as one (1), and so each object is represented by the symbol "1". So we count them, 1 plus another 1 makes 2, plus another 1 makes 3, plus another 1 makes 4, etc.. Each "1", must necessarily represent a distinct and separate object from every other "1", or else we would not have the multiplicity implied by the count, "2" "3" "4", etc.. It's not the case that the fourth object counted, when we point to it and count it as "4", is represented as 4, each distinct object is represented as 1. And, that each 1 represents a distinct object is absolutely necessary, or else the count would be invalid.

ps -- I should add this so you understand why you are wrong. It's a basic principle of math that the same symbol means exactly the same thing each time it's used in an argument or equation. — fishfry

You are clearly wrong, and have given this absolutely no thought, or else you would see how wrong you are. When I say I have 2 chairs at the table, and I need another 2 chairs at the table to have 4, so that I can accommodate my guests, it is very obvious that each instance of "2" must represent a distinct pair of chairs. If the two 2s represented the same pair, I could not get four chairs out of them. I would be stuck with only one pair of chairs.

Likewise when we say 4 + 4 = 8, it's basic to all rational enterprise that the symbol '4' refers to the exact same thing each time it's used. — fishfry

Again, you are very obviously wrong here, and you have clearly given this no thought or else you would see immediately how wrong you are. In the equation "4+4=8", each "4" must represent a distinct group of four things, or else they could not produce the sum of eight things. If both the 4s represented the same group of four things, there is no way to get a group of eight things, which is what is signified by "8".

If you deny that the number 4 is the same as the number 4 you are entitled to your opinion, but that kind of sophistry is of no interest to me. — fishfry

I just explained this. When the symbol "4" is used twice in "4+4=8", it must signify a different thing in each of the two instances, or else 4+4 would not equal 8. If the two 4's both signified the same group of four, there would not be eight, by putting together the two things represented by the two 4's, there would only be the same four. Therefore the two 4's in 4+4 must signify different things or else 4+4 could not equal 8.

If you have anything of relevance to say, address my post, show me how it is possible that when you count, and you add 1+1+1+1 etc., each instance of "1" signifies the same thing. If you cannot address this issue you are just blowing smoke, saying that "1", or "2", or "4", always represents the same thing.

But in the end you have now said, and not for the first time, that you don't believe the number 4 is the same as the number 4. There is no conversation to be had (at least on this topic) with someone who professes such an obvious falsehood. — fishfry

To be clear, I do not believe there is any such thing as the number four. Aristotle decisively disproved this Pythagorean idealism (currently known as Platonic realism) many centuries ago. What is the case, is that we use this symbol, written as "4", and each time it is used it signifies something, usually something different from the last time. When it is used, it may or may not signify the very same thing as in another instance of use, but in the vast majority of instances it signifies something different each time. Therefore the symbol, or numeral "4", does not represent the number four. This is a false assumption.

ps -- Wiki agrees with me. — fishfry

I was expecting this sort of reply, and I've already addressed it:

And if you insist that this is "the conventional" interpretation, that is not a justification. All this means is that "the conventional" interpretation is wrong, as I've demonstrated. — Metaphysician Undercover

The number 2 is identical to the number 2. — fishfry

I went through this with Zuhair already. It is impossible that the numeral, the symbol "2" represents the same object every time it occurs. If it did, then both the 2's in "2+2" would refer to the same thing, and 2+2 would not equal four because there would just be the same two.

This is fundamental to the nature of counting. Each thing referred to by "1" must be a different thing, or else there would not be a multiplicity. "1+1" must represent two distinct things, or else it would not equal to two things. And "1+1+1" must represent three distinct things or else there would not be three. And so on, and so forth, each occurrence of the same numeral "1", must represent a different thing when we count, or else there is no multiplicity, only the same thing over and over and over again; and the sum of the count would be invalid because there would only be one thing being counted,.over and over again.

But in ZFC, the domain of discourse in which you originally claimed that identity differs from equality, I tell you that you are incorrect. But I have said nothing new, I've written the same things over and over. — fishfry

That's what I've been saying, you keep asserting the same thing over and over and over again, without justifying your claim. I've demonstrated how equality is different from identity. So unless you can demonstrate how it is that equality is identity, in set theory, all you are doing is demonstrating that you misinterpret.

How can you possibly judge the 'rightness' or 'wrongness' of the direction of speculation? The idea doesn't even make sense. Speculation is just that, meaning we don't know if it's right or wrong before we test it. — Isaac

I disagree, metaphysics can guide us in the right direction through the use of logic. So for example things which are impossible and don't need to be tested, because we can know that they are impossible without testing them, ought to be excluded from speculation. But I'm not saying that string theory is speculation into impossibilities, because I don't know enough about it to make that judgement. This is just an example of how it is possible to know that speculation is in the wrong direction.

Furthermore, all speculation proceeds from principles, fundamental judgements, and I believe that some judgements at the base of modern speculative physics are incorrect. Principally, they employ a notion of time which is inconsistent with what we experience. That's what's wrong about it.

I meant why the distinction between static space and active space, since the shape of an object is not necessarily static. — leo

Well I went through this already. An object must really be a static thing, because if it changes it is no longer the same object. Sure we say that it is the same object, only changed, but logically if it has changed, it can no longer be the very same thing. Aristotle tried to deal with this problem by employing the concept of matter, which allowed that the object would remain the same object, despite changing its form, so long as its matter stayed the same.

So Aristotle distinguished change of shape or form, from locomotion, as two distinct types of activity. In modern times, we have come to understand change of shape as the locomotion of a thing's parts. So we no longer have these two distinct types of activity, all is understood under the terms of locomotion. Change of the shape of an object, is supposed to be the movement of parts relative to each other. But then the parts are themselves objects, moving relative to each other, and there is no justification for the claim that a multitude of objects is really one object, the original "object". Either the circumstances being observed is a multitude of objects, or it is one object, but it can't be both at the same time because this is contradictory.

That is the problem with the part/whole ontology. Saying that an entity, an object which exists as a single, individual unity, is composed of other objects which are parts, is really contradictory. This is because we then consider the same thing to be both one object, and a multiplicity of objects, at the same time, and this is contradictory, like saying 1 is at the same time, 2. If we divide the one unity into parts, then it is no longer one unity. It cannot be divided and whole at the same time. So the one object, as a unity is divisible into parts, but it cannot actually be composed of parts, if the parts are considered to be objects themselves.

If the object, as a unity is not composed of parts, then it cannot be changing. If it is composed of parts, and changing, then the parts cannot be considered to be objects, and their activities cannot be understood as objects moving relative to each other.

No I'm not saying that, I said that the definitions refer to it like a thing, some sort of container in which objects move. In physics space used to be thought as a medium (the luminiferous aether), then failures to detect it experimentally led to abandon the idea of it as a medium (as Einstein did with special relativity in which there is no more reference to an absolute space but instead to relative reference frames), and then Einstein reintroduced it as some sort of a medium in general relativity since in it space has properties such as curvature. But even though in his theory space has properties, Einstein was well aware that space is a "tool of thought" (that's his own words), in no way did he pretend that his theory somehow proved that space is an actual medium that really does curve, only people who misinterpret him and misinterpret the function of scientific theories say that. — leo

I accept this description, but it does not explain how objects exist within space, yet space is just a tool of thought. The inconsistency, or contradiction, remains. If the conceptions of "space" model space as a medium within which objects exist, then it is absolutely incorrect to say that space is a "tool of thought". Space is something which is modelled as a medium within which objects exist. It is not modeled as a tool of thought, so it is incorrect to say that space is a tool of thought, because it is represented by the models as a medium within which objects exist. If we model water as something we can swim in, then it is incorrect to say that water is a tool of thought, that is not how it is modelled.

It could be that there really is a medium that permeates everything, or it could be that there is pure void between things, both ideas are compatible with what we observe. If there is pure void between things then space isn't a medium, it isn't an actual thing. — leo

It doesn't matter if you call this medium "pure void", it's still a medium. So your claim of two possibilities, medium, and pure void, is inaccurate because "pure void" is really just a special type of medium, and so there is really only one choice, medium. Many people speak of "pure void" as if it were something other than medium. But when we come to realize that "pure void" just refers to a special type of medium, an absolute medium which consists of absolutely nothing but itself, then we realize that it doesn't make sense even to speak of "pure void".

It does make sense if it is said conceptually and not literally. — leo

I don't understand this distinction. Do you recognize that a model must model something? If one were to make a model, and it didn't model anything, it would just be random nonsense, and not a model at a all.

So if you model planets as moving through space, it makes no sense to say that this is just what the model shows, and the planets are not really moving through space, we've just modelled them that way. If you model planets as moving through space, and insist that the planets aren't really moving through space, it's just that the model shows them as moving through space, then all you are doing is asserting that the model is wrong.

If simultaneously one person can imagine space as flat, some other person as curved, some other person as shrinking and expanding, some other person as being displaced by objects, do you not see that space is a concept, and that people conceptualize it by analogy with what they do observe? — leo

Not at all. What I would conclude from this is that space is a real thing, because many people are talking about it, but they just don't understand it, and this is evident because their concepts of it vary. It's very similar to when a few people try to recount an incident from many years ago. Some will remember it in one way, others in another way. This doesn't mean that the incident isn't a real thing which really happened, it just means that the people haven't conceptualized it well.

I don't know how it could be a plane, but I don't believe in fate and determinism, so I've never given it much thought.

Breaking down the sci-fi part, there's a plane of existence, (think of it as overcoming a mountain, though it instead of over it), that allows these two beings to meet, across the set of all possible worlds. — Wallows

"Across the set of all possible worlds" implies necessity. So that meeting was necessitated. This is sometimes called "fate", which determinists take for granted. To meet was their fate.

Speculative physicists are headed in the wrong direction.

I suppose Trump's pulling the troops from Syria was just the fulfilling of an election promise - one made to the Russians.

I don't know why you make a distinction there. In both cases measurements are involved, in both cases the measurements can change (the shape of an object can change, so can the distance between objects). — leo

Do you not see a difference between measuring an object, and measuring the distance between two objects? In the first case, you would be dealing with the properties of one individual object, and in the second case you would be dealing with a relation between two objects.

There are other conceptions of space. The one customarily used in physics is something like:

a boundless three-dimensional extent in which objects and events occur and have relative position and direction (Merriam-Webster dictionary)
the dimensions of height, depth, and width within which all things exist and move (Oxford dictionary)

Notice how these definitions do not refer specifically to measurements of objects or measurements between objects, they refer to a thing within which objects exist and move. — leo

If space is "a thing within which objects exist and move", how can it not be a substance? You are saying that it is a thing, like a medium, within which objects exist, like they exist in water, or air. How could there be a thing, with objects existing within it, and this thing does not have substantial existence?

For instance in classical physics, when two objects move towards each other they move in space, space doesn't shrink between them. Sure the distance between them decreases, the unoccupied volume between them shrinks, but the reference background relative to which objects are tracked, space, doesn't shrink. — leo

OK, so there is a thing, with objects moving within it, just like objects move in water or air, but this thing is called "space". How can the objects move within this "space" without changing this thing? If an object moved, wouldn't some of the space be displaced, and therefore itself be moved? If the objects moved closer to each other, than the amount of space between them would necessarily shrink, as some would have to move aside, or else it might compress.

Now of course that reference background is not something we observe or detect, it is a reference frame that is defined from things we do observe, which is why I say that this background is not something tangible, is not a material substance, it's a concept, a tool of thought, and to treat it as tangible like an object is the fallacy of reification. — leo

Now you are contradicting what you said above. You said that space is a thing within which objects exist. How could this thing (space) be just a concept, or tool of thought? Either there is a thing (space), within which objects exist, or space is just a concept, a tool of thought. But it doesn't make sense to say that the thing within which objects exist, and move around, is a concept. Which do you believe? Is space a medium which has objects within it, as you say is the customary definition in physics, or is space just a concept or tool of thought, as it is in you ontology?

This is the problem I told you about already. Our definitions, concepts and models, treat space as a real, substantial thing, a medium within which objects exist,. Also, you use and refer to those concepts in your argumentation. Yet you assert an ontological principle which contradicts this, that space is only conceptual. Do you not realize that the definitions you cite do not support, and are actually opposed to the principle you assert?

The definition I use would be something like a material with particular physical characteristics (Cambridge dictionary), whereas your definition seems to be something like the essential nature underlying phenomena (Oxford dictionary). So obviously if we're not using the same definition we talk past each other when we talk about substance. — leo

OK, since we have different ideas of what substance means, lets leave that word. Let's just focus on your definition of "space" as a thing within which objects exist, and we'll forget about whether this thing is properly called a substance or not. Clearly you must see that this thing is not merely conceptual. How could objects exist within it if it were only conceptual?

Now that you know in what sense I use the words "space" and "substance", and so as to not get too carried away, the whole point of the discussion is what does it mean to say that space curves? Plenty of people say that gravity is the curvature of space, that planets orbit the Sun because space is curved around the Sun and because they follow straight lines in curved space, people are made to believe that we have found the cause of gravity, that this cause is that space is curved, as if space was a tangible thing, a tangible material, a tangible substance that we have detected to curve, and as I keep saying this is false, we have detected no such thing, the curvature of space is an abstraction, a concept, a tool of thought, not something that is physically detected in any way, and to treat that abstraction as a material thing is the fallacy of reification. — leo

OK, now according to your definition, space is a thing, like a medium, within which objects exist and move. Would you agree that there is a property of this medium (space) which causes things to move in a curved trajectory when we would otherwise think that these things ought to travel in a straight line, and that this is why some people talk about a curved space? If it is not a property of this thing, called space, then what could it possibly be that causes this? It cannot be that the concept of space, or that the tool of thought causes this curved motion, because the concept is simply supposed to represent, model, or demonstrate an understanding of this curvature.

People are made to believe that we can't model gravity precisely without invoking a curved space, as a supposed proof that space really is a tangible material that really does curve even though we don't directly observe it, this is false, we can model observations as precisely without invoking a curved space. — leo

OK, let's suppose that this is true, space can be modeled with or without the curvature, and each model is as accurate, and reliable as the other. What does this indicate other than the fact that we really don't know what space is?

You CLAIM they have different meanings but have not even attempted to defend or explain your claim but only seem to be avoiding the question. — fishfry

This is ridiculous. I've explained numerous times in this thread how equality differs from identity. "Identity" applies to one thing, the same thing, its identity. So "identity" relates to what makes one specified thing other than everything else. "Equality" applies to two distinct things which are judged to be "the same" in a specific way. You might consider that "identity means "the same" in an absolute way, whereas "equal" means "the same" in a qualified, relative way. The example I gave is that two human beings are equal because they have the same rights, but they are not the same, because they each have a distinct identity.

Your task, as it has been since we first engaged in this thread, is to demonstrate that in mathematics "equality" is "identity".

I deny that mathematical equality differs from identity in set theory, except in a handful of casual conventions that can easily be rigorized on demand. — fishfry

That is the point you keep asserting, without justifying. All the information you referred me to speaks of "equality", and there is no axiom which indicates that equality is identity. Your so-called proof relied on the premise, that "=" means identical, but the axioms don't bare this out. The information you referred me to spoke of "equality" not identity, so that premise is taken as false unless you can justify it. So unless you can justify your claim, produce this information whereby it is dictated that equality is to be interpreted as identity, I will continue to conclude that you wrongly interpret these axioms.

And if you insist that this is "the conventional" interpretation, that is not a justification. All this means is that "the conventional" interpretation is wrong, as I've demonstrated.