In the sense that God is said to know the future, time knows the future and that includes all our choices. — Gregory

It is not necessarily true that God knows the future. This problem was investigated by Augustine at some length. If God can know the future, it appears like the possibility of free will is denied. And if the human being definitely does have free will, then God cannot know the future. The indeterminacy of the future, which is required for free will, denies the possibility that anyone, even God, could know the future. God knows all that is, but the future does not exist yet, so that is not necessarily included within "what is".

Please forgive this primitive naif. I have been enjoying our exchange, but now I see that it has been an annoyance to you. Still, I cannot help myself : I feel that I must continue to put my prattle before the public. So please deign to consider this poor bumpkin's thoughts. — Real Gone Cat

I wouldn't say it's an annoyance to me, or I wouldn't participate. I enjoy it, so don't worry about that.

If time is taken as continuous, the Arrow Paradox is resolved. Calculus helps. From the IEP : — Real Gone Cat

I am familiar with this so-called resolution, and I would call it an illusion of a resolution, rather than a true resolution. I believe it's based in a principle which rounds off the infinitely small to zero, and calls this "approaching zero", or something like that, while treating it as zero. This is the same sort of principle which treats .999... as 1. It's not a real resolution, it's just saying that we can get on with our calculations very well, without resolving the issue.

1. Is your theory of time-instants-being-distinct-universes widely held in philosophy? Can you cite sources that I might peruse? (Full disclosure : I do know of one somewhat prominent thinker who shares a similar outlook, but I'll hold off until you tell me who you read.) — Real Gone Cat

No I don't think it is a widely held solution to the problems with "time". In fact I don't even hold it myself. I just rolled with it, because it was how you characterized the point I was making. I was saying that things in the past could be characterized as not existing in the universe. You proposed that they must be in a different universe then, not wanting to allow that they were completely "outside" any universe, as this was the point of discussion, things outside the universe. So I went along with that proposal of yours, that things outside one universe would be in another universe.

Then, I tried to explain how this doesn't relieve us of the need for something which is fundamentally out side of any, and every universe. Consider, as I explained, that the human being, would necessarily staddle a multitude of universes. Since this "being" comprises a relationship between a number of universes, it has some aspect which is necessarily outside of all of them, to account for its unity independent of any particular universe. That was the point, that by proposing a multitude of universes we do not avoid the need to assume something outside of all these universes.

To summarize then, I've been insisting on the need to assume something, or things, outside the universe. You proposed that the things outside the universe would be within other universes. I then argued that we still need to assume something outside of all universes.

2. Do you think time is continuous or discrete? I.e., do instants have duration? — Real Gone Cat

Personally, I believe in a two dimensional time. I believe that the time line which we understand as duration of time, and as a continuity, is actually composed of discrete "instants", which appear to us as a continuity, like that produced from a movie of still frames. However, each still frame, or "instant" is not itself still, or a static point, but consists of a second type of temporal passage, which is very distinct from the one we understand, hence the second dimension. The second dimension of time passing, we have not even recognized so much as to posit principles toward understanding it. But it is required to assume the second dimension, in order to understand how moments of time overlap, or the relationship between the "universes" described above. The second dimension of time cannot be described as anything within this universe, or in any universe, when distinct universes are defined as moments on the continuous time line.

3. Are all, some, or no causes do to God? In the burnt hand example, what is the causal chain? Does God play a role? — Real Gone Cat

Referring to the above description of two dimensional time, causation as we know it, in the sense of efficient cause, is a simple relationship along the timeline of instances. But when each instant has a duration, and activity, proper to that distinct dimension of time, and the possibility of parallel timelines, and other timelines which are diagonal, then we have to consider different sorts of causation. For instance, consider a moment just prior to another moment on the standard timeline. If each of these moments are given breadth, then one side of the prior moment might end up being posterior to the other side of the posterior moment through a diagonal timeline. So that diagonal, or cross relationship between the two moments, would put the prior moment as posterior, in that diagonal timeline.

As for the causes which are due to God, as I said before, that is the relationship between moments. God created time (as the cause of it) in such and such a way, so as to have the relationships between moments which are the true ones.

I am familiar with this so-called resolution, and I would call it an illusion of a resolution, rather than a true resolution. — Metaphysician Undercover

Hmmm, just to let you know, I'm a math professor at a medium-sized college in upstate New York, so I know a little about this stuff (been teaching classes from Calculus I through Differential Equations for almost 30 years). Actually, there is no ambiguity here. The limit concept has been well understood since the middle of the 19th Century (Cauchy, Weierstrass, et al.). True, its rather abstract and difficult to master - Newton and Leibniz didn't know it. In fact, it was almost the last idea defined in the development of Calculus (only the definition of number followed it). But it stands on solid ground. The concept of "approaching zero" is just an informal definition to help the newbs get some idea.

No I don't think it is a widely held solution — Metaphysician Undercover

That's fine. I just wondered if I was missing out on some secret cabal of universe-pancake conspiracy folks. :wink:

I said I knew someone who held this position - check out Stephen Wolfram's book A New Kind of Science.

I believe that the time line which we understand as duration of time, and as a continuity, is actually composed of discrete "instants", which appear to us as a continuity — Metaphysician Undercover

OK, you give me something to think about. Discrete instants would mean Zeno's Arrow is back in play. But continuity would suggest something else : if time is continuous and universe are instants of time, then universes also form a continuity. This means not many universes, but one (long, continuous) universe. But your answer is more nuanced than that. I'll have to chew on it a bit.

With respect to your last answer (about causes and God), I wonder if you could give an example. Maybe the burnt hand situation? Your idea is new to me and I'm having trouble following it.

The limit concept has been well understood since the middle of the 19th Century (Cauchy, Weierstrass, et al.). — Real Gone Cat

I'm not saying that it's not well understood, nor am I saying that it's at all ambiguous. I'm just saying that it does not provide a real solution to the issues which cause the paradox. I might say that it provides a "work around". Consider for example, the concept of instantaneous velocity. Velocity is a concept which is time dependent, meaning that a thing could only have a velocity if it exists over a period of time. So what could velocity at an instant mean? It must mean that an instant consists of a very small period of time. That's fine, but now what about the instant that divides one period of time from another, when we perform a measurement of a period of time. If the instant contains a duration of time then the measurement is necessarily imprecise, ambiguous. The result of the "work around" is the acceptance of imprecise measurement

So it doesn't resolve Zeno's paradox, because all it does is assume that we cannot determine the precise location of a moving object, because it is moving, therefore it doesn't have a precise location, all it has is a velocity therefore it is necessarily in a multitude of places at an instant in time. If we accept this as the reality of physical existence then we accept as reality that there is no objective position of any object, (all objects being in some form of motion). Therefore we have a measurement problem and an uncertainty principle in quantum physics. The uncertainty principle is not necessarily a feature of reality, it is a product of the way that we choose to look at reality, through our mathematical principles, and what is implied by those principles; that nothing has a precise location because it is moving. The issue which creates the paradox is not resolved, it is just deferred, to create a different problem.

OK, you give me something to think about. Discrete instants would mean Zeno's Arrow is back in play. But continuity would suggest something else : if time is continuous and universe are instants of time, then universes also form a continuity. — Real Gone Cat

This is the same problem as saying that a line is composed of points. If a point has no spatial dimension, then no matter how many points you stack up, you do not get a line which has spatial dimension. We can either say that the line is what exists between points, or we can assume that there is some sort of dimension within points, so that we might put a bunch together and have a line. What I suggested for time, synthesizes both of these. The dimension of time which we know and understand is what exists between points, Within a point in time, there is no temporal extension in that sense of duration. However, within a point in time there is another dimension of time, a type of "time" which is completely different from the temporal duration which we know because it involves a different sort of activity. But we have absolutely no understanding of this dimension of time until we posit the possibility of its reality, look for the evidence of it, and establish a way of relating the dimension which we know, to the other dimension which we do not.

With respect to your last answer (about causes and God), I wonder if you could give an example. Maybe the burnt hand situation? Your idea is new to me and I'm having trouble following it. — Real Gone Cat

OK, I'll give it a try. Let's start with Newton's first law of motion, inertia. Look at that law this way, as saying that whatever has been going on in the past, will continue to go on indefinitely into the future, as time passes, unless something causes that to change. Notice the role of "cause" here. It is assumed that things will remain the same, therefore a "cause" is required to produce change. But Newton stated that his first law was dependent on the will of God. So the theological way of looking at this is that inertia, i.e. the tendency for things to stay the same, what Newton took for granted, actually is caused. And when we consider the position of free will, as I explained already, we see that it is necessary for this cause to act at every moment of passing time. So the mystical way of understanding this is that God creates the entire universe anew at each passing moment of time.

To take your example then, of the burnt hand, consider that God must recreate your hand, (as well as your entire body, even the universe), at each moment of passing time, to maintain the continuous existence of that hand. That is how we account for the inertia of that mass. If you burn your hand, something interferes with that cause of existence of your hand, its being recreated as it was in the past, at each moment of passing time. See how the role of "cause" is reversed? Instead of saying something caused your hand to be damaged, we can say that something interfered with the cause of continued existence of your hand.

Velocity is a concept which is time dependent, meaning that a thing could only have a velocity if it exists over a period of time. So what could velocity at an instant mean? It must mean that an instant consists of a very small period of time. — Metaphysician Undercover

Yours is the classical interpretation of velocity (pre-calculus), not the modern one (post-calculus). In fact, your definition is what we now call the average velocity over the interval. To point out a problem with your definition, imagine a moving object that is accelerating over the small period of time. Clearly its velocity at the beginning of that period of time is less than its velocity at the end (no matter how short the period is). So how can we assign a single value to its velocity?

So why does the classical view of velocity exist? Zeno, Archimedes, et al., were doing the best they could with the limited math of the day. The classical view works perfectly well for objects moving with constant velocity. Which was all they could handle. Think of Newtonian physics being replaced by Einsteinian. Newtonian worked fine for the simpler problems, but not so well as the 20th Century dawned.

If a point has no spatial dimension, then no matter how many points you stack up, you do not get a line which has spatial dimension. — Metaphysician Undercover

But that's looking at it backwards. Sure, stacking up dimensionless points gets us nowhere, but when we draw a line we say it contains an infinite number of points. And nowhere on the line is a place "between" points.

One thing to remember is that there are two types of infinities : countable infinities and uncountable infinities. Your notion of stacking up points creates a countable infinity. But the continuum (the set of real numbers that are one-to-one with points on a line) is uncountable.

The dimension of time which we know and understand is what exists between points, Within a point in time, there is no temporal extension in that sense of duration. However, within a point in time there is another dimension of time, a type of "time" which is completely different from the temporal duration which we know because it involves a different sort of activity. But we have absolutely no understanding of this dimension of time until we posit the possibility of its reality, look for the evidence of it, and establish a way of relating the dimension which we know, to the other dimension which we do not. — Metaphysician Undercover

Ooh, this really smacks of speculation (sorry). You mention looking for evidence - do you have any? This would really shake up the scientific community, if true.

...consider that God must recreate your hand, (as well as your entire body, even the universe), at each moment of passing time, to maintain the continuous existence of that hand. That is how we account for the inertia of that mass — Metaphysician Undercover

Couple questions :

1. If God is creating the universe at each moment in time, how is free will possible? Let's say I wish to reach out for the hot pan. By your argument, God is the one creating the moment of contact, not me. In fact, God created the moment when I decided to reach out. Through infinite regress, God creates all causes. It sounds like your arguing for determinism.

2. Does God ever withhold temporal ordering? ("I'm gonna mess with you sinners and make every day Monday!") If the claim is that God has been creating temporal order at every instant since the beginning of time, how would we know? Is the claim testable? Is there any evidence?

3. Does God actively order other continuums (the line, the set of reals, etc.)? Could 37 suddenly be less than 2?

The problem with positing God is that you have to find something for God to do.

Yours is the classical interpretation of velocity (pre-calculus), not the modern one (post-calculus). In fact, your definition is what we now call the average velocity over the interval. To point out a problem with your definition, imagine a moving object that is accelerating over the small period of time. Clearly its velocity at the beginning of that period of time is less than its velocity at the end (no matter how short the period is). So how can we assign a single value to its velocity?

So why does the classical view of velocity exist? Zeno, Archimedes, et al., were doing the best they could with the limited math of the day. The classical view works perfectly well for objects moving with constant velocity. Which was all they could handle. Think of Newtonian physics being replaced by Einsteinian. Newtonian worked fine for the simpler problems, but not so well as the 20th Century dawned. — Real Gone Cat

You missed the point. Velocity, no matter how you interpret it, classically or in the modern way, implies motion. Motion implies that the thing moving has no definitive location. That's the real outcome of Zeno's paradox, we cannot say that a moving thing has a definite location. And since all things are moving, relatively speaking, nothing has a true location. In the modern interpretation, this creates problems like the uncertainty principle. So Zeno's paradox is not resolved, it has just taken another form.

But that's looking at it backwards. Sure, stacking up dimensionless points gets us nowhere, but when we draw a line we say it contains an infinite number of points. And nowhere on the line is a place "between" points. — Real Gone Cat

Yes that's exactly the point. Think about it. An infinite number of points cannot make a line, as you say yourself, stacking up points will not get us anywhere. Therefore your claim that a line consists of an infinite number of points with nothing between them is an invalid conclusion from the two premises, 1) a point has no dimension, and 2) a line has dimension. Your statement "when we draw a line we say it contains an infinite number of points. And nowhere on the line is a place 'between' points" is self-contradicting under the accepted definitions of points and lines. It is "what we say", but it's easy to say things that are contradictory.

Ooh, this really smacks of speculation (sorry). — Real Gone Cat

It's all good, there's nothing wrong with speculation, so long as it is presented as such, and it's somewhat reasonable. I speak metaphysics, so that it's speculation should be taken for granted.

1. If God is creating the universe at each moment in time, how is free will possible? Let's say I wish to reach out for the hot pan. By your argument, God is the one creating the moment of contact, not me. In fact, God created the moment when I decided to reach out. Through infinite regress, God creates all causes. It sounds like your arguing for determinism. — Real Gone Cat

I thought I explained my resolution to this issue in the succession of universes analogy. It is a question which many theologians have given considerable thought to. That God puts one moment of time after the last, does not necessitate that God determines everything within each moment. In fact, it is this break, between one moment and the next which allows for free will. If God wanted to determine everything, there would be no such break, just one continuous existence. It is this proposal, that the universe is recreated at each moment, which allows that we can act, and produce something which wasn't there in the last moment, so this is actually God's way of providing us with the possibility of free will.

2. Does God ever withhold temporal ordering? ("I'm gonna mess with you sinners and make every day Monday!") If the claim is that God has been creating temporal order at every instant since the beginning of time, how would we know? Is the claim testable? Is there any evidence? — Real Gone Cat

I haven't seen it, have you? This in general, is the problem of induction. So all the laws of physics are based in induction, and we assume that because things have been in such and such a way for so long, they will continue to be that way (eg, the sun will rise tomorrow). That's why Newton said his first law of motion depends on the will of God. God fearing creatures will be worried that God could pull out his support at any moment.

3. Does God actively order other continuums (the line, the set of reals, etc.)? Could 37 suddenly be less than 2? — Real Gone Cat

This is a more complex subject, because we have the issue of the human imagination intermingling with the issue of God's will. Many people like to insist that human orders, numerology are actually divine orders, or the same as, but I think it is necessary to maintain a separation, to account for the fallibility of human orders. So I propose that mathematical orders are really the product of the free willing human mind, and not determined by God. We produce these orders (sometimes with the intent of understanding the divine order), but since we are only human and fallible, so are the principles of order we produce. Sometimes they are faulty and lead us astray.

This fallibility is evident in your proposal that a line consists of an infinite number of points and nothing else, which under analysis is actually illogical. Points have no dimension, so even an infinite number of them could not produce the dimensionality required for a line. So it's examples like this which lead me to propose a distinction between true order (divine order) and orders created by the minds of human beings.

The problem with positing God is that you have to find something for God to do. — Real Gone Cat

God doesn't have to do anything. As "creator", everything is already done by the time we are present.

You missed the point. Velocity, no matter how you interpret it, classically or in the modern way, implies motion. Motion implies that the thing moving has no definitive location. That's the real outcome of Zeno's paradox, we cannot say that a moving thing has a definite location. And since all things are moving, relatively speaking, nothing has a true location. In the modern interpretation, this creates problems like the uncertainty principle. So Zeno's paradox is not resolved, it has just taken another form. — Metaphysician Undercover

This is simply not the modern view of motion. The modern theory of motion is sometimes call "at-at" :

Motion is : being at different places at different times.

Math helps. A graph representing an object's motion can be drawn as position vs. time. Each point on the curve is a location the object is at, at a given moment in time. Then velocity is defined as the slope of the tangent through that point.

But the early philosophers and mathematicians had no access to these ideas. So the classical theory of motion was the best the early thinkers could do before the development of the Cartesian coordinate system and (most importantly) calculus. And the classical theory works fine for linear motion (constant velocity), because then the slope of the tangent and the slope of the graph of position are equal. But it fails utterly for more complicated cases. In fact, it was this problem - amongst others - which spurred the development of calculus.

An infinite number of points cannot make a line, as you say yourself, stacking up points will not get us anywhere. — Metaphysician Undercover

Again, you need to differentiate between countable infinities (stacking up points) and uncountable infinities (a line). The integers are a countable infinity, but the real numbers are not. Stacked points can be put into a one-to-one relationship with the integers (you can count them as you stack). But the points on a line have a one-to-one relationship with the reals. Now the integers are a subset of the reals. So this implies that your stacked points - even though infinite - are a subset of the line.

(Again, math. Kinda my thing.)

That God puts one moment of time after the last, does not necessitate that God determines everything within each moment. In fact, it is this break, between one moment and the next which allows for free will. — Metaphysician Undercover

Two points :

1. But I thought you said God creates the universe at each instant of time. So either God is determining all that exists in that instant, or God is being directed by us (i.e., told what to do).

2. The breaks you posit between one moment and the next means that time is not continuous, and Zeno's Arrow pops back up. You can't have continuous time consisting of discrete instants anymore than you can have a married bachelor.

God fearing creatures will be worried that God could pull out his support at any moment. — Metaphysician Undercover

The problem here is that you are positing a solution to a problem that doesn't seem to exist. You have to first assume that time could potentially go haywire under a lack of divine intervention (based on what I don't know), then insert God to fix it. This is what I meant by, "The problem with positing God is that you have to find something for God to do."

And why would God "pull his support"? Is God whimsical? Easily angered? Cruel? Such a God would be petty and beneath contempt.

This is simply not the modern view of motion. The modern theory of motion is sometimes call "at-at" :

Motion is : being at different places at different times. — Real Gone Cat

This is not true, that's the problem. This is not what the math represents. It's just like your claim that a line is composed of an infinite number of points. There is a disjunct between what you claim is represented, and what the mathematics actually represents. If your statement here was true, you could not claim to have resolved Zeno's arrow paradox, because that paradox is the direct result of representing motion as "being at different places at different times". Each different "place" can be represented as a point in space, and each different time is a point in time. From this, we have the Zeno problem of how the arrow gets from one point to the next. Representing motion as "being at different places at different times" does not represent the actual "motion" which is the activity that occurs between the different places and different times, how the arrow gets from one place to another.

But this is not how calculus is used to represent motion. In calculus the point is a limit, and what is represented by the function is what is between the points, hence the use of "approaching the limit" in common descriptions. Therefore the object is never represented as being at a place, it is always represented as approaching a place. And your statement above ought to read "Motion is: being at an indefinite place during an indefinite period of time". The concept of "approaching the limit" produces the illusion of definition, when clearly "approaching" is not a well defined spatial temporal position.

Again, you need to differentiate between countable infinities (stacking up points) and uncountable infinities (a line). — Real Gone Cat

Sorry, but a "countable infinity" is blatant contradiction to me, so you might try to justify this distinction you're talking about, but I think you'd rapidly discover that you'll only be wasting your time.

(Again, math. Kinda my thing.) — Real Gone Cat

Discrediting common mathematical axioms is kinda my thing, so you have fair warning now. I hope you don't have emotional attachment to your principles, as some on this forum display.

1. But I thought you said God creates the universe at each instant of time. So either God is determining all that exists in that instant, or God is being directed by us (i.e., told what to do). — Real Gone Cat

This is just a strawman. To create something, does not mean to determine all within. When an artist creates a work of art, there is much (the features of the medium for example) which is not determine by the artist. So God simply has to intentionally allow for freedom of will, in what He creates, intentionally creating indeterminacy, as we see in the nature of "the future", and there is no such problem. You seem to be assuming that when someone, or God, creates something, every aspect of the thing created must be determined by the creator, when this is simply not the true nature of creating.

2. The breaks you posit between one moment and the next means that time is not continuous, and Zeno's Arrow pops back up. You can't have continuous time consisting of discrete instants anymore than you can have a married bachelor. — Real Gone Cat

I think I addressed this already. I claim that continuity is an illusion. Continuous time is not true, just like a continuous line created from an infinity of points is not true. So, we have a number of points in time, and we might claim that the arrow has true existence at each place, and each point in time. This produces the Zeno paradox, how does the arrow get from point A to point B. Instead of going the calculus route, to say that the arrow never is at point A or point B, these are simply limits which it approaches, I say that the arrow really is at point A and point B, but these "points" have a completely different type of existence from what we understand.

This is the requirement for the second dimension of time I referred to. So within the point itself, there is time, which is completely different from the time between points. And it is completely different from the time between points, because the spatial activity within the point is completely different from "motion", which is a description of what the arrow does between points. For example, consider the concept of spatial expansion. This is an "activity" which is understood as completely distinct from "motion". The activity which happens because of spatial expansion cannot be understood by the principles of "motion", so this is said to be not motion. Now place this type of activity as within the point, as only being able to be understood through a second dimension of time.

The problem here is that you are positing a solution to a problem that doesn't seem to exist. You have to first assume that time could potentially go haywire under a lack of divine intervention (based on what I don't know), then insert God to fix it. This is what I meant by, "The problem with positing God is that you have to find something for God to do."

And why would God "pull his support"? Is God whimsical? Easily angered? Cruel? Such a God would be petty and beneath contempt. — Real Gone Cat

Obviously there is a very real problem, which God is posited as the fix of, but you just don't understand it yet. Look, you think that calculus portrays motion as being at different places at different times, when really it portrays motion as being at an indefinite place at an indefinite time. That my description is true, rather than yours, is justified by the evidence of this model's manifestation, the uncertainty principle.

...what is represented by the function is what is between the points — Metaphysician Undercover

Holy cow. You need to talk to some mathematicians. I'm not kidding. Where did you get this? I have to read that source. This upends every geometry class being taught in US high schools.

I took this from Math Insight, but you can find these ideas in any elementary description of infinity :

A set is countably infinite if its elements can be put in one-to-one correspondence with the set of natural numbers. Countably infinite is in contrast to uncountable, which describes a set that is so large, it cannot be counted even if we kept counting forever.

The points on a line are an uncountable infinite set. Thus they "fill" the line. There is NO space between points. Much of your misunderstanding of calculus (and time as a continuum) starts here.

Sorry, but a "countable infinity" is blatant contradiction to me... — Metaphysician Undercover

Same as above. Its climate-change-denial, flat-earth talk. ANY elementary text on infinite sets will explain this.

Discrediting common mathematical axioms is kinda my thing... — Metaphysician Undercover

I guess so.

I'm going to leave it here.

If I go half a distance, then I have to go half that otherwise there is no space let. And half that otherwise there is no space left. This goes to infinity, so nothing is discrete in the world. This is not a trick but instead logic

You need to talk to some mathematicians. — Real Gone Cat

I have, there is a number of them in my family. Also, I've had numerous, (some very lengthy), discussions with mathematicians in this forum, some concerning these same issues. You don't seem to understand what I wrote. You just dismissed it as inconsistent with what you believe, therefore wrong.

Same as above. Its climate-change-denial, flat-earth talk. ANY elementary text on infinite sets will explain this. — Real Gone Cat

Why do mathematicians always seem to get so emotional when their principles are subjected to skepticism, and alternative belief systems? It appears to me like they are somehow trained to believe that what they are taught is the absolute truth. Doesn't this seem like dogmatism to you?

If I go half a distance, then I have to go half that otherwise there is no space let. And half that otherwise there is no space left. This goes to infinity, so nothing is discrete in the world. This is not a trick but instead logic — Gregory

If motion is not as you think it is (i.e. continuous), then this is not true. Think about how you walk, one foot on the ground here, then the next one a yard or so away. Your feet only cover the ground in those spots where they land, all the ground in between is not covered. Yet to measure how far you walked, we'd measure the ground. That's the way motion is, it doesn't necessarily cover all the spatial points by which it is measured, that's just an assumption made by the measurer.

So Aristotle was wrong to say that matter is infinitely divisible? If it's infinitely divisible the infinite infinitesimal are there. But how can matter find in itself something that is space but is indivisible? Space we know of always is divisible.

I can't make sense of your post. "Matter" and "space", though related, are distinct conceptions. I don't know what you mean by matter finding space within itself. Matter is potential, for Aristotle, space is formal, therefore actual. The two are categorically distinct.

Whether matter has two principle, form and prime matter, or one it still is spatial. You are saying it's made of discrete parts yet you say infinite points don't make a line. Contradiction?

I don't see your point. The concept of "matter" is not compatible with the concept of a "line", in any conceptual scheme that I'm aware of. Simply put, a line is not spatial because it has only one dimension, and no conception of space which I'm aware of describes space as one dimensional. Nor is a point a spatial concept.

How do you know you can't comprehend? Try to, and see what happens. — Ciceronianus

:smirk:

Lines in three dimensions make extension, which is the first attribute of matter. And you didn't explicate how something discrete can be partless and yet be spatial

You don't seem to understand what I wrote. You just dismissed it as inconsistent with what you believe, therefore wrong. — Metaphysician Undercover

My apologies for being a bit harsh - I was tired and lacking sleep.

Not everyone has math concepts at the forefront of their mind. I think about math a lot because its my job.

I will caution this however : If you don't understand a concept, you don't get to make up your own interpretations and expect everyone else to agree. And your ideas about infinite sets (and lines, etc.) are not consistent with any text, course at university, or discussion on this subject.

An analogy : I am not a philosophy major. In fact, I have never taken a philosophy course. When discussions on TPF get too esoteric, I know to back off and not add my two cents. If I find the thread interesting but beyond my immediate understanding, I'll either look up the sources, or I'll sit back and read the exchange of comments.

It's OK to talk about math if you're not a math major. Just make sure you're on solid ground with your ideas.

I'm not going to teach a lesson in set theory - there are innumerable easily-understood texts on the subject. I'll just say this : countable does not mean finite. I went to Youtube, and one of the first videos I found was this one

https://www.youtube.com/watch?v=fRhdpyaOhEo

We actually do not teach this to most high school geometry students in the US (they're just told a line consists of points - they simply don't have the background to understand the explanation). But the notion that the points of a line form an uncountable infinite set underpins geometry, calculus, topology, and every topic more complicated than arithmetic.

Here's a weird fact : Because the points on a line are uncountable, if a number line consisted only of rational numbers (a countable infinite set), you would not even see the line. Countable infinite sets are that much smaller than uncountable ones.

Once you wrap your mind around it, you might want to re-think your ideas of time and motion (time being represented by a line and thus an uncountable infinite set of instants). Or you can dig your heels in and keep inventing your own version of math.

Lines in three dimensions make extension, which is the first attribute of matter. — Gregory

You can say that a line is extension, but a line only has one dimension. You can define space to be three dimensional, described by three lines in relation two each other, but then the three lines are the extensions of space, not of matter.

I will caution this however : If you don't understand a concept, you don't get to make up your own interpretations and expect everyone else to agree. And your ideas about infinite sets (and lines, etc.) are not consistent with any text, course at university, or discussion on this subject. — Real Gone Cat

I only state things that I believe I understand. And you haven't shown that I misunderstand. You started talking about things not relevant to what I said. I wrote about the concept of approaching a limit, and I explained how I understood this concept. You simply asserted that I have no understanding of infinity without even explaining how your concept of infinity is related to what I was talking about, approaching a limit. And you imply that you believe that this relationship between approaching a point, and infinity, somehow resolves Zeno's paradox, when clearly the application of the concept "infinity" could in no way resolve the paradox. "Infinity doesn't resolve anything because it doesn't resolve

But the notion that the points of a line form an uncountable infinite set underpins geometry, calculus, topology, and every topic more complicated than arithmetic. — Real Gone Cat

All you are attesting to, is that an incoherent, illogical concept, (that non-dimensional points could somehow form a dimensional line), underpins a vast part of modern mathematics. What does that say about the mathematics which is underpinned by this incoherent concept? The fact that it underpins all this mathematics doesn't make the concept any less incoherent, it just says that much mathematics is underpinned by an incoherent concept.

Once you wrap your mind around it, you might want to re-think your ideas of time and motion (time being represented by a line and thus an uncountable infinite set of instants). Or you can dig your heels in and keep inventing your own version of math. — Real Gone Cat

Actually, you are the one who needs to reconsider. Once you recognize that much mathematics is underpinned by an incoherent concept, you might want to rethink your ideas of time and motion, perhaps come up with something more logical like my ideas. Or, you could dig in, and keep insisting that this idea is not incoherent, without any justification.

How much mathematics so you know?

I only state things that I believe I understand. And you haven't shown that I misunderstand. — Metaphysician Undercover

Actually, I have. But I fear that you will refuse to accept any explanation that counters the ideas you have invented for yourself. That is the way of all true-believers : the more they are shown reason, the harder they cling to the irrational. (That's why so many still support Trump.)

Pick up any set theory textbook. Search Youtube. The explanations are not that difficult to understand. And they are certainly not open to speculation. (In fact, the "weirdness" of the infinite might appeal to you.)

All you are attesting to, is that an incoherent, illogical concept, (that non-dimensional points could somehow form a dimensional line), underpins a vast part of modern mathematics. — Metaphysician Undercover

And again you fail to bother to learn about the difference between countable and uncountable. Your initial notion of stacking points is dealing with a countable infinite set, but the points on a line are an uncountable infinite set. Both sets are infinite, but they're not the same size.

Your claim of an "incoherent, illogical concept" underpinning math is like knowing half the alphabet and then claiming the dictionary is faulty. And refusing to learn otherwise.

I wrote about the concept of approaching a limit, and I explained how I understood this concept. — Metaphysician Undercover

Alright, try again. Admittedly, I've lost the thread of some of your ideas. On second thought, don't bother. If you won't accept that a line is made up of an uncountable infinite set of points, your definition of limit will be your own invention.

I will ask again : Where do you come by your ideas? Who else believes them?

Actually, I have. But I fear that you will refuse to accept any explanation that counters the ideas you have invented for yourself. — Real Gone Cat

No you haven't explained. And that you say you fear I will refuse to accept your explanation, is admittance that you haven't explained, because you are afraid to.

Pick up any set theory textbook. Search Youtube. The explanations are not that difficult to understand. And they are certainly not open to speculation. (In fact, the "weirdness" of the infinite might appeal to you.) — Real Gone Cat

We were very explicitly talking about calculus, and your claim that it has resolved Zeno's arrow paradox. Then you jumped to infinity, and now you've jumped to set theory. Clearly it's you who is incapable of following the conversation, and needs to do a google search on "calculus".

And again you fail to bother to learn about the difference between countable and uncountable. Your initial notion of stacking points is dealing with a countable infinite set, but the points on a line are an uncountable infinite set. Both sets are infinite, but they're not the same size. — Real Gone Cat

As I told you, "infinite", whether countable or uncountable, is irrelevant. Neither is the size of a set relevant. We were not talking about infinities, nor were we talking about sets. We were talking about points, and lines. A point has no dimension, a line has dimension. There is no number of points which could be added together to make a dimensional line. Nor is there any number of times you could divide a line and be left with just points. Those are obviously incoherent ideas. Where would the dimension all of a sudden come from when adding up points? Alternatively, when dividing a line, at what point would you suddenly have no dimensionality left to the parts created through that division, just dimensionless points left? Where could the dimensionality have gone? If the whole line which was divided exists within the parts, going nowhere else, then the parts must always have dimensionality, no matter how many divisions you make. If you cannot see how obviously it is incoherent nonsense, what you propose, then provide for me a demonstration. Show me how a dimensional line can be divided, such that you would produce parts, all of which have no dimension. Show me where the dimension, which was the line, ends up after the division takes place?

I will ask again : Where do you come by your ideas? Who else believes them? — Real Gone Cat

I look at what other people say, and judge whether what has been said has logical consistency or not. If so, then I am prone to accepting it. If not, I reject it. Your claim that "a line is made up of an uncountable infinite set of points" is simply illogical. A point has zero dimension. A line has one dimension. No matter how many zeros you put together, you do not get one. Likewise, no matter how many times you divide one, you do not get zero. Therefore I reject your principle. You seem to have a very unreliable understanding of the relationship between "zero" and "one".

I concede the floor. I am no match for your brilliance. But I beg of you one thing - please do not deny the math community access to these ideas. Believe me when I tell you that they are ground-breaking. No one has seen their like before. I implore - on bended knee - write them up and send them off to prestigious math journals. They will fight to be the first to publish your insights.

And I'll be able to say, I was there. I was the first to doubt, but be brought into the light.

In particular, mention that the line does not contain an uncountable infinite set of points, then explain the limit concept. We've been languishing under the epsilon-delta definition for far too long.

We can let ourselves know that we don't (fully) comprehend God by the existence of apophatic theology, the way of negation/denial (via negativa). It seems we're more certain of what/who God is not than what/who God is. The Hindus have a similar, let's just agree, technique known as neti neti (not this, not that).

Is it proper to say that I know/grasp/comprehend x if all I "know" is what x is not? Have you, for instance, come across a book on Mars that goes "Mars is neither an apple nor a dog. Mars is not green. Mars is not 3 million cubic meters in volume, etc."?

The reason I keep pressing you to name a source for your ideas is that I intend on Tuesday (Monday's a holiday) to reveal to my students that lines do not consist of points. When I inevitably get called in by my chairperson, I would like to be able to defend myself.

I concede the floor. I am no match for your brilliance. But I beg of you one thing - please do not deny the math community access to these ideas. Believe me when I tell you that they are ground-breaking. No one has seen their like before. I implore - on bended knee - write them up and send them off to prestigious math journals. They will fight to be the first to publish your insights.

And I'll be able to say, I was there. I was the first to doubt, but be brought into the light. — Real Gone Cat

You're not the first, if you check my history on this site, I've already been engaged in fulfilling your wishes. In mathematics we are taught to take the principles for granted, and move along. There is a vast amount of material to cover, and have not the time to understand the principles of each axiom. But that's why I didn't do well in math, I wanted to clearly understand each step of the way, and the class left me behind.

In particular, mention that the line does not contain an uncountable infinite set of points, then explain the limit concept. We've been languishing under the epsilon-delta definition for far too long. — Real Gone Cat

Right, and I can tell you what the issue is. Within the mathematical community there is a field which many call "pure mathematics". Within that disciplined, it is allowed that mathematical axioma are formulated completely and absolutely, independent from reference to physical reality. They are what many call "abstract". I discussed this to some length with a member of this forum, named fishfry. He admitted that axioms of pure math are completely imaginary, and argued that mathematicians ought not be constrained by the reality of the physical world in creating their axioms.

So you can see, that unlike science, within which we hold the theories to rigid standards of empirical verification, the theories of mathematics are not held to such standards. Further, we cannot hold mathematics to any standards of empirical verification because they extend to principles which are fundamentally not empirical themselves, as the means by which we understand empirical observations. Therefore to ensure the veracity of mathematical axioms we have nothing to employ except rigorous logic. In the case of the line and the point, what I've explained is that there is a fundamental incoherency in the relation between zero and one, which inheres within your principle. You do not allow for a true zero point. The zero is allowed to always contain some part of the one.

The reason I keep pressing you to name a source for your ideas is that I intend on Tuesday (Monday's a holiday) to reveal to my students that lines do not consist of points. When I inevitably get called in by my chairperson, I would like to be able to defend myself. — Real Gone Cat

Isn't the logic clear to you? We take a line with dimension, and divide it. we end up with two lines, each with dimension. We divide those lines, and end up with more lines, each with dimension. No matter how many times we do these divisions, we will always end up with more and more, shorter and shorter lines, always with dimension.

Are you familiar with the concept of "infinitesimal"? This concept was fundamental in the development of calculus. By this concept we might say that the line is composed of infinitesimals. Then it's no longer zero dimensional points which composed the line, but infinitesimal lines. But if we define the point as infinitesimal then we cannot claim it to be zero dimensions. This produces a requirement to determine the shape and size of a point, because we've removed the point from the status of being purely abstract.

I think you actually have to take courses in calculus to understand this. You failed, btw, to give an alternative picture except by saying every object is discrete (lol). That's all for me

:lol: :up:

You can't.