In the sense that God is said to know the future, time knows the future and that includes all our choices. — Gregory
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
If time is taken as continuous, the Arrow Paradox is resolved. Calculus helps. From the IEP : — Real Gone Cat
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
2. Do you think time is continuous or discrete? I.e., do instants have duration? — Real Gone Cat
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
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
No I don't think it is a widely held solution — Metaphysician Undercover
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
The limit concept has been well understood since the middle of the 19th Century (Cauchy, Weierstrass, et al.). — Real Gone Cat
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
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
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
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
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
...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
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
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
Ooh, this really smacks of speculation (sorry). — Real Gone Cat
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
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
3. Does God actively order other continuums (the line, the set of reals, etc.)? Could 37 suddenly be less than 2? — Real Gone Cat
The problem with positing God is that you have to find something for God to do. — 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. — Metaphysician Undercover
An infinite number of points cannot make a line, as you say yourself, stacking up points will not get us anywhere. — Metaphysician Undercover
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
God fearing creatures will be worried that God could pull out his support at any moment. — 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. — Real Gone Cat
Again, you need to differentiate between countable infinities (stacking up points) and uncountable infinities (a line). — Real Gone Cat
(Again, math. Kinda my thing.) — Real Gone Cat
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
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
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
...what is represented by the function is what is between the points — Metaphysician Undercover
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.
Sorry, but a "countable infinity" is blatant contradiction to me... — Metaphysician Undercover
Discrediting common mathematical axioms is kinda my thing... — Metaphysician Undercover
You need to talk to some mathematicians. — Real Gone Cat
Same as above. Its climate-change-denial, flat-earth talk. ANY elementary text on infinite sets will explain this. — Real Gone Cat
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
:smirk:How do you know you can't comprehend? Try to, and see what happens. — Ciceronianus
You don't seem to understand what I wrote. You just dismissed it as inconsistent with what you believe, therefore wrong. — Metaphysician Undercover
Lines in three dimensions make extension, which is the first attribute of matter. — Gregory
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
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
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
I only state things that I believe I understand. And you haven't shown that I misunderstand. — Metaphysician Undercover
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
I wrote about the concept of approaching a limit, and I explained how I understood this concept. — 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. — Real Gone Cat
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
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
I will ask again : Where do you come by your ideas? Who else believes them? — Real Gone Cat
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
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
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
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