The concept of infinite regress

[Tinker Grey]

Whether there is infinite time or not, nothing is traversing it.

 

[Ana the Ist]

Try counting from negative infinity to zero.

I don't get what that would have to do with it. Even upon an infinite time scale it would have to be at some point called the present (wherever that is) so why couldn't that point be now?

 

[Chany]

I don't get what that would have to do with it. Even upon an infinite time scale it would have to be at some point called the present (wherever that is) so why couldn't that point be now?

Because, assuming that time works in a linear causal chain of events (a view that is most likely not true), the causal chain would have to have an infinite number of causes happening before the present. An number of infinite actions, similiar to the act of counting from negative infinity, would have to occur to reach the present (0). You can't skip any numbers to get there. Because their is an infinite number of causes receding in the past and each cause is necessary to get somewhere, it is impossible to get anywhere, much like it is impossible to reach infinity by counting every number.

 

[Ana the Ist]

Because, assuming that time works in a linear causal chain of events (a view that is most likely not true), the causal chain would have to have an infinite number of causes happening before the present. An number of infinite actions, similiar to the act of counting from negative infinity, would have to occur to reach the present (0). You can't skip any numbers to get there. Because their is an infinite number of causes receding in the past and each cause is necessary to get somewhere, it is impossible to get anywhere, much like it is impossible to reach infinity by counting every number.

Sure, but somewhere on that infinite chain it has to be "now" doesn't it?

 

[Chany]

Sure, but somewhere on that infinite chain it has to be "now" doesn't it?

The entire infinite chain concept is supposed to be a paradox and impossible because of it. You can't have a single, infinite causal chain in a traditional sense. You can't reach infinity by counting. Because the chain is infinite, no definite causal event will ever reached. There would be no "now" on an infinite causal chain in the traditional sense because the very concept is impossible from the start.

1. "Now" is unattainable without the necessary causal events to reach it.

2. All steps must happen before "now" can be achieved and are necessary causal events.

3. In a standard, single-line infinite causal chain, the number of events before "now" is infinite.

4. The is an infinite number of necessary causal events that must happen before "now" achieved.

5. Because there are an infinite number of causal events, it is impossible for all of them to be achieved, just like it is impossible to count to infinite.

6. Because it is impossible for all the necessary causal events to be achieved, "now" can never happen.

7. "Now" is currently happening.

8. Therefore, a traditional infinite causal chain is impossible, at least in terms of past events.

 

[Freodin]

The entire infinite chain concept is supposed to be a paradox and impossible because of it. You can't have a single, infinite causal chain in a traditional sense. You can't reach infinity by counting. Because the chain is infinite, no definite causal event will ever reached. There would be no "now" on an infinite causal chain in the traditional sense because the very concept is impossible from the start.

1. "Now" is unattainable without the necessary causal events to reach it.

2. All steps must happen before "now" can be achieved and are necessary causal events.

3. In a standard, single-line infinite causal chain, the number of events before "now" is infinite.

4. The is an infinite number of necessary causal events that must happen before "now" achieved.

5. Because there are an infinite number of causal events, it is impossible for all of them to be achieved, just like it is impossible to count to infinite.

6. Because it is impossible for all the necessary causal events to be achieved, "now" can never happen.

7. "Now" is currently happening.

8. Therefore, a traditional infinite causal chain is impossible, at least in terms of past events.

I still that that this reasoning is false.

It is not impossible to count to infinite. You just need infinite time to do it. And if you assume an infinite regression / progression of events, you do have infinite time.

 

[Ana the Ist]

The entire infinite chain concept is supposed to be a paradox and impossible because of it. You can't have a single, infinite causal chain in a traditional sense. You can't reach infinity by counting. Because the chain is infinite, no definite causal event will ever reached. There would be no "now" on an infinite causal chain in the traditional sense because the very concept is impossible from the start.

1. "Now" is unattainable without the necessary causal events to reach it.

2. All steps must happen before "now" can be achieved and are necessary causal events.

3. In a standard, single-line infinite causal chain, the number of events before "now" is infinite.

4. The is an infinite number of necessary causal events that must happen before "now" achieved.

5. Because there are an infinite number of causal events, it is impossible for all of them to be achieved, just like it is impossible to count to infinite.

6. Because it is impossible for all the necessary causal events to be achieved, "now" can never happen.

7. "Now" is currently happening.

8. Therefore, a traditional infinite causal chain is impossible, at least in terms of past events.

I'll accept that maybe I'm seeing this differently, or perhaps I'm just not getting it at all...

For a moment though....let's think of two points in time 2 seconds exactly one second apart. If we begin dividing that one second of time between the beginning of those two seconds, we'd have half a second, then a quarter, than an eighth...etc etc etc.

Could we not continue dividing it infinitely? To smaller and smaller fractions of time?

And yet we well know that infinity is crossed in the space of one second. In fact, every fraction of a second from when we began at the beginning of the first second to when we reached the second second was always "now" and though it crosses an infinity...don't we still arrive at the beginning of the second second?

I guess I'm looking at it as an infinite causal chain that's always only now.

 

[Eudaimonist]

The entire infinite chain concept is supposed to be a paradox and impossible because of it. You can't have a single, infinite causal chain in a traditional sense. You can't reach infinity by counting. Because the chain is infinite, no definite causal event will ever reached. There would be no "now" on an infinite causal chain in the traditional sense because the very concept is impossible from the start.

Agreed.

It seems to me that the reason that an infinite regress seems achievable is that mathematics begs for a "Platonic" view of things, instead of dealing with thought experiments based on one's experience of reality. It's easy to talk about "infinities" when discussing math, but what exactly does that refer to in reality?

For a moment though....let's think of two points in time 2 seconds exactly one second apart. If we begin dividing that one second of time between the beginning of those two seconds, we'd have half a second, then a quarter, than an eighth...etc etc etc.

Could we not continue dividing it infinitely? To smaller and smaller fractions of time?

The problem with that is that you'd end up having to divide up that time infinitely, meaning that you would be traversing an infinite number of intervals of precisely zero length in order to travel those 2 seconds. It's basically Calculus.

I don't see how this really solves the problem. You really are travelling 2 seconds, not an infinite amount of time.


eudaimonia,

Mark

 

[ebia]

. One might argue that to progress through an infinite regression, you would need to have an infinite amount of time.

Of course you don't. An infinite sequence can have a finite sum. For example, if each cause took half as long as it's successor.

 

[ebia]

It is not impossible to count to infinite. You just need infinite time to do it. .

Or if your counting can speed up quickly enough to make a fine sum.

Of course, since time itself is part of this caused universe, those infinitely regressing causes are not part of time anyway.

 

[Radagast]

It's all in Zeno, all in Zeno: Bless me, what do they teach them at these schools?

 

[KCfromNC]

Try counting from negative infinity to zero.

If I can't, does that imply that 1 doesn't exist?

 

[leftrightleftrightleft]

An infinite regress doesn't necessarily mean going from negative infinity to 0.

It could mean going from 1 to 0 in smaller and smaller increments.

 

[quatona]

Try counting from negative infinity to zero.

So the scale of negative numbers is finite?

 

[Eudaimonist]

So the scale of negative numbers is finite?

Is one of the numbers on that scale "negative infinity" would be a better question.

However, a much better question is: when counting upwards from "negative infinity", where does one start? And if one can't start without backing up because there are an infinite number of negative numbers before one's starting point, how can one ever reach zero?


eudaimonia,

Mark

 

[quatona]

Yeah, I suspect "infinite regress" and "progress from infinity" aren´t the same concepts.

 

[Eudaimonist]

Yeah, I suspect "infinite regress" and "progress from infinity" aren´t the same concepts.

Agreed. Which is why I usually imagine a round trip.

Start from zero and count towards "negative infinity". Then count all the way back to zero. Divide the time it takes by two, because you are only interested in how long it takes to make the return trip. The result is infinite. You never reach zero because you are forever heading towards negative infinity. The return trip never starts.


eudaimonia,

Mark

 

[ebia]

Borrowed from Godel's Esher Bach:

Suppose you have a lamp, from which comes a djinni. And you make a wish. But in this case the djinni cannot grant the wish directly. What he does is pull out a lamp, and summon a meta-djinni, but he does it in half the time. And that meta-djinni pulls out a lamp and summons a meta-meta-djinni (twice as quickly again) ... And so forth. Until the granted request comes back down the chain again. Since each djinni is twice as quick as the one that summoned it, the whole process takes a finite time.

 

[GrowingSmaller]

However, a much better question is: when counting upwards from "negative infinity", where does one start? And if one can't start without backing up because there are an infinite number of negative numbers before one's starting point, how can one ever reach zero?

I don't think you can count from infinity, its not a number AFAIK, so yo're right in a sense.

So the idea of an infinite regress, all the way 'to infinity' (conceived as a point), is perhaps invalid, or absurd. That would be "language gone on holiday" to use a Wittgensteinian phrase.

From my stock knowledge, infinite regress means something depends on another thing to come to existence, and this other thing depends on still another thing to come to existence, and so on and on and on without any end, in the series of one thing depending on another thing to come to existence, and then this depending on another thing anterior to it to come to existence

Infinity AFAIK is not at a point on a line, its a property of the line (ie extended, rather than intersected at a point).

So the very act of looking for a starting point, in an infinite regress, is logically absurd. Because infinity is not at a point.

So any discrete (extended) amount, you cannot hold to be part of an known infinity. Thats because to know such and such (eg ten light minutes) to be, one has to have put a limit on it in space time quotients or quantize it. Even physicists have the planck length, planck time and planck mass. Basically, defining in terms of measurable units.

So it is with "counting backwards": counting involves discrete numbers and infinity is not an number, so it cant be "localised" in the mind or on paper as belonging somewhere on a number line. So its a priori impossible to find infinity somewhere, a contradiction in terms perhaps?

But what of a causal regress? Well, a cause is an extended quanta of physical stuff IMO. If the universe has no cause (true, because there is no non-universe to cause it, no extended stuff outside of it), perhaps the search for the cause of the universe is in vain. So maybe there can be a causal regress without reaching THE CAUSE [sup]TM[/sup], because there is no such thing as THE CAUSE in ordinary terms.

Well, physicists have the singularity, which is as small as a cause can get on paper AFAICT. But that, perhaps, is uncaused, because all before that singular event is "beyond measurement" (i.e. beyond quantisation in planck terms, and therefore analogous to infinity, at least, because it cant be counted out, measured or apportioned in physical terms). So the singularity is perhaps the cause of what we know, but the "cause of that" is not a sensible matter for investigation.

The singularity is so many years away in an relativistic or measured universe, in "the beginning" in units or quantised space-time, but from a unmeasured perspective, which gets to its nature it is everywhere and nowhere all at once. But thats a guess.

So whats left after that dogs dinner of a post? I am more of a "dual aspect theorist" (to borrow another philosophical term). The universe is uncaused at or beneath the quantum level of the strange world of planck length, and caused at the classical level of relativity. One universe, two aspects. Maybe this indicates it could possibly be both finite and infinite too? All regressions, ingressions or progressions, are finite yet and end up at infinity, or at least end up at a certain impasse, ie an incalculability at the planck domain?

And asking "did I cause this?" (as in is the will free?) perhaps it is also both caused at one time, and uncaused at the same "time" ( or a timelessness which defies ordinary denotative words.) There is a finite regress - and a measurable causal chain - unto my planck dimension; and yet from there on and there in (out, spread all about, or whatever), well, who knows? Maybe its the eternal and uncaused aspect of me?

Salam,

GS.