Why is infinite regression held to be impossible?

[ivebeenshown]

A set can be both countable and infinite. Regression only requires the set to be countable…

Premise.) For each item removed from an infinite quantity of items, the aforementioned quantity remains infinite

Can we agree on this?

 

[TheTrueCentrist]

You absolutely need to determine the difference between an actual infinity (one that actually exists) and a potential infinity (one that, in theory, could exist but has no ontological analog). You are completely lost in the details of the entire thread and are arguing points that amount to nonsense. The debate is about why a potential infinity does not indicate an actual infinity, not more and more about a potential infinity that you are doing.

No. The original question is “why is infinite regression held to be impossible?” The correct way to approach this question is to either show that assuming an actually infinite something causes logical contradictions or to show that an actual infinity is impossible.

Certainly people have been proposing possible “hypothetical” explanations of what an actual infinity might look like. If it is the case that actual infinities are impossible then there should be a single argument to prove that all the hypothesis including an actual infinity are invalid. So far you have offered little defense aside from simply denying the hypothesis on the grounds that they are hypothetical. If that were an admissible line of reasoning, an atheist would be perfectly justified in rejecting God by simply saying that his existence was “hypothetical.”

 

[empther]

The A-team’s quibbling never ends:

Quote:
Originally Posted by Alberti_Devoveo

forums.catholic-questions.org/images/buttons_khaki/viewpost.gif
You absolutely need to determine the difference between an actual infinity (one that actually exists) and a potential infinity (one that, in theory, could exist but has no ontological analog). You are completely lost in the details of the entire thread and are arguing points that amount to nonsense. The debate is about why a potential infinity does not indicate an actual infinity, not more and more about a potential infinity that you are doing.

No. The original question is “why is infinite regression held to be impossible?” The correct way to approach this question is to either show that assuming an actually infinite something causes logical contradictions or to show that an actual infinity is impossible.

Certainly people have been proposing possible “hypothetical” explanations of what an actual infinity might look like. If it is the case that actual infinities are impossible then there should be a single argument to prove that all the hypothesis including an actual infinity are invalid. What the heck does that mean? Absolutely nothing. :hey_bud: It is the obligatory A-team nonsense sentence buried in the middle of the paragraph so you won’t notice it’s nonsense, but seems to provide a transition from point A to point B so you’ll think the whole paragraph is logical. ] So far you have offered little defense aside from simply denying the hypothesis on the grounds that they are hypothetical. If that were an admissible line of reasoning, an atheist would be perfectly justified in rejecting God by simply saying that his existence was “hypothetical.”

There cannot be an infinite number of anything countable,
or an infinite amount of anything measurable.

Anybody who doesn’t understand this simple concept is in bad shape.

 

[JDaniel]

The A-team’s quibbling never ends:

There cannot be an infinite number of anything countable,
or an infinite amount of anything measurable.

Anybody who doesn’t understand this simple concept is in bad shape.

God bless,
jd

 

[TheTrueCentrist]

The A-team’s quibbling never ends:

There cannot be an infinite number of anything countable,
or an infinite amount of anything measurable.

Anybody who doesn’t understand this simple concept is in bad shape.

There are an infinite number of counting numbers (i.e. natural numbers.) If you think there are not, then tell me the largest one.

 

[empther]

There are an infinite number of counting numbers (i.e. natural numbers.) If you think there are not, then tell me the largest one.

Natural numbers have no real existence.

This has already been pointed out.

You’re in bad shape. :bighanky:

 

[ThinkingSapien]

Premise.) For each item removed from an infinite quantity of items, the aforementioned quantity remains infinite

Can we agree on this?

I think you can get a notational agreement on this. However math notations don’t always have mappings or applicability to the real world. Even if agreement were agreed on the notation that doesn’t apply that there is agreement that this notion has isomorphism with any systems in the real world.

I don’t want to post the entire thing here but the book “Where Math comes from…” had a section where it talked about the concept of infinity.

 

[JDaniel]

No. The original question is “why is infinite regression held to be impossible?” The correct way to approach this question is to either show that assuming an actually infinite something causes logical contradictions or to show that an actual infinity is impossible.

Certainly people have been proposing possible “hypothetical” explanations of what an actual infinity might look like. If it is the case that actual infinities are impossible then there should be a single argument to prove that all the hypothesis including an actual infinity are invalid. So far you have offered little defense aside from simply denying the hypothesis on the grounds that they are hypothetical. If that were an admissible line of reasoning, an atheist would be perfectly justified in rejecting God by simply saying that his existence was “hypothetical.”

TTC:

What Alberti Devoveo is saying (I believe) is that ANY mathematical hypotheses of “actual” infinities are confusions and/or conflations of the abstract with the real. Mathematics is the second order of abstraction and is only quasi-real and only insofar as it is directly grounded in some objective, real, thing(s). (Ob-jectum is the Latin and means that which strikes the senses. Real is from the Latin res, which means, oddly enough, “thing” or “object.”) In objective reality there are no actualized infinities - anywhere or any when. If you think that there are, then please tell me the two numbers on either side of it, if not the number itself - and, I don’t mean by the use of another constructive abstraction, such as +1 or -1.

God, on the other hand, is not an abstraction. God, invisible to us though He is, is a necessary conclusion grounded upon: (1) physics, (2) philosophy, and (3) Revelation. That He is one’s “personal God” is the subject matter of Theology and Faith.

God bless,
jd

 

[JDaniel]

There are an infinite number of counting numbers (i.e. natural numbers.) If you think there are not, then tell me the largest one.

TTC:

But YOU are the one saying “infinite number!” You need to tell us what THAT number is.

Besides, it would be excellent if you would prove that there are an infinite number of counting numbers. Perhaps you could start today, right after reading this post! Let us know when you’re finished.

God bless,
jd

 

[ivebeenshown]

I think you can get a notational agreement on this. However math notations don’t always have mappings or applicability to the real world. Even if agreement were agreed on the notation that doesn’t apply that there is agreement that this notion has isomorphism with any systems in the real world.

You may say that, but then I would have to ask this: if there were some infinite quantity of items and you removed one of the items from the set, what would the quantity of the remaining items be?

 

[ThinkingSapien]

You may say that, but then I would have to ask this: if there were some infinite quantity of items and you removed one of the items from the set, what would the quantity of the remaining items be?

**Short answer : ** I think this can never happen. I can’t project what my behaviour would be for situations that I find to be conceptually impossible.

Detailed Answer:

The earth has a mass of 5.9736×1024 kg. If I were to take a few tons and toss it out into space some where then how much mass is the earth left with? The answer is 5.9736×1024 kg. Now this mass is far less than infinite but we could still use it as a system to illustrate what I think you are trying to get at. The amount subtracted is insignificant when compared to the larger set from which it was taken. We can find other systems to which this concept is applicable. How much is left in the ocean if I remove a cup of water from the ocean? If I remove a few skin cells from some one’s body what will be the difference in their weight before and after I’ve removed the cells? If Keep going down this path and one might find enough similar scenarios such that it inspires a very useful “rule of thumb.” Here’s such a rule:

When I remove a very small amount from a large set I can treat the result as though I had not removed anything.

Subtract 1 from X and you still have X

That rule could be applied to answer your question of what do you have when you remove an item from some infinite quantity of items.

This rule only appears to be valid in within the limitations of the precision available to us (both on the quantities and on the change in the quantities). Given a sufficient level of precision we start to notice that X - 1 does not result in X being left. Or if the removal operation is repeated enough times eventually the difference may approach a difference that is within the reach of the precision available to us and it becomes apparent that the subtraction operation is eroding the set.

What that being said let’s review the first part of your question.

…]if there were some infinite quantity of items…]

As far as I know an infinite quantity of physical items is a useful but imaginary concept. If I’m wrong could you identify some set of infinite items? I don’t think that this is a condition that could ever occur. I’ll continue with the large set in consideration. Given an extremely large set of items if I were to remove one I would probably treat the set as though it were unaltered. The precision to which I can know the size of the set is limited as is my cognition for internally conceptualizing it beyond the string of digits that represents its size. It may even go beyond my limits for distinguishing between experiences involving the large sets (ex: What is the difference in the experience of being in a room with 20,000 flies and a room with 21,000 flies?).

 

[ivebeenshown]

As far as I know an infinite quantity of physical items is a useful but imaginary concept. If I’m wrong could you identify some set of infinite items? I don’t think that this is a condition that could ever occur.

I cannot think of a set of physical items that would meet that criteria; however, we know of the integers, which are a countably infinite set. Before one begins to count the integers, they are face with an infinite quantity of integers that have not yet been counted. However, even after one counts… say, a million of them, they are still faced with an infinite quantity of integers that have not yet been counted.

Now translate this to the idea of an infinite quantity of ordered events in physical motion…

 

[Alberti_Devoveo]

No. The original question is “why is infinite regression held to be impossible?” The correct way to approach this question is to either show that assuming an actually infinite something causes logical contradictions or to show that an actual infinity is impossible.

The title is that, but if you look at the OP, the question asked is:

Are each of these not infinite regressions?

If the universe itself contains these infinite regressions, why should there not be an infinite regression of causes?

And ‘these’ refers to things like the repeating decimals of 1/3 and pi. Qoeleth is taking mathematical infinities and asking why these are not actual infinities.

Certainly people have been proposing possible “hypothetical” explanations of what an actual infinity might look like. If it is the case that actual infinities are impossible then there should be a single argument to prove that all the hypothesis including an actual infinity are invalid. So far you have offered little defense aside from simply denying the hypothesis on the grounds that they are hypothetical. If that were an admissible line of reasoning, an atheist would be perfectly justified in rejecting God by simply saying that his existence was “hypothetical.”

I have provided a single argument: a finite object cannot make an infinite object. There is a finite number of atoms in our universe, hence there can never be an object with infinite dimension. Outside of that definition, I have tried correcting your point of view about what is the difference between an actual infinity and a potential infinity, because you (among others) keep mixing them up.

 

[ThinkingSapien]

…]however, we know of the integers, which are a countably infinite set. Before one begins to count the integers, they are face with an infinite quantity of integers that have not yet been counted. However, even after one counts… say, a million of them, they are still faced with an infinite quantity of integers that have not yet been counted.

What is being talked about here is a conceptual description of something that won’t ever happen. Forget about infinity for a moment. Think about the number 452,109,435,709,123. It’s less abstract than infinity. Now think about some one counting to it. You’ll find that over a short period of time their counting will slow down. Eventually the person won’t be able to use their cognitive resources to keep track of a the number so an external device like paper and pen are needed and the process becomes limited by both their mental resources and the mechanical speed at which the numbers can be represented as symbols on paper. And of course there is the ultimate terminal interruption, death.

Now translate this to the idea of an infinite quantity of ordered events in physical motion…

Sounds like a perpetual motion machine. This concept does not seem to extend to the real world. You are describing what Aristotle labeled as “potential infinity” which was distinguished from “actual infinity.”

 

[ivebeenshown]

What is being talked about here is a conceptual description of something that won’t ever happen. Forget about infinity for a moment. Think about the number 452,109,435,709,123. It’s less abstract than infinity. Now think about some one counting to it. You’ll find that over a short period of time their counting will slow down. Eventually the person won’t be able to use their cognitive resources to keep track of a the number so an external device like paper and pen are needed and the process becomes limited by both their mental resources and the mechanical speed at which the numbers can be represented as symbols on paper. And of course there is the ultimate terminal interruption, death.

I guess this comes down to ‘all analogies fail’.

Sounds like a perpetual motion machine. This concept does not seem to extend to the real world. You are describing what Aristotle labeled as “potential infinity” which was distinguished from “actual infinity.”

I agree, it does not extend to the real world! But those that posit a universe or material reality that has always existed and always will exist are positing exactly that – that there is an infinite ordered set of physical events.

 

[Qoeleth]

I guess this comes down to ‘all analogies fail’.

I agree, it does not extend to the real world! But those that posit a universe or material reality that has always existed and always will exist are positing exactly that – that there is an infinite ordered set of physical events.

OK, here’s an attempt at an actual infinity:

Q. What is the distance from earth to the end of the universe?
A. Actual infinity.

So, here is an actual, physical infinity.

Now, granted, it is present as a progression, but if I reverse it, and say:
Q. What is the earth’s distance from the end of the universe?
The answer is an infinite regression…

 

[Alberti_Devoveo]

OK, here’s an attempt at an actual infinity:

Q. What is the distance from earth to the end of the universe?
A. Actual infinity.

So, here is an actual, physical infinity.

No it absolutely is not infinity meters away. Nor is infinity light-years away. We can only logically &experimentally claim knowledge of the distance to the edge of the observable universe. There are several hypotheses about what the universe that we do not see (the unobservable universe) is and how big it is. But none of them can be guaranteed correctness and, thus, are only hypothetical. That is to say, the edge of the total universe is completely unknown, its distance is potentially anything larger than 15 billion light-years. Hence, not an actual infinity.

Now, granted, it is present as a progression, but if I reverse it, and say:
Q. What is the earth’s distance from the end of the universe?
The answer is an infinite regression…

Similarly, this answer is wrong because we do not actually know how far the edge of the total universe is from our current position.

 

[ThinkingSapien]

OK, here’s an attempt at an actual infinity:

Q. What is the distance from earth to the end of the universe?
A. Actual infinity.

A. Actual unknown.

We can’t observe space beyond the limits of the speed of light. Given the estimated age of the universe of 13.7 billion years this means we can’t observe any light or electromagnetic radiation from any further than 13.7 billion light years away. This gives a total viewing diameter of 27.4 billion light years. There could be stars and other matter beyond that distance. In another billion years we’ll be able to “see” what is 14.7 billion light years away if it hasn’t red shifted too much.

 

[empther]

OK, here’s an attempt at an actual infinity:

Q. What is the distance from earth to the end of the universe?
A. Actual infinity.

So, here is an actual, physical infinity.

That’s impossible.
Somewhere beyond the furthest star, space ends. There is nothing beyond that, not even nothing!!

Space is where matter and energy is. “Where” there is no matter or anything else, there is no “where”. Don’t ask me to explain it. That’s what the scientists tell us.

 

[TheTrueCentrist]

That’s impossible.
Somewhere beyond the furthest star, space ends. There is nothing beyond that, not even nothing!!

Space is where matter and energy is. “Where” there is no matter or anything else, there is no “where”. Don’t ask me to explain it. That’s what the scientists tell us.

But this is the problem. We are trying to determine why it is impossible. Assertions like yours have permeated that thread but don’t get us closer to an answer. The OP was curious why people believe actual infinity is impossible, and your answer was “because actual infinity is impossible.”

While we could talk about the limits of this universe, we can’t say anything (scientific (yet)) about universes outside our own. Unless you have a general reason why any actual infinity can’t exist, we have not really gotten anywhere.

I suspect that such a reason will not be given because the Christian conception of God is a being comprised of at least one actual infinity. Therefore, if there were a well articulated reason why a general actual infinity could not exist, it would also apply to God.