Actual Infinity in Reality?

[GrandizerII]

Ok, but you can still use a certain type of argument to disprove it. You get that, right? And in fact, that's what you have been trying to do anyway ... but you keep failing.

Well, some of that has to do with your attention or your comprehension (or both).

Or some of that has to do with you skipping over my refutations, and just mindlessly repeating the same shit which has been refuted regardless.

You haven't addressed the infinity - infinity explanations that both polymath and I have provided various times throughout this thread. All you do is when confronted with the maths is blabber on about how mathematics only applies to the abstract world, even though your argument is pretty much saying that even mathematically, infinity leads to absurdities.

Look, it's clear you're not that good at mathematics. That's fine, but then you can't do proper philosophy of mathematics if you can't even understand the mathematics under discussion.

I did make an argument--I even presented it formally. Here it is again (with a new line to be clearer). 

1. An actual infinite consists of real (not abstract) objects.
2. In 100% of our experiences and 100% of our scientific inquiries, quantities of real objects can have all the operations of addition, subtraction, multiplication and division applied to them. 
3. As Hilbert's Hotel shows, these operations cannot be applied to the concept of an actual infinite without creating contradictions and absurdities
4. Classical propositional logic does not allow for contradictory statements to be true. 
5. Therefore an actual infinite of real objects is logically impossible.

Infinite set theory is not a defeater for (2) because infinite set theory is not itself a conclusion derived from a logical process. To defeat (2) you have to give logical reasons why we should expect an infinite quantity of objects to behave fundamentally different than a finite quantity of objects. 

So, tell me where I "keep failing".

From the start, your argument is a failure.

Premise 1 is false.

Premise 3: There are no contradictions or absurdities. We have put in so much effort to point this out to you. I can guarantee that you didn't EVER bother to address directly the mathematics throughout this thread.

So due to false premises, your argument is at best not sound.

Sure if you have a mathematical purpose to do so. We don't.

Everytime you talk about operations on groups, that implies mathematics right there. You need mathematics to clarify what is going on in this case.

And I believe that even your compadre Poly corrected you in thinking there is nothing to count back into infinity and therefore trigger the problem of traversing an actual infinite. I thought you dropped the argument. My mistake. If you still think there is no problem, I can't help that.

Did you note the response to that where I actually told him I agree pretty much with what he said from the start? And the kudos to that response? And actually, I don't think you understood what polymath was saying to me.

[SteveII]

This is probably where you should have taken the intro to philosophy class before all your math classes. It skews reality for students to think they are the center of the world.

Mathematics is its own discipline. Math employs a type of logic: mathematical logic. There is a whole host of things that have to do with philosophy and logic that have nothing to do with math. (see the link I posted that discusses 9 different types of logic --a BRANCH of philospohy)


What in the world do you think the tens of thousands of pages written on Zeno's paradoxes alone have been discussing? If you can discuss infinity dividing a distance, you are not talking about mathematics. 

You have a way over-inflated view of mathematics. It is not the end all. Only mathematicians who don't know anything about philosophy/metaphysics think that. 


Certainly not. The idea of an infinite series of things is not itself a mathematical concept. Grandizer likes to champion an infinite series of causes. Philosophers for millennium have discussed infinite regresses (and how to avoid them). The concept also comes up in religion, computer science, physics, engineering, and a bunch of other disciplines. 

Again, mathematics is no where near the center of the universe.

And in computer science, physics, engineering, etc, the way it is discussed is through math, not philosophy. There is a good reason for that. Mathj is MUCH more logical and precise than philosophy will ever be.

It looks to me like you need to take a bit of your own advice: philosophy isn't the be all and end all of knowledge. At *best* it can explore possibilities. At worst, it leads to dogmatism and fanaticism.

I don't think math is th end all. But it is a MUCH better way to investigate ideas than philosophy as demonstrated by its track record. When there is a conflict between math and philosophy, I'll go for the math any day. But if there is a conflict between physics and philosophy, I'll go for the physics any day.

Those areas of logic that have nothing to do with math are those that are the least logical: Aristotelian 'logic' and informal logic. The rest: propositional, predicate, and modal, are ALL part of math.

By rejecting math (which you have done repeatedly), you are only showing your own ignorance. By insisting on ideas that were properly abandoned a century or more ago, you show yourself to be dogmatic. Until you can overcome those limitations, you have decided to give up on logic and rationality. And at that point, there is nothing worth saying.

I will continue to correct you when you are wrong in your math and physics. But your ideas about infinity are clearly outdated and too firmly held to be worth debating.

Wait a minute. I have never rejected math. I reject your use of mathematical concepts where it is not appropriate. The fact that I do not think that infinite set theory has any translation whatsoever in the real world is not limited to me. I still find it extraordinary that you and Grand are so sure, but it seems neither could produce a single article on the subject. We have had nothing but assertions and your misapplication of mathematical concepts to things that do not pertain to math. 

So I see that you favor math over philosophy and physics over philosophy. How about when physics and math don't agree:

Physical infinities
So infinities in modern physics have become separate from the study of infinities in mathematics. One area in physics where infinities are sometimes predicted to arise is aerodynamics or fluid mechanics. For example, you might have a wave becoming very, very steep and non-linear and then forming a shock. In the equations that describe the shock wave formation some quantities may become infinite. But when this happens you usually assume that it's just a failure of your model. You might have neglected to take account of friction or viscosity and once you include that into your equations the velocity gradient becomes finite — it might still be very steep, but the viscosity smoothes over the infinity in reality. In most areas of science, if you see an infinity, you assume that it's down to an inaccuracy or incompleteness of your model. https://plus.maths.org/content/does-infinity-exist

I am also done debating infinity. I have heard nothing new for 30 pages and no one seems to be able to answer my objections with a coherent counterargument.

[polymath257]

And in computer science, physics, engineering, etc, the way it is discussed is through math, not philosophy. There is a good reason for that. Mathj is MUCH more logical and precise than philosophy will ever be.

It looks to me like you need to take a bit of your own advice: philosophy isn't the be all and end all of knowledge. At *best* it can explore possibilities. At worst, it leads to dogmatism and fanaticism.

I don't think math is th end all. But it is a MUCH better way to investigate ideas than philosophy as demonstrated by its track record. When there is a conflict between math and philosophy, I'll go for the math any day. But if there is a conflict between physics and philosophy, I'll go for the physics any day.

Those areas of logic that have nothing to do with math are those that are the least logical: Aristotelian 'logic' and informal logic. The rest: propositional, predicate, and modal, are ALL part of math.

By rejecting math (which you have done repeatedly), you are only showing your own ignorance. By insisting on ideas that were properly abandoned a century or more ago, you show yourself to be dogmatic. Until you can overcome those limitations, you have decided to give up on logic and rationality. And at that point, there is nothing worth saying.

I will continue to correct you when you are wrong in your math and physics. But your ideas about infinity are clearly outdated and too firmly held to be worth debating.

Wait a minute. I have never rejected math. I reject your use of mathematical concepts where it is not appropriate. The fact that I do not think that infinite set theory has any translation whatsoever in the real world is not limited to me. I still find it extraordinary that you and Grand are so sure, but it seems neither could produce a single article on the subject. We have had nothing but assertions and your misapplication of mathematical concepts to things that do not pertain to math. 

So I see that you favor math over philosophy and physics over philosophy. How about when physics and math don't agree:

Physical infinities
So infinities in modern physics have become separate from the study of infinities in mathematics. One area in physics where infinities are sometimes predicted to arise is aerodynamics or fluid mechanics. For example, you might have a wave becoming very, very steep and non-linear and then forming a shock. In the equations that describe the shock wave formation some quantities may become infinite. But when this happens you usually assume that it's just a failure of your model. You might have neglected to take account of friction or viscosity and once you include that into your equations the velocity gradient becomes finite — it might still be very steep, but the viscosity smoothes over the infinity in reality. In most areas of science, if you see an infinity, you assume that it's down to an inaccuracy or incompleteness of your model. https://plus.maths.org/content/does-infinity-exist

I am also done debating infinity. I have heard nothing new for 30 pages and no one seems to be able to answer my objections with a coherent counterargument.

In situations where physics and math disagree, if we are talking about reality, then physics gets the win. And yes, in mnay situations, having an infinity in the equations of physics means you have neglected something. In fluid mechanics, the obvious point of neglect is the molecular structure of all physical objects. And in the singularity of the Big Bang model, the likelihood is that quantum mechanics smooths things out.

But, when talking about an infinite duration or infinite space, those considerations no longer apply: we aren't saying that mass goes infinite, or density. We are saying that space or time does. And no 'quantity' is then involved. So there, an actual infinity has no barrier holding it back.

[GrandizerII]

I am also done debating infinity. I have heard nothing new for 30 pages and no one seems to be able to answer my objections with a coherent counterargument.

Your objections have been answered over and over again.

Infinity - infinity is going to yield different answers just as finity - finity is going to yield different answers (in terms of real numbers) when we're describing different situations and contexts and sets. Again, there's a reason why infinity - infinity is indeterminate when we lack contextual constraints in a given problem. 0/0 is also indeterminate without contextual constraints.

I wish you had paid more to the math part to understand exactly how they're not contradictions rather than just jumping hastingly to arguing the abstract doesn't apply to the real world, because at least then you would've had a chance to learn something interesting and mind-opening about infinity. But instead, we get repeated foot stomping and an evident unwillingness to be openminded to being wrong. You've made up your mind already (because, in your view, an actual infinity existing cannot comport with your conception of God) and so there's nothing any of us here can say/do to change your mind about this.

[GrandizerII]

Oh, and in response to this:

The fact that I do not think that infinite set theory has any translation whatsoever in the real world is not limited to me. I still find it extraordinary that you and Grand are so sure, but it seems neither could produce a single article on the subject.

Check this thread:
https://atheistforums.org/thread-53666-p...09645.html

Not our problem you don't read enough articles on cosmology.

[RoadRunner79]

Oh, and in response to this:

The fact that I do not think that infinite set theory has any translation whatsoever in the real world is not limited to me. I still find it extraordinary that you and Grand are so sure, but it seems neither could produce a single article on the subject.

Check this thread:
https://atheistforums.org/thread-53666-p...09645.html

Not our problem you don't read enough articles on cosmology.

LOL.... They say speculative.... I say highly imaginative  (perhaps science fiction would be a better category.)

[GrandizerII]

Oh, and in response to this:


Check this thread:
https://atheistforums.org/thread-53666-p...09645.html

Not our problem you don't read enough articles on cosmology.

LOL.... They say speculative.... I say highly imaginative  (perhaps science fiction would be a better category.)

Well, that's your ignorance speaking. I'm sure most people laughed in the past at the idea of the earth being round and not being the center of the universe, but little did they know how wrong they were. You keep laughing in your ignorance, while scientists (people far smarter than you and I) continue to do a great job in their respective domains.

And the multiverse idea is speculative in the sense that there is no hardcore evidence for it, but there are good reasons to take it seriously. And that is why these smart people do take it seriously. Finite universe is speculation as well, and it's getting less and less likely over time as opposed to an infinite universe.

[RoadRunner79]

Back to the topic.... I think there is an question that wasn't answered, that should be.

  If it is said, that a line contains a continuum of points (however you choose to define them).  Despite the fact, that this supposed infinity ends at 1 which is contradictory to saying that it is infinite in number in itself. (note:  I'll use one as a destination in this writing, although it may be another length)   What is the point immediately prior to 1?  There is necessarily an instance, where you transition from "not 1" to "1" while traveling along this line. 

I don't think that those proposing an actual infinite can answer the question.   I believe that this question shows the bait and switch that is occurring (whether the presenter knows it or not).  I think it is also why I have found difficulty in these conversations in having someone define what the term "point" is.  (It much easier to play fast and loose, if you do not define your terms).  If the points along the line are in fact infinite, then there cannot be a transition from "not 1" to "1".  As the argument goes, no matter how small the number is between our last point and the destination, we can always make up another number which is yet smaller (nature of the decimal system).  And we can repeat this over and over again, never reaching 1.  The time doesn't matter; this will never end (which is correctly the definition of infinite) .   This is what Zeno's dichotomy (runners) paradox shows .   And I don't think that this is being addressed.  To get from "not 1" to "1"  you have to end the infinity (thus not infinite).

If you follow the logic and the procedure that is used to get an infinity in this way, then you cannot logically reach the destination either (not if you are consistent).  Adding an infinity of points of time, does not change here that the process will never end (which is why time is inconsequential).  The fact, that it does end, and that motion is possible, shows that this idea of a infinity in any given line and any given motion, shows that this idea is not logical (or at least the way it is argued is not logical).  

---

LOL.... They say speculative.... I say highly imaginative  (perhaps science fiction would be a better category.)

Well, that's your ignorance speaking. I'm sure most people laughed in the past at the idea of the earth being round and not being the center of the universe, but little did they know how wrong they were. You keep laughing in your ignorance, while scientists (people far smarter than you and I) continue to do a great job in their respective domains.

And the multiverse idea is speculative in the sense that there is no hardcore evidence for it, but there are good reasons to take it seriously. And that is why these smart people do take it seriously. Finite universe is speculation as well, and it's getting less and less likely over time as opposed to an infinite universe.

Ok.... and the skeptic in me asks what are those "good reasons"?  But that is not the topic here.

[SteveII]

Well, some of that has to do with your attention or your comprehension (or both).

Or some of that has to do with you skipping over my refutations, and just mindlessly repeating the same shit which has been refuted regardless. 

You haven't addressed the infinity - infinity explanations that both polymath and I have provided various times throughout this thread. All you do is when confronted with the maths is blabber on about how mathematics only applies to the abstract world, even though your argument is pretty much saying that even mathematically, infinity leads to absurdities.

Look, it's clear you're not that good at mathematics. That's fine, but then you can't do proper philosophy of mathematics if you can't even understand the mathematics under discussion.

Since you took the time to kind of reply to my syllogism...

You are incapable of separating the concept of a mathematical infinity with one in real life or a logically possible infinity. That's why you think this question has been answered. I have shown conclusively that the concept of infinity in mathematics is not the same. It was not derived from a logical process. It is assumed for the purpose of further math calculations. Period. End of story. If you use the mathematical concept of infinity as an argument against anything related to infinity with real objects (like Hilbert's Hotel), you are question begging. By one of your previous comments, you seem to think this is okay to do. It is NOT. 

For the 40th time, all you have to do is produce an article that talks about the possibility of an actual infinity. This does not mean an article that mentions a multiverse. That is not a discussion on the concept of infinity (the subject of this thread). I am talking about an article that discusses the concept. This should be easy if I am "mindlessly repeating the same shit which has been refuted regardless". 

Why do I keep asking for an article? Because, no offense, the nuances of this subject are beyond you. You stumble along with complete confidence that is not warranted by your piss-poor critical thinking, argumentation and discussion skills. I am not usually as blunt, but your cockiness and condescension is getting to me. 

I did make an argument--I even presented it formally. Here it is again (with a new line to be clearer). 

1. An actual infinite consists of real (not abstract) objects.
2. In 100% of our experiences and 100% of our scientific inquiries, quantities of real objects can have all the operations of addition, subtraction, multiplication and division applied to them. 
3. As Hilbert's Hotel shows, these operations cannot be applied to the concept of an actual infinite without creating contradictions and absurdities
4. Classical propositional logic does not allow for contradictory statements to be true. 
5. Therefore an actual infinite of real objects is logically impossible.

Infinite set theory is not a defeater for (2) because infinite set theory is not itself a conclusion derived from a logical process. To defeat (2) you have to give logical reasons why we should expect an infinite quantity of objects to behave fundamentally different than a finite quantity of objects. 

So, tell me where I "keep failing".

From the start, your argument is a failure.

Premise 1 is false.

I will clarify the obvious:

1' An actual infinite in the physical world consists of real (not abstract) objects.

Premise 3: There are no contradictions or absurdities. We have put in so much effort to point this out to you. I can guarantee that you didn't EVER bother to address directly the mathematics throughout this thread.

So from Hilbert's Hote we get:
infinity + infinity = infinity
infinity + infinity = infinity/2
infinity - 1 = infinity
infinity / 2 = infinity
infinity - infinity = 3

These are contradictory statements resulting from simple arithmetic operations (from 2). 

You CANNOT use infinite set theory constraints to explain away the contradictions because infinite set theory is not derived from a logical process. It is assumed in mathematics by the Axiom of Infinity. So the defeater you offer is exactly the same as "let's assume there is no contradictions". 

So due to false premises, your argument is at best not sound.

You are in over your head. 

Sure if you have a mathematical purpose to do so. We don't.

Everytime you talk about operations on groups, that implies mathematics right there. You need mathematics to clarify what is going on in this case.

When talking about rooms and guest (actual objects), all we need is basic arithmetic (from 2). We do not need "groups". It is painfully obvious this is an attempt to sneak in your beloved infinite set theory constraints. 

And I believe that even your compadre Poly corrected you in thinking there is nothing to count back into infinity and therefore trigger the problem of traversing an actual infinite. I thought you dropped the argument. My mistake. If you still think there is no problem, I can't help that.

Did you note the response to that where I actually told him I agree pretty much with what he said from the start? And the kudos to that response? And actually, I don't think you understood what polymath was saying to me.

LOL. read it again or ask Poly to clarify. You would get a kudo from those people if I said "white" and you said "black".

[Kernel Sohcahtoa]

Back to the topic.... I think there is an question that wasn't answered, that should be.

  If it is said, that a line contains a continuum of points (however you choose to define them).  Despite the fact, that this supposed infinity ends at 1 which is contradictory to saying that it is infinite in number in itself. (note:  I'll use one as a destination in this writing, although it may be another length)   What is the point immediately prior to 1?  There is necessarily an instance, where you transition from "not 1" to "1" while traveling along this line. 

I don't think that those proposing an actual infinite can answer the question.   I believe that this question shows the bait and switch that is occurring (whether the presenter knows it or not).  I think it is also why I have found difficulty in these conversations in having someone define what the term "point" is.  (It much easier to play fast and loose, if you do not define your terms).  If the points along the line are in fact infinite, then there cannot be a transition from "not 1" to "1".  As the argument goes, no matter how small the number is between our last point and the destination, we can always make up another number which is yet smaller (nature of the decimal system).  And we can repeat this over and over again, never reaching 1.  The time doesn't matter; this will never end (which is correctly  the definition of infinite) .   This is what Zeno's dichotomy (runners) paradox shows .   And I don't think that this is being addressed.  To get from "not 1" to "1"  you have to end the infinity (thus not infinite).

If you follow the logic and the procedure that is used to get an infinity in this way, then you cannot logically reach the destination either (not if you are consistent).  Adding an infinity of points of time, does not change here that the process will never end (which is why time is inconsequential).  The fact, that it does end, and that motion is possible, shows that this idea of a infinity in any given line and any given motion, shows that this idea is not logical (or at least the way it is argued is not logical).  

Roadrunner, if you are interested, then you may want to study real analysis, as this subject will  provide answers to your questions (though you may not personally agree with them). Specifically, it covers the following material, which IMO, is relevant to your inquiries: sets and cardinalities of sets; the limit concept; infinite series and sequences; properties of real numbers such as least upper bounds, greatest lower bounds, and the completeness and density of the real numbers.  IMO, you may find these topics interesting, and taking a real analysis course, may be the only way to fully understand/appreciate these ideas; taking this course would also give you more tools to formally prove/disprove various mathematical ideas.