Mathematician here. I have never seen the term "actual infinity" in any mathematical literature. This is because the foundations of mathematics do not distinguish the "real" from the "unreal". All of pure mathematics is about the definitions and rules we construct and the consequences of those rules. All of pure mathematics is conceptual. Any time we use mathematics to describe something in the "real world" we are using a model, and all models have some potential for error. If mathematics implies something weird about the nature of the world an experienced mathematician is going to question the validity of the model before questioning the weirdness of the world.
@towellight9400 The concepts of countable and uncountable infinity are a different matter altogether. Hilbert's Hotel and Grim Reaper Paradoxes posit countable actual infinities. An example of an uncountable infinity is the number of points in a one-meter line segment.
@@michaeleldredge4279 Out of curiosity, what's your view of the Mandelbrot set in terms of inifinity? I always describe it as infinitely complex within a finite boundary, but I've never discussed it with an actual mathematician!
@@Leszek.Rzepecki The idea of "complexity" as in the boundary of the Mandelbrot set is difficult to define. There are proxies that you can use for it like "fractal dimension", but those fail to some extent because there are sets that intuitively feel more complicated but will have a lower fractal dimension. The set does have some interesting properties. It is a connected region that has a non-smooth boundary. It has a relatively simple definition and given a specific point it is usually fairly straightforward to determine if the point is in the set or not. I guess what I am saying is that mathematicians love their definitions, and without a precise definition of complexity I am reluctant to either agree or disagree that the shape has infinite complexity. I will agree that it is a fascinating shape though.
@@michaeleldredge4279 Ah, so it's a "yes it is, but then again, no it isn't" answer! Well, seriously, I'm sure it's hard to state mathematical propositions clearly in English plain to a non-mathematician. I'm a biologist by training, and found the Mandelbrot set, and associated fractals, well beyond fascinating, showing how a simple equation and iterative process could result in almost unfathomably complex behaviour. Even the notion of a fractal (or is it fractional?) dimension boggles my mind. From a biological POV, it has been a beacon light illuminating how nature can produce vast complexity using fairly simple rules, thus obviating a vastly more complex designer to generate it. It's absolutely mesmerising, and its almost biological shape and texture rings so many bells and whistles - to mix my metaphors - that I feel pretty certain it has explanatory power well beyond being a simple mathematical curiosity, if only as an example. Maybe it's not this particular version that's applicable, but something along the lines. Anyhoo, thanks for taking the time to respond. It's always a bit of a wonder how math manages to describe some aspect of the real world. If there is a god, which I doubt, it's definitely a mathematician!
As a mathematician, I always roll my eyes whenever theists try to explain what is wrong with infinity, and then posit the existence of an infinite being. They don’t even attempt to engage with the mathematical literature about infinity, such as set theory or limits, and instead just be like “Infinity weird, therefore contradiction.” As much as I criticize William Lane Craig, I appreciate that he sees the value in infinite sets, though he tries to bootstrap it for his narrative.
The Grim Reaper Paradox shows the logical impossibility of the Grim Reaper Paradox. Just because _some_ actual infinities contain contradictions, that does not mean that all actual infinities contain contradictions. We can just as well construct finite contradictions, but that does not mean that all actual finites are impossible. So we cannot have a infinite series of reapers following these particular rules. That's nice to know, but it tells us nothing about other infinite series that follow different rules.
I must have missed it, but I didn't catch the part where the Theist can actually get to grips with what they choose to call "Actual infinity." Other than "It was God all along," which isn't really much of an explanation.
"It was God all along" is not a explanation for pretty much anything. Not only for that, but also for the things that theists usually explain with God. For example, if i ask "how was the universe formed?", the answer "it was God" doesn't answer the question at all: I asked for a 'how', not a 'who'.
Hey man, been checking you out for about a year, now. And I just wanted to say. I really appreciate how measured and civil your responses can be. I’ve never felt like you’re talking down or patronising. As much as I can enjoy the comedy the more acerbic response channels can be, I wholly prefer genuine attempts at discourse. Respect, my dude
7:30 The barber is a woman, is a boy who hasn't yet started to grow a beard, or travels to another village to get shaved by the barber there. The paradox needs to be more precisely worded to be a problem. The barber could *also* have a beard, but that might be blocked by "doesn't shave" preventing the growth of beards by requiring every to shave or be shaved.
Women, prepubescent boys, and people who travel to other villages to get shaved are still in the category of people who do not shave themselves. The paradox is not about real life. It's about self-reference. The real-life example of barbers is just illustrative. You cannot solve a fundamental limit of logical thinking with a cheeky trick.
@@andreab380 People who don't grow beards though don't need to be shaved. At least not as far as the other ways I've seen this paradox presented have allowed for, where it's been presented more as a puzzle than a paradox - like the one where a boy is injured in an accident that kills his father, the boy is brought to hospital and the surgeon can't operate because "This is my son!" (the obvious solution being a female surgeon or a gay couple).
@@dreadlindwyrm I think the people who presented it to you didn't phrase it right. It's not "people who don't need to shave". It's just "people who don't shave themselves". The focus is on self-referentiality: doing the thing that you do to yourself. It's meant to illustrare a logical problem in set theory, which is a genuine paradox . If you try to think of "a set of all sets that contain themselves", it can neither contain itself nor not contain itself, because both alternatives lead to a contradiction.
For someone who chose to argue that atheism doesn't explain infinity, he failed to explain why his god would make the concept explainable. If he was going to do so by saying that his god is infinite, then that's a claim which would have to be demonstrated.
The theist arguement of the contradictory nature of infinity is used as part of the greater arguement. In a nut shell, if there is no such thing as infinity then the universe must have had a beginning. They then assert god, titans, great turtles, etc are the cause of the beginning of the universe. The arguement is not limited to a single definition of the christian God. But then you get to the larger primary mover or unmoved mover which theists solve with special pleading for God or gods as the primary mover rather than an infinite chain of causes or an infinite universe.
@@leopard3131Except that the principles of casualty presuppose a spacetime continuum. Trying to extend our intuitions about causality beyond the Big Bang (the point at which spacetime became actualized) is itself incoherent.
@@leopard3131 Rather than an infinite multiverse within which our universe is an infinitessimally small part, theists prefer an infinite god that they can personity, relate to, and project their personal prejudices on to. Theists always want to reduce a god to their own puny dimensions. They couldn't deal with a really infinite one bigger than a multiverse.
Which do you like better? "There are two infinites: human capacity for misunderstanding, and human potential for compassion - and I'm endlessly amazed by the latter." "There are two infinites: the depths of human confusion, and the heights of human creativity - and I'm constantly in awe of the latter." "There are two infinites: human limitations, and human imagination - and the second one never ceases to inspire me."
@@darkofalltrades I completely misread your latter respons I thought it was some form of "riddle"!🤣 This is now edited. I've really enjoyed this. Good exercise for an old brain with a young spirit. Many thanks from Denmark 👍
I don’t believe in any gods… therefore I cannot conceptualize infinity with my limited mind. I mean… unlike theists? The majority of which believe that their God is beyond their understanding? I can’t even understand what that guy’s point is, much less have the infinite mind required to properly conceive any infinite.
I can appreciate the effort, but there's that one huge problem with these preacher boys: they should start focusing on explaining their own position if they cared at all what outsiders think, but no, this is for the slaves deceiving them to believe their nonsplanation makes them all better.
These paradoxes are often solved by the calculus technique of summation of infinitesimals, and it may be that space-time, like energy, has its own minimum quantum. And in any case, the fact that these are paradoxes means that no one has solved them, including theists.
If there IS someone who can honnestly interact with actual infinity, I'd be glad to have a chat with them. The closest I had the chance to talk to was an astrophysicist that was an atheist. The religious people that claimed to have a grasp of infinity were just reducing it to something that paled compared to my finite understanding of things. They were not very... Science oriented.
I have thought for a while that theists have a conceptual problem with inifinity and solve that by replacing inifities with god, without considering the infinities inherit to the god concept. Such as they solve infinite regress by using god as a beginning point via special pleading
This was one of the more interesting ones, but when you boil it all down to its basic core, this was just another example of "You can't explain X, therefore God." It's just as fallacious regardless of how it's presented.
I don't think this guy realizes that this is not an "atheist problem" but a "human/finite being problem." 99% of people do not understand or comprehend infinity. Infinity is extremely complex and takes a lot of thought to understand. Even if you understand some infinites, that will not mean you will understand all types of infinites. Even many mathematicians take quite some time to actually come to understand various types of infinity. I've studied various types of infinity, but I will not claim to be able to understand them all, much less explain them to others for them to understand.
The basic concept is very simple. Something just doesn't end. Most people have a hard time wrapping their head around that for some reason. They usually don't even get to the point where they discover that there's more than one kind of infinity.
Here's a version of the Kalam: P1: All things come to an end. P2: The universe is a thing: C: The universe comes to an end. Totally irrefutable, just like the original, and as pointless! :) Perhaps ∞ as a concept has its uses in maths, but eventually, practically speaking even adding another 1 to a seemingly infinite series is going to become impossible because the person doing the adding expires. Not only does ∞ not imply a god, except to those desperate to believe in one, it couldn't distinguish between the gods. I doubt the god of maths is particularly interested in apes, in any case.
It also runs into the same pitfall as the original in that the term "end" is ambiguous. We never see things "end" in the sense of vanishing from existence. They just become inert, break down, and are (eventually) reconstituted into something else. If the universe "ends" in Heat Death, there will still technically not be nothing, because all of the energy will still be there (just in an unusable form).
@@chameleonx9253 Yeah, agreed, so far as we can tell. Of course, we can't really tell how it started yet, so guessing how it ends is also pretty much a guess. To most of us, infinity is a quantity too vast to be imagined. My personal response to questions of what the universe is, or whether it has an actual beginning or end, and in relation to what else, is a firm "I don't know!" I despise folk who make shit up and call it religion.
@Leszek.Rzepecki "I don't know" is the only honest answer. It's unfortunate that so many people would rather have an emotionally comforting answer than the truth.
@@chameleonx9253 Well, it's even worse, it's settling for an imaginary answer rather than accepting we don't know "the truth." That's the problem with religion: it pretends to provide answers for questions that we not only don't have immediate answers for, but that might be in principle unanswerable. Science searches for truth, but we should be able to admit that maybe sometimes we won't be able to find it.
@Leszek.Rzepecki I would argue that science doesn't necessarily seek out "truth," per say, so much as practical applications for the truth. If a question ultimately has no answer, then it has no value insofar as providing us new technology or ways of navigating the world we live in, and thus science isn't really going to devote our limited time and resources to it. "I don't know" has the advantage of leaving open a possiblity of future discovery, while "we can't know" is a dead end.
This is nothing more than an attempt to make Christian beliefs appear more rational than atheism. Christianity depends upon the acceptance of astonishing claims that cannot possibly be demonstrated to be true. I see no logic in blindly accepting Christian claims. I was never troubled by concepts of infinity in my former electronics work. Numbers often became increasingly insignificant as the got larger. Electrons might as well have been infinitely small, given their minute size.
I have no issue with infinity, and there is no need or requirement for athiests to explain or justify it. It's an inelegant mathematical concept that has no practical use. It is, by nature, indefinable. To say that God can not only contain infinity, but solve for it, is a facile deepity, and an attempt to define God into existence that fails on its own terms. Christian athiests are really just humanists who aren't quite ready to let the safety blanket of the church go.
I do find Joe Shmidt's (Majesty of Reason) response to the Grim Reaper Paradox to be pretty sufficient. Essentially, the paradox doesn't require infinity to create such paradoxes. As such, the paradox is paradoxical for reasons that have nothing to do with infinity.
Math says the infinite can’t be divided. Our reality relies on interactions. H2 must interact with O to make water. An infinite distance prevents this, so math’s infinity isn’t here.
Infinity is just a mathematical tool. To search it in the real world is at best misleading. And I speak as a prettily good mathematician, who could say a lot more on the subject... except that it's really hard to tell that in english. Maintenant, s'il y a quelqu'un qui veut que je m'étende sur le sujet en français, qu'il m'interpelle.
Well given math has nothing inherently to do with whether or not a god exists. I don't see why it is brought up as an issue for atheists. The claim that a god or any number of gods does not exist, or is not known to exist, has no basis in whether infinites are logically consistent or not. Then there is the fact that there are an infinite number of infinites from whole infinites, even or odd infinites, indivisible infinites, infinity between each whole number, imaginary number infinities, negative infinites, and on and on the series goes. But that is purely mathematical, and not something the human mind evolved to be able to understand or conceptualize in anything resembling intuitive sense. this cognitive limitation doesn't imply any connection to theological claims. The assertion that a god does or does not exist remains a separate matter, reliant on evidence, philosophy, and personal belief-not the logical properties of infinite sets in mathematics.
Well the "problem" with Hilbert's Hotel is in the premises. Is it full or not? if it is full no more giests can be accommodated regardless if the hotel is finite or infinite, that is the definition of full lol
@ArrantPrac full, occupied, use any synonyms you wish. If they are all occupied, there are no unoccupied rooms regardless if the hotel is finite or infinite, no more guests can be accommodated.
@@leopard3131 "Full" specifically means no more can be added. "All rooms are occupied" _implies_ that no more can be added, in any real life situation. The entire point of the example is that with an infinite number of rooms, that is no longer the case. You can always add another person and still end up with every guest having a room, even if there are no unoccupied rooms to begin with.
@ArrantPrac, you fail to understand infinity. There are an infinite number of rooms all occupied by an infinite number of guests. By definition, you can not add a room. They are all occupied to infinity and beyond . There is no such thing as infinity +1 The paradox only exists because you break the rules. The only way to accommodate an adding guest is to have infinite rooms but finite guests. This breaks the rule that they are all occupied. If you have infinite rooms but a finite number of guests, you can always add more, but that is not the case as you have infinite rooms mapped 1:1 with infinite guests, otherwise the rooms are not all occupied. If you add a room or roo.s without adding a guest or guests you violation the premise that all the rooms are occupied thus you create a paradox by violation of the premise.
@@leopard3131That’s the paradox. The hotel is full, all it’s rooms are occupied and yet you can fit more people in. It’s very counterintuitive and that’s why it’s called a paradox.
I've always understood paradoxes as unsolvable by their very nature (as well as the best way to defeat the inevitable android/AI uprising), thus his blathering about atheism being unable to "solve" the paradoxes is pointless. About the only other thing I have to contribute is that I don't think the barber situation is an actual paradox, because I would assume that he shaved himself because why wouldn't he? Also, the initial setup says nothing about a hard-and-fast rule regarding whom the barber shaves, only that he shaves those who do not shave themselves. This also does not mean that he couldn't have a beard, either, thus negating the need to shave/be shaved. Also also, if there are men in the village that shave themselves, the barber could ask/pay one of them to do it. Oh, I thought of another thing: the question of whether a set of all sets contains itself. I think the logical response is "yes, but it might end up causing a recursive loop and maybe lock up the system, so probably don't try getting the universe to do that. Rebooting a universe does a factory reset and I'm not ready for that yet."
Mathematician here.
I have never seen the term "actual infinity" in any mathematical literature. This is because the foundations of mathematics do not distinguish the "real" from the "unreal". All of pure mathematics is about the definitions and rules we construct and the consequences of those rules. All of pure mathematics is conceptual. Any time we use mathematics to describe something in the "real world" we are using a model, and all models have some potential for error. If mathematics implies something weird about the nature of the world an experienced mathematician is going to question the validity of the model before questioning the weirdness of the world.
Yep, the terms mathematics use is "countable infinity" and "uncountable infinity."
@towellight9400
The concepts of countable and uncountable infinity are a different matter altogether.
Hilbert's Hotel and Grim Reaper Paradoxes posit countable actual infinities.
An example of an uncountable infinity is the number of points in a one-meter line segment.
@@michaeleldredge4279 Out of curiosity, what's your view of the Mandelbrot set in terms of inifinity? I always describe it as infinitely complex within a finite boundary, but I've never discussed it with an actual mathematician!
@@Leszek.Rzepecki
The idea of "complexity" as in the boundary of the Mandelbrot set is difficult to define. There are proxies that you can use for it like "fractal dimension", but those fail to some extent because there are sets that intuitively feel more complicated but will have a lower fractal dimension.
The set does have some interesting properties. It is a connected region that has a non-smooth boundary. It has a relatively simple definition and given a specific point it is usually fairly straightforward to determine if the point is in the set or not.
I guess what I am saying is that mathematicians love their definitions, and without a precise definition of complexity I am reluctant to either agree or disagree that the shape has infinite complexity. I will agree that it is a fascinating shape though.
@@michaeleldredge4279 Ah, so it's a "yes it is, but then again, no it isn't" answer! Well, seriously, I'm sure it's hard to state mathematical propositions clearly in English plain to a non-mathematician. I'm a biologist by training, and found the Mandelbrot set, and associated fractals, well beyond fascinating, showing how a simple equation and iterative process could result in almost unfathomably complex behaviour.
Even the notion of a fractal (or is it fractional?) dimension boggles my mind. From a biological POV, it has been a beacon light illuminating how nature can produce vast complexity using fairly simple rules, thus obviating a vastly more complex designer to generate it. It's absolutely mesmerising, and its almost biological shape and texture rings so many bells and whistles - to mix my metaphors - that I feel pretty certain it has explanatory power well beyond being a simple mathematical curiosity, if only as an example.
Maybe it's not this particular version that's applicable, but something along the lines. Anyhoo, thanks for taking the time to respond. It's always a bit of a wonder how math manages to describe some aspect of the real world. If there is a god, which I doubt, it's definitely a mathematician!
As a mathematician, I always roll my eyes whenever theists try to explain what is wrong with infinity, and then posit the existence of an infinite being. They don’t even attempt to engage with the mathematical literature about infinity, such as set theory or limits, and instead just be like “Infinity weird, therefore contradiction.” As much as I criticize William Lane Craig, I appreciate that he sees the value in infinite sets, though he tries to bootstrap it for his narrative.
The Grim Reaper Paradox shows the logical impossibility of the Grim Reaper Paradox. Just because _some_ actual infinities contain contradictions, that does not mean that all actual infinities contain contradictions. We can just as well construct finite contradictions, but that does not mean that all actual finites are impossible. So we cannot have a infinite series of reapers following these particular rules. That's nice to know, but it tells us nothing about other infinite series that follow different rules.
Especially since there are no actual Grim Reapers at all.
I must have missed it, but I didn't catch the part where the Theist can actually get to grips with what they choose to call "Actual infinity." Other than "It was God all along," which isn't really much of an explanation.
"It was God all along" is not a explanation for pretty much anything. Not only for that, but also for the things that theists usually explain with God. For example, if i ask "how was the universe formed?", the answer "it was God" doesn't answer the question at all: I asked for a 'how', not a 'who'.
Hey man, been checking you out for about a year, now. And I just wanted to say. I really appreciate how measured and civil your responses can be. I’ve never felt like you’re talking down or patronising. As much as I can enjoy the comedy the more acerbic response channels can be, I wholly prefer genuine attempts at discourse.
Respect, my dude
7:30
The barber is a woman, is a boy who hasn't yet started to grow a beard, or travels to another village to get shaved by the barber there. The paradox needs to be more precisely worded to be a problem.
The barber could *also* have a beard, but that might be blocked by "doesn't shave" preventing the growth of beards by requiring every to shave or be shaved.
Women, prepubescent boys, and people who travel to other villages to get shaved are still in the category of people who do not shave themselves.
The paradox is not about real life. It's about self-reference. The real-life example of barbers is just illustrative.
You cannot solve a fundamental limit of logical thinking with a cheeky trick.
@@andreab380 People who don't grow beards though don't need to be shaved.
At least not as far as the other ways I've seen this paradox presented have allowed for, where it's been presented more as a puzzle than a paradox - like the one where a boy is injured in an accident that kills his father, the boy is brought to hospital and the surgeon can't operate because "This is my son!" (the obvious solution being a female surgeon or a gay couple).
@@dreadlindwyrm I think the people who presented it to you didn't phrase it right.
It's not "people who don't need to shave". It's just "people who don't shave themselves".
The focus is on self-referentiality: doing the thing that you do to yourself.
It's meant to illustrare a logical problem in set theory, which is a genuine paradox . If you try to think of "a set of all sets that contain themselves", it can neither contain itself nor not contain itself, because both alternatives lead to a contradiction.
I've never liked the casual throwing around of infinity. Infinity is a limit, not a number.
For someone who chose to argue that atheism doesn't explain infinity, he failed to explain why his god would make the concept explainable. If he was going to do so by saying that his god is infinite, then that's a claim which would have to be demonstrated.
The theist arguement of the contradictory nature of infinity is used as part of the greater arguement. In a nut shell, if there is no such thing as infinity then the universe must have had a beginning. They then assert god, titans, great turtles, etc are the cause of the beginning of the universe. The arguement is not limited to a single definition of the christian God.
But then you get to the larger primary mover or unmoved mover which theists solve with special pleading for God or gods as the primary mover rather than an infinite chain of causes or an infinite universe.
@@leopard3131Except that the principles of casualty presuppose a spacetime continuum. Trying to extend our intuitions about causality beyond the Big Bang (the point at which spacetime became actualized) is itself incoherent.
@@leopard3131 Rather than an infinite multiverse within which our universe is an infinitessimally small part, theists prefer an infinite god that they can personity, relate to, and project their personal prejudices on to. Theists always want to reduce a god to their own puny dimensions. They couldn't deal with a really infinite one bigger than a multiverse.
So god explains infinity? Doubt it. Another god of the gaps.
Since infinity doesn't and cannot exist as a quantity, only as a useful mathematical concept, nothing can interact with infinity in reality.
Albert Einstein:
Only two things are
Infinite.
The universe and
human stupidity, and
I'm not sure about the former
Which do you like better?
"There are two infinites: human capacity for misunderstanding, and human potential for compassion - and I'm endlessly amazed by the latter."
"There are two infinites: the depths of human confusion, and the heights of human creativity - and I'm constantly in awe of the latter."
"There are two infinites: human limitations, and human imagination - and the second one never ceases to inspire me."
@@darkofalltrades
You are not able, to
be in two separate infinites at the same
time.
One of them excludes the other
I may disagree. Things can be part of two infinities, and I can give examples if you'd like. Whether I as a person can, I am not sure.
@@darkofalltrades
I completely misread
your latter respons
I thought it was some
form of "riddle"!🤣
This is now edited.
I've really enjoyed this.
Good exercise for an
old brain with a young
spirit.
Many thanks from
Denmark 👍
I don’t believe in any gods… therefore I cannot conceptualize infinity with my limited mind.
I mean… unlike theists? The majority of which believe that their God is beyond their understanding?
I can’t even understand what that guy’s point is, much less have the infinite mind required to properly conceive any infinite.
Nice video. I don't think an actual infinite series is possible either, but I must confess I don't really get many of these paradoxes lol
They get really complicated. I don't fault you for a moment!
I can appreciate the effort, but there's that one huge problem with these preacher boys: they should start focusing on explaining their own position if they cared at all what outsiders think, but no, this is for the slaves deceiving them to believe their nonsplanation makes them all better.
These paradoxes are often solved by the calculus technique of summation of infinitesimals, and it may be that space-time, like energy, has its own minimum quantum. And in any case, the fact that these are paradoxes means that no one has solved them, including theists.
If there IS someone who can honnestly interact with actual infinity, I'd be glad to have a chat with them. The closest I had the chance to talk to was an astrophysicist that was an atheist. The religious people that claimed to have a grasp of infinity were just reducing it to something that paled compared to my finite understanding of things. They were not very... Science oriented.
I have thought for a while that theists have a conceptual problem with inifinity and solve that by replacing inifities with god, without considering the infinities inherit to the god concept. Such as they solve infinite regress by using god as a beginning point via special pleading
This is why God has no time to care about us humans, he desperately tries to solve conceptual problems involving infinities.
Infinity is not compatible with Christianity as infinite regress, a form of infinity, would screw their creation myths over.
This was one of the more interesting ones, but when you boil it all down to its basic core, this was just another example of "You can't explain X, therefore God." It's just as fallacious regardless of how it's presented.
I don't think this guy realizes that this is not an "atheist problem" but a "human/finite being problem."
99% of people do not understand or comprehend infinity. Infinity is extremely complex and takes a lot of thought to understand. Even if you understand some infinites, that will not mean you will understand all types of infinites.
Even many mathematicians take quite some time to actually come to understand various types of infinity. I've studied various types of infinity, but I will not claim to be able to understand them all, much less explain them to others for them to understand.
Precisely.
It's more a limit of the human perception than an ""atheist/theist"" problem.
The basic concept is very simple. Something just doesn't end.
Most people have a hard time wrapping their head around that for some reason. They usually don't even get to the point where they discover that there's more than one kind of infinity.
Here's a version of the Kalam:
P1: All things come to an end.
P2: The universe is a thing:
C: The universe comes to an end.
Totally irrefutable, just like the original, and as pointless! :) Perhaps ∞ as a concept has its uses in maths, but eventually, practically speaking even adding another 1 to a seemingly infinite series is going to become impossible because the person doing the adding expires. Not only does ∞ not imply a god, except to those desperate to believe in one, it couldn't distinguish between the gods. I doubt the god of maths is particularly interested in apes, in any case.
It also runs into the same pitfall as the original in that the term "end" is ambiguous. We never see things "end" in the sense of vanishing from existence. They just become inert, break down, and are (eventually) reconstituted into something else.
If the universe "ends" in Heat Death, there will still technically not be nothing, because all of the energy will still be there (just in an unusable form).
@@chameleonx9253 Yeah, agreed, so far as we can tell. Of course, we can't really tell how it started yet, so guessing how it ends is also pretty much a guess. To most of us, infinity is a quantity too vast to be imagined. My personal response to questions of what the universe is, or whether it has an actual beginning or end, and in relation to what else, is a firm "I don't know!" I despise folk who make shit up and call it religion.
@Leszek.Rzepecki "I don't know" is the only honest answer. It's unfortunate that so many people would rather have an emotionally comforting answer than the truth.
@@chameleonx9253 Well, it's even worse, it's settling for an imaginary answer rather than accepting we don't know "the truth." That's the problem with religion: it pretends to provide answers for questions that we not only don't have immediate answers for, but that might be in principle unanswerable. Science searches for truth, but we should be able to admit that maybe sometimes we won't be able to find it.
@Leszek.Rzepecki I would argue that science doesn't necessarily seek out "truth," per say, so much as practical applications for the truth.
If a question ultimately has no answer, then it has no value insofar as providing us new technology or ways of navigating the world we live in, and thus science isn't really going to devote our limited time and resources to it.
"I don't know" has the advantage of leaving open a possiblity of future discovery, while "we can't know" is a dead end.
This is nothing more than an attempt to make Christian beliefs appear more rational than atheism. Christianity depends upon the acceptance of astonishing claims that cannot possibly be demonstrated to be true. I see no logic in blindly accepting Christian claims. I was never troubled by concepts of infinity in my former electronics work. Numbers often became increasingly insignificant as the got larger. Electrons might as well have been infinitely small, given their minute size.
I have no issue with infinity, and there is no need or requirement for athiests to explain or justify it. It's an inelegant mathematical concept that has no practical use. It is, by nature, indefinable. To say that God can not only contain infinity, but solve for it, is a facile deepity, and an attempt to define God into existence that fails on its own terms.
Christian athiests are really just humanists who aren't quite ready to let the safety blanket of the church go.
I do find Joe Shmidt's (Majesty of Reason) response to the Grim Reaper Paradox to be pretty sufficient. Essentially, the paradox doesn't require infinity to create such paradoxes. As such, the paradox is paradoxical for reasons that have nothing to do with infinity.
Math says the infinite can’t be divided. Our reality relies on interactions. H2 must interact with O to make water. An infinite distance prevents this, so math’s infinity isn’t here.
Infinity is just a mathematical tool. To search it in the real world is at best misleading. And I speak as a prettily good mathematician, who could say a lot more on the subject... except that it's really hard to tell that in english. Maintenant, s'il y a quelqu'un qui veut que je m'étende sur le sujet en français, qu'il m'interpelle.
Well given math has nothing inherently to do with whether or not a god exists. I don't see why it is brought up as an issue for atheists. The claim that a god or any number of gods does not exist, or is not known to exist, has no basis in whether infinites are logically consistent or not. Then there is the fact that there are an infinite number of infinites from whole infinites, even or odd infinites, indivisible infinites, infinity between each whole number, imaginary number infinities, negative infinites, and on and on the series goes. But that is purely mathematical, and not something the human mind evolved to be able to understand or conceptualize in anything resembling intuitive sense. this cognitive limitation doesn't imply any connection to theological claims. The assertion that a god does or does not exist remains a separate matter, reliant on evidence, philosophy, and personal belief-not the logical properties of infinite sets in mathematics.
...should it?
Is infinity a girl? That would explain why I can't interact then.
I have seen nothing to even conclude that any infinity exists, well, except for the ignorance of humans
Adding a pre-emptive like and comment.
Well the "problem" with Hilbert's Hotel is in the premises. Is it full or not? if it is full no more giests can be accommodated regardless if the hotel is finite or infinite, that is the definition of full lol
The premise is that every room is occupied. There are no rooms without people in them.
@ArrantPrac full, occupied, use any synonyms you wish. If they are all occupied, there are no unoccupied rooms regardless if the hotel is finite or infinite, no more guests can be accommodated.
@@leopard3131 "Full" specifically means no more can be added. "All rooms are occupied" _implies_ that no more can be added, in any real life situation. The entire point of the example is that with an infinite number of rooms, that is no longer the case. You can always add another person and still end up with every guest having a room, even if there are no unoccupied rooms to begin with.
@ArrantPrac, you fail to understand infinity. There are an infinite number of rooms all occupied by an infinite number of guests. By definition, you can not add a room. They are all occupied to infinity and beyond . There is no such thing as infinity +1
The paradox only exists because you break the rules. The only way to accommodate an adding guest is to have infinite rooms but finite guests. This breaks the rule that they are all occupied.
If you have infinite rooms but a finite number of guests, you can always add more, but that is not the case as you have infinite rooms mapped 1:1 with infinite guests, otherwise the rooms are not all occupied.
If you add a room or roo.s without adding a guest or guests you violation the premise that all the rooms are occupied thus you create a paradox by violation of the premise.
@@leopard3131That’s the paradox. The hotel is full, all it’s rooms are occupied and yet you can fit more people in. It’s very counterintuitive and that’s why it’s called a paradox.
As a general rule, only bridge salesmen cite low bar bill as a scholar.
A hotel with infinite rooms could never be full.
What if you have infinite guests and assign a guest to every room?
@@dwaneanderson8039 As long as the hotel and the guests have the same Cardinality there will be room for more
@@nafetz1687 If they have the same cardinality, there will be a guest in every room.
All these problems against infinity by philosophers just shows their lack of understanding of infinity
Is God infinite or Infinity is God? " To infinity and beyond"
Infinity doesn't exist in the universe and is only a man made concept. Everything is finite. Simple as that.
I've always understood paradoxes as unsolvable by their very nature (as well as the best way to defeat the inevitable android/AI uprising), thus his blathering about atheism being unable to "solve" the paradoxes is pointless.
About the only other thing I have to contribute is that I don't think the barber situation is an actual paradox, because I would assume that he shaved himself because why wouldn't he?
Also, the initial setup says nothing about a hard-and-fast rule regarding whom the barber shaves, only that he shaves those who do not shave themselves.
This also does not mean that he couldn't have a beard, either, thus negating the need to shave/be shaved.
Also also, if there are men in the village that shave themselves, the barber could ask/pay one of them to do it.
Oh, I thought of another thing: the question of whether a set of all sets contains itself. I think the logical response is "yes, but it might end up causing a recursive loop and maybe lock up the system, so probably don't try getting the universe to do that. Rebooting a universe does a factory reset and I'm not ready for that yet."
My mom adds: "Send the Grim Reapers to Hilbert's Hotel and that will fix everything."