Rob Osborn Posted January 20, 2012 Posted January 20, 2012 (edited) I have been struggling for quite some time since a post a while back about infinity and where and how God fits into it. In the scriptures there are times when it is written about something to be "without end". A classic example is in Moses-4 And, behold, thou art my son; wherefore alook, and I will show thee the bworkmanship of mine chands; but not all, for my dworks are without eend, and also my fwords, for they never cease.(Pearl of Great Price |Moses 1:4) 35 But only an account of this earth, and the inhabitants thereof, give I unto you. For behold, there are many worlds that have passed away by the word of my power. And there are many that now stand, and innumerable are they unto man; but all things are numbered unto me, for they are mine and I aknow them.(Pearl of Great Price | Moses 1:35) Here we are told in those two verses what appears to be contradicitions. On the one hand we are told that God's works are without number or "innumerable", and yet on the other hand we are told that they are all numbered unto God. This brings up the point I want to discuss. Are God's works truly infinite- his worlds he has created, populated, etc? Or does this just mean that His works never cease but in fact they are of a finite order at any given time? When we look out into space we see a seemingly never-ending amount of stars, planets, galaxies, etc. If they are the works of God, then to us it may truly appear to be never-ending and perhaps even infinite. But to God is this really the case? Has he truly created a universe with separate but countable parts that goes on forever?I am left somewhat to believe that logically they only appear to us to be innumerable because of our lack of telescope power, technology, etc. and that To God they truly are all numbered being of a finite order.I have been often intrigued by Cantor's work in mathematics with "infinity" but I am always drawn to conclude that there is no such thing as an infinity of something because it can't be known or proven, even for God. What say ye? Edited January 20, 2012 by Rob Osborn 1
selek1 Posted January 20, 2012 Posted January 20, 2012 I doubt, Rob, that you'll get any kind of useful answer on this thread because you are asking finite minds to comprehend- or worse, explain- the infinite.In that sense, your question is simply a variation of one that has been raised countless times: "Can God make a rock so big that he cannot lift it?" The question is a logical contradiction in that either answer limits the ability of a God who is without limits.Theologians and philosophers have been debating this for thousands of years- and the only consistent answer has been, "Would you like fries with that?"
CV75 Posted January 20, 2012 Posted January 20, 2012 What say ye?I think infinity is a man-made concept to help talk about “boundlessness” (in the many way it is considered), and even that from our finite point of view. I think it is a quantitative construct and not meant to speak of qualitative matters.Perhaps “innumerable” has a different meaning than “without end” or to “never cease." If so, God’s creations in the present tally are innumerable only to man, but God can number them; they are at the same time “without end” and “never cease” in terms of being eternal. In this passage, I’d say that “innumerable” refers to quantities comprehensible to man, and “without end” refers to qualities.
Tarski Posted January 20, 2012 Posted January 20, 2012 (edited) I have been struggling for quite some time since a post a while back about infinity and where and how God fits into it. In the scriptures there are times when it is written about something to be "without end". A classic example is in Moses-4 And, behold, thou art my son; wherefore alook, and I will show thee the bworkmanship of mine chands; but not all, for my dworks are without eend, and also my fwords, for they never cease.(Pearl of Great Price |Moses 1:4) 35 But only an account of this earth, and the inhabitants thereof, give I unto you. For behold, there are many worlds that have passed away by the word of my power. And there are many that now stand, and innumerable are they unto man; but all things are numbered unto me, for they are mine and I aknow them.(Pearl of Great Price | Moses 1:35) Here we are told in those two verses what appears to be contradictions. On the one hand we are told that God's works are without number or "innumerable", and yet on the other hand we are told that they are all numbered unto God. This brings up the point I want to discuss. Are God's works truly infinite- his worlds he has created, populated, etc? Or does this just mean that His works never cease but in fact they are of a finite order at any given time? When we look out into space we see a seemingly never-ending amount of stars, planets, galaxies, etc. If they are the works of God, then to us it may truly appear to be never-ending and perhaps even infinite. But to God is this really the case? Has he truly created a universe with separate but countable parts that goes on forever?I am left somewhat to believe that logically they only appear to us to be innumerable because of our lack of telescope power, technology, etc. and that To God they truly are all numbered being of a finite order.Infinity is a human concept. What we mean by it, what mathematicians mean by it, is totally up to us. We wish to make our use of that word both as precise as possible in a given context and as useful as possible. We also want to the not be led into contradictions.But, non-mathematicians are notoriously confused about the the difference between contradiction and counter-intuitiveness. Many of the results about non-Euclidean geometry are counter-intuitive but they are not contradictions.Now, I submit that you are using words imprecisely. Can it mean anything to say that an infinite set is "numbered". Well, that is up to us. Can we come up with a useful and logical extension of the usual notion that works for finite sets?Well, yes. This is the notion of cardinality. You may have expectations that are not met by this concept but so what? Infinite sets have other measures of size such as so called "measure" - a technical notion at the foundations of probability theory. This notion serves different purposes but also generalizes the notion of the size of a finite set.Perhaps God in some sense knows the cardinality of his creations (some cardinalities being "bigger "than others). Or maybe he sees that there is a natural measure function (a la measure theory) that applies to his creations. Or maybe there is only us humans with our various mental and social constructs such as "infinity", "fame", or "price".The bottom line is that you are nowhere near thinking about infinity in the right spirit. It is too medieval and metaphysical in the pejorative sense (angels on the head of a pin).Leave the real stuff to mathematicians, logicians and people who catch onto what we are doing.I have been often intrigued by Cantor's work in mathematics with "infinity" but I am always drawn to conclude that there is no such thing as an infinity of something because it can't be known or proven, even for God. What say ye?This is confused and mathematically illiterate. It (infinity) is our (human's) word, our concept and it has been refined and made precise by mathematicians for human purposes. Look how imprecise your language is: You say that there can be no such thing as infinity because it can't be proven. What do you even mean?? What is this "it" and what would it mean for "it" to be "proven"? Propositions are proven. What proposition did you have in mind?The following sentence is not even wrong (it makes no sense which is worse than being wrong)."Infinity cannot be proven". (huh??)Most theologians are generating nonsense on this topic and that is because they are centuries behind.Cantor blows Anselm out of the water on this topic. History happened you see. We found a way to be clearer and more precise. Edited January 20, 2012 by Tarski
Analytics Posted January 20, 2012 Posted January 20, 2012 Cantor blows Anselm out of the water on this topic. History happened you see. We found a way to be clearer and more precise.Didn't Cantor believe that his theorem's involving infinity had bearing on the nature of God?
Rob Osborn Posted January 20, 2012 Author Posted January 20, 2012 Infinity is a human concept. What we mean by it, what mathematicians mean by it, is totally up to us. We wish to make our use of that word both as precise as possible in a given context and as useful as possible. We also want to the not be led into contradictions.But, non-mathematicians are notoriously confused about the the difference between contradiction and counter-intuitiveness. Many of the results about non-Euclidean geometry are counter-intuitive but they are not contradictions.Now, I submit that you are using words imprecisely. Can it mean anything to say that an infinite set is "numbered". Well, that is up to us. Can we come up with a useful and logical extension of the usual notion that works for finite sets?Well, yes. This is the notion of cardinality. You may have expectations that are not met by this concept but so what? Infinite sets have other measures of size such as so called "measure" - a technical notion at the foundations of probability theory. This notion serves different purposes but also generalizes the notion of the size of a finite set.Perhaps God in some sense knows the cardinality of his creations (some cardinalities being "bigger "than others). Or maybe he sees that there is a natural measure function (a la measure theory) that applies to his creations. Or maybe there is only us humans with our various mental and social constructs such as "infinity", "fame", or "price"."Cardinality" or "size"- its all semantics. Only mathematicians get bothered over this. We know what I was talking about.The bottom line is that you are nowhere near thinking about infinity in the right spirit. It is too medieval and metaphysical in the pejorative sense (angels on the head of a pin).Leave the real stuff to mathematicians, logicians and people who catch onto what we are doing.I think that I know the subject "logically" quite well. I am inly asking logically about God and the notion of infinity and if it relates to God. This is confused and mathematically illiterate. It (infinity) is our (human's) word, our concept and it has been refined and made precise by mathematicians for human purposes. Look how imprecise your language is: You say that there can be no such thing as infinity because it can't be proven. What do you even mean?? What is this "it" and what would it mean for "it" to be "proven"? Propositions are proven. What proposition did you have in mind?The following sentence is not even wrong (it makes no sense which is worse than being wrong)."Infinity cannot be proven". (huh??)Infinity- the parts of an infinite set, if it were exist cannot be proven and checked by proofs in math. We can say that something has endless or "infinite" possiblities but what we can't know is that "all" of them can be known which is impossible to know. As it relates to what I was saying about the universe is that it cannot be proven that the universe goes on infinitely because all points checked will only be a finite distance apart. In fact, logically it can be proven that all points within what is "known" within the universe have finite proportions and distances at any time. What I am saying here is that it is logically impossible to find two separate locations in the universe that have an infinite amount of distance between them.Most theologians are generating nonsense on this topic and that is because they are centuries behind.Cantor blows Anselm out of the water on this topic. History happened you see. We found a way to be clearer and more precise.But what did Cantor really prove about numbers and the infinite? Inmy opinion he added no real truths other than different ways to look at finite numbers.
Duncan Posted January 20, 2012 Posted January 20, 2012 being of the pragmatic tradition I see God saying to Moses to me they are numbered but to you and the rest of mankind they are not numbered and innumerable, I don't think God wanted to confuse him or us
The Nehor Posted January 20, 2012 Posted January 20, 2012 (edited) Moses wasn't good with numbers or counting so God was going easy on him. There are 8 worlds. Edited January 20, 2012 by The Nehor 3
Flyonthewall Posted January 21, 2012 Posted January 21, 2012 The Lord stated in the scriptures that He would limit Abraham's revelation to only the things that concern this earth, which tells me that He speaks relatively to us, not neccesarily in absolutes or in full details. As a parent speaks with a child in a way they can understand, I believe God does not speak beyond our capabilities to understand.He does not tell us details about other worlds, only that they exist.A child that can only count to 10 would have a very hard time, if not impossible, understanding what 100 is, or 1000, or 1000000. To them it is just a big number...innumerable so to speak.
blackstrap Posted January 21, 2012 Posted January 21, 2012 It is possible ,and quite easy,to add up an infinite number of numbers(convergent geometric sequence).There is a finite limit. Perhaps there is a similar expression that applies to creations.There is an infinite number of them,but there is a limit to creation itself.
blackstrap Posted January 21, 2012 Posted January 21, 2012 An interesting problem in calculus deals with a figure created by revolving a line about an axis,thereby forming a volume.The surface of the figure was infinite,but its volume had a limit. So,technically there was no way to paint it unless one was to fill it up with paint. Strange stuff.
DarkScythe Posted January 21, 2012 Posted January 21, 2012 In short, This universe is vast. Also God is not only king of this universe but I do believe the King of the Multi-verse.
The Nehor Posted January 21, 2012 Posted January 21, 2012 In short, This universe is vast. Also God is not only king of this universe but I do believe the King of the Multi-verse.Azathoth would like to have a word with you.
DarkScythe Posted January 21, 2012 Posted January 21, 2012 me and him have lunch on Tuesdays. We do talk about stuff. I did ask him about his job. Right now, He is just caretaker of this universe but he loves to mess with certain mortals heads. 1
altersteve Posted January 21, 2012 Posted January 21, 2012 I've always interpreted it to mean that there are so many worlds that we don't have a number for it. Counting them is impossible for us simply because of how many there are. 1
Tarski Posted January 21, 2012 Posted January 21, 2012 (edited) "Cardinality" or "size"- its all semantics.No it is not "just" semantics. It is a matter of logical proofs and precision. It is a matter of conceptual clarity, a matter of avoiding contradiction etc. It is a big, solid, and developed subject with plenty of proofs.Only mathematicians get bothered over this. We know what I was talking about.You absolutely do not know what you are talking about as witnessed by several of your assertions.The mathematics was developed to sort out the rampant confusion that you are still subject to.I think that I know the subject "logically" quite well.I am quite sure that you do not. You seem unware of the multivalent nature of the word "infinity" and unwilling to face up to the various clarified notions that have been developed so that we can actually finally say something true and provable.I am inly asking logically about God and the notion of infinity and if it relates to God.Who knows? Your notion of God is vague enough that one could never be sure. But if you knew the math and logic, then you could at least be clear about what is possible in principle.Infinity- the parts of an infinite set, if it were exist cannot be proven and checked by proofs in math. That was an awkward sentence but maybe it will suffice to point out that we do prove things about the various precise notions of infinity in math. There are thousands of book filled with such proofs. Cantor made the first seminal steps toward rigor in this regard and it hasn't stopped since.We can say that something has endless or "infinite" possiblities but what we can't know is that "all" of them can be known which is impossible to know. *sigh*Consider this: We know and can prove that the set of prime natural numbers is a denumerablly infinite set. Yet we are not aquinted with each individual prime and so in that sense do not know them. But we still know the set is infinite and we know at least one property of each of its members. (notice I said the word prove".)As it relates to what I was saying about the universe is that it cannot be proven that the universe goes on infinitely because all points checked will only be a finite distance apart. In fact, logically it can be proven that all points within what is "known" within the universe have finite proportions and distances at any time. What I am saying here is that it is logically impossible to find two separate locations in the universe that have an infinite amount of distance between them.Exhibit A. This is mathematically illiterate. The task of showing that a metric space is infinite in diameter is not the same as finding two points at an infinite distance from each other.But what did Cantor really prove about numbers and the infinite? In my opinion he added no real truths other than different ways to look at finite numbers.You are 100% wrong. He proved plenty and is famous to this day for it. His proofs still appear in textbooks and undergraduates routinely understand them and why the the proofs work.If I were talking to Zeta Flux or Asbestosman (two mathematically literate posters) we might get into disagreements and puzzles about metamathematical notion of mathematical "truth", the ontological status of mathematical abstracta, foundational questions about set theoretic systems such as ZFC and the puzzling Löwenheim–Skolem theorem. But trust me, you are not ready for such a discussion.Your first step should just be to understand why anyone would say that the cardinality of the power set of a given set is larger than that of the set itself (leading for example to the notion that the cardinality of the real numbers is greater than that of the natural numbers).Actually, it might be interesting for you to ask yourself how it is that your finite mind could even be talking about the infinite. How is it you and other humans even grasp the meaning if you cannot fully grasp any examples. If the supposed real true notion of infinity is beyond the ken of even mathematicians, then what in the world is it we are talking about? What are you talking about? Edited January 21, 2012 by Tarski
Rob Osborn Posted January 21, 2012 Author Posted January 21, 2012 Tarski,I see you are an intellectual snob. No problem- oh happy day!You can belittle my intelligence all you like but I am trying to honestly discuss this matter in a reasonable manner. I don't mind discussing why Cantor was wrong but I would wish to do so in a more civil manner. I don't belittle your intelligence so show me some respect also.
Stargazer Posted January 21, 2012 Posted January 21, 2012 (edited) Well, Stargazer wants to chime in on this, because it is right up his alley."And there are many that now stand, and innumerable are they unto man; but all things are numbered unto me, for they are mine and I know them."As to the worlds being "innumerable ... unto man", of course they cannot be counted by man because we can't see them all -- in fact we can't see hardly any of them! Our galaxy alone has so much obscuring dust and intervening stars that we can see only the barest pittance of them from where we sit out here in the Perseus Arm. And don't get me started about extra-Milky Way galaxies, because there are more galaxies in just the Universe we can see (let alone the portion we can't) than there are stars in our own galaxy. Of course we can't number them. Duh!God numbers them because he CAN see them all. In detail.As to "for my works are without end, and also my words, for they never cease," well, Duh! again. You need to take a class or read a book in Introductory Astronomy. Our sun is approximately 5 billion years old. It has about 5 billion more years left on the "Main Sequence", before it burns itself into a white dwarf. It's actually going to last about 1 billion more years in its current state as a "yellow dwarf", and then it will start to expand and eventually turn into a "red giant" and burn all life off the earth. Father's works are without end because He continues to create new ones as the old ones burn out. Take a look:http://apod.nasa.gov...d/ap120118.htmlThis is a deep infrared image of Cygnus X, the largest known star forming region in the entire Milky Way Galaxy. There are enormously many more of them, both here and in every galaxy we can see, and of course in the ones we can't see. These regions churn out new stars on a steady pace -- though the process is slow and we haven't been observing them long enough to actually document a single one popping out.Of course Father's works never cease.Now stop tripping yourself up on things your tiny little mind can't possibly comprehend! And don't worry, my mind is just as tiny as yours, comparatively speaking. Edited January 21, 2012 by Stargazer 1
Tarski Posted January 21, 2012 Posted January 21, 2012 (edited) An interesting problem in calculus deals with a figure created by revolving a line about an axis,thereby forming a volume.The surface of the figure was infinite,but its volume had a limit. So,technically there was no way to paint it unless one was to fill it up with paint. Strange stuff.Which is just one more reason that it pays to specify precisely what one means by infinite and what it is that one is referring to.One might jokingly wonder if, like Gabriel's Horn, the works of God are finite in volume but infinite in surface area.(http://en.wikipedia.org/wiki/Gabriel's_Horn) (Edit: you have to type this in to get to it. For some reason the "_Horn" gets dropped).Think carefully..........Infinite in what sense? Rob never specifies this. Yet it makes all the difference in the world.Infinite in time?Infinite dimensional? (Which notion of dimension are we speaking of?)In volume?In hypervolume?In some measure theoretic sense?In cardinality?In the sense of hyperreal numbers?Noncomputable? Inaccessible?Unbounded (e.g topologically having no boundary points)?Unbounded metrically?In some other sense such as infinite as in inconcievability (unknowable)?All of these are different and there may be many more senses unmentioned here and many more as yet undiscovered.Once this is decided we must look to the laws and logics that such infinties follow (e.g. transfinite arithmetic, theory of limits, etc ), Edited January 21, 2012 by Tarski
Tepui Posted January 21, 2012 Posted January 21, 2012 Jan 11, 2012- Astronomers See More Planets Than Stars in Galaxyhttp://abcnews.go.com/Technology/wireStory/astronomers-planets-stars-galaxy-15340717"One study shows that in our Milky Way, most stars have planets. And since there are a lot of stars in our galaxy — about 100 billion — that means a lot of planets."
Rob Osborn Posted January 21, 2012 Author Posted January 21, 2012 Tarski, maybe you didn't understand my opening post. I am asking if it is possible that he truly created "worlds" that are infinite in number. That is pretty simple- that is what I was asking. Many have responded exactly knowing what I meant. As it relates to God is intriguing to me because it appears that because God knows "all" his creations and they are "numbered" unto him it seems rather apparent that He doesn't truly have an infinite amount of creations but rather a finite amount of them at any given moment. It may also say something about the mystery of the universe- that as far as God's works go, he has his dominion or that which he has created and they can all be numbered in a finite manner. Now this may not say much about ownership of planets in the entire universe, but it may shed some light on how we view numbering sets- even at the god level. Might i propose that the gods don't work with any abstract of the infinite becaus eit has no value to them. I read the scriptures and it seems rather apparent to me that God's works ar every numerous, maybe even astonishingly more numerous than we can comprhend but never are they at or nearing some level of infinite measure.
Stargazer Posted January 21, 2012 Posted January 21, 2012 Tarski, maybe you didn't understand my opening post. I am asking if it is possible that he truly created "worlds" that are infinite in number. That is pretty simple- that is what I was asking. Many have responded exactly knowing what I meant.I thought I should make an addendum to my astronomy lesson, and that is that when you see the word "infinite" being used in the scriptures, it doesn't mean what you might think it means. Even when God makes reference to terms that seem to suggest this, such as "worlds without end" and the like, we see in DC 19:10-12 that Endless is simply one of His names. 10 For, behold, the mystery of godliness, how great is it! For, behold, I am endless, and the punishment which is given from my hand is endless punishment, for Endless is my name. Wherefore—11 Eternal punishment is God’s punishment.12 Endless punishment is God’s punishment.God is Endless because He just keeps going on. His creations are Endless because He created them, and He will just continue to create more of them, and will not stop doing so. So Endless is infinite enough.
Rob Osborn Posted January 21, 2012 Author Posted January 21, 2012 I thought I should make an addendum to my astronomy lesson, and that is that when you see the word "infinite" being used in the scriptures, it doesn't mean what you might think it means. Even when God makes reference to terms that seem to suggest this, such as "worlds without end" and the like, we see in DC 19:10-12 that Endless is simply one of His names.God is Endless because He just keeps going on. His creations are Endless because He created them, and He will just continue to create more of them, and will not stop doing so. So Endless is infinite enough.That is precisely how I relate these terms in scripture also. It's kind of like me and you- suppose we are good friends forever from this point on. It could be said that our experiences we share will be endless not that all of them we ever share at any point will actually be endless.
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