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# Is It This, or is It That?

 Posts: 3,375 Add as FriendChallenge to a DebateSend a Message 5/24/2014 4:03:05 PMPosted: 4 years agoThe word infinity basically means without end, or unlimited. To define something means to set a limit, bound, or end. In defining infinity, aren't our actions in opposition to its very meaning? The act of defining is to say something is this, as opposed to that: a dog is an animal; it is not a plant. However, in defining that which, by definition, is not definable, we are creating a paradox.
 Posts: 6,138 Add as FriendChallenge to a DebateSend a Message 5/24/2014 6:41:45 PMPosted: 4 years agoAt 5/24/2014 4:03:05 PM, s-anthony wrote:The word infinity basically means without end, or unlimited. To define something means to set a limit, bound, or end. In defining infinity, aren't our actions in opposition to its very meaning? The act of defining is to say something is this, as opposed to that: a dog is an animal; it is not a plant. However, in defining that which, by definition, is not definable, we are creating a paradox.There are different kinds of infinity. Counting numbers start at 1 then go on to infinity. There is no end but there is a beginning and it is endless it a particular direction.I think it was Aristotle who said there was greater infinity and small infinity. Greater being descriptive by addition and small being by division (which is now termed infinitesimal)So I don't see a confusion. I know some people think infinity has to be endless in all directions and so immense that it can not be bound. There is a very special case and not usually the infinities we work with.
 Posts: 3,749 Add as FriendChallenge to a DebateSend a Message 5/24/2014 7:44:12 PMPosted: 4 years agoAt 5/24/2014 4:03:05 PM, s-anthony wrote:The word infinity basically means without end, or unlimited. To define something means to set a limit, bound, or end.But as you said, it is defined as without end or unlimited, how is that setting a limit.?In defining infinity, aren't our actions in opposition to its very meaning?Not if it's defined properly.The act of defining is to say something is this, as opposed to that: a dog is an animal; it is not a plant. However, in defining that which, by definition, is not definable, we are creating a paradox.No, because It isn't true that infinity is "not definable by definition"."It is one of the commonest of mistakes to consider that the limit of our power of perception is also the limit of all there is to perceive." " C. W. Leadbeater
 Posts: 9,513 Add as FriendChallenge to a DebateSend a Message 5/24/2014 9:18:24 PMPosted: 4 years agoWell, that's kind of the thing about infinity. It's bounded by a definition, but it's not finite. In mathematics, there is a sharp distinction drawn between something's being bounded and its being finite. Consider: you could take some arbitrary subset of the real numbers--for convenience, we will play it safe and use the closed interval [0, 1]. Very clear boundaries. However, if you were asked to write, one by one, each member of the set of real numbers within this interval, you'd never make it further than zero: the interval is continuous, which means the members of the corresponding set are uncountable. In other words, you could write any specific member of the set, e.g., 0.0063784267846, but you can't write the next member of the set, because there are infinitely many down to infinitesimal size. So, you've got boundedness, but you're also stuck with infinity. This is why mathematical definitions for weird things often take the form "X is the thing such that..." It's s little kooky, but it checks out when you actually do the footwork.
 Posts: 8,234 Add as FriendChallenge to a DebateSend a Message 5/24/2014 9:24:12 PMPosted: 4 years agoAt 5/24/2014 9:18:24 PM, Cody_Franklin wrote:Well, that's kind of the thing about infinity. It's bounded by a definition, but it's not finite. In mathematics, there is a sharp distinction drawn between something's being bounded and its being finite. Consider: you could take some arbitrary subset of the real numbers--for convenience, we will play it safe and use the closed interval [0, 1]. Very clear boundaries. However, if you were asked to write, one by one, each member of the set of real numbers within this interval, you'd never make it further than zero: the interval is continuous, which means the members of the corresponding set are uncountable. In other words, you could write any specific member of the set, e.g., 0.0063784267846, but you can't write the next member of the set, because there are infinitely many down to infinitesimal size. So, you've got boundedness, but you're also stuck with infinity. This is why mathematical definitions for weird things often take the form "X is the thing such that..." It's s little kooky, but it checks out when you actually do the footwork.Defining something does not necessarily set boundaries on it. It simply describes it so everyone understands what concept the word conveys.Lack of understanding creates the boundaries in peoples minds.
 Posts: 587 Add as FriendChallenge to a DebateSend a Message 5/24/2014 9:27:24 PMPosted: 4 years agoAt 5/24/2014 9:24:12 PM, Skyangel wrote:Defining something does not necessarily set boundaries on it. It simply describes it so everyone understands what concept the word conveys.Lack of understanding creates the boundaries in peoples minds.Different kind of boundary."The book you are looking for hasn't been written yet. What you are looking for you are going to have to find yourself, it's not going to be in a book..." -Sidewalker
 Posts: 8,234 Add as FriendChallenge to a DebateSend a Message 5/24/2014 9:30:13 PMPosted: 4 years agoAt 5/24/2014 9:27:24 PM, Poetaster wrote:At 5/24/2014 9:24:12 PM, Skyangel wrote:Defining something does not necessarily set boundaries on it. It simply describes it so everyone understands what concept the word conveys.Lack of understanding creates the boundaries in peoples minds.Different kind of boundary.Yes, its the kind where people are stuck in a rut and cannot think outside the box.
 Posts: 587 Add as FriendChallenge to a DebateSend a Message 5/24/2014 9:32:50 PMPosted: 4 years agoAt 5/24/2014 9:30:13 PM, Skyangel wrote:Yes, its the kind where people are stuck in a rut and cannot think outside the box.And that's exactly the kind of "boundary" that isn't relevant to the immediate topic here."The book you are looking for hasn't been written yet. What you are looking for you are going to have to find yourself, it's not going to be in a book..." -Sidewalker
 Posts: 8,234 Add as FriendChallenge to a DebateSend a Message 5/24/2014 9:36:40 PMPosted: 4 years agoAt 5/24/2014 9:32:50 PM, Poetaster wrote:At 5/24/2014 9:30:13 PM, Skyangel wrote:Yes, its the kind where people are stuck in a rut and cannot think outside the box.And that's exactly the kind of "boundary" that isn't relevant to the immediate topic here.Sure its relevant because if a person cannot understand the concept of infinity being something that never ends, the problem must be in their own understanding. Their own thinking is limited.
 Posts: 587 Add as FriendChallenge to a DebateSend a Message 5/24/2014 9:42:59 PMPosted: 4 years agoAt 5/24/2014 4:03:05 PM, s-anthony wrote:However, in defining that which, by definition, is not definable, we are creating a paradox."By definition undefinable"? You're mistaking your own incoherent choice of words for an absurdity in the idea of infinity. Mathematical infinities exhibit plenty of weirdness, we can all agree, but you certainly haven't touched on it here."The book you are looking for hasn't been written yet. What you are looking for you are going to have to find yourself, it's not going to be in a book..." -Sidewalker
 Posts: 587 Add as FriendChallenge to a DebateSend a Message 5/24/2014 9:49:35 PMPosted: 4 years agoAt 5/24/2014 9:36:40 PM, Skyangel wrote:Sure its relevant because if a person cannot understand the concept of infinity being something that never ends, the problem must be in their own understanding. Their own thinking is limited.Cody_Franklin was talking about the mathematical notion of a boundary, say B, of a set of points S, where B is the set of points generated by the closure of S intersected with the closure of its complement. Has nothing to do with psychology."The book you are looking for hasn't been written yet. What you are looking for you are going to have to find yourself, it's not going to be in a book..." -Sidewalker
 Posts: 3,375 Add as FriendChallenge to a DebateSend a Message 5/24/2014 10:48:55 PMPosted: 4 years agoAt 5/24/2014 6:41:45 PM, Mhykiel wrote:At 5/24/2014 4:03:05 PM, s-anthony wrote:The word infinity basically means without end, or unlimited. To define something means to set a limit, bound, or end. In defining infinity, aren't our actions in opposition to its very meaning? The act of defining is to say something is this, as opposed to that: a dog is an animal; it is not a plant. However, in defining that which, by definition, is not definable, we are creating a paradox.There are different kinds of infinity. Counting numbers start at 1 then go on to infinity. There is no end but there is a beginning and it is endless it a particular direction.The end is your inability to count indefinitely.I think it was Aristotle who said there was greater infinity and small infinity. Greater being descriptive by addition and small being by division (which is now termed infinitesimal)Either extreme is beyond experience and, therefore, meaningless.So I don't see a confusion. I know some people think infinity has to be endless in all directions and so immense that it can not be bound. There is a very special case and not usually the infinities we work with.No. Just endless.
 Posts: 3,375 Add as FriendChallenge to a DebateSend a Message 5/24/2014 11:06:44 PMPosted: 4 years agoAt 5/24/2014 7:44:12 PM, Sidewalker wrote:At 5/24/2014 4:03:05 PM, s-anthony wrote:The word infinity basically means without end, or unlimited. To define something means to set a limit, bound, or end.But as you said, it is defined as without end or unlimited, how is that setting a limit.?Anytime you say something is this but not that, you are setting a limit.In defining infinity, aren't our actions in opposition to its very meaning?Not if it's defined properly.The act of defining is to say something is this, as opposed to that: a dog is an animal; it is not a plant. However, in defining that which, by definition, is not definable, we are creating a paradox.No, because It isn't true that infinity is "not definable by definition".In- means no; -finity means end.De- means to set; -fine means an end.
 Posts: 3,375 Add as FriendChallenge to a DebateSend a Message 5/24/2014 11:14:58 PMPosted: 4 years agoAt 5/24/2014 9:18:24 PM, Cody_Franklin wrote:Well, that's kind of the thing about infinity. It's bounded by a definition, but it's not finite. In mathematics, there is a sharp distinction drawn between something's being bounded and its being finite. Consider: you could take some arbitrary subset of the real numbers--for convenience, we will play it safe and use the closed interval [0, 1]. Very clear boundaries. However, if you were asked to write, one by one, each member of the set of real numbers within this interval, you'd never make it further than zero: the interval is continuous, which means the members of the corresponding set are uncountable. In other words, you could write any specific member of the set, e.g., 0.0063784267846, but you can't write the next member of the set, because there are infinitely many down to infinitesimal size. So, you've got boundedness, but you're also stuck with infinity. This is why mathematical definitions for weird things often take the form "X is the thing such that..." It's s little kooky, but it checks out when you actually do the footwork.Infinity's boundaries are you, in other words, your inability to demonstrate this mathematical claim.
 Posts: 9,513 Add as FriendChallenge to a DebateSend a Message 5/25/2014 3:11:25 AMPosted: 4 years agoAt 5/24/2014 11:14:58 PM, s-anthony wrote:At 5/24/2014 9:18:24 PM, Cody_Franklin wrote:Well, that's kind of the thing about infinity. It's bounded by a definition, but it's not finite. In mathematics, there is a sharp distinction drawn between something's being bounded and its being finite. Consider: you could take some arbitrary subset of the real numbers--for convenience, we will play it safe and use the closed interval [0, 1]. Very clear boundaries. However, if you were asked to write, one by one, each member of the set of real numbers within this interval, you'd never make it further than zero: the interval is continuous, which means the members of the corresponding set are uncountable. In other words, you could write any specific member of the set, e.g., 0.0063784267846, but you can't write the next member of the set, because there are infinitely many down to infinitesimal size. So, you've got boundedness, but you're also stuck with infinity. This is why mathematical definitions for weird things often take the form "X is the thing such that..." It's s little kooky, but it checks out when you actually do the footwork.Infinity's boundaries are you, in other words, your inability to demonstrate this mathematical claim.As has been mentioned, we are dealing here with two kinds of boundaries. I am speaking, not of conceptual boundaries, but of boundaries in the formal sense. You must understand, infinity is not monolithic: there are several different sizes of infinity, some with boundaries, some without. Some are countable, others are not. The integers are infinite, unbounded, and countable; the real numbers are infinite, unbounded, but uncountable. The subset of real numbers between zero and one is bounded by definition--zero on one side, one on the other--but also uncountable. It is for this same reason that the easy way of conceptualizing infinity--beginning at one and perpetually increasing--is as easy to understand as it is inaccurate. People like to imagine infinity temporally, but all of the members of the set are always already there. We simply cannot make each member explicit, requiring instead some kind of shorthand (e.g., aleph null, 0.999 repeating).Anyway, I just wanted to make it clear that the boundaries of which I speak are of a technical nature, not a conceptual or psychological one.
 Posts: 3,749 Add as FriendChallenge to a DebateSend a Message 5/25/2014 6:08:09 AMPosted: 4 years agoAt 5/24/2014 11:06:44 PM, s-anthony wrote:At 5/24/2014 7:44:12 PM, Sidewalker wrote:At 5/24/2014 4:03:05 PM, s-anthony wrote:The word infinity basically means without end, or unlimited. To define something means to set a limit, bound, or end.But as you said, it is defined as without end or unlimited, how is that setting a limit.?Anytime you say something is this but not that, you are setting a limit.Nonsense, if you say something is this (unlimited), but not that (limited), you are not saying it is limited. On the contrary, you are saying it is not limited.In defining infinity, aren't our actions in opposition to its very meaning?Not if it's defined properly.The act of defining is to say something is this, as opposed to that: a dog is an animal; it is not a plant. However, in defining that which, by definition, is not definable, we are creating a paradox.No, because It isn't true that infinity is "not definable by definition".In- means no; -finity means end.De- means to set; -fine means an end.You are contradicting yourself.What is it about the concept of infinity that causes people to want to think it is so mystical and esoteric.Mathematically, the idea of a repeating series is about as simple a mathematical concept as can be, yet people try to make 1/3 into some kind of inconceivable, transcendent, impossible thing, I just don't understand it.A definition that says it doesn't end is an end, unlimited means limited, unbounded means bounded, someone said infinity and I hear the sound of one hand clapping....really?"It is one of the commonest of mistakes to consider that the limit of our power of perception is also the limit of all there is to perceive." " C. W. Leadbeater
 Posts: 3,375 Add as FriendChallenge to a DebateSend a Message 5/25/2014 8:36:26 AMPosted: 4 years agoAt 5/25/2014 3:11:25 AM, Cody_Franklin wrote:At 5/24/2014 11:14:58 PM, s-anthony wrote:At 5/24/2014 9:18:24 PM, Cody_Franklin wrote:Well, that's kind of the thing about infinity. It's bounded by a definition, but it's not finite. In mathematics, there is a sharp distinction drawn between something's being bounded and its being finite. Consider: you could take some arbitrary subset of the real numbers--for convenience, we will play it safe and use the closed interval [0, 1]. Very clear boundaries. However, if you were asked to write, one by one, each member of the set of real numbers within this interval, you'd never make it further than zero: the interval is continuous, which means the members of the corresponding set are uncountable. In other words, you could write any specific member of the set, e.g., 0.0063784267846, but you can't write the next member of the set, because there are infinitely many down to infinitesimal size. So, you've got boundedness, but you're also stuck with infinity. This is why mathematical definitions for weird things often take the form "X is the thing such that..." It's s little kooky, but it checks out when you actually do the footwork.Infinity's boundaries are you, in other words, your inability to demonstrate this mathematical claim.As has been mentioned, we are dealing here with two kinds of boundaries. I am speaking, not of conceptual boundaries, but of boundaries in the formal sense.All boundaries are conceptual boundaries. You can't conceive something and, then, say it's not conceptual.You must understand, infinity is not monolithic: there are several different sizes of infinity, some with boundaries, some without.Infinity's only size is the size we give it. It is not any larger or any smaller than our imaginations.Some are countable, others are not. The integers are infinite, unbounded, and countable; the real numbers are infinite, unbounded, but uncountable. The subset of real numbers between zero and one is bounded by definition--zero on one side, one on the other--but also uncountable.You can't have the capacity, for doing something, and, then, say you're not able to do it.It is for this same reason that the easy way of conceptualizing infinity--beginning at one and perpetually increasing--is as easy to understand as it is inaccurate. People like to imagine infinity temporally, but all of the members of the set are always already there. We simply cannot make each member explicit, requiring instead some kind of shorthand (e.g., aleph null, 0.999 repeating).Since we are temporal beings, temporally is the only way we can imagine infinity, or anything else, for that matter.The members that are there are the members that are explicit, to us.Anyway, I just wanted to make it clear that the boundaries of which I speak are of a technical nature, not a conceptual or psychological one.All boundaries are conceptual and psychological.
 Posts: 3,375 Add as FriendChallenge to a DebateSend a Message 5/25/2014 9:58:28 AMPosted: 4 years agoAt 5/25/2014 6:08:09 AM, Sidewalker wrote:At 5/24/2014 11:06:44 PM, s-anthony wrote:At 5/24/2014 7:44:12 PM, Sidewalker wrote:At 5/24/2014 4:03:05 PM, s-anthony wrote:The word infinity basically means without end, or unlimited. To define something means to set a limit, bound, or end.But as you said, it is defined as without end or unlimited, how is that setting a limit.?Anytime you say something is this but not that, you are setting a limit.Nonsense, if you say something is this (unlimited), but not that (limited), you are not saying it is limited. On the contrary, you are saying it is not limited.Exactly. If I say something is unlimited, I am not saying it is limited.In defining infinity, aren't our actions in opposition to its very meaning?Not if it's defined properly.The act of defining is to say something is this, as opposed to that: a dog is an animal; it is not a plant. However, in defining that which, by definition, is not definable, we are creating a paradox.No, because It isn't true that infinity is "not definable by definition".In- means no; -finity means end.De- means to set; -fine means an end.You are contradicting yourself.My point exactly, and so is anyone else who says infinity is indefinite and, then, sets out to define it.What is it about the concept of infinity that causes people to want to think it is so mystical and esoteric.I don't know.Mathematically, the idea of a repeating series is about as simple a mathematical concept as can be, yet people try to make 1/3 into some kind of inconceivable, transcendent, impossible thing, I just don't understand it.Neither can I.A definition that says it doesn't end is an end, unlimited means limited, unbounded means bounded, someone said infinity and I hear the sound of one hand clapping....really?
 Posts: 13,776 Add as FriendChallenge to a DebateSend a Message 5/25/2014 11:02:06 AMPosted: 4 years agoBut infinity does have bounds, for if it didn't, it would be nothingness. In defining infinity, we are not defining it to have bounds as a concept, we are placing bounds on what it is not. It is "bounded" in the sense that it can't have bounds. If infinity actually had no bounds in the sense you mean, it would be a meta-paradox. Why? Because if it didn't have bounds, it would have them, for it could not prevent itself from having them. But then it wouldn't be a paradox because nothingness cannot be anything, yet it would be a paradox becuase it can't "not" be anything either.
 Posts: 13,776 Add as FriendChallenge to a DebateSend a Message 5/25/2014 11:14:57 AMPosted: 4 years agoEssentially, there is nothing that has "no bounds", because then it would have them.
 Posts: 9,513 Add as FriendChallenge to a DebateSend a Message 5/25/2014 1:05:35 PMPosted: 4 years agoAt 5/25/2014 8:36:26 AM, s-anthony wrote:At 5/25/2014 3:11:25 AM, Cody_Franklin wrote:As has been mentioned, we are dealing here with two kinds of boundaries. I am speaking, not of conceptual boundaries, but of boundaries in the formal sense.All boundaries are conceptual boundaries. You can't conceive something and, then, say it's not conceptual.Then we mean different things by conceptual.You must understand, infinity is not monolithic: there are several different sizes of infinity, some with boundaries, some without.Infinity's only size is the size we give it. It is not any larger or any smaller than our imaginations.No, it isn't. Infinity has demonstrably different sizes, and some are larger than others. The real number line and the integers are both infinite; the integers are a subset of the real numbers; the cardinality of the set of integers is smaller than the cardinality of the set of real numbers, which is to say that the infinity of real numbers is larger. There is even a largest infinity, which is the set containing as members all the cardinalities of infinity.Some are countable, others are not. The integers are infinite, unbounded, and countable; the real numbers are infinite, unbounded, but uncountable. The subset of real numbers between zero and one is bounded by definition--zero on one side, one on the other--but also uncountable.You can't have the capacity, for doing something, and, then, say you're not able to do it.What, counting? In the case of uncountable infinities, I said explicitly that you can only enumerate individual members of the set. I challenge you to give me the positive real number immediately adjacent to zero.It is for this same reason that the easy way of conceptualizing infinity--beginning at one and perpetually increasing--is as easy to understand as it is inaccurate. People like to imagine infinity temporally, but all of the members of the set are always already there. We simply cannot make each member explicit, requiring instead some kind of shorthand (e.g., aleph null, 0.999 repeating).Since we are temporal beings, temporally is the only way we can imagine infinity, or anything else, for that matter.The act of thinking of infinity is temporal. It takes place on time. Infinity is not itself temporal--the mathematical sense of infinity is not "counting up forever". If you have even the most rudimentary understanding of set theory, you'd understand that members aren't being perpetually added in: they're always already there, even if we can't think or write them all. It isn't contingent on or cognitive access to it.The members that are there are the members that are explicit, to us.Anyway, I just wanted to make it clear that the boundaries of which I speak are of a technical nature, not a conceptual or psychological one.All boundaries are conceptual and psychological.Boundaries are a concept, but not always conceptual in the sense I mean it. This is why I draw the line between threes and mathematical boundaries. You're welcome to call them whatever you want, as long as you're clear about what sits behind the sign.
 Posts: 3,375 Add as FriendChallenge to a DebateSend a Message 5/25/2014 1:59:42 PMPosted: 4 years agoAt 5/25/2014 1:05:35 PM, Cody_Franklin wrote:At 5/25/2014 8:36:26 AM, s-anthony wrote:At 5/25/2014 3:11:25 AM, Cody_Franklin wrote:As has been mentioned, we are dealing here with two kinds of boundaries. I am speaking, not of conceptual boundaries, but of boundaries in the formal sense.All boundaries are conceptual boundaries. You can't conceive something and, then, say it's not conceptual.Then we mean different things by conceptual.You must understand, infinity is not monolithic: there are several different sizes of infinity, some with boundaries, some without.Infinity's only size is the size we give it. It is not any larger or any smaller than our imaginations.No, it isn't. Infinity has demonstrably different sizes, and some are larger than others. The real number line and the integers are both infinite; the integers are a subset of the real numbers; the cardinality of the set of integers is smaller than the cardinality of the set of real numbers, which is to say that the infinity of real numbers is larger. There is even a largest infinity, which is the set containing as members all the cardinalities of infinity.Demonstrate it.Some are countable, others are not. The integers are infinite, unbounded, and countable; the real numbers are infinite, unbounded, but uncountable. The subset of real numbers between zero and one is bounded by definition--zero on one side, one on the other--but also uncountable.You can't have the capacity, for doing something, and, then, say you're not able to do it.What, counting? In the case of uncountable infinities, I said explicitly that you can only enumerate individual members of the set. I challenge you to give me the positive real number immediately adjacent to zero.It is for this same reason that the easy way of conceptualizing infinity--beginning at one and perpetually increasing--is as easy to understand as it is inaccurate. People like to imagine infinity temporally, but all of the members of the set are always already there. We simply cannot make each member explicit, requiring instead some kind of shorthand (e.g., aleph null, 0.999 repeating).Since we are temporal beings, temporally is the only way we can imagine infinity, or anything else, for that matter.The act of thinking of infinity is temporal. It takes place on time. Infinity is not itself temporal--the mathematical sense of infinity is not "counting up forever". If you have even the most rudimentary understanding of set theory, you'd understand that members aren't being perpetually added in: they're always already there, even if we can't think or write them all. It isn't contingent on or cognitive access to it.You know they're always there, even if you haven't the cognitive capacity to access all of them? In other words, you know, that which you don't know. Sorry, but that's called a contradiction.The members that are there are the members that are explicit, to us.Anyway, I just wanted to make it clear that the boundaries of which I speak are of a technical nature, not a conceptual or psychological one.All boundaries are conceptual and psychological.Boundaries are a concept, but not always conceptual in the sense I mean it. This is why I draw the line between threes and mathematical boundaries. You're welcome to call them whatever you want, as long as you're clear about what sits behind the sign.
 Posts: 3,375 Add as FriendChallenge to a DebateSend a Message 5/25/2014 2:09:57 PMPosted: 4 years agoAt 5/25/2014 11:02:06 AM, dylancatlow wrote:But infinity does have bounds, for if it didn't, it would be nothingness. In defining infinity, we are not defining it to have bounds as a concept, we are placing bounds on what it is not. It is "bounded" in the sense that it can't have bounds. If infinity actually had no bounds in the sense you mean, it would be a meta-paradox. Why? Because if it didn't have bounds, it would have them, for it could not prevent itself from having them. But then it wouldn't be a paradox because nothingness cannot be anything, yet it would be a paradox becuase it can't "not" be anything either.If we weren't able to conceive it, it would have no meaning, to us.Even nothingness has bounds, in that nothingness is not something.