• Metaphysician Undercover
    8.6k
    Where can I actualy read anyone explaining the concept of numbers that way?TonesInDeepFreeze

    Didn't you just read it?
  • synthesis
    915
    With a closed mind, you will always be wasting your time.
  • jgill
    1.2k
    With a closed mind, you will always be wasting your timesynthesis

    Good troll thread, eh doctor? :cool:
  • TonesInDeepFreeze
    263
    Where can I actualy read anyone explaining the concept of numbers that way?
    — TonesInDeepFreeze

    Didn't you just read it?
    Metaphysician Undercover

    The post to which you responded didn't say it. So would you please link to a post or reference anything on the Internet or anywhere else?
  • fishfry
    2.2k
    The notion of an actual infinite makes zero sense if, as per my assumption, actual means what it seems to mean to wit, completed in one sense or another for it flies against the definition of infinity as being necessarily that which can't be completed.

    Maths, set theoretical infinities, kind courtesy of Georg Cantor, is an altogther different story as maths is essentially an axiomatic system, anything goes so long as you don't contradict yourself within one.
    TheMadFool

    I am in agreement with this. Whatever it is that physicists mean by infinity, they surely don't mean mathematical infinity. The set of positive integers is infinite by construction in Peano arithmetic, or by the axiom of infinity in set theory. But I do not believe such an infinite set can be instantiated in the real world.

    I have another idle thought ... that the next revolution in physics will be the discovery of the actual infinite in the real world. By analogy, non-Euclidean geometry was thought to be a mathematical parlor trick of no use to physicists. Then Einstein came along and non-Euclidean geometry became real to the physicists.

    Physically realized actual infinity has the same status in physics today as non-Euclidean geometry had in physics in the 1840s. The future genius to make this next breakthrough hasn't been born yet. Perhaps.
  • Metaphysician Undercover
    8.6k

    What do you need a link for? If you don't understand what I said, just show me what you do not understand, and I'll explain. If you understand but disagree, just tell me what you disagree with, and maybe we can hash it out.
  • TonesInDeepFreeze
    263
    There is a fundamental problem with the concept of numbers. The numeral "1" represents a basic unity. an individual. The "2" represents two of those individuals together, and "3" represents three, etc. But then we want "2" and "3", each to represent a distinct unity as well. So we have to allow that "1" represents a different type of unity than "2" does, or else we'd have the contradiction of "2" representing both one and also two of the same type of unity.Metaphysician Undercover

    I thought you meant that there is a fundamental problem with:

    "The numeral "1" represents a basic unity. an individual. The "2" represents two of those individuals together, and "3" represents three, etc. But then we want "2" and "3", each to represent a distinct unity as well."

    And that your supposed solution to the supposed problem is:

    "[...] we have to allow that "1" represents a different type of unity than "2" does [...]"

    So I was wondering who you have in mind as having said or written anywhere that:

    "The numeral "1" represents a basic unity. an individual. The "2" represents two of those individuals together, and "3" represents three, etc. But then we want "2" and "3", each to represent a distinct unity as well."

    Or are you saying that you yourself holds that:

    "The numeral "1" represents a basic unity. an individual. The "2" represents two of those individuals together, and "3" represents three, etc. But then we want "2" and "3", each to represent a distinct unity as well."?

    Or perhaps you would make clear which parts of your passage are ones you are critiquing and which parts are ones you are claiming.
  • synthesis
    915
    Is that the big building where the big kids go to school? :)

    My friend, just because it doesn't happen to make sense to you doesn't mean that you should not consider it.

    I would bet that if we compared credentials (and experience), you just might end up on the short end. Fortunately, none of that matters in the least as even the least educated among us have attained great realization.
  • synthesis
    915
    I have another idle thought ... that the next revolution in physics will be the discovery of the actual infinite in the real world. By analogy, non-Euclidean geometry was thought to be a mathematical parlor trick of no use to physicists. Then Einstein came along and non-Euclidean geometry became real to the physicists.

    Physically realized actual infinity has the same status in physics today as non-Euclidean geometry had in physics in the 1840s. The future genius to make this next breakthrough hasn't been born yet. Perhaps.
    fishfry

    What's interesting about this is that whereas it is quite easy to see how mathematics (at its extremes) makes no sense, everything else knowable is EXACTLY the same. It's just more difficult to see.
  • fishfry
    2.2k
    What's interesting about this is that whereas it is quite easy to see how mathematics (at its extremes) makes no sensesynthesis

    I totally agree. Bertrand Russell nailed it:

    Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true..

    Tru dat.
  • Metaphysician Undercover
    8.6k
    I thought you meant that there is a fundamental problem with:

    "The numeral "1" represents a basic unity. an individual. The "2" represents two of those individuals together, and "3" represents three, etc. But then we want "2" and "3", each to represent a distinct unity as well."

    And that your supposed solution to the supposed problem is:

    "[...] we have to allow that "1" represents a different type of unity than "2" does [...]"
    TonesInDeepFreeze

    There is no proposed solution. The issue was stated as a fundamental problem with numbers, without a solution.

    Or perhaps you would make clear which parts of your passage are ones you are critiquing and which parts are ones you are claiming.TonesInDeepFreeze

    I am not critiquing anything, the whole thing is what I am claiming. I am claiming that there is a fundamental problem with numbers. If "1", "2", "3", etc. , are used to represent unities, then "2" and "3" must represent a different type of unity from "1", for the reason I explained.

    Now here is a proposal for a solution. If "2" and "3" are said to represent numbers, then maybe we ought to say that "1" represents something other than a number.
  • TonesInDeepFreeze
    263
    I am claiming that there is a fundamental problem with numbers. If "1", "2", "3", etc. , are used to represent unities,Metaphysician Undercover

    Yes, as I thought, you find that there is a problem with the notion (whatever it means) that 'the numeral "1" represents a basic unity. an individual. The "2" represents two of those individuals together, and "3" represents three, etc".

    But (aside from even trying to parse the broken phrases) I don't know who says anything along the lines of 'the numeral "1" represents a basic unity. an individual. The "2" represents two of those individuals together, and "3" represents three, etc". So I don't see why you think it is a problem that needs to be addressed.
  • Metaphysician Undercover
    8.6k
    Yes, as I thought, you find that there is a problem with the notion (whatever it means) that 'the numeral "1" represents a basic unity. an individual. The "2" represents two of those individuals together, and "3" represents three, etc".TonesInDeepFreeze

    No, I see no problem with that in itself. The problem is when we want to say that, and also that "2" and "3" represent a type of unity.

    But (aside from even trying to parse the broken phrases) I don't know who says anything along the lines of 'the numeral "1" represents a basic unity. an individual. The "2" represents two of those individuals together, and "3" represents three, etc". So I don't see why you think it is a problem that needs to be addressed.TonesInDeepFreeze

    I don't know about you, but I always use "1", "2", and "3" in that way. If you don't ever talk about 1 chair, 2 or 3, or any number of other things like that, then I guess you don't use them the same way. But if someone asks you how old you are, do you answer with a number?
  • TonesInDeepFreeze
    263
    I see no problem with that in itself. The problem is when we want to say that, and also that "2" and "3" represent a type of unity.Metaphysician Undercover

    I understood that; I thought you meant that you do want to take '2' and '3' as representing a type of unity, while you think that that is contradicted by 'the numeral "1" represents a basic unity. an individual. The "2" represents two of those individuals together, and "3" represents three, etc" so that it needs correction .

    Am I not correct that that is your view?

    More basically, I don't know why one would fret over any of this, since I don't know anyone who claims "the numeral "1" represents a basic unity. an individual. The "2" represents two of those individuals together, and "3" represents three, etc" or anyone who claims "'2" and "3" represent some kind of unity". Moreover, aside from the ill-formed English, I don't know that you're not using such terms as 'unity' and 'represents' other than in a personal idiosyncratic way. Also, I would wonder what are your rigorous mathematical or philosophical definitions of 'basic unity', 'individuals together'. In sum, I can't make sense of what you're trying to say.

    Suggestion: You could reference some actual piece of mathematical or philosophical writing that you disagree with and show how you think you can correct it.
  • Metaphysician Undercover
    8.6k
    I understood that; I thought you meant that you do want to take '2' and '3' as representing a type of unity, while you think that that is contradicted by 'the numeral "1" represents a basic unity. an individual. The "2" represents two of those individuals together, and "3" represents three, etc" so that it needs correction .

    Am I not correct that that is your view?
    TonesInDeepFreeze

    That's pretty close, except I do not necessarily want to take "2" and "3" as representing unities, that's why I said "if" we want to. I see the numeral as representing a group with a specific number of things in that group, but the unity of that group is questionable.

    .
    More basically, I don't know why one would fret over any of this, since I don't know anyone who claims "the numeral "1" represents a basic unity. an individual.TonesInDeepFreeze

    I find that very strange I hear them used that way all the time. I suppose I didn't explain very well. Isn't this how we count? One represents one unit, two represents two of those, etc.. If you're put off by the terminology, "unity", "represent", etc., that's understandable, but why don't you just relax and enjoy the simplicity of the terms. It seems to me like there's always some people who get really flustered, and then have difficulty understanding simple terms, as soon as you mention any sort of problems within the systems of mathematics.

    In sum, I can't make sense of what you're trying to say.TonesInDeepFreeze

    Yes, I can see that. You haven't really ever thought about such fundamental issues as how we use numerals, and you don't really understand why anyone else would. Why did you engage me, if what I was saying appeared so foreign to you?

    Suggestion: You could reference some actual piece of mathematical or philosophical writing that you disagree with and show how you think you can correct it.TonesInDeepFreeze

    I've addressed particular pieces of mathematical writing which I disagree with before, in the past, but I cannot think of any way to correct these issues. So people have told me that if I don't have a solution, then don't point out a problem. But I think that's nonsense. I think we have to find the problems, and get a good clear understanding of why and how they are problems, before we can move toward an adequate solution. Solutions don't come easily, they require a thorough understanding of the problems.
  • TonesInDeepFreeze
    263
    So your argument outline is: If someone wants P, he is reminded that P contradicts Q, which he might also want, so we think about a way to adjust so that there is not a contradiction.

    But neither P nor Q are stated coherently by you. And there's no reason to think anyone wants P or Q anyway.

    More basically, I don't know why one would fret over any of this, since I don't know anyone who claims "the numeral "1" represents a basic unity. an individual.
    — TonesInDeepFreeze

    I find that very strange I hear them used that way all the time.
    Metaphysician Undercover

    You cut off the rest of my quote of you.

    "the numeral "1" represents a basic unity. an individual. The "2" represents two of those individuals together, and "3" represents three, etc"TonesInDeepFreeze

    Of course the notion of 'one' is related to that of a unity. But even aside from parsing, I don't know who in particular you think holds that "The "2" represents two of those individuals together, and "3" represents three, etc". It would help if you would cite at least one particular written passage by someone that you think is properly rendered as "the numeral "1" represents a basic unity. an individual. The "2" represents two of those individuals together, and "3" represents three, etc" and "'2" and "3" represent some kind of unity".

    You haven't really ever thought about such fundamental issues as how we use numerals, and you don't really understand why anyone else would.Metaphysician Undercover

    You don't know that I haven't thought about numerals. Actually in another thread, in posts directly with you, I posted a fair amount on the subject. And, most pointedly, I have never written that I don't understand why anyone would be interested in the subject.
  • Metaphysician Undercover
    8.6k
    But neither P nor Q are stated coherently by you. And there's no reason to think anyone wants P or Q anyway.TonesInDeepFreeze

    Then I conclude that what needs to be discussed is clarification of P and Q.

    Of course the notion of 'one' is related to that of a unity. But even aside from parsing, I don't know who in particular you think holds that "The "2" represents two of those individuals together, and "3" represents three, etc". It would help if you would cite at least one particular written passage by someone that you think is properly rendered as "the numeral "1" represents a basic unity. an individual. The "2" represents two of those individuals together, and "3" represents three, etc" and "'2" and "3" represent some kind of unity".TonesInDeepFreeze

    Whenever we count something it is like this. Count the books on the shelf for example. "Book" signifies the type of unity being counted, "1" signifies that a unity called "a book" has been identified, and a first one has been counted , "2" signifies two of these units, etc..

    t would help if you would cite at least one particular written passage by someone that you think is properly rendered as "the numeral "1" represents a basic unity. an individual.TonesInDeepFreeze

    I assume you know how to use Google or some other search facility. You could simply search this if you need such a confirmation, instead of asking me to do your research for you. Here is the first paragraph from the Wikipedia entry on "1":

    1 (one, also called unit, and unity) is a number and a numerical digit used to represent that number in numerals. It represents a single entity, the unit of counting or measurement. For example, a line segment of unit length is a line segment of length 1. In conventions of sign where zero is considered neither positive nor negative, 1 is the first and smallest positive integer.[1] It is also sometimes considered the first of the infinite sequence of natural numbers, followed by 2, although by other definitions 1 is the second natural number, following 0. — Wikipedia

    Also, if you actually are interested (which you don't seem to be by your half-hearted replies, and refusal to do any research yourself, and near complete denial of the relation between one and unity), you could look into number theory, and the reason why 1 is generally determined as not a prime number. Here's the first entry I get when I Google that question, is 1 a prime number: https://blogs.scientificamerican.com/roots-of-unity/why-isnt-1-a-prime-number/
    Here's a passage from that article:
    In the very most basic example, we can ask whether the number -2 is prime. The question may seem nonsensical, but it can motivate us to put into words the unique role of 1 in the whole numbers. The most unusual aspect of 1 in the whole numbers is that it has a multiplicative inverse that is also an integer. (A multiplicative inverse of the number x is a number that when multiplied by x gives 1. The number 2 has a multiplicative inverse in the set of the rational or real numbers, 1/2: 1/2×2=1, but 1/2 is not an integer.) The number 1 happens to be its own multiplicative inverse. No other positive integer has a multiplicative inverse within the set of integers.* The property of having a multiplicative inverse is called being a unit. The number -1 is also a unit within the set of integers: again, it is its own multiplicative inverse. We don’t consider units to be either prime or composite because you can multiply them by certain other units without changing much. We can then think of the number -2 as not so different from 2; from the point of view of multiplication, -2 is just 2 times a unit. If 2 is prime, -2 should be as well.

    *This sentence was edited after publication to clarify that no other positive integer has a multiplicative inverse that is also an integer.
    — * reference above
  • TonesInDeepFreeze
    263
    near complete denial of the relation between one and unityMetaphysician Undercover

    I had said in the very post to which you now replied, "Of course the notion of 'one' is related to that of a unity." So I couldn't possibly be in denial about it. You are very confused.

    Then I conclude that what needs to be discussed is clarification of P and Q.Metaphysician Undercover

    Then you need to clarify them, since you are the one who mentioned them, and you have not shown what anyone else said that is properly rendered as you did. But now you do clarify:

    Count the books on the shelf for example. "Book" signifies the type of unity being counted, "1" signifies that a unity called "a book" has been identified, and a first one has been counted , "2" signifies two of these units, etc..Metaphysician Undercover

    That might be sharpened a little, but I guess it's okay on its own. However, "The "2" represents two of those individuals together, and "3" represents three, etc" is garbled, so I asked for an example of anything said by anyone that you think is properly rendered that way. First you said that I had just read it. But, as far as I can tell, it's not in the posts of the poster you quoted. Then you said that it's actually your own notion. Then you came back around to telling me that I can find it on the Internet somewhere.

    I assume you know how to use Google or some other search facility. You could simply search this if you need such a confirmation, instead of asking me to do your research for you.Metaphysician Undercover

    I didn't ask you to research for me. I just wanted to know of a particular example that YOU consider to be properly rendered by "The "2" represents two of those individuals together, and "3" represents three, etc" and "'2" and "3" represent some kind of unity". I can find all kinds of things about units and unity on the Internet. But that wouldn't tell me what in particular YOU have in mind as being properly rendered by "The "2" represents two of those individuals together, and "3" represents three, etc" and "'2" and "3" represent some kind of unity".

    Here's the first entry I get when I Google that question, is 1 a prime numberMetaphysician Undercover

    I said in the very post to which you now replied:

    Of course the notion of 'one' is related to that of a unity. But even aside from parsing, I don't know who in particular you think holds that "The "2" represents two of those individuals together, and "3" represents three, etc". It would help if you would cite at least one particular written passage by someone that you think is properly rendered as "the numeral "1" represents a basic unity. an individual. The "2" represents two of those individuals together, and "3" represents three, etc" and "'2" and "3" represent some kind of unity".TonesInDeepFreeze

    So I made clear I wasn't asking about 1 but about the part where you write, "The "2" represents two of those individuals together, and "3" represents three, etc" and "'2" and "3" represent some kind of unity".

    So your example about 1 not being a prime number does not address this.

    Anyway, after first telling me that I had already read someone who said this, then saying instead that it was your own notion, then saying it is on the Internet (but citing an example not addressing it), we did get something of a better statement by you as I mentioned earlier in this post. Such long and unnecessary detours by you. As well as you flatly claimed the opposite about me when you said that I'm in "near denial" about the relation between the notions of one and unity when I had actually explicitly stated that there is a relation.
  • TonesInDeepFreeze
    263
    There is a fundamental problem with the concept of numbers. The numeral "1" represents a basic unity. an individual. The "2" represents two of those individuals together, and "3" represents three, etc. But then we want "2" and "3", each to represent a distinct unity as well. So we have to allow that "1" represents a different type of unity than "2" does, or else we'd have the contradiction of "2" representing both one and also two of the same type of unity.Metaphysician Undercover

    Now that you've somewhat clarified that, here's the best I can make of it (I don't claim to represent what you have in mind, but this is the best I can make sense of it):

    1 is the count at the first member of the set, a particular unity (whatever it is). 2 is the count at the second member of the set. Etc. And '1' and '2' name different individual numbers. And 1 is the count of the members of the set with one unit. And 2 is the count of the members of a unity that is a set with two members. And a set with one member is a different kind of unity from a set with two members.

    I think that's all okay. But then you conclude:

    "we'd have the contradiction of "2" representing both one and also two of the same type of unity."

    '2' denotes the number 2. The number 2 is the count of a set with two members. And a set of two members is itself a unity as a set. But '2' does not denote a unity; it does not denote the set that it counts. It denotes the COUNT of a set that is itself a unity. When we say that a set is a unity, we mean that it is one set, while we recognize that the number of members of the set may be greater than one.

    {'War And Peace' 'Portnoy's Complaint'} is one set, which is a unity. But the count of {'War And Peace' 'Portnoy's Complaint'} is 2.

    I don't see a contradiction.
  • Proximate1
    24
    Semantics- the foundation on which we stand, The term infinite has various meanings. The original old French term means simply 'not finite' or in simple terms undefined, There will always be that which lies outside of our ability to ascertain or even comprehend. We can experience such a paltry slice of the universe that it is simply hubris that one attempts to make grand declarations of reality must be. Who cares what physicists believe- we are children in a sandbox.
  • Present awareness
    78
    The spaceship can keep going, because the universe is expanding faster than the speed of light. The spaceship won't catch up with the expansion of the universe.Down The Rabbit Hole

    The universe is not expanding, objects in the universe are simply moving away from each other and the space within which they are moving, in is infinite.
  • Metaphysician Undercover
    8.6k
    1 is the count at the first member of the set, a particular unity (whatever it is). 2 is the count at the second member of the set. Etc. And '1' and '2' name different individual numbers. And 1 is the count of the members of the set with one unit. And 2 is the count of the members of a unity that is a set with two members. And a set with one member is a different kind of unity from a set with two members.TonesInDeepFreeze

    I do not assume any sets, or numbers, to begin with. Numerals are used fundamentally for counting things, objects like chairs, cars, etc.. There is no such thing as "the count", without things that are counted. So in that situation "1" signifies the existence of one object counted, "2" signifies two, etc..

    '2' denotes the number 2. The number 2 is the count of a set with two members. And a set of two members is itself a unity as a set. But '2' does not denote a unity; it does not denote the set that it counts. It denotes the COUNT of a set that is itself a unity. When we say that a set is a unity, we mean that it is one set, while we recognize that the number of members of the set may be greater than one.TonesInDeepFreeze

    The inconsistency arises now, if we say that numerals signify numbers rather than the things being counted. Let's call the number, "the count" which seems acceptable to both of us. Let me look at the difference between a count of one, and a count of two.

    To have a count of one, there must be an object which is counted. In order for the count to be a valid count, there must be something which is counted. This is not the number 1 which is counted. It is something independent, an object like a chair, or a car, one of the things which is going to be counted. What validates the count of one, is an independent object, what I call a fundamental unity, which is counted.

    Now let's consider a count of two. The count of two is justified by the existence of two such objects. But you want to say that "the count" itself is an object, the number two. So we have two distinct types of objects referred to with "a count of two". We have the two material objects, which have been counted, justifying the count of two as a valid count, and also we have the count itself, as an abstract object, which is called the number.

    So, if we assume the reality of abstract objects, numbers, then when we use "2", there is always, if it is a valid use of "2", two distinct types of objects referred to. There is a number, 2, which as a unified object, as "the count", and there is also two of another type of unity, being the things counted, in order that the count is a true and valid count. In the case of "1" however, we can say that the number is the fundamental unity, the thing being counted, and also the abstract unity, represented as "the count", because they are each one simple unity. Therefore we would have consistency saying that the number 1 is both the thing being counted, making a valid count, and an abstract object itself.

    To summarize now. Let's say that "1" refers to the number 1, which represents the count, and is also the thing counted, abstract numbers. We cannot use "2" in the same way. "2" might refer to a number, which represents "the count", as an object, or it might refer to the two distinct objects which are counted. It cannot refer to both, due to the inconsistency of one being one object, and the other two. My contention is, that if we use "2" to refer to "the count" itself, as the number 2, an abstract object, and this is what you are doing in your post, then the count itself is rendered false or invalid, because "2" cannot refer to both one object and two objects at the same time without contradiction.
  • Down The Rabbit Hole
    99


    The universe is not expanding, objects in the universe are simply moving away from each other and the space within which they are moving, in is infinite.Present awareness

    So there wasn't a big bang that started an expanding universe?
  • TonesInDeepFreeze
    263
    Let's say that "1" refers to the number 1, which represents the count, and is also the thing countedMetaphysician Undercover

    No, let's not say that 1 is the thing counted.

    The things that are counted are, in this case, the books.

    '1' is a numeral.

    1 is the number denoted by the numeral '1'.

    1 is the count of the books.

    1 is not a book.
  • Metaphysician Undercover
    8.6k

    Right, but do you agree that it is necessary that there is a thing counted, a book in this case? So as much as the numeral "1" "denotes" what you call the number 1, which is a property of "the count", it must also refer to the one book, or else the count is not a true count. For "the count" to qualify as a true count, there must be something which is counted. If "1" does not refer to the book, as well as what you call the number, then there is nothing being counted, and therefore no count, because if there is nothing being counted, this does not qualify as a count.

    Therefore, we cannot dispense with the fact that "1" must refer to the object being counted, a book, as well as what you call the number 1, or else we have annihilated "the count" as false because we cannot have a count with nothing being counted. But we cannot annihilate the count, because that is what gives logical coherency to the numbers.

    If this is not clear to you, imagine that you go to count the books, and you count the same book over and over again, 1, 2, 3, 4, etc., such that you could have an infinite number of books, by counting the same book over and over again. That is not a valid or true count. To have a true count, "1" must refer to the first book, "2" refers to the first and second together, "3" refers to those two with a third, etc.. If we remove the need to have distinct objects being counted, then the count is not a valid or true count.
  • Primordial Light
    1
    The Infinite is a personality, who is beyond time and mathematics -
    The Creator of the Universe, who is revealed only to the pure in heart.
  • frank
    7k
    Since Aristotle, the philosophers say that there is only the potentially infinite.spirit-salamander

    I think this just implies that if Greene's spaceship was pimped out with an odometer, we wouldn't expect it to ever read "infinite.". It's always going to show a finite number no matter how far we go.

    I don't think Greene would deny that. I don't think it's relevant to his stance.

    BTW, did you see the Space Time episode where he explained why they think the universe is flat?
  • TonesInDeepFreeze
    263
    In ordinary English, we use these senses:

    (1) A count is an instance of counting. "Do a count of the books."

    (2) A count is the result of counting. "The count of the books is five."

    A number (we're talking about natural numbers in this context) is a count in sense (2). That doesn't preclude that a number is a mathematical object.

    do you agree that it is necessary that there is a thing countedMetaphysician Undercover

    To have a count (in sense (1)), you need something to count. (Except in the base case, there is the empty count.)

    If "1" does not refer to the book, as well as what you call the number, then there is nothing being countedMetaphysician Undercover

    Numbers also have other aspects than being counts (or 'results of counts' depending on how exactly we might define 'count').

    we cannot dispense with the fact that "1" must refer to the object being counted, a bookMetaphysician Undercover

    We better dispense with that notion. It's nuts. A number is not a book.

    To have a true count, "1" must refer to the first book, "2" refers to the first and second togetherMetaphysician Undercover

    '1' does not denote a book. And 'together' is not defined by you.

    The most common mathematical understanding of counting is bijection.

    For a set with only one book - 'War And Peace' - in the set, the count is the greatest number in the range of the bijection between the set {'War And Peace'} and the set {1}, and that greatest number is 1.

    The bijection is {<'War And Peace' 1>}.

    For a set with only two books - 'War And Peace' and 'Portnoy's Complaint' - in the set, the count is the greatest number in the range of the bijection between the set {'War And Peace' and 'Portnoy's Complaint'} and the set {1 2}, and that greatest number is 2.

    The bijection is {<'War And Peace' 1> <'Portnoy's Complaint' 2>}.

    So the numeral does not denote a book, but rather it denotes the number that is paired to the book in the bijection (or, in everyday terms, in the pairing off procedure we call 'counting').

    We pair 'War And Peace' to 1, then we pair 'Portnoy's Complaint' to 2. That's counting.

    We don't say "''1' denotes 'War And Peace' and '2' denotes 'War And Peace' together with 'Portnoy's Complaint'". That's crazy.
  • Present awareness
    78
    So there wasn't a big bang that started an expanding universe?Down The Rabbit Hole

    At the moment of conception, there is a rapid expansion of cells, like a Big Bang, only on a biological scale if you will. Looking at our observable universe, we see what conception looks like on a cosmic scale. Since space is infinite, there may be an infinite number of Big Bangs, but we’ll never observe them from earth because of the enormous distances involved. The light from a universe 100 billion light years away, won’t arrive on earth for another 86 billion years.
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