Page 5 of 8 FirstFirst ... 34567 ... LastLast
Results 41 to 50 of 74

Thread: The Concept of the Infinite

  1. #41
    tWebber mattdamore's Avatar
    Join Date
    Jan 2017
    Location
    Houston, TX
    Faith
    Christian
    Gender
    Male
    Posts
    40
    Amen (Given)
    0
    Amen (Received)
    4
    Quote Originally Posted by Boxing Pythagoras View Post
    No worries! Happens to the best of us, from time to time.
    Hello! It's been a long time! I hope you're doing well. I haven't forgotten about this conversation, thank goodness. Dr. Craig's class on God and Abstract objects starts Monday, and I'm excited to ask him about hyperreal numbers and infinity. If you'd like, perhaps you can type your question here, and I could read it to him in class. This is because I don't want to misrepresent you, ha. If I remember correctly, hyperreal numbers enable me to perform subtraction/division with transfinite numbers without paradox, and therefore serves as a sort of undercutting defeater to the thesis that an actual infinite is metaphysically impossible due to the paradoxes its instantiation in reality would lead to. Please let me know of any misrepresentation. Thanks!

  2. #42
    tWebber shunyadragon's Avatar
    Join Date
    Jan 2014
    Location
    Hillsborough, NC
    Faith
    Agnostic
    Gender
    Male
    Posts
    12,820
    Amen (Given)
    1251
    Amen (Received)
    870
    Quote Originally Posted by mattdamore View Post
    Hello! It's been a long time! I hope you're doing well. I haven't forgotten about this conversation, thank goodness. Dr. Craig's class on God and Abstract objects starts Monday, and I'm excited to ask him about hyperreal numbers and infinity. If you'd like, perhaps you can type your question here, and I could read it to him in class. This is because I don't want to misrepresent you, ha. If I remember correctly, hyperreal numbers enable me to perform subtraction/division with transfinite numbers without paradox, and therefore serves as a sort of undercutting defeater to the thesis that an actual infinite is metaphysically impossible due to the paradoxes its instantiation in reality would lead to. Please let me know of any misrepresentation. Thanks!
    The problem with considering actual infinities impossible is that they used to describe actual natural infinite sets in nature.

    Source: https://plus.maths.org/content/do-infinities-exist-nature-0



    Do infinities exist in nature?
    By Marianne Freiberger and Rachel Thomas

    Submitted by Marianne on September 26, 2013
    What would you see if you came to the edge of the Universe? It's hard to imagine so it's tempting to conclude that the Universe doesn't have an edge and therefore that it must be infinite. That's not a necessary conclusion however. There are things that are finite in extent but still don't have an edge, the prime example being the surface of a sphere. It's got a finite area but when you walk around on it you'll never fall over an edge. The question of whether the Universe is finite or infinite is one that still hasn't been answered, and there are mathematical models that allow for both possibilities. More generally, the question of whether any infinite quantities can arise in the Universe is a deep one. In April this year philosophers, cosmologists and physicists came together at the University of Cambridge, as part of a conference series on the philosophy of cosmology, in order to discuss it. Plus went along to find out more (and you can also listen to the interviews we did in our podcast).

    Infinity that doesn't bite

    John D. Barrow

    People have been studying infinity and its relation to reality for a long time. "The idea of studying infinities in physics really began with Aristotle," says the Cambridge cosmologist John D. Barrow. "Aristotle made a clear distinction between two types of infinity. One he called potential infinities and he was quite happy to allow for those to appear in descriptions of the world. These are just like lists that never end. The ordinary numbers are an example; one, two, three, four, five, and so on, the list goes on forever. It's infinite, but you never reach or experience the infinity. In a subject like cosmology, there are lots of infinities like that and most people are quite happy with them. For example, the Universe might have infinite size; it might have an infinite past age, it might be destined to have an infinite future age. These are all potential infinities, so they don't bite you as it were, they're just ways of saying that things are limitless, they're unbounded, like that list of numbers."

    © Copyright Original Source

    Glendower: I can call spirits from the vasty deep.
    Hotspur: Why, so can I, or so can any man;
    But will they come when you do call for them? Shakespeare’s Henry IV, Part 1, Act III:

    go with the flow the river knows . . .

    Frank

    I do not know, therefore everything is in pencil.

  3. #43
    tWebber mattbballman31's Avatar
    Join Date
    Feb 2014
    Faith
    Christian
    Gender
    Male
    Posts
    192
    Amen (Given)
    2
    Amen (Received)
    60
    Quote Originally Posted by shunyadragon View Post
    The problem with considering actual infinities impossible is that they used to describe actual natural infinite sets in nature.
    I feel like I'm going to regret responding to you, but I can't resist . . . sorry. So . . . you're claim is:

    - Actual infinities are used to describe "actual natural infinite sets in nature".

    . . . I have no idea what it means for an actual infinite set to be natural.

    It's hard to imagine so it's tempting to conclude that the Universe doesn't have an edge and therefore that it must be infinite. That's not a necessary conclusion however.
    How the heck doesn't this contradict what you just said? I'll keep reading . . .

    The question of whether the Universe is finite or infinite is one that still hasn't been answered, and there are mathematical models that allow for both possibilities.
    Irrelevant. Actual infinities are mathematically possible. No one denies this. Metaphysical possibility is the issue.

    "Aristotle made a clear distinction between two types of infinity. One he called potential infinities and he was quite happy to allow for those to appear in descriptions of the world. These are just like lists that never end.
    Wow. No one denies that potential infinities are real. Irrelevant.

    So . . . . . . . . . . nothing you quoted supports your claim. I thought in my time off here you'd get a little smarter. Guess not.
    Many and painful are the researches sometimes necessary to be made, for settling points of [this] kind. Pertness and ignorance may ask a question in three lines, which it will cost learning and ingenuity thirty pages to answer. When this is done, the same question shall be triumphantly asked again the next year, as if nothing had ever been written upon the subject.
    George Horne

  4. #44
    tWebber shunyadragon's Avatar
    Join Date
    Jan 2014
    Location
    Hillsborough, NC
    Faith
    Agnostic
    Gender
    Male
    Posts
    12,820
    Amen (Given)
    1251
    Amen (Received)
    870
    Quote Originally Posted by mattbballman31 View Post
    I feel like I'm going to regret responding to you, but I can't resist . . . sorry. So . . . you're claim is:

    - Actual infinities are used to describe "actual natural infinite sets in nature".

    . . . I have no idea what it means for an actual infinite set to be natural.



    How the heck doesn't this contradict what you just said? I'll keep reading . . .



    Irrelevant. Actual infinities are mathematically possible. No one denies this. Metaphysical possibility is the issue.



    Wow. No one denies that potential infinities are real. Irrelevant.

    So . . . . . . . . . . nothing you quoted supports your claim. I thought in my time off here you'd get a little smarter. Guess not.
    Metaphysical or physical? I believe you are misrepresenting Craig's argument.

    Craig claims this by claiming our universe (physical existence) cannot be past infinite.

    Source: http://spot.colorado.edu/~morristo/craig-on-the-actual-infinite.pdf



    Craig on the actual infinite
    wes morriston
    Department of Philosophy, University of Colorado at Boulder, 169 Hellems, Campus
    Box 232, Boulder, CO 80309-0232
    Abstract : In a series of much discussed articles and books, William Lane Craig
    defends the view that the past could not consist in a beginningless series of events.
    In the present paper, I cast a critical eye on just one part of Craig’s case for the
    finitude of the past – viz. his philosophical argument against the possibility of
    actually infinite sets of objects in the ‘real world’. I shall try to show that this
    argument is unsuccessful. I shall also take a close look at several considerations that
    are often thought to favour the possibility of an actual infinite, arguing in each case
    that Craig’s response is inadequate.

    © Copyright Original Source



    Craig's problem with infinities gets worse when he proposes the bogus old Hilbert's Hotel argument.

    Source: https://www.youtube.com/watch?v=j_q802eboxA


    William Lane Craig explains why the universe had a beginning and is not infinite using the Hilbert's Hotel example. Since the universe had a beginning, it had to have a cause. That cause had to be enormously powerful and extremely intelligent, i.e. God.Feb 19, 2010
    William Lane Craig explains Hilbert's Hotel, Infintiy, Kalam - YouTube
    https://www.youtube.com/watch?v=j_q802eboxA

    © Copyright Original Source



    One easy response is simply begin with an infinite Hilbert's Hotel that is empty. Now, try and fill the hotel.
    Last edited by shunyadragon; 11-24-2017 at 11:38 AM.
    Glendower: I can call spirits from the vasty deep.
    Hotspur: Why, so can I, or so can any man;
    But will they come when you do call for them? Shakespeare’s Henry IV, Part 1, Act III:

    go with the flow the river knows . . .

    Frank

    I do not know, therefore everything is in pencil.

  5. #45
    tWebber mattbballman31's Avatar
    Join Date
    Feb 2014
    Faith
    Christian
    Gender
    Male
    Posts
    192
    Amen (Given)
    2
    Amen (Received)
    60
    Quote Originally Posted by shunyadragon View Post
    Metaphysical or physical? I believe you are misrepresenting Craig's argument.
    Well, then you've been hating on him too much to know that I'm not.

    Craig claims this by claiming our universe (physical existence) cannot be past infinite.
    And how does this contradict the point that the past-eternal, physical existence of the universe is a metaphysical impossibility?

    Abstract : In a series of much discussed articles and books, William Lane Craig
    defends the view that the past could not consist in a beginningless series of events.
    In the present paper, I cast a critical eye on just one part of Craig’s case for the
    finitude of the past – viz. his philosophical argument against the possibility of
    actually infinite sets of objects in the ‘real world’. I shall try to show that this
    argument is unsuccessful. I shall also take a close look at several considerations that
    are often thought to favour the possibility of an actual infinite, arguing in each case
    that Craig’s response is inadequate.
    See the bold stuff? That's referring to metaphysical possibility. That has absolutely nothing to do with whether the universe is physical or not,

    Craig's problem with infinities gets worse when he proposes the bogus old Hilbert's Hotel argument.
    Well, thank goodness I don't just take your word for it. Why is it bogus? Sounds good to me!

    One easy response is simply begin with an infinite Hilbert's Hotel that is empty. Now, try and fill the hotel.
    That was perspicuous, lol. The response is completely misconceived. Great, you've emptied it out. In this possible world, Craig's metaphysical absurdities involving contradictions in transfinite arithmetic wouldn't arise with regard to people leaving and accommodating a potentially infinite amount of new guests when an actual infinite amount of guests are already in the hotel. In the new scenario, the hotel would never fill up! That's Craig's second philosophical argument: the metaphysical impossibility of forming an actual infinite via successive addition. Thanks for illustrating Hilbert's Hotel in a way that doesn't threaten Craig's argument at all!
    Many and painful are the researches sometimes necessary to be made, for settling points of [this] kind. Pertness and ignorance may ask a question in three lines, which it will cost learning and ingenuity thirty pages to answer. When this is done, the same question shall be triumphantly asked again the next year, as if nothing had ever been written upon the subject.
    George Horne

  6. Amen Jedidiah amen'd this post.
  7. #46
    tWebber shunyadragon's Avatar
    Join Date
    Jan 2014
    Location
    Hillsborough, NC
    Faith
    Agnostic
    Gender
    Male
    Posts
    12,820
    Amen (Given)
    1251
    Amen (Received)
    870
    Quote Originally Posted by mattbballman31 View Post
    Well, then you've been hating on him too much to know that I'm not.



    And how does this contradict the point that the past-eternal, physical existence of the universe is a metaphysical impossibility?


    See the bold stuff? That's referring to metaphysical possibility. That has absolutely nothing to do with whether the universe is physical or not,



    Well, thank goodness I don't just take your word for it. Why is it bogus? Sounds good to me!



    That was perspicuous, lol. The response is completely misconceived. Great, you've emptied it out. In this possible world, Craig's metaphysical absurdities involving contradictions in transfinite arithmetic wouldn't arise with regard to people leaving and accommodating a potentially infinite amount of new guests when an actual infinite amount of guests are already in the hotel. In the new scenario, the hotel would never fill up! That's Craig's second philosophical argument: the metaphysical impossibility of forming an actual infinite via successive addition. Thanks for illustrating Hilbert's Hotel in a way that doesn't threaten Craig's argument at all!
    I do not propose emptying anything. I propose beginning with a potentially infinite hotel that is empty. Now try and fill it. Hilbert's Hotel fits in my hotel.

    Craig proposes that our (universe) physical existence cannot be 'past infinite.' That is not metaphysical issue.
    Last edited by shunyadragon; 11-28-2017 at 01:10 AM.
    Glendower: I can call spirits from the vasty deep.
    Hotspur: Why, so can I, or so can any man;
    But will they come when you do call for them? Shakespeare’s Henry IV, Part 1, Act III:

    go with the flow the river knows . . .

    Frank

    I do not know, therefore everything is in pencil.

  8. #47
    tWebber Tassman's Avatar
    Join Date
    Jan 2014
    Location
    Sydney/Phuket
    Faith
    Atheist
    Gender
    Male
    Posts
    8,984
    Amen (Given)
    2212
    Amen (Received)
    1517
    Quote Originally Posted by mattbballman31 View Post


    And how does this contradict the point that the past-eternal, physical existence of the universe is a metaphysical impossibility?

    Given you acknowledge that actual infinities are mathematically possible metaphysical possibility is no longer the issue. A metaphysician can be mistaken in his deductions, just as a scientist can. But even if these are impeccable, he will not necessarily succeed if he argues correctly from premises that are unacceptable because they lack the necessary foundation in fact.
    “He felt that his whole life was a kind of dream and he sometimes wondered whose it was and whether they were enjoying it.” - Douglas Adams.

  9. Amen shunyadragon amen'd this post.
  10. #48
    tWebber mattbballman31's Avatar
    Join Date
    Feb 2014
    Faith
    Christian
    Gender
    Male
    Posts
    192
    Amen (Given)
    2
    Amen (Received)
    60
    Quote Originally Posted by shunyadragon View Post
    I do not propose emptying anything. I propose beginning with a potentially infinite hotel that is empty. Now try and fill it. Hilbert's Hotel fits in my hotel.
    Craig would have no problem saying you can't fill a hotel with a potentially infinite amount of rooms. His philosophical arguements don't even apply to a hotel with a potentially infintine amount of rooms in a hotel. What are you talking about?

    Craig proposes that our (universe) physical existence cannot be 'past infinite.' That is not metaphysical issue.
    Yes it is. Seriously. How is that not a metaphysical issue? The claims are,

    1. An infinite temporal regress of events is an actual infinite
    2. An actual infinite cannot exist.
    3. Therefore, an infinite temporal regress of events cannot exist.

    1 and 2 are metaphysical propositions, and so is the conclusion.
    Many and painful are the researches sometimes necessary to be made, for settling points of [this] kind. Pertness and ignorance may ask a question in three lines, which it will cost learning and ingenuity thirty pages to answer. When this is done, the same question shall be triumphantly asked again the next year, as if nothing had ever been written upon the subject.
    George Horne

  11. #49
    tWebber mattbballman31's Avatar
    Join Date
    Feb 2014
    Faith
    Christian
    Gender
    Male
    Posts
    192
    Amen (Given)
    2
    Amen (Received)
    60
    Quote Originally Posted by Tassman View Post
    Given you acknowledge that actual infinities are mathematically possible metaphysical possibility is no longer the issue. A metaphysician can be mistaken in his deductions, just as a scientist can. But even if these are impeccable, he will not necessarily succeed if he argues correctly from premises that are unacceptable because they lack the necessary foundation in fact.
    I'm so lost right now. When Craig is saying that an actual infinite is mathematically possible, he saying that you shouldn't deny the "mathematical legitimacy to the actual infinite", like the intuitionists do. "Cantor's system and axiomatized set theory may be taken to be simply a universe of discourse, a mathematical system based on certain adopted axioms and conventions, which carries no ontological commitments." Ontological commitments is the modal realm of metaphysical possibility, or broad logical possibility, which is in terms of actualizability. Like David Hilbert said, "The infinite is nowhere to be found in reality. It neither exists in nature nor provides a legitimate basis for rational thought . . . The role that remains for the infinite to play is solely that of an idea." So, just because you think there's mathematical legitimacy to the idea of actual infinites in infinite set theory, it does not follow that it is metaphysically possible to put into one-to-one correspondence each member of such a set and a concrete or a Platonically conceived abstract object. Craig doesn't even believe mathematical objects exist. Craig says, " . . . it is open to the mutakallim to hold that while the actual infinite is a fruitful and consistent concept within the postulated universe of discourse, it cannot be transposed into the real world."
    Many and painful are the researches sometimes necessary to be made, for settling points of [this] kind. Pertness and ignorance may ask a question in three lines, which it will cost learning and ingenuity thirty pages to answer. When this is done, the same question shall be triumphantly asked again the next year, as if nothing had ever been written upon the subject.
    George Horne

  12. #50
    tWebber shunyadragon's Avatar
    Join Date
    Jan 2014
    Location
    Hillsborough, NC
    Faith
    Agnostic
    Gender
    Male
    Posts
    12,820
    Amen (Given)
    1251
    Amen (Received)
    870
    Quote Originally Posted by mattbballman31 View Post
    I'm so lost right now. When Craig is saying that an actual infinite is mathematically possible, he saying that you shouldn't deny the "mathematical legitimacy to the actual infinite", like the intuitionists do. "Cantor's system and axiomatized set theory may be taken to be simply a universe of discourse, a mathematical system based on certain adopted axioms and conventions, which carries no ontological commitments." Ontological commitments is the modal realm of metaphysical possibility, or broad logical possibility, which is in terms of actualizability. Like David Hilbert said, "The infinite is nowhere to be found in reality. It neither exists in nature nor provides a legitimate basis for rational thought . . . The role that remains for the infinite to play is solely that of an idea." So, just because you think there's mathematical legitimacy to the idea of actual infinites in infinite set theory, it does not follow that it is metaphysically possible to put into one-to-one correspondence each member of such a set and a concrete or a Platonically conceived abstract object. Craig doesn't even believe mathematical objects exist. Craig says, " . . . it is open to the mutakallim to hold that while the actual infinite is a fruitful and consistent concept within the postulated universe of discourse, it cannot be transposed into the real world."
    As Tassman noted, William Craig and David Hilbert may be mistaken in their deductions. Actual infinities are actually used in science to describe the physical nature of our existence. Actual infinities would descriptive of attributes of our physical existence within a greater potential infinity.
    Glendower: I can call spirits from the vasty deep.
    Hotspur: Why, so can I, or so can any man;
    But will they come when you do call for them? Shakespeare’s Henry IV, Part 1, Act III:

    go with the flow the river knows . . .

    Frank

    I do not know, therefore everything is in pencil.

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •