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Cogito ergo sum

Here in the Philosophy forum we will talk about all the "why" questions. We'll have conversations about the way in which philosophy and theology and religion interact with each other. Metaphysics, ontology, origins, truth? They're all fair game so jump right in and have some fun! But remember...play nice!

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The Concept of the Infinite

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  • #31
    Originally posted by mattdamore View Post
    I appreciate your links. I'll give those articles a look and have something probably by the weekend. Dr. Craig and I have had a professor/student relationship for the past year, and we've dined together as a class. In one-on-one conversation, he's a really nice, down-to-earth, pleasant guy.
    I definitely get that feeling from seeing his interactions with his students, and I've always thought him to be utterly sincere in his discussions. Despite the fact that I disagree with him on a great many things, I do have a great deal of respect for Dr. Craig.

    Perhaps I could bring these things up and see what he thinks.
    That'd be awesome! Thanks!

    My problem is that I haven't had much exposure to the way "infinity" is used in that particular project Dr. Craig had. So I have a lot of reading to do.
    By all means, start by listening to the audio from Dr. Craig's Excursus on Natural Theology , parts 9 and 10 (or watch the video, which I think is available as well). Then read over my articles again to see if I have treated Dr. Craig's arguments fairly. After that, I can help point you to good references which discuss these concepts independently of theology, so you can judge whether I treat them accurately.
    "[Mathematics] is the revealer of every genuine truth, for it knows every hidden secret, and bears the key to every subtlety of letters; whoever, then, has the effrontery to pursue physics while neglecting mathematics should know from the start he will never make his entry through the portals of wisdom."
    --Thomas Bradwardine, De Continuo (c. 1325)

    Comment


    • #32
      Originally posted by Boxing Pythagoras View Post
      I definitely get that feeling from seeing his interactions with his students, and I've always thought him to be utterly sincere in his discussions. Despite the fact that I disagree with him on a great many things, I do have a great deal of respect for Dr. Craig.

      That'd be awesome! Thanks!

      By all means, start by listening to the audio from Dr. Craig's Excursus on Natural Theology , parts 9 and 10 (or watch the video, which I think is available as well). Then read over my articles again to see if I have treated Dr. Craig's arguments fairly. After that, I can help point you to good references which discuss these concepts independently of theology, so you can judge whether I treat them accurately.
      I've already put on the wish-list: The Blackwell Companion to Natural Theology, The Kalam Cosmological Argument, and I think I'll read his articles on his website as well. I'll start with the Excursus on Natural Theology, and get to your articles after that. I have a full load doing Graduate Studies and now I have more homework. No worries, though! I'll fit this in as soon as I can. I'll see this as prep for when I talk to him next about you. I saw that Dr. Craig reviews Jordan Howard Sobel's Logic and Theism: Arguments for and against Belief in God, and Sobel mentions hyperreal numbers. It's strange Dr. Craig wouldn't mention it in the review. But I think I will read through Dr. Craig's review and another article he wrote on just that portion of the book focused on The Kalam.

      Comment


      • #33
        Originally posted by mattdamore View Post
        I'll start with the Excursus on Natural Theology, and get to your articles after that.
        For the sake of ease, here are the videos and transcripts for Dr. Craig's Excursus parts 9 and 10:

        Transcript of Excursus Part 9


        Transcript of Excursus Part 10

        I have a full load doing Graduate Studies and now I have more homework. No worries, though! I'll fit this in as soon as I can.
        I fully understand that. I certainly know how difficult it can be to find time for such things. The discussion will definitely be here whenever you're ready for it, though.

        I saw that Dr. Craig reviews Jordan Howard Sobel's Logic and Theism: Arguments for and against Belief in God, and Sobel mentions hyperreal numbers. It's strange Dr. Craig wouldn't mention it in the review. But I think I will read through Dr. Craig's review and another article he wrote on just that portion of the book focused on The Kalam.
        Very interesting. I've just added Sobel's work to my ever-growing reading list.
        "[Mathematics] is the revealer of every genuine truth, for it knows every hidden secret, and bears the key to every subtlety of letters; whoever, then, has the effrontery to pursue physics while neglecting mathematics should know from the start he will never make his entry through the portals of wisdom."
        --Thomas Bradwardine, De Continuo (c. 1325)

        Comment


        • #34
          Originally posted by mattdamore View Post
          Hmmm. I've known Dr. Craig for the past two semesters at Houston Baptist University, and have gotten to know the wonderful faculty and friends in that particular academic circle, and I can assure you that there's not the least hint - that I've discerned - of deception in any area of academic research and study. I realize I could be wrong, but I'm typically a good reader of character, and after many conversations with Dr. Craig, I can tell you the guy is a very nice, sincere person, who has been very caring toward me, and everyone in our class. I'm sorry you've gotten that impression, however. I really am. It's just hard to hear that said about someone I've known for a year who clearly evidences indicators of a stalwart character. But I don't want to sidetrack the issue from the concept of the "infinite" too much. I just wanted to tell you my perspective, and perhaps we can just agree to disagree.
          I do not want to dwell on this to derail the thread which is yours, but it would interesting if you would ask others at your college and WLC to get feed back on why the math of infinity they use in their arguments does not address the concept of hyperreal numbers and contemporary set theory as Boxing Pythagoras describes.

          I can understand someone like 'hansgeorge,' a Twebber, who simply upfront denies contemporary math and everything since and including Cantor's set theory, but I do not have an explanation from WLC.

          I have a good math background up to the graduate level, but nothing close to Boxing Pythagoras that is why I differ to him here and learn from him concerning math. Based on my background I easily understand the concepts as described by Boxing Pythagoras, and the problems with WLC's math.

          You could simply refer to Boxing Pythagoras's essays and ask for an explanation.
          Last edited by shunyadragon; 03-09-2017, 04:56 PM.
          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.

          Comment


          • #35
            Originally posted by shunyadragon View Post
            I do not want to dwell on this to derail the thread which is yours, but it would interesting if you would ask others at your college and WLC to get feed back on why the math of infinity they use in their arguments does not address the concept of hyperreal numbers and contemporary set theory as Boxing Pythagoras describes.
            To be fair, Set Theory is a particularly confusing area of mathematics, which is why Cantor was so controversial at first. I honestly don't expect non-mathematicians to be fully familiar with it.

            The Hyperreal numbers are, unfortunately, a bit more obscure. While I would love to see non-standard analysis replace the ε,δ-limit foundation upon which modern Calculus is taught, it has not yet gained anywhere near as widespread recognition. As such, it is entirely unsurprising that a non-mathematician might be wholly ignorant of the entire field of non-standard analysis.

            My problem isn't so much that Dr. Craig is ignorant of these concepts-- most people are. Rather, it is that he has attempted to pronounce on the topic of infinity, and has spread those pronouncements to his rather sizable audience, while making mistakes about very basic properties of the math which he is trying to invoke in order to prove his point. His audience is generally even more ignorant of the math than he is-- which, again, is not meant as any sort of indictment upon them-- so they tend to trust Dr. Craig and his multiple PhD's when he speaks on the subject.

            You could simply refer to Boxing Pythagoras's essays and ask for an explanation.
            As I suggested to Matt, I would like for him to start by seeing what Dr. Craig has to say, then read my work to be sure that I am treating Dr. Craig's argument irenically, and then to other mathematical works to be sure that I am representing the math properly. I don't pretend to be any sort of real authority on the subject. I don't have any fancy letters after my name. I'm just a dude who really, really enjoys mathematics and has a particular fondness for the mathematics of infinity.

            By all means, I am perfectly willing to discuss any questions about the work which I have written. However, I wouldn't want anyone to simply ignore those who disagree with me and look to my writings as if they are some absolute truth of the matter. If Matt can bring my complaints to the attention of Dr. Craig for his opinion, I absolutely welcome such an endeavor!
            "[Mathematics] is the revealer of every genuine truth, for it knows every hidden secret, and bears the key to every subtlety of letters; whoever, then, has the effrontery to pursue physics while neglecting mathematics should know from the start he will never make his entry through the portals of wisdom."
            --Thomas Bradwardine, De Continuo (c. 1325)

            Comment


            • #36
              Oh my goodness, what is going on? This new website format is throwing me for a loop! Is anyone else having trouble? I was about to start my response and I don't know how to quote now! ha, ha.

              Comment


              • #37
                Originally posted by mattdamore View Post
                Oh my goodness, what is going on? This new website format is throwing me for a loop! Is anyone else having trouble? I was about to start my response and I don't know how to quote now! ha, ha.
                I am not presently having trouble.

                How to quote: [quote=Me] La de da da [/quote ]

                I added a space after the second quote. Take it out and it will read;
                Originally posted by Me
                La de da da
                Citation follows the same format; [cite=Me] La de da da [/cite ]

                I added a space after the second cite. Take it out and it will read;
                Source: Me

                La de da da

                © Copyright Original Source

                Last edited by shunyadragon; 03-10-2017, 01:36 PM.
                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.

                Comment


                • #38
                  [QUOTE=shunyadragon;424171]I am not presently having trouble.

                  How to quote:
                  Originally posted by Me
                  La de da da [/quote ]

                  I added a space after the second quote. Take it out and it will read;

                  Citation follows the same format; [cite=Me] La de da da [/cite ]

                  I added a space after the second cite. Take it out and it will read;
                  Source: Me

                  La de da da

                  © Copyright Original Source

                  Thank you Shunya. I did already know that. But when I used to click on "go advanced", it would take me to a screen that had a whole panoply of options without the rigmarole of including the HTML coding manually. Did it change for you too? This would make it much more difficult for me to write responses. There used to be a veritable console of different tools that would automatically assist in providing HTML coding. I'm saddened that it's no longer here, unless my computer is wigging out.

                  Comment


                  • #39
                    Oh my goodness! I fixed it! Yay! I went to the bottom of the screen and clicked a link called "see full site", or some such locution. I'm so sorry. Ignore the above post. I feel foolish.

                    Comment


                    • #40
                      Originally posted by mattdamore View Post
                      Oh my goodness! I fixed it! Yay! I went to the bottom of the screen and clicked a link called "see full site", or some such locution. I'm so sorry. Ignore the above post. I feel foolish.
                      No worries! Happens to the best of us, from time to time.
                      "[Mathematics] is the revealer of every genuine truth, for it knows every hidden secret, and bears the key to every subtlety of letters; whoever, then, has the effrontery to pursue physics while neglecting mathematics should know from the start he will never make his entry through the portals of wisdom."
                      --Thomas Bradwardine, De Continuo (c. 1325)

                      Comment


                      • #41
                        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!

                        Comment


                        • #42
                          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.

                          Comment


                          • #43
                            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

                            Comment


                            • #44
                              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, 06:38 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.

                              Comment


                              • #45
                                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

                                Comment

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