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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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  • #46
    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; 11-27-2017, 08:10 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


    • #47
      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.

      Comment


      • #48
        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

        Comment


        • #49
          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

          Comment


          • #50
            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.

            Comment


            • #51
              Originally posted by mattbballman31 View Post
              Craig would have no problem saying you can't fill a hotel with a potentially infinite amount of rooms. His philosophical arguments don't even apply to a hotel with a potentially infintine amount of rooms in a hotel. What are you talking about?
              Potential infinities would only exist as infinite sets within a greater potential infinity.


              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.
              No, they describe limits on the potential infinite nature of our physical existence as Craig proposes. Actually the claim that an actual infinity cannot exist is false.
              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


              • #52
                Originally posted by shunyadragon View Post
                Potential infinities would only exist as infinite sets within a greater potential infinity.
                Uh, potential infinities are finite sets.


                No, they describe limits on the potential infinite nature of our physical existence as Craig proposes. Actually the claim that an actual infinity cannot exist is false.
                Uh, yes. I don't care what they describe. I care about the nature of their descriptions. And your last point is completely irrelevant to that issue. Great! You think they can't exist. I disagree. But to say they can't exist is a metaphysical proposition about the impossibility of an actual infinite. The fact that you can't understand these simple distinctions means you just haven't read or understood the literature on the topic.
                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


                • #53
                  Originally posted by mattbballman31 View Post
                  Uh, potential infinities are finite sets.

                  Actual infinities are defined as 'completed' closed sets of infinities.

                  Source: https://www.iep.utm.edu/infinite/#H1


                  For purposes of doing mathematics and science, the actual infinite has turned out to be the most useful of the three concepts. Using the idea proposed by Bolzano that was mentioned above, the concept of the actual infinite was precisely defined in 1888 when Richard Dedekind redefined the term “infinity” for use in set theory and George Cantor made the infinite, in the sense of infinite set, an object of mathematical study. Before this turning point, the philosophical community generally believed Aristotle’s concept of potential infinity should be the concept used in mathematics and science.

                  © Copyright Original Source



                  Source: https://math.vanderbilt.edu/schectex/courses/thereals/potential.html


                  Completed infinity, or actual infinity, is an infinity that one actually reaches; the process is already done. For instance, let's put braces around that sequence mentioned earlier:
                  { 1, 2, 3, 4, ... }
                  With this notation, we are indicating the set of all positive integers. This is just one object, a set. But that set has infinitely many members. By that I don't mean that it has a large finite number of members and it keeps getting more members. Rather, I mean that it already has infinitely many members.

                  We can also indicate the completed infinity geometrically. For instance, the diagram at right shows a one-to-one correspondence between points on an infinitely long line and points on a semicircle. (see reference for diagram) There are no points for plus or minus infinity on the line, but it is natural to attach those "numbers" to the endpoints of the semicircle.

                  Isn't that "cheating," to simply add numbers in this fashion? Not really; it just depends on what we want to use those numbers for. For instance, f(x)=1/(1+x2) is a continuous function defined for all real numbers x, and it also tends to a limit of 0 when x "goes to" plus or minus infinity (in the sense of potential infinity, described earlier). Consequently, if we add those two "numbers" to the real line, to get the so-called "extended real line," and we equip that set with the same topology as that of the closed semicircle (i.e., the semicircle including the endpoints), then the function f is continuous everywhere on the extended real line. This has some advantages in advanced mathematics: The topology of the closed semicircle is compact and metrizable. Compact metric spaces have very nice topological properties; for instance, every sequence has a convergent subsequence. Even if we're really just interested in the properties of the ordinary (finite) real numbers, we can discover and prove some of those properties more easily by viewing that set of numbers as a subset of this larger, compact metric space.

                  © Copyright Original Source




                  Uh, yes. I don't care what they describe. I care about the nature of their descriptions. And your last point is completely irrelevant to that issue. Great! You think they can't exist. I disagree. But to say they can't exist is a metaphysical proposition about the impossibility of an actual infinite. The fact that you can't understand these simple distinctions means you just haven't read or understood the literature on the topic.
                  Read my posts again and respond intelligently. Math is descriptive of our physical nature and math is not material objects that exist nor not exist. Actual infinities exists as descriptions of the physical properties of our physical existence.

                  If your care what they describe, they actually do exist as descriptions of attributes of our physical universe.

                  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

                  Last edited by shunyadragon; 02-18-2018, 04:45 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


                  • #54
                    Originally posted by shunyadragon View Post
                    Actual infinities are defined as closed sets of infinities.
                    You really are dense.

                    YOU SAID THE POTENTIAL INFINITE WAS AN INFINITE SET, YOU MORON.

                    Then I said that the potential infinite was a finite set.

                    And your response is to mention that ACTUAL INFINITIES ARE DEFINED AS CLOSED SETS OF INFINITIES????

                    NO DUH! It's like I'm talking to a darn wall. I wasn't talking about actual infinites, moron. I was responding to your claim that potential infinites are infinite sets. They aren't. Got that, moron? So, your dumb IEP quote is idiotically irrelevant, moron. Learn to read and stop wasting my time.

                    Read my posts again and respond intelligently.
                    Why don't you follow your own genius advice?

                    Math is descriptive of our physical nature and math is not material objects that exist nor not exist. Actual infinities exists as descriptions of the physical properties of our physical existence.
                    Did you even read my last post, moron? I said that . . . Craig . . . does not deny the mathematical legitimacy of the actual infinite. THAT MEANS I DON'T DENY THAT MATH IS DESCRIPTIVE OF PHYSICAL NATURE, MORON. How in the freaking world does this have anything to do with the idea that " . . . 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."

                    And then you just quote these huge block quotes I've already addressed, dunce. Marianne Freiberger and Rachel Thomas don't say ANYTHING addressing the point. And Barrow is only talking about POTENTIAL infinities. You either really suck at reading and comprehension or you're so blinded by your own bias that any semblance of objectivity has evaporated into the stratosphere and beyond.

                    I can't wait what nonsense you'll spew next! Stay tuned!
                    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


                    • #55
                      Originally posted by mattbballman31 View Post
                      You really are dense.

                      YOU SAID THE POTENTIAL INFINITE WAS AN INFINITE SET, YOU MORON.

                      Then I said that the potential infinite was a finite set.

                      And your response is to mention that ACTUAL INFINITIES ARE DEFINED AS CLOSED SETS OF INFINITIES????

                      NO DUH! It's like I'm talking to a darn wall. I wasn't talking about actual infinites, moron. I was responding to your claim that potential infinites are infinite sets. They aren't. Got that, moron? So, your dumb IEP quote is idiotically irrelevant, moron. Learn to read and stop wasting my time.



                      Why don't you follow your own genius advice?



                      Did you even read my last post, moron? I said that . . . Craig . . . does not deny the mathematical legitimacy of the actual infinite. THAT MEANS I DON'T DENY THAT MATH IS DESCRIPTIVE OF PHYSICAL NATURE, MORON. How in the freaking world does this have anything to do with the idea that " . . . 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."

                      And then you just quote these huge block quotes I've already addressed, dunce. Marianne Freiberger and Rachel Thomas don't say ANYTHING addressing the point. And Barrow is only talking about POTENTIAL infinities. You either really suck at reading and comprehension or you're so blinded by your own bias that any semblance of objectivity has evaporated into the stratosphere and beyond.

                      I can't wait what nonsense you'll spew next! Stay tuned!
                      I apologize for the typo. It is actual infinities that are 'complete' closed sets. They are description of attributes of our physical existence.

                      I correctly described it in the next post. In this context actual infinities do indeed exist in nature.
                      Last edited by shunyadragon; 02-18-2018, 06:40 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


                      • #56
                        Originally posted by shunyadragon View Post
                        I apologize for the typo. It is actual infinities that are 'complete' closed sets. They are description of attributes of our physical existence.

                        I correctly described it in the next post. In this context actual infinities do indeed exist in nature.
                        Wow. Admission of error. We're making progress! There's hope for you yet.

                        The quote you gave doesn't show that actual infinities exist in nature at all. It's like you copy/past some mathematical explanation and are unable to connect the dots to metaphysical reality. All the quote does is define, mathematically, an actual infinite (something Craig affirms), extend such a definition geometrically from points on a line to points on a semicircle (something Craig wouldn't deny), and show how it wouldn't be 'cheating' if such a topological extension is done in geometry. Wow. Cool. Oooh! Ahhh! Shuny can quote blocks of irrelevant bilge. Craig denies none of this, and it has nothing (absolutely nothing!) to do with saying that actual infinities exist in nature.

                        Oh, and because you're such a Craig-expert, quote me exactly where Craig addresses the very point your clumsily trying to target that because one can successfully utilize actual infinites relative to topological geometrical structures for whatever the mathematician 'wants to use the numbers for', that this therefore implies the begged metaphysical question of whether the topological structure of space itself is metaphysically identical to the structure as delineated in geometry. He addresses it! It's in his literature on the topic! And rather than hold your hand and quote it for you, either admit that you don't have a sufficient grasp on the argument as Craig has presented it since freaking 1979 or that you're an embarrassing armchair block-quote copy and paster whose only concern is the appearance of sophistication, an appearance that itself is a laughable disguise. I'm so sick of pseudo-intellectuals like you thinking that you can just throw some stupid gotchya-spaghetti against the wall, and you actually are convinced that you've GOT CRAIG WITH HIS BACK AGAINST THE WALL. It's absurd. He's explored the darn argument almost into the ground, and these silly 'arguments' you bring up would just be laughed out of your normal philosophy conference.
                        Last edited by mattbballman31; 02-18-2018, 09:56 PM.
                        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


                        • #57
                          This article by Morriston addresses the problems with Craig's arguments concerning actual infinities in great detail.


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



                          In a series of much discussed articles and books, William Lane Craig has
                          vigorously defended the view that the past could not consist in a beginningless
                          series of events.1 Craig’s goal, of course, is to make a strong case for the existence
                          of God. If the past has a beginning, then so does the universe, and a familiar line
                          of argument suggests that there must be a First Cause.2 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 in the ‘real
                          world’.3 If this argument were to succeed, then an actually infinite series of past
                          events would have been proved impossible, and we could go on to ask about the
                          cause of the very first event. However, I do not believe that Craig has succeeded in
                          proving that actually infinite sets are impossible. As far as this particular line of
                          argument is concerned, I shall try to show that it remains an open question
                          whether the past could consist in a beginningless series of events.
                          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



                          My previous references confirm that actual infinities do exist in nature.
                          Last edited by shunyadragon; 02-19-2018, 10:23 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


                          • #58
                            Originally posted by shunyadragon View Post
                            My previous references confirm that actual infinities do exist in nature.
                            No they didn't. I read through the whole article you referenced in post #53, and not once did I see the authors make the claim that actual infinities have been confirmed to exist in nature.

                            Comment


                            • #59
                              Originally posted by Chrawnus View Post
                              No they didn't. I read through the whole article you referenced in post #53, and not once did I see the authors make the claim that actual infinities have been confirmed to exist in nature.
                              Yes it demonstrated Craig's assertions as false, as well as other references describing actual infinities in nature. More to follow.

                              Self imposed ignorance leers its ugly head.

                              Again this article discusses actual infinities as they exist in describing their properties using math to describe nature.

                              Source: https://plus.maths.org/content/does-infinity-exist


                              Does infinity exist? by John D. Barrow
                              Submitted by Marianne on July 2, 2012

                              In the latest poll of our Science fiction, science fact project you told us that you wanted to know if infinity exists. Here is an answer, based on an interview with the cosmologist John D. Barrow. Click here to see other articles on infinity and here to listen to our interview with Barrow as a podcast.

                              . . .


                              But generally Cantor's ideas have been accepted and today they form their own sub-branch of pure mathematics. This has led some philosophers, and even some theologians, to rethink their ancient attitudes to infinities. Because there are quite different varieties of infinity, it is clear that you don't have to regard the appearance of mathematical infinity as some sort of challenge to the divine as the medieval theologians believed. Cantor's ideas were at first actually taken up more enthusiastically by contemporay theologians than by mathematicians.

                              Scientists also started to distinguish between mathematical and physical infinities. In mathematics, if you say something "exists", what you mean is that it doesn't introduce a logical contradiction given a particular set of rules. But it doesn't mean that you can have one sitting on your desk or that there's one running around somewhere. Unicorns are not a logical impossibility but that doesn't mean that one exists biologically. When mathematicians demonstrated that non-Euclidean geometries can exist, they showed that there's an axiomatic system which permits them that is not self-contradictory. (You can find out more about non-Euclidean geometries in the article Strange geometries.)

                              Physical infinities
                              So infinities in modern physics have become separate from the study of infinities in mathematics. One area in physics where infinities are sometimes predicted to arise is aerodynamics or fluid mechanics. For example, you might have a wave becoming very, very steep and non-linear and then forming a shock. In the equations that describe the shock wave formation some quantities may become infinite. But when this happens you usually assume that it's just a failure of your model. You might have neglected to take account of friction or viscosity and once you include that into your equations the velocity gradient becomes finite — it might still be very steep, but the viscosity smoothes over the infinity in reality. In most areas of science, if you see an infinity, you assume that it's down to an inaccuracy or incompleteness of your model.

                              string diagram
                              Two particles meeting form a sharp corner (left) but two loops coming together are like two pairs of trousers sown together. (The trouser diagram has time going downwards and space horizontal.)

                              In particle physics there has been a much longer-standing and more subtle problem. Quantum electrodynamics is the best theory in the whole of science, its predictions are more accurate than anything else that we know about the Universe. Yet extracting those predictions presented an awkward problem: when you did a calculation to see what you should observe in an experiment you always seemed to get an infinite answer with an extra finite bit added on. If you then subtracted off the infinity, the finite part that you were left with was the prediction you expected to see in the lab. And this always matched experiment fantastically accurately. This process of removing the infinities was called renormalisation. Many famous physicists found it deeply unsatisfactory. They thought it might just be a symptom of a theory that could be improved.

                              This is why string theory created great excitement in the 1980s and why it suddenly became investigated by a huge number of physicists. It was the first time that particle physicists found a finite theory, a theory which didn't have these infinities popping up. The way it did it was to replace the traditional notion that the most basic entities in the theory (for example photons or electrons) should be point-like objects that move through space and time and so trace out lines in spacetime. Instead, string theory considers the most basic entities to be lines, or little loops, which trace out tubes as they move. When you have two point-like particles moving through space and interacting, it's like two lines hitting one another and forming a sharp corner at the place where they meet. It's that sharp corner in the picture that's the source of the infinities in the description. But if you have two loops coming together, it's rather like two legs of a pair of trousers. Then two more loops move out from the interaction — that's like sewing another pair of trousers onto the first pair. What you get is a smooth transition. This was the reason why string theory was so appealing, it was the first finite theory of particle physics.

                              Cosmological infinities
                              Black hole
                              Simulated view of a black hole. Image: Alain Riazuelo.

                              Another type of infinity arises in gravitation theory and cosmology. Einstein's theory of general relativity suggests that an expanding Universe (as we observe ours to be) started at a time in the finite past when its density was infinite — this is what we call the Big Bang. Einstein's theory also predicts that if you fell into a black hole, and there are many black holes in our Galaxy and nearby, you would encounter an infinite density at the centre. These infinities, if they do exist, would be actual infinities.

                              © Copyright Original Source

                              Last edited by shunyadragon; 02-19-2018, 09:54 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


                              • #60
                                Originally posted by shunyadragon View Post
                                Yes it demonstrated Craig's assertions as false, as well as other references describing actual infinities in nature. More to follow.

                                Self imposed ignorance leers its ugly head.

                                Again this article discusses actual infinities as they exist in describing their properties using math to describe nature.

                                Source: https://plus.maths.org/content/does-infinity-exist


                                Does infinity exist? by John D. Barrow
                                Submitted by Marianne on July 2, 2012

                                In the latest poll of our Science fiction, science fact project you told us that you wanted to know if infinity exists. Here is an answer, based on an interview with the cosmologist John D. Barrow. Click here to see other articles on infinity and here to listen to our interview with Barrow as a podcast.

                                . . .


                                But generally Cantor's ideas have been accepted and today they form their own sub-branch of pure mathematics. This has led some philosophers, and even some theologians, to rethink their ancient attitudes to infinities. Because there are quite different varieties of infinity, it is clear that you don't have to regard the appearance of mathematical infinity as some sort of challenge to the divine as the medieval theologians believed. Cantor's ideas were at first actually taken up more enthusiastically by contemporay theologians than by mathematicians.

                                Scientists also started to distinguish between mathematical and physical infinities. In mathematics, if you say something "exists", what you mean is that it doesn't introduce a logical contradiction given a particular set of rules. But it doesn't mean that you can have one sitting on your desk or that there's one running around somewhere. Unicorns are not a logical impossibility but that doesn't mean that one exists biologically. When mathematicians demonstrated that non-Euclidean geometries can exist, they showed that there's an axiomatic system which permits them that is not self-contradictory. (You can find out more about non-Euclidean geometries in the article Strange geometries.)

                                Physical infinities
                                So infinities in modern physics have become separate from the study of infinities in mathematics. One area in physics where infinities are sometimes predicted to arise is aerodynamics or fluid mechanics. For example, you might have a wave becoming very, very steep and non-linear and then forming a shock. In the equations that describe the shock wave formation some quantities may become infinite. But when this happens you usually assume that it's just a failure of your model. You might have neglected to take account of friction or viscosity and once you include that into your equations the velocity gradient becomes finite — it might still be very steep, but the viscosity smoothes over the infinity in reality. In most areas of science, if you see an infinity, you assume that it's down to an inaccuracy or incompleteness of your model.

                                string diagram
                                Two particles meeting form a sharp corner (left) but two loops coming together are like two pairs of trousers sown together. (The trouser diagram has time going downwards and space horizontal.)

                                In particle physics there has been a much longer-standing and more subtle problem. Quantum electrodynamics is the best theory in the whole of science, its predictions are more accurate than anything else that we know about the Universe. Yet extracting those predictions presented an awkward problem: when you did a calculation to see what you should observe in an experiment you always seemed to get an infinite answer with an extra finite bit added on. If you then subtracted off the infinity, the finite part that you were left with was the prediction you expected to see in the lab. And this always matched experiment fantastically accurately. This process of removing the infinities was called renormalisation. Many famous physicists found it deeply unsatisfactory. They thought it might just be a symptom of a theory that could be improved.

                                This is why string theory created great excitement in the 1980s and why it suddenly became investigated by a huge number of physicists. It was the first time that particle physicists found a finite theory, a theory which didn't have these infinities popping up. The way it did it was to replace the traditional notion that the most basic entities in the theory (for example photons or electrons) should be point-like objects that move through space and time and so trace out lines in spacetime. Instead, string theory considers the most basic entities to be lines, or little loops, which trace out tubes as they move. When you have two point-like particles moving through space and interacting, it's like two lines hitting one another and forming a sharp corner at the place where they meet. It's that sharp corner in the picture that's the source of the infinities in the description. But if you have two loops coming together, it's rather like two legs of a pair of trousers. Then two more loops move out from the interaction — that's like sewing another pair of trousers onto the first pair. What you get is a smooth transition. This was the reason why string theory was so appealing, it was the first finite theory of particle physics.

                                Cosmological infinities
                                Black hole
                                Simulated view of a black hole. Image: Alain Riazuelo.

                                Another type of infinity arises in gravitation theory and cosmology. Einstein's theory of general relativity suggests that an expanding Universe (as we observe ours to be) started at a time in the finite past when its density was infinite — this is what we call the Big Bang. Einstein's theory also predicts that if you fell into a black hole, and there are many black holes in our Galaxy and nearby, you would encounter an infinite density at the centre. These infinities, if they do exist, would be actual infinities.

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                                Can you please bold the part that you misunderstood to confirm the existence of actual infinities in nature?

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