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  • Originally posted by Adrift View Post
    Yes he does. He often uses Hilbert's paradox, or some other such coherent defense. At least, I find his argument against actual infinite coherent.
    Hilbert's hotel isn't actually a paradox. Nor is it an argument to show that actual infinites cannot exist.

    Dr. Craig's problem, when discussing infinity, is that he constantly makes the mistake of trying to use infinity as a number. Infinity is not a number, and as such, you cannot perform mathematical operations on infinity. There are numbers which are infinite, however, and one can perform mathematical operations on these numbers. Unfortunately for Dr. Craig, these numbers can resolve the alleged problems which he cites for infinity fairly easily.

    For example, insofar as Hilbert's Hotel is concerned, let's say that the Hotel in question has N rooms, where N is an infinite Hyperreal such that N=(1,2,3,4,5,...). This defines a situation in which the Hotel has the same number of rooms as there are Natural numbers, and let's say that all of these rooms are occupied by a single patron. That means there are N patrons staying in the Hotel. Now, let's say 3 people check out of the Hotel. Sure enough, the number of patrons remaining in the Hotel is still infinite, but it is not the same number of patrons as it had originally. Now, there are N-3 patrons, where N-3=(-2,-1,0,1,2,...). It is not true that N=N-3.

    Now let's say that instead of 3 patrons, all of the patrons in the even numbered rooms check out. Sure enough, this means that an infinite number of patrons are checking out of the Hotel-- but again, it is not the same infinite number as we had originally. In this case, we see that N/2=(0.5,1.0,1.5,2.0,2.5,...) patrons have left, and again, it is not true that N=N/2.

    Dr. Craig doesn't have a very good understanding of the mathematics which he attempts to describe.
    Last edited by Boxing Pythagoras; 01-10-2017, 08:48 AM.
    "[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


    • Originally posted by Adrift View Post
      Anyhow, this is all neither here nor there, since it isn't an instance where Craig is referring to the cause that his Kalam argument points back to. I can't think of any time in any of his debates where he told an interlocutor, or even an audience member "read my book" when it came to explaining why God is the best reason for the cause of the universe.
      As I don't have any examples to hand, I'll certainly cede this point, for now. I'll see if I can find any. If I can't, I'll certainly admit that I was mistaken.
      "[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


      • Originally posted by Boxing Pythagoras View Post
        Hilbert's hotel isn't actually a paradox. Nor is it an argument to show that actual infinites cannot exist.

        Dr. Craig's problem, when discussing infinity, is that he constantly makes the mistake of trying to use infinity as a number. Infinity is not a number, and as such, you cannot perform mathematical operations on infinity. There are numbers which are infinite, however, and one can perform mathematical operations on these numbers. Unfortunately for Dr. Craig, these numbers can resolve the alleged problems which he cites for infinity fairly easily.

        For example, insofar as Hilbert's Hotel is concerned, let's say that the Hotel in question has N rooms, where N is an infinite Hyperreal such that N=(1,2,3,4,5,...). This defines a situation in which the Hotel has the same number of rooms as there are Natural numbers, and let's say that all of these rooms are occupied by a single patron. That means there are N patrons staying in the Hotel. Now, let's say 3 people check out of the Hotel. Sure enough, the number of patrons remaining in the Hotel is still infinite, but it is not the same number of patrons as it had originally. Now, there are N-3 patrons, where N-3=(-2,-1,0,1,2,...). It is not true that N=N-1.

        Now let's say that instead of 3 patrons, all of the patrons in the even numbered rooms check out. Sure enough, this means that an infinite number of patrons are checking out of the Hotel-- but again, it is not the same infinite number as we had originally. In this case, we see that N/2=(0.5,1.0,1.5,2.0,2.5,...) patrons have left, and again, it is not true that N=N/2.

        Dr. Craig doesn't have a very good understanding of the mathematics which he attempts to describe.
        Of course he does, and he's in good company. We've been over this before, but it's worth repeating:

        Source: Abraham Robinson, "Formalism 64," in Selected Papers, vol. 2, 507


        My position concerning the foundations of mathematics is based on the following two main points or principles.

        i) Infinite totalities do not exist in any sense of the word (i.e., either really or ideally). More precisely, any mention, or purported mention, of infinite totalities is, literally, meaningless.

        ii) Nevertheless, we should continue the business of Mathematics "as usual", i.e., we should act as if infinite totalities really existed.

        © Copyright Original Source



        Source: David Hilbert

        Finally, let us return to our original topic, and let us draw the conclusion from all our reflections on the infinite. The overall result is then: The infinite is nowhere realized. Neither is it present in nature nor is it admissible as a foundation of our rational thinking – a remarkable harmony between being and thinking.

        © Copyright Original Source



        Source: Confessions of an Apostate Mathematician by Edward Nelson, Department of Mathematics, Princeton University


        Let me conclude with a brief but passionate apologia for formalism.

        As a description of what mathematicians have been doing, and cherishing, for well over two millenia, it is accurate and leaves nothing out. What we devote our lives to is seeking for proofs; if a proof follows the formal rules, it is correct; if it does not, it is not a proof and is worthless unless it suggests a way to find a proof. No other field of human endeavor has maintained such a consensus over such a vast extent of space and time.

        Formalism denies the relevance of truth to mathematics. But, one might object, mathematics works -- the evidence is all around us. Does this not imply that there is truth in mathematics? Not in the slightest. Suppose we find a primitive people, or an advanced people, but a people with a world-view utterly alien to ours, who have an herb that is quite effective for a certain illness. They explain its efficacy in terms of the divine action of the shuki on the body's okrus. We find that the herb is equally effective in our society. How much evidence does this provide for belief in the shuki? None at all. The syntax is correct; the semantics is irrelevant. So it is with mathematics. It works. But this is no evidence whatsoever that the religion of mathematics has any truth in it.

        In mathematics, reality lies in the symbolic expressions themselves, not in any abstract entities they are thought to denote. The symbol ∃ is simply a backwards E. If we conclude that a certain entity exists just because we have derived in a certain formal system a formula beginning with ∃, we do so at our peril. The dwelling place of meaning is syntax; semantics is the home of illusion.

        How can I continue to be a mathematician when I have lost my faith in the semantics of mathematics? Why should I want to continue doing mathematics if I no longer believe that numbers and stochastic processes and Hilbert spaces exist? Well, why should a composer want to compose music that is not program music? Mathematics is the last of the arts to become nonrepresentational.

        And mathematics is slowly beginning to become non-representational. Slowly in departments of mathematics, but quickly in computer science departments. Those who do computer science know that they are inventing and not discovering, and they are making beautiful and deep results concerning the nature of feasible computations. If we who are in traditional departments don't want to miss the boat, it behooves us to saddle a formalist horse pronto.

        Abstract beliefs affect concrete actions. Despite its complete lack of justification, the semantic view of mathematics -- the discovery of properties of entities existing in a Pythagorean world -- has served mathematics reasonably well for a very long time. But now it is time to move forward, to reject the semantic view, and concentrate on what is real in mathematics. And what is real in mathematics is the notation, not an imagined denotation.

        Let one brief example suffice. Abraham Robinson's creation of nonstandard analysis was a revolutionary simplification and extension of mathematical practice, but the mathematical community has been very slow, or unwilling, to adopt it because it conflicts with the Pythagorean religion.

        We are too timid. If we cannot achieve the depth of Eudoxus, we can at least emulate his willingness to break with universally held opinion.

        © Copyright Original Source



        I mean, Craig isn't a nutter for holding the views he holds on infinities. You may not agree with that, but that doesn't mean he doesn't have a good understanding of what he's talking about.

        Also, plenty of mathematicians call Hilbert's Hotel a paradox. Are you disputing that?

        Comment


        • Originally posted by JimL View Post
          I don't think that the idea of the physical laws breaking down at the singularity means that the laws no longer exist, I think that it just means that we can no longer calculate the physical laws.
          Sorry if you read what I said that way. I don't mean that they no longer exist but we cannot assume that the laws we use currently apply to the singularity.

          Originally posted by JimL View Post
          Singularities within the universe, black holes wherein the physical laws break down, don't come from nothing, they come from collapsing stars. If the Big Bang were to reverse itself into a Big crunch ending in a singularity, even though the physical laws would "break down" at that point, said singularity would not have come from nothing. Perhaps within an area of the Greater Cosmos the entropy decreases to form a sort of singularity wherein the physical laws are obscured and hidden from us, in the same way as they are hidden with respect to black holes, and can only be understood when the singularity, within the which the laws exist, begins to expand. I don't know, again I'm no physicist, and this is just a laymans musings, but the idea is not exactly a presupposing, its based upon what we can observe of how things work within our universe itself and extrapolating that as an explanation of its own origins.
          The presupposition is when it is thought that the laws of our universe apply to a singularity or whatever (if anything) came before our universe.

          Comment


          • Originally posted by Adrift View Post
            I mean, Craig isn't a nutter for holding the views he holds on infinities.
            I didn't say he was. I said he does a poor job of defending his views on infinities because he doesn't have a very good grasp of the mathematics involved.

            You may not agree with that, but that doesn't mean he doesn't have a good understanding of what he's talking about.
            Nor have I said that it does. I don't claim that Craig has a poor understanding of mathematics because he thinks actual infinities cannot exist. I claim that Craig has a poor understanding of mathematics because he makes statements about mathematics which are entirely incorrect.

            For example, when Craig says, "[Actual] infinity is symbolized by the Hebrew letter aleph (ℵ)," he is wrong. The symbol ℵ in set theory refers to the cardinality of infinite sets. It is not a symbol for the concept of infinity, actual or otherwise.

            For another example, look to how Craig's description of Hilbert's Hotel from that same talk consistently treats infinity as if it is a number, despite the fact that Craig recognizes earlier in the lecture that infinity is not a number. Or how, after discussing Hilbert's Hotel, he says, "Someone might say that you can’t do inverse operations with mathematical quantities. Not on paper perhaps, but there is no way you can stop people from checking out of a real hotel." Now, obviously, he meant to say "infinite quantities," here, not "mathematical quantities;" but even so, he's incorrect. Subtraction and division, for example, are not defined in Transfinite Arithmetic, as Craig notes earlier in the talk; but Transfinite Arithmetic doesn't add, multiply, or exponentiate cardinal numbers. Since cardinal numbers are the focus of Craig's Hilbert Hotel discussion, Transfinite Arithmetic is not really relevant. There certainly ARE number systems which include infinite numbers, are logically consistent, and define subtraction and division on infinite numbers-- for example, the Hyperreals or the Surreals. I gave examples of how the Hyperreals quite easily resolve the absurdities which Craig alleges result from Hilbert's Grand hotel.

            Also, plenty of mathematicians call Hilbert's Hotel a paradox. Are you disputing that?
            I am certainly disputing that Hilbert's Hotel is a paradox. There's nothing self-contradictory about a hotel with an infinite number of rooms.
            Last edited by Boxing Pythagoras; 01-10-2017, 10:06 AM.
            "[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


            • Originally posted by Boxing Pythagoras View Post
              For example, when Craig says, "[Actual] infinity is symbolized by the Hebrew letter aleph (ℵ)," he is wrong. The symbol ℵ in set theory refers to the cardinality of infinite sets. It is not a symbol for the concept of infinity, actual or otherwise.
              Doesn't the fuller quote give context to exactly that,

              By contrast with that, the actual infinite is an infinite which is, as it were, complete. The number of items in the collection is not growing toward infinity; it is infinite! It is complete and static and involves an actually infinite number of things.

              This type of infinity is symbolized by the Hebrew letter aleph (ℵ) and is used in set theory. In set theory, mathematicians talk about sets like the set of natural numbers which have an actually infinite number of members in the set. The collection is not growing toward infinity as a limit. It is infinity. There are an actually infinite number of natural numbers in this set.



              Originally posted by Boxing Pythagoras View Post
              For another example, look to how Craig's description of Hilbert's Hotel from that same talk consistently treats infinity as if it is a number, despite the fact that Craig recognizes earlier in the lecture that infinity is not a number.
              What are you referring to exactly? I don't see anywhere in which Craig uses Hilbert's Hotel differently from Hilbert. And they both come to the same conclusion. As Hilbert states, "The overall result is then: The infinite is nowhere realized. Neither is it present in nature nor is it admissible as a foundation of our rational thinking – a remarkable harmony between being and thinking."


              Originally posted by Boxing Pythagoras View Post
              Or how, after discussing Hilbert's Hotel, he says, "Someone might say that you can’t do inverse operations with mathematical quantities. Not on paper perhaps, but there is no way you can stop people from checking out of a real hotel." Now, obviously, he meant to say "infinite quantities," here, not "mathematical quantities;" but even so, he's incorrect. Subtraction and division, for example, are not defined in Transfinite Arithmetic, as Craig notes earlier in the talk; but Transfinite Arithmetic doesn't add, multiply, or exponentiate cardinal numbers. Since cardinal numbers are the focus of Craig's Hilbert Hotel discussion, Transfinite Arithmetic is not really relevant. There certainly ARE number systems which include infinite numbers, are logically consistent, and define subtraction and division on infinite numbers-- for example, the Hyperreals or the Surreals. I gave examples of how the Hyperreals quite easily resolve the absurdities which Craig alleges result from Hilbert's Grand hotel.
              Craig is not the one who alleges that absurdities result from Hilbert's Hotel. That is, he did not come up with this idea that Hilbert's Hotel results in absurdities. You're acting like he came up with all of this all by himself, and is making a fool of himself for having discovered these absurdities, but as I've already pointed out, he's simply mimicking others who've come to similar conclusions. In the end, I can't help but feel that your issue with Craig is less to do with his misuse of math, and more that you disagree with those mathematicians that he relies on. There are mathematicians, good mathematicians, that do not believe that actual infinities can exist in the real world. I imagine even they would not accept that the use of hyperreals could resolve absurdities with infinities in real life.

              I'm no mathematician though, and I know enough to know when I'm out of my depth. So I suppose there's something really obvious here that I'm missing. Have you emailed Dr. Craig your solution to Hilbert's Hotel using hyperreals? He answers emails all the time on both his website and podcast. I couldn't find anyplace where Craig discusses hyperreals to solve Hilbert's Hotel Paradox, but I did find this interesting discussion between the skeptic mathematician Jeffrey Shallit, and a poster named Wade. Wade makes a number of very interesting points that you might want to look over.

              Originally posted by Boxing Pythagoras View Post
              I am certainly disputing that Hilbert's Hotel is a paradox. There's nothing self-contradictory about a hotel with an infinite number of rooms.
              I realize you are disputing that Hilbert's Hotel is a paradox. Do you dispute that other mathematicians refer to it as a paradox? It appears as though even The Concise Oxford Dictionary of Mathematics (2009) considers it a paradox.

              Comment


              • Originally posted by 37818 View Post

                Hilbert's paradox actually explains paradox quite well I think.
                Thanks - have been sampling the others too. They're all good.
                Jorge: Functional Complex Information is INFORMATION that is complex and functional.

                MM: First of all, the Bible is a fixed document.
                MM on covid-19: We're talking about an illness with a better than 99.9% rate of survival.

                seer: I believe that so called 'compassion' [for starving Palestinian kids] maybe a cover for anti Semitism, ...

                Comment


                • Originally posted by Adrift View Post
                  Doesn't the fuller quote give context to exactly that,

                  By contrast with that, the actual infinite is an infinite which is, as it were, complete. The number of items in the collection is not growing toward infinity; it is infinite! It is complete and static and involves an actually infinite number of things.

                  This type of infinity is symbolized by the Hebrew letter aleph (ℵ) and is used in set theory. In set theory, mathematicians talk about sets like the set of natural numbers which have an actually infinite number of members in the set. The collection is not growing toward infinity as a limit. It is infinity. There are an actually infinite number of natural numbers in this set.
                  The fuller quote doesn't correct the problem to which I pointed. The symbol ℵ does not represent a "type of infinity," as Craig claims. Rather, it represents the cardinality of infinite sets. The cardinality of an infinite set isn't a "type of infinity." The cardinality of an infinite set is a description of an algorithm which one might use in listing the elements of that set.

                  What are you referring to exactly? I don't see anywhere in which Craig uses Hilbert's Hotel differently from Hilbert. And they both come to the same conclusion. As Hilbert states, "The overall result is then: The infinite is nowhere realized. Neither is it present in nature nor is it admissible as a foundation of our rational thinking – a remarkable harmony between being and thinking."
                  I'm referring particularly to when Craig says this:

                  Suppose all the people in the odd-numbered rooms check out – 1, 3, 5, 7, and so forth. How many guests are left? Well, all the even-numbered guests. An infinite number of guests are still left in the hotel even though an equal number has already checked out and left the hotel. But now let’s suppose instead that all of the guests in the rooms 3, 4, 5, 6, 7, out to infinity checked out. How many guests are left now? If there is a room #0, just three are left. Yet, the same number of guests checked out this time as when all of the odd-numbered guests left. You subtract identical quantities from identical quantities and you get non-identical results, which is absurd.


                  I have highlighted the particularly offending portion. It is not the case that the same number of guests checked out in each of those cases. Each case describes an infinite number of guests checking out, to be sure, but not the same infinite number. This is not a case of subtracting identical quantities from identical quantities to receive non-identical results, as Craig alleges.

                  Craig is not the one who alleges that absurdities result from Hilbert's Hotel. That is, he did not come up with this idea that Hilbert's Hotel results in absurdities. You're acting like he came up with all of this all by himself, and is making a fool of himself for having discovered these absurdities, but as I've already pointed out, he's simply mimicking others who've come to similar conclusions.
                  Whether Craig came up with them himself or is simply repeating something he's heard others claim is irrelevant. The fact of the matter is that he presents a misunderstanding of the mathematics in order to support his claim that actual infinites do not exist.

                  In the end, I can't help but feel that your issue with Craig is less to do with his misuse of math, and more that you disagree with those mathematicians that he relies on.
                  Nope, it's due to his misuse of math. If Craig were making legitimate mathematical arguments, I might disagree with him, but I wouldn't accuse him of being ignorant of mathematics. Our disagreement, in that case, would likely be a philosophical one, and I would cite those reasons for my disagreement. I have done exactly that, in fact, when I've discussed Dr. Norman Wildberger's view on the subject. Dr. Wildberger is a mathematics professor at the University of New South Wales. He understands the mathematics under discussion, but objects to some of the axioms underlying that mathematics.

                  However, Craig doesn't understand the mathematics. He makes claims about the mathematics which are incorrect in order to support his claims about actual infinites.

                  There are mathematicians, good mathematicians, that do not believe that actual infinities can exist in the real world. I imagine even they would not accept that the use of hyperreals could resolve absurdities with infinities in real life.
                  Those mathematicians would argue that the axioms underlying the Hyperreals do not apply to the real world. They would not argue that Hilbert's Hotel on the Hyperreal number system results in mathematical absurdities.

                  I'm no mathematician though, and I know enough to know when I'm out of my depth. So I suppose there's something really obvious here that I'm missing. Have you emailed Dr. Craig your solution to Hilbert's Hotel using hyperreals?
                  I have not. Even if Dr. Craig were to answer such a question, it would likely be a one-off reply, on his part. Given the complexity of the matter, and given Dr. Craig's numerous misunderstandings of the mathematics with which he is somewhat aware, I have no confidence that such a one-sided correspondence would be at all useful, on my part.

                  I couldn't find anyplace where Craig discusses hyperreals to solve Hilbert's Hotel Paradox, but I did find this interesting discussion between the skeptic mathematician Jeffrey Shallit, and a poster named Wade. Wade makes a number of very interesting points that you might want to look over.
                  Wade doesn't seem to have any understanding of the Hyperreals, either. When the user Gareth McCaughan mentions them, Wade misunderstands and thinks the gentleman is referring to Transfinite arithmetic.

                  Beyond that, the discussion definitely illustrates some of the problems I have with Craig's discussion of Hilbert's Hotel. Wade mistakes the fact that subtraction is not defined on Transfinite arithmetic for implying that it is impossible to perform subtraction on infinite numbers. Then, after noting that subtraction is not defined, he tries to draw conclusions about that subtraction, which is preposterous. That'd be like bringing up an Onomblattive in a conversation, noting that you have no definition for what an "Onomblattive" actually is, then proceeding to claim that the Onomblattive therefore proves your point.

                  I realize you are disputing that Hilbert's Hotel is a paradox. Do you dispute that other mathematicians refer to it as a paradox? It appears as though even The Concise Oxford Dictionary of Mathematics (2009) considers it a paradox.
                  I certainly don't! People often use the phrase "paradox" colloquially to refer to something which is counter-intuitive or which can easily be misunderstood as self-contradictory. For example, the Twin Paradox of Special Relativity isn't actually a paradox, but because a simple misunderstanding can make it appear to be paradoxical, the name has stuck despite the problem having been resolved. Similarly, even some people who don't actually consider Hilbert's Hotel to be self-contradictory have referred to it as a "paradox," in this colloquial sense.

                  If there are mathematicians who do still consider the thought experiment to be an actual paradox, I will be happy to disagree with them.
                  "[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


                  • Originally posted by Boxing Pythagoras View Post
                    Hilbert's hotel isn't actually a paradox. Nor is it an argument to show that actual infinites cannot exist.

                    Dr. Craig's problem, when discussing infinity, is that he constantly makes the mistake of trying to use infinity as a number. Infinity is not a number, and as such, you cannot perform mathematical operations on infinity. There are numbers which are infinite, however, and one can perform mathematical operations on these numbers. Unfortunately for Dr. Craig, these numbers can resolve the alleged problems which he cites for infinity fairly easily.

                    For example, insofar as Hilbert's Hotel is concerned, let's say that the Hotel in question has N rooms, where N is an infinite Hyperreal such that N=(1,2,3,4,5,...). This defines a situation in which the Hotel has the same number of rooms as there are Natural numbers, and let's say that all of these rooms are occupied by a single patron. That means there are N patrons staying in the Hotel. Now, let's say 3 people check out of the Hotel. Sure enough, the number of patrons remaining in the Hotel is still infinite, but it is not the same number of patrons as it had originally. Now, there are N-3 patrons, where N-3=(-2,-1,0,1,2,...). It is not true that N=N-3.

                    Now let's say that instead of 3 patrons, all of the patrons in the even numbered rooms check out. Sure enough, this means that an infinite number of patrons are checking out of the Hotel-- but again, it is not the same infinite number as we had originally. In this case, we see that N/2=(0.5,1.0,1.5,2.0,2.5,...) patrons have left, and again, it is not true that N=N/2.

                    Dr. Craig doesn't have a very good understanding of the mathematics which he attempts to describe.
                    See, I'm not a math guy and can't go into this kind of detail. My argument against Craig is philosophical.

                    The series of numbers is an accidentally ordered series, that is, a series which does not depend on the continued existence of any of the prior elements. The existence of 3 is not dependent on the continued existence of 2. A classical example is fathers and sons: a father has to bring a son into existence, but after the son's conception, the father does not have to continue to exist. Craig has to demonstrate that there is a logical incomprehensibility of having an infinite series, which he can't.

                    What Craig would have to show is that the past-finitude of the universe is an essentially ordered series, one where there cannot logically fail to have been some sort of first cause. For him to do that, he has to assume A-theory of time, which, while not necessarily in conflict with modern physics, isn't as self-evident as Craig seems to believe.

                    Comment


                    • What is in evidence that our known universe has an infinite past?
                      . . . the gospel of Christ: for it is the power of God unto salvation to every one that believeth; . . . -- Romans 1:16 KJV

                      . . . that Christ died for our sins according to the scriptures; And that he was buried, and that he rose again the third day according to the scriptures: . . . -- 1 Corinthians 15:3-4 KJV

                      Whosoever believeth that Jesus is the Christ is born of God: . . . -- 1 John 5:1 KJV

                      Comment


                      • Originally posted by 37818 View Post
                        What is in evidence that our known universe has an infinite past?
                        Other than mathematical models? Nothing.

                        Incidentally, that's exactly the same amount of evidence as we have for our known universe having a finite past.
                        "[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


                        • Originally posted by Boxing Pythagoras View Post
                          Other than mathematical models? Nothing.

                          Incidentally, that's exactly the same amount of evidence as we have for our known universe having a finite past.
                          Actually that is not true. The prevailing view is that our known universe began 13.8 billion years ago is that of a finite past based on the evidence.
                          . . . the gospel of Christ: for it is the power of God unto salvation to every one that believeth; . . . -- Romans 1:16 KJV

                          . . . that Christ died for our sins according to the scriptures; And that he was buried, and that he rose again the third day according to the scriptures: . . . -- 1 Corinthians 15:3-4 KJV

                          Whosoever believeth that Jesus is the Christ is born of God: . . . -- 1 John 5:1 KJV

                          Comment


                          • Originally posted by 37818 View Post
                            Actually that is not true. The prevailing view is that our known universe began 13.8 billion years ago is that of a finite past based on the evidence.
                            That prevailing view is based upon mathematical models. The oldest physical data available to us are from hundreds of thousands of years after the Big Bang. While this is incredibly close to the event, on cosmological scales, the simple fact of the matter is that we have no physical data earlier than this.

                            All cosmological claims about times prior to the CMB are simply based upon mathematical models. There exist models in which the universe is past finite, and others in which the universe is past infinite.
                            "[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


                            • Originally posted by Boxing Pythagoras View Post
                              That prevailing view is based upon mathematical models. The oldest physical data available to us are from hundreds of thousands of years after the Big Bang. While this is incredibly close to the event, on cosmological scales, the simple fact of the matter is that we have no physical data earlier than this.

                              All cosmological claims about times prior to the CMB are simply based upon mathematical models. There exist models in which the universe is past finite, and others in which the universe is past infinite.
                              Show the math for a red shift and an infinite past. It does not exist.
                              . . . the gospel of Christ: for it is the power of God unto salvation to every one that believeth; . . . -- Romans 1:16 KJV

                              . . . that Christ died for our sins according to the scriptures; And that he was buried, and that he rose again the third day according to the scriptures: . . . -- 1 Corinthians 15:3-4 KJV

                              Whosoever believeth that Jesus is the Christ is born of God: . . . -- 1 John 5:1 KJV

                              Comment


                              • Originally posted by 37818 View Post
                                Show the math for a red shift and an infinite past. It does not exist.
                                Are you claiming that mathematical models of a universe with a past-infinite time dimension cannot account for red shift in the CMB? Or perhaps red shift in the motion of galaxies?
                                "[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)

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