Miracles

[JimL]

Well Boxing, according to the quotes by Adrift it all seems quite nebulous. So really, I would like to know, and not for the sake of argument, what do you think numbers are?



No, infinities are not connected to reality. And again, don't some of those who Adrift quoted, agree?



See Boxing, you are usually pretty honest but here I really think you are fudging. A finite number of miles could have an actual number - like 100. What number do you give to an endless number of miles?

Unless you too were infinite and eternal along with the universe then your question "could you ever reach the end of the infinite?" makes no sense. Finite is the exact opposite of infinite, and temporal is the exact opposite of eternal. So how could you, being a finite part of an infinite whole, ever expect to traverse the infinite? So, how could infinite many events take place within it then? Because it is eternal and infinite! Things that begin to exist are temporal and finite with respect to themselves, but they are eternal and infinite with respect to that of which they are a part. So, the answer to your question "how can a finite thing possibly come to be at this point within the infinite, is because it is not a thing that came to be within the infinite, it is part of the infinite itself. Again, you have the same cunundrm to deal with concerning God. How, if God is infinite, could you traverse all the related thoughts that led up to the one, 14 billion years ago, in which he decided to create the universe? If your argument against that is that "thoughts" for God are not relational in time, then God is not a thinking thing, not a mind, but infinitely fixed, aka a determined thing.

[seer]

Again, you have the same cunundrm to deal with concerning God. How, if God is infinite, could you traverse all the related thoughts that led up to the one, 14 billion years ago, in which he decided to create the universe? If your argument against that is that "thoughts" for God are not relational in time, then God is not a thinking thing, not a mind, but infinitely fixed, aka a determined thing.

God does not have to move through and infinite number of physical events. And since God is not in time limited by time, I have no idea what God's ideas or thoughts would look like in a timeless realm.

So how could you, being a finite part of an infinite whole, ever expect to traverse the infinite? So, how could infinite many events take place within it then? Because it is eternal and infinite! Things that begin to exist are temporal and finite with respect to themselves, but they are eternal and infinite with respect to that of which they are a part. So, the answer to your question "how can a finite thing possibly come to be at this point within the infinite, is because it is not a thing that came to be within the infinite, it is part of the infinite itself.

Asserting this does not make it so Jim. In my example of an infinite number of miles, I will give you an eternity to walk. It will make no difference for there never would a point when you didn't still have an infinite number of miles ahead.

[JimL]

God does not have to move through and infinite number of physical events. And since God is not in time limited by time, I have no idea what God's ideas or thoughts would look like in a timeless realm.

Well again, if your argument is that time, however time is defined, is not a characteristic of the infinite, then the nature of that infinite, whether it be an eternal Cosmos or God, is a fixed and determined nature. Saying that you have no idea how relational thoughts, or change of any kind, can take place within a timeless realm is to ignore reason, which tells you that they can not.

Asserting this does not make it so Jim. In my example of an infinite number of miles, I will give you an eternity to walk. It will make no difference for there never would a point when you didn't still have an infinite number of miles ahead.

And again, you are correct, being that you are a finite part of a never ending infinite whole, the answer to your question is self evident. You could never, since there is no end to it, traverse the infinite. But the infinite itself is not about time, the infinite is all there, all the time, and universes can pop up anywhere within the infinite. Time only becomes manifest for those changes taking place within the infinite, but the infinite itself within which these changes occur, is all there, in all of infinite time, so it makes no sense to ask if an eternally infinite whole can be traversed by a temporally finite part of itself. But, just because the infinite can not be finitely traversed, prima facie, doesn't prohibit the fact that the infinite whole is made up of finite parts on into infinity.

[Boxing Pythagoras]

Well Boxing, according to the quotes by Adrift it all seems quite nebulous. So really, I would like to know, and not for the sake of argument, what do you think numbers are?

Numbers are well-defined descriptions of quantity.

No, infinities are not connected to reality. And again, don't some of those who Adrift quoted, agree?

Some of them, sure. But they do so knowing that (a) their position has not been demonstrated any more fully than the one they oppose, and (b) their position leads to severe consequences for the study and applicability of mathematics. You do not seem to understand either of these things.

See Boxing, you are usually pretty honest but here I really think you are fudging. A finite number of miles could have an actual number - like 100. What number do you give to an endless number of miles?

Since this is a hypothetical situation, you can define it to be any infinite number. If you would like a simple example, we could say that the number of miles is M, where

[seer]

Numbers are well-defined descriptions of quantity.

Ok, that sounds good.

Some of them, sure. But they do so knowing that (a) their position has not been demonstrated any more fully than the one they oppose, and (b) their position leads to severe consequences for the study and applicability of mathematics. You do not seem to understand either of these things.

You are correct, but here is the problem - where does the layman go, or who does he believe, when the experts disagree? And don't tell me to study the issue more because you have experts who have spent a life time on these issues but still disagree. For instance you said that you disagreed with Edward Nelson, a Professor of Mathematics at Princeton. Boxing are you really as educated as Nelson in this field? Why should I believe you to be correct and him not?

But I am still waiting for you to point to an actual infinity of objects.

Since this is a hypothetical situation, you can define it to be any infinite number. If you would like a simple example, we could say that the number of miles is M, where

Really Boxing? I may not know a lot about math but I do know that an endless number of miles has no actual number, because it is endless.

[Boxing Pythagoras]

You are correct, but here is the problem - where does the layman go, or who does he believe, when the experts disagree? And don't tell me to study the issue more because you have experts who have spent a life time on these issues but still disagree. For instance you said that you disagreed with Edward Nelson, a Professor of Mathematics at Princeton. Boxing are you really as educated as Nelson in this field? Why should I believe you to be correct and him not?

If you, as a layman, do not know what to believe and you do not want to study the issue more, then the most reasonable solution is to accept the view held by the vast majority of experts in a field. Edward Nelson was a brilliant mathematician, but he would have been the first to tell you that his ultrafinitism was an extreme minority position, and that the vast majority of mathematicians disagreed with him.

If a person was looking into scholarship on the historical Jesus, and he did not know what to believe and did not want to study the issue for himself, do you think it would be reasonable for that person to adopt the views of Richard Carrier over against the majority of scholarship? Of course not! Similarly, it is not reasonable to accept a minority position on the philosophy of mathematics without educating yourself on that view.

But I am still waiting for you to point to an actual infinity of objects.

And I'm still waiting for you to tell me why it's relevant to this discourse.

Really Boxing? I may not know a lot about math but I do know that an endless number of miles has no actual number, because it is endless.

Then you don't even know as much about math as you think you know. The mathematics of infinite numbers was formalized over half a century ago, and has been proven to hold true if and only if the Real number system holds true. Therefore, if you deny that infinite numbers are actual numbers, you also need to deny that things like π and √2 are actual numbers.

[Paprika]

Is it possible to reach the end of something that is endless?

Wait and see.

[seer]

If you, as a layman, do not know what to believe and you do not want to study the issue more, then the most reasonable solution is to accept the view held by the vast majority of experts in a field. Edward Nelson was a brilliant mathematician, but he would have been the first to tell you that his ultrafinitism was an extreme minority position, and that the vast majority of mathematicians disagreed with him.

If a person was looking into scholarship on the historical Jesus, and he did not know what to believe and did not want to study the issue for himself, do you think it would be reasonable for that person to adopt the views of Richard Carrier over against the majority of scholarship? Of course not! Similarly, it is not reasonable to accept a minority position on the philosophy of mathematics without educating yourself on that view.

See Boxing you are telling me that the position of a Nelson or Robinson is in the minority. How do you know that? And will it be the minority in the future? And it is different than a Carrier - with that discipline I can understand the language.

And I'm still waiting for you to tell me why it's relevant to this discourse.

Because YOU SAID that you could show us an actual infinity of objects. Or you agree that infinities do not correspond to anything in reality.

Then you don't even know as much about math as you think you know. The mathematics of infinite numbers was formalized over half a century ago, and has been proven to hold true if and only if the Real number system holds true. Therefore, if you deny that infinite numbers are actual numbers, you also need to deny that things like π and √2 are actual numbers.

Giving a label to infinities tells us nothing about how one can actually move through and infinite number of miles.

[Boxing Pythagoras]

See Boxing you are telling me that the position of a Nelson or Robinson is in the minority. How do you know that? And will it be the minority in the future? And it is different than a Carrier - with that discipline I can understand the language.

I know it from asking expert mathematicians about the consensus view regarding infinities. I see no reason to think that it won't be the minority view in the future.

And it is certainly no different than the case with Carrier. If someone who doesn't "understand the language," as you've phrased it, espouses Carrier's position without having actually done any study in the field, and despite knowing that Carrier's position is an extreme minority, you would rightly conclude that this person has adopted an unreasonable view. Similarly, you do not "understand the language," and yet you are adopting an extreme minority position without any thought or desire toward actually studying it. This is why I find your view to be unreasonable.

Because YOU SAID that you could show us an actual infinity of objects. Or you agree that infinities do not correspond to anything in reality.

I did say that I can show an actual infinite quantity of objects. I also said that it is irrelevant to the conversation at hand, since you do not believe that it is necessary to demonstrate an actual physical quantity represented by a number in order for it to be an actual number.

Giving a label to infinities tells us nothing about how one can actually move through and infinite number of miles.

I never said that it did. However, giving a strict definition for a number tells us a great deal about how one can actually traverse that number of miles. To that end, I offered a strictly defined number of miles for us to discuss.

[Adrift]

I know it from asking expert mathematicians about the consensus view regarding infinities. I see no reason to think that it won't be the minority view in the future.

And it is certainly no different than the case with Carrier. If someone who doesn't "understand the language," as you've phrased it, espouses Carrier's position without having actually done any study in the field, and despite knowing that Carrier's position is an extreme minority, you would rightly conclude that this person has adopted an unreasonable view. Similarly, you do not "understand the language," and yet you are adopting an extreme minority position without any thought or desire toward actually studying it. This is why I find your view to be unreasonable.

I get what you're saying, but maybe Carrier is not the best example. Unlike Nelson, Carrier is speaking on a field that isn't exactly within his expertise. Carrier is an unemployed PhD in Ancient History, not a scholar of the NT, and while intelligent he's certainly not brilliant. Also, he has a clear anti-Christian agenda (that he's discussed quite often) behind his minority position.

[Paprika]

But isn't the use of set theory just a convenient sort of axiom to solve the issue without actually dealing with the real-world scenario? Sets are abstract objects. How would that be practical in the real world if you honestly had to traverse a real number of actual infinite miles, or a real number of actual infinite past events?

1) Use of set theory isn't merely 'convenient' because it is the convention to define the number system using some type of set theory.

2) Numbers are abstract objects, and concepts such 'finite' and 'infinite' are likewise abstract. By using the concept of numbers one are using abstract concepts to describe real things of events. In particular, Seer himself is implicitly invoking some kind of notion of the infinite as he tries to derive either a contradiction or an absurdity to make his case.

If you want to argue that certain abstract objects or concepts have no relevance to reality, it has to be demonstrated; you can't cogently beg the question that in general there is no real infinite set to argue there cannot be a real infinite series of events.

[Boxing Pythagoras]

I get what you're saying, but maybe Carrier is not the best example. Unlike Nelson, Carrier is speaking on a field that isn't exactly within his expertise. Carrier is an unemployed PhD in Ancient History, not a scholar of the NT, and while intelligent he's certainly not brilliant. Also, he has a clear anti-Christian agenda (that he's discussed quite often) behind his minority position.

Carrier was simply an example with which I knew Seer would be familiar, and upon whose position we both agree.

I could have gone with a more esoteric minority viewpoint, but I wouldn't have been sure that Seer knew either the viewpoint or even the subject matter which I was discussing. For example, had I pointed out that Rickson Gracie's belief that Jiu-Jitsu is the only martial art a fighter needs to know when stepping into an MMA ring, I would have illustrated the same point; but it's quite possible that Seer has no idea who Rickson is, what Jiu-Jitsu is, or what martial arts are important to the sport of MMA.

[seer]

I know it from asking expert mathematicians about the consensus view regarding infinities. I see no reason to think that it won't be the minority view in the future.

OK

I did say that I can show an actual infinite quantity of objects. I also said that it is irrelevant to the conversation at hand, since you do not believe that it is necessary to demonstrate an actual physical quantity represented by a number in order for it to be an actual number.

OK, so it is irrelevant to our present discussion, so what? I am still curious. I really don't think that infinities actually correspond to anything in reality - that there is no such thing as an actual infinite quantity of objects. I'm not saying that using the concept infinities is not helpful in some way - but you would know more than me on that.

I never said that it did. However, giving a strict definition for a number tells us a great deal about how one can actually traverse that number of miles. To that end, I offered a strictly defined number of miles for us to discuss.

What is the end number of endless miles?

[JonathanL]

Wait and see.

[Boxing Pythagoras]

OK, so it is irrelevant to our present discussion, so what? I am still curious.

Cool. That's all I was looking for. As I said, earlier, once we were agreed on the irrelevance, I'd be more than willing to satisfy your curiosity.

In that case, I'll use one of my favorite examples. The quantity of actual longitudinal positions on the surface of the Earth which lie exactly on the equator is infinite. These positions in space are actual, physical things. You can see them, occupy them, traverse through them, and assign each one of them a distinct label which clearly differentiates it from all of the others. The total quantity of these positions is infinite.

What is the end number of endless miles?

What do you mean by "end number?" If we are using the example I provided, the number of miles is M.