Infinite time?

[charris]

It seems to me possible that there is an infinite time, specifically that of the past. All that would be required is for a previous event or cause (depending on you interpretation of QM).

I mentioned this, and was met with the objection, "If the past was infinite, then it would have taken an infinite amount of time to get here." I personally think this objection is pointless, so maybe if you think this is the case you could expound upon it. If you disagree, then if you could post your reasons as well I would appreciate it.

Also, if you disagree because of other reasons, I would like to hear them.

[charris]

First and foremost, models should not be confused with the actual real world. Infinity is useful in mathematics. I can derive the volume of a sphere by calculating triple integrals, using calculus to add together the volumes of an infinite number of infinitesmal cubes. But it's just an abstraction, one with interesting and useful properties - but an abstraction none the less. But try actually chopping up a sphere into an infinite number of infinitesmal cubes. You can't. It's not real world. The question about time is real world. Just because you can conceptualize time extending infinitely in both directions does not make it so. And incidentally, Craig didn't invent the idea of potential infinity. Aristotle dealt with it. Finally, it’s not pointless at all – it’s at the heart of the very real arrow of time .

Do you even know what a model is? It's a description of the real world. Spacetime is a model, does that mean spacetime isn't real? No. You're basically rewording the complaint "such-and-such is only a theory!" Of course it is, but theories/models explain what we find. Your objection to this is pointless.

Any “when� implies a specific point in past time, and it happened a finite number of days ago. You’re basically trying to give the argument that we can just keep right on counting into the infinite past. Yep, you could certainly do that if the past were infinite, but you must first assume the past is infinite in order to start this endless counting. This doesn't make a case for it actually BEING infinite. You're confusing your ability to conceptualize an infinity with it actually existing in reality. A conceptual observation like this certainly does not in any way refute my statement. How can an infinite past NOT entail an infinite number of past days? Clearly, it does.

Yes, any 'when' is a point in time. So?
I am assuming that the past is infinite, that's what this whole conversation is about. If the past were infinite, then we could just keep on counting. I'm not using this to prove that time is infinite, I'm using to explain how any objections to infinite time are pointless. (Otherwise, I would be begging the question.) But again, you ask 'How can an infinite past NOT entail an infinite number of past days?' This is what I'm talking about, an infinite amount of days since when? Infinity isn't a specific number.

Your statement assumes an infinite past, it doesn’t prove there can be one and doesn’t refute my statement that there would have to be an infinite number of past days.

Again, I'm explaining it, not proving it.

Here’s how: big bang happens, time begins. Going forward, we see the days proceeding one after another and no reason for this to stop; ie the future is potentially infinite.

Time doesn't necessarily begin at the big bang, first of all. We use it as time=0 because that's what we know for certain.

Again, you are presupposing an infinite past when you say, “if a person has always been walking…� How can that be?

Same as before, I'm not using this to prove an infinite past, I'm using it as an explanation of it. I'm sure this was just a miscommunication between us.

How about supporting this assertion. Here’s my support for it being asymmetric:
The past is completed, the future is not completed
The past is immutable, the future is not
Time proceeds in one direction only; there is an arrow of time

Certainly.
First, you are misunderstanding what I mean when I say time is symmetric. I'm not saying that we can travel back in time or that there is no arrow of time, I'm saying that the laws of physics work the same no matter what 'direction' of time you're moving in.
Here's a quote from the particle physicist Victor Stenger about it (not to be used as proof, but an explanation):

A slight time asymmetry in reaction rates on the order of 0.1 percent is observed in the weak interactions of elementary particles. This does not account for the macroscopic arrow of time. Time asymmetry does not forbid reverse processes from occurring; the reaction rate in one direction is simply different than in the other. Even this slight asymmetry goes away if... you change all the particles to antiparticles and take the mirror-image event: that is, you perform the combined operation CPT [charge, parity, time]. Quantum time reversibility does not mean that humans can travel back in time or that time-travel paradoxes do not exist for macroscopic systems. But what it does mean is that one should not assume a direction of time when one is talking about the fundamental processes of nature. The common notion that cause always precedes effect must be modified, so that cause and effect are interchangeable. What we call the effect can just as well be the cause, and the beginning can just as well be the end.

Time symmetry and CPT symmetry. "Space-time symmetry is put to the test" from the CERN Courier. No violations of the combined operation CPT have ever been observed. I can give you a much more detailed explanation if you like, given by Prof. Stenger. I recommend two of his books, "Timeless Reality" and "Comprehensible Cosmos," and the book by Prof. Sean Carroll called "From Eternity to Here." All deal with symmetries used in physics (some books more than others).

You’re being fooled by the math. He defined x(t) to be a function that computes the spatial position at time t. He then integrates this position function over an infinite time span, and calculates a finite number. This implies that over an infinite period of time (that is what he is integrating over), it is possible to traverse a finite distance. That certainly doesn’t demonstrate anything relevant. Integration is a mathematical technique for simultaneously adding together infinitesmals. In this case, it’s infinitesimal distances that are being added together, and they are added together simultaneously. Math is great for being able to do this. However, it’s not a real world transversal of time because in the real world, time intervals (no matter how small) occur one after the other, not simultaneously.

I'm not being fooled by the math at all, actually. He clearly stated that "all that was asked is 'is it logically possible?' and the answer is yes." ("It" being an infinite past.) Did he say that this proves there is an infinite past? No, he said it proves that it is logically possible; you can have infinities and get a finite number. You're still arguing about models, which is pointless.

[fredonly]

First and foremost, models should not be confused with the actual real world. Infinity is useful in mathematics. I can derive the volume of a sphere by calculating triple integrals, using calculus to add together the volumes of an infinite number of infinitesmal cubes. But it's just an abstraction, one with interesting and useful properties - but an abstraction none the less. But try actually chopping up a sphere into an infinite number of infinitesmal cubes. You can't. It's not real world. The question about time is real world. Just because you can conceptualize time extending infinitely in both directions does not make it so. And incidentally, Craig didn't invent the idea of potential infinity. Aristotle dealt with it. Finally, it’s not pointless at all – it’s at the heart of the very real arrow of time .

Do you even know what a model is? It's a description of the real world. Spacetime is a model, does that mean spacetime isn't real? No. You're basically rewording the complaint "such-and-such is only a theory!" Of course it is, but theories/models explain what we find. Your objection to this is pointless.

It depends on which model you’re talking about. I wasn’t actually referring to a theoretical model of spacetime, but let’s go ahead and get into that. If you’re referring to a cosmological model of the big bang, based on general relativity – then I completely agree with you. However, the standard model, which is based on general relativity, does not point to a in infinite past at all. Speculative models that attempt to describe a broader context, such as oscillating big bang/big crunch, multi-verses, colliding branes, etc cannot be argued as “descriptions of reality� – they aren’t complete (e.g. they rely on incomplete and unsupported quantum gravity models, and have practically no empirical support).

What I was actually referring to in my prior post was a generic mathematical model, formulae that can be computed out to infinity. A number line can conceptually extend from –infinity to +infinity; this is a simple mathematical model. My point was that this is just an abstraction, and that this doesn’t necessarily map into reality.

Any “when� implies a specific point in past time, and it happened a finite number of days ago. You’re basically trying to give the argument that we can just keep right on counting into the infinite past. Yep, you could certainly do that if the past were infinite, but you must first assume the past is infinite in order to start this endless counting. This doesn't make a case for it actually BEING infinite. You're confusing your ability to conceptualize an infinity with it actually existing in reality. A conceptual observation like this certainly does not in any way refute my statement. How can an infinite past NOT entail an infinite number of past days? Clearly, it does.

Yes, any 'when' is a point in time. So?

Here’s the “so� -- Let’s use a conceptual number line, representing time from –infinity to +infinity, centered at 0 (now). “when� is a specific point on this timeline and is a finite number of days from now.

I am assuming that the past is infinite, that's what this whole conversation is about. If the past were infinite, then we could just keep on counting. I'm not using this to prove that time is infinite, I'm using to explain how any objections to infinite time are pointless. (Otherwise, I would be begging the question.)

You ARE begging the question. All you are doing is assuming the past is infinite, and refusing to answer the question I posed, and dancing around it. The question I posed is the first step in the logical argument against an infinite past.

But again, you ask 'How can an infinite past NOT entail an infinite number of past days?' This is what I'm talking about, an infinite amount of days since when? Infinity isn't a specific number.

There is no “since when� as I said. Your question is a diversion. You are evading the key question that leads to the logical inconsistency of an infinite past. Let me make it easy, please answer yes or no to these questions:
1. Is the past infinite?
2. (assume the past is infinite):Does the past include an infinite number of days?
3. (assume the past is infinite and the number of past days is infinite): Are each of the past days completed (i.e. are they over and done with)?

Please don’t evade the questions.

Your statement assumes an infinite past, it doesn’t prove there can be one and doesn’t refute my statement that there would have to be an infinite number of past days.

Again, I'm explaining it, not proving it.

Explaining what? You are doing nothing but making an assertion that the past is infinite. You seem vaguely unhappy with the notion that an infinite past implies an infinite number of past days, but you haven’t countered it.

And how can you have an infinite future without an infinite past? The ability to change it is irrelevant.

Here’s how: big bang happens, time begins. Going forward, we see the days proceeding one after another and no reason for this to stop; ie the future is potentially infinite.

Time doesn't necessarily begin at the big bang, first of all. We use it as time=0 because that's what we know for certain.

I was answering your question, explaining how there can be an infinite future without an infinite past. I assume you accept my answer. To be clear, I’m not insisting that time began at the big bang, that’s simply what the standard model predicts. You were the one who said this about models: “Do you even know what a model is? It's a description of the real world.� I’ll point out that to assume time did NOT begin at the big bang is getting beyond the accepted model and into the realm of speculation. However, this is a tangent - not directly related to the impossibility of an infinite past. It doesn't matter if time started at the big bang, or goes further back. There's still a logical problem.

Again, you are presupposing an infinite past when you say, “if a person has always been walking…� How can that be?

Same as before, I'm not using this to prove an infinite past, I'm using it as an explanation of it. I'm sure this was just a miscommunication between us.

Maybe so. I thought you were insisting the past is infinite. Maybe you simply saying that you don’t know, and that you reject my argument; is that it? I’m OK with that position, but you should give a reason why you reject it. As I said earlier, it’s just seems to be a vague unease.

How about supporting this assertion. Here’s my support for it being asymmetric:
The past is completed, the future is not completed
The past is immutable, the future is not
Time proceeds in one direction only; there is an arrow of time

Certainly.
First, you are misunderstanding what I mean when I say time is symmetric. I'm not saying that we can travel back in time or that there is no arrow of time, I'm saying that the laws of physics work the same no matter what 'direction' of time you're moving in.
Here's a quote from the particle physicist Victor Stenger about it (not to be used as proof, but an explanation):

A slight time asymmetry in reaction rates on the order of 0.1 percent is observed in the weak interactions of elementary particles. This does not account for the macroscopic arrow of time. Time asymmetry does not forbid reverse processes from occurring; the reaction rate in one direction is simply different than in the other. Even this slight asymmetry goes away if... you change all the particles to antiparticles and take the mirror-image event: that is, you perform the combined operation CPT [charge, parity, time]. Quantum time reversibility does not mean that humans can travel back in time or that time-travel paradoxes do not exist for macroscopic systems. But what it does mean is that one should not assume a direction of time when one is talking about the fundamental processes of nature. The common notion that cause always precedes effect must be modified, so that cause and effect are interchangeable. What we call the effect can just as well be the cause, and the beginning can just as well be the end.

Time symmetry and CPT symmetry. "Space-time symmetry is put to the test" from the CERN Courier. No violations of the combined operation CPT have ever been observed. I can give you a much more detailed explanation if you like, given by Prof. Stenger. I recommend two of his books, "Timeless Reality" and "Comprehensible Cosmos," and the book by Prof. Sean Carroll called "From Eternity to Here." All deal with symmetries used in physics (some books more than others).

That’s certainly interesting, but the points I made still hold. The past and future are different. The past is completed, and the future is not realized, is not complete, but it has potential. It is the notion of ‘completeness’ that presents the problem of an infinite past. An infinite past implies an actual infinite number of days have been completed. You previously expressed displeasure at my suggestion that there’s a difference between actual infinity and potential infinity. These are most certainly very real distinctions, and are at the heart of the matter. You can’t make the distinction go away. An infinite past implies an actual, completed infinity; an infinite future does not – it only implies a potential infinity. This difference is part of the asymmetry of time, and it is the reason it is logically impossible for the past to be infinite. It is logically impossible to have a completed infinity. It seems possible, on the surface, if you consider the symmetric nature of a number line you might draw to represent time. This is the mistake most people make. You have to think deeper than this representation. Time proceeds one day at a time (which is not apparent on a number line). The only way to reach today, from an infinite past, is for an infinite number of days to be completed. But this is impossible, because infinity entails incompleteness. The future is always incomplete; you can always go out one more day, and then another, and so on. If time were symmetric, going both forward and backward, then one could say the same thing about the past. But it's not symmetric. TIme moves in one direction. The past has no potential. What's done is done. We can't add one more day to the past (like we can the future) because the past is already completed.

You’re being fooled by the math. He defined x(t) to be a function that computes the spatial position at time t. He then integrates this position function over an infinite time span, and calculates a finite number. This implies that over an infinite period of time (that is what he is integrating over), it is possible to traverse a finite distance. That certainly doesn’t demonstrate anything relevant. Integration is a mathematical technique for simultaneously adding together infinitesmals. In this case, it’s infinitesimal distances that are being added together, and they are added together simultaneously. Math is great for being able to do this. However, it’s not a real world transversal of time because in the real world, time intervals (no matter how small) occur one after the other, not simultaneously.

I'm not being fooled by the math at all, actually. He clearly stated that "all that was asked is 'is it logically possible?' and the answer is yes." ("It" being an infinite past.) Did he say that this proves there is an infinite past? No, he said it proves that it is logically possible; you can have infinities and get a finite number. You're still arguing about models, which is pointless.

The assertion he would need to disprove was: “it is impossible to traverse an infinite amount of time by successive addition.� He didn’t do this. What he did was to show that an infinite amount of time could be traversed by addition. But it was through the simultaneous addition of integral calculus, not successive addition. This is what makes traversal of an infinite past impossible; you have to traverse it one day at a time; you can’t traverse it all at once.

[charris]

First and foremost, models should not be confused with the actual real world. Infinity is useful in mathematics. I can derive the volume of a sphere by calculating triple integrals, using calculus to add together the volumes of an infinite number of infinitesmal cubes. But it's just an abstraction, one with interesting and useful properties - but an abstraction none the less. But try actually chopping up a sphere into an infinite number of infinitesmal cubes. You can't. It's not real world. The question about time is real world. Just because you can conceptualize time extending infinitely in both directions does not make it so. And incidentally, Craig didn't invent the idea of potential infinity. Aristotle dealt with it. Finally, it’s not pointless at all – it’s at the heart of the very real arrow of time .

Do you even know what a model is? It's a description of the real world. Spacetime is a model, does that mean spacetime isn't real? No. You're basically rewording the complaint "such-and-such is only a theory!" Of course it is, but theories/models explain what we find. Your objection to this is pointless.

It depends on which model you’re talking about. I wasn’t actually referring to a theoretical model of spacetime, but let’s go ahead and get into that. If you’re referring to a cosmological model of the big bang, based on general relativity – then I completely agree with you. However, the standard model, which is based on general relativity, does not point to a in infinite past at all. Speculative models that attempt to describe a broader context, such as oscillating big bang/big crunch, multi-verses, colliding branes, etc cannot be argued as “descriptions of reality� – they aren’t complete (e.g. they rely on incomplete and unsupported quantum gravity models, and have practically no empirical support).

What I was actually referring to in my prior post was a generic mathematical model, formulae that can be computed out to infinity. A number line can conceptually extend from –infinity to +infinity; this is a simple mathematical model. My point was that this is just an abstraction, and that this doesn’t necessarily map into reality.

I was referring to spacetime itself, not the big bang. I'm sure you're aware, the standard model is incomplete, and the people who came up with it have stated it's wrong because it doesn't take into account quantum mechanics. Since the standard model is incomplete, you can't use it (by your own reasoning) to say that time must be finite.

Any “when� implies a specific point in past time, and it happened a finite number of days ago. You’re basically trying to give the argument that we can just keep right on counting into the infinite past. Yep, you could certainly do that if the past were infinite, but you must first assume the past is infinite in order to start this endless counting. This doesn't make a case for it actually BEING infinite. You're confusing your ability to conceptualize an infinity with it actually existing in reality. A conceptual observation like this certainly does not in any way refute my statement. How can an infinite past NOT entail an infinite number of past days? Clearly, it does.

Yes, any 'when' is a point in time. So?

Here’s the “so� -- Let’s use a conceptual number line, representing time from –infinity to +infinity, centered at 0 (now). “when� is a specific point on this timeline and is a finite number of days from now.

Yes, if you pick a point on a number line, any point you pick is a finite distance away (as long as you aren't dividing).

I am assuming that the past is infinite, that's what this whole conversation is about. If the past were infinite, then we could just keep on counting. I'm not using this to prove that time is infinite, I'm using to explain how any objections to infinite time are pointless. (Otherwise, I would be begging the question.)

You ARE begging the question. All you are doing is assuming the past is infinite, and refusing to answer the question I posed, and dancing around it. The question I posed is the first step in the logical argument against an infinite past.

I'm not begging the question at all, contrary to what you insist. I will state again, I'm not using explanations that assume an infinite past to prove an infinite past. That would just be absurd. You asked how could we progress in time if it were infinite, and I described how that is irrelevant if[/it] it were infinite. I'm explaining away your objection, not proving it is the truth. There is a difference.

But again, you ask 'How can an infinite past NOT entail an infinite number of past days?' This is what I'm talking about, an infinite amount of days since when? Infinity isn't a specific number.

There is no “since when� as I said. Your question is a diversion. You are evading the key question that leads to the logical inconsistency of an infinite past. Let me make it easy, please answer yes or no to these questions:
1. Is the past infinite?
2. (assume the past is infinite):Does the past include an infinite number of days?
3. (assume the past is infinite and the number of past days is infinite): Are each of the past days completed (i.e. are they over and done with)?

Please don’t evade the questions.

I haven't been evading any question at all.
1. It is logically possible.
2. This question makes no sense because you're using infinity as a number, which it is not. Is there a day before today? Yes. Is there a day before that day? Yes. Continue with this, and you will still not reach infinity (even if you could). Why? Because you haven't been doing this for infinity. The only way this question even makes the slightest amount of sense is if you have always been counting. That means there is no beginning an infinite amount of time ago, you've just always been counting.
3. If I were to assume what you propose, then yes. The objection 'we could never reach now' is still irrelevant because you can always add. 1+1=2 2+1=3 3+1=4 etc. etc.

Your statement assumes an infinite past, it doesn’t prove there can be one and doesn’t refute my statement that there would have to be an infinite number of past days.

Again, I'm explaining it, not proving it.

Explaining what? You are doing nothing but making an assertion that the past is infinite. You seem vaguely unhappy with the notion that an infinite past implies an infinite number of past days, but you haven’t countered it.

I'm not making an assertion at all, I'm explaining how an infinite past is logically possible. The only thing I'm unhappy with is that you continuously accuse me of committing a logical fallacy, which I have not.

And how can you have an infinite future without an infinite past? The ability to change it is irrelevant.

Here’s how: big bang happens, time begins. Going forward, we see the days proceeding one after another and no reason for this to stop; ie the future is potentially infinite.

Time doesn't necessarily begin at the big bang, first of all. We use it as time=0 because that's what we know for certain.

I was answering your question, explaining how there can be an infinite future without an infinite past. I assume you accept my answer. To be clear, I’m not insisting that time began at the big bang, that’s simply what the standard model predicts. You were the one who said this about models: “Do you even know what a model is? It's a description of the real world.� I’ll point out that to assume time did NOT begin at the big bang is getting beyond the accepted model and into the realm of speculation. However, this is a tangent - not directly related to the impossibility of an infinite past. It doesn't matter if time started at the big bang, or goes further back. There's still a logical problem.

If you say that there can be an infinite future, then you are left with the same 'problem' that you propose with an infinite past. Why? Because if you were to proceed an infinite number of days in the future (whatever that means), then the past would be an infinite number of days in the past, thus 'you couldn't have traveled in time.'

Again, you are presupposing an infinite past when you say, “if a person has always been walking…� How can that be?

Same as before, I'm not using this to prove an infinite past, I'm using it as an explanation of it. I'm sure this was just a miscommunication between us.

Maybe so. I thought you were insisting the past is infinite. Maybe you simply saying that you don’t know, and that you reject my argument; is that it? I’m OK with that position, but you should give a reason why you reject it. As I said earlier, it’s just seems to be a vague unease.

That's exactly it. We can't measure back to a point called 'infinity,' we can only measure back finite times ago. But, since we know that you can always subtract a number on a time line, I see no logical objection as to why it couldn't be applied to time.

How about supporting this assertion. Here’s my support for it being asymmetric:
The past is completed, the future is not completed
The past is immutable, the future is not
Time proceeds in one direction only; there is an arrow of time

Certainly.
First, you are misunderstanding what I mean when I say time is symmetric. I'm not saying that we can travel back in time or that there is no arrow of time, I'm saying that the laws of physics work the same no matter what 'direction' of time you're moving in.
Here's a quote from the particle physicist Victor Stenger about it (not to be used as proof, but an explanation):

A slight time asymmetry in reaction rates on the order of 0.1 percent is observed in the weak interactions of elementary particles. This does not account for the macroscopic arrow of time. Time asymmetry does not forbid reverse processes from occurring; the reaction rate in one direction is simply different than in the other. Even this slight asymmetry goes away if... you change all the particles to antiparticles and take the mirror-image event: that is, you perform the combined operation CPT [charge, parity, time]. Quantum time reversibility does not mean that humans can travel back in time or that time-travel paradoxes do not exist for macroscopic systems. But what it does mean is that one should not assume a direction of time when one is talking about the fundamental processes of nature. The common notion that cause always precedes effect must be modified, so that cause and effect are interchangeable. What we call the effect can just as well be the cause, and the beginning can just as well be the end.

Time symmetry and CPT symmetry. "Space-time symmetry is put to the test" from the CERN Courier. No violations of the combined operation CPT have ever been observed. I can give you a much more detailed explanation if you like, given by Prof. Stenger. I recommend two of his books, "Timeless Reality" and "Comprehensible Cosmos," and the book by Prof. Sean Carroll called "From Eternity to Here." All deal with symmetries used in physics (some books more than others).

That’s certainly interesting, but the points I made still hold. The past and future are different. The past is completed, and the future is not realized, is not complete, but it has potential. It is the notion of ‘completeness’ that presents the problem of an infinite past. An infinite past implies an actual infinite number of days have been completed. You previously expressed displeasure at my suggestion that there’s a difference between actual infinity and potential infinity. These are most certainly very real distinctions, and are at the heart of the matter. You can’t make the distinction go away. An infinite past implies an actual, completed infinity; an infinite future does not – it only implies a potential infinity. This difference is part of the asymmetry of time, and it is the reason it is logically impossible for the past to be infinite. It is logically impossible to have a completed infinity. It seems possible, on the surface, if you consider the symmetric nature of a number line you might draw to represent time. This is the mistake most people make. You have to think deeper than this representation. Time proceeds one day at a time (which is not apparent on a number line). The only way to reach today, from an infinite past, is for an infinite number of days to be completed. But this is impossible, because infinity entails incompleteness. The future is always incomplete; you can always go out one more day, and then another, and so on. If time were symmetric, going both forward and backward, then one could say the same thing about the past. But it's not symmetric. TIme moves in one direction. The past has no potential. What's done is done. We can't add one more day to the past (like we can the future) because the past is already completed.

So you hold to a point that is rejected by almost every working physicist, and certainly every working quantum physicist? When anyone says that time is symmetric, again, we aren't saying you can travel back in time or that something hasn't happened. We're saying that the laws of physics work whether you are at point t=2011->infinity or t=-2011-> -infinity. Not to mention that, in quantum mechanics, we see things happen that violate the normal notions of causality.

You’re being fooled by the math. He defined x(t) to be a function that computes the spatial position at time t. He then integrates this position function over an infinite time span, and calculates a finite number. This implies that over an infinite period of time (that is what he is integrating over), it is possible to traverse a finite distance. That certainly doesn’t demonstrate anything relevant. Integration is a mathematical technique for simultaneously adding together infinitesmals. In this case, it’s infinitesimal distances that are being added together, and they are added together simultaneously. Math is great for being able to do this. However, it’s not a real world transversal of time because in the real world, time intervals (no matter how small) occur one after the other, not simultaneously.

I'm not being fooled by the math at all, actually. He clearly stated that "all that was asked is 'is it logically possible?' and the answer is yes." ("It" being an infinite past.) Did he say that this proves there is an infinite past? No, he said it proves that it is logically possible; you can have infinities and get a finite number. You're still arguing about models, which is pointless.

The assertion he would need to disprove was: “it is impossible to traverse an infinite amount of time by successive addition.� He didn’t do this. What he did was to show that an infinite amount of time could be traversed by addition. But it was through the simultaneous addition of integral calculus, not successive addition. This is what makes traversal of an infinite past impossible; you have to traverse it one day at a time; you can’t traverse it all at once.

Why, if you have been counting for an infinite amount of time, could you not reach a time infinitely far away? You've always been counting, you'll always bee counting, and ta da! You've reached 'now.'

"Time, Successive Addition, and Kalam Cosmological Arguments" by Graham Oppy

[fredonly]

First and foremost, models should not be confused with the actual real world. Infinity is useful in mathematics. I can derive the volume of a sphere by calculating triple integrals, using calculus to add together the volumes of an infinite number of infinitesmal cubes. But it's just an abstraction, one with interesting and useful properties - but an abstraction none the less. But try actually chopping up a sphere into an infinite number of infinitesmal cubes. You can't. It's not real world. The question about time is real world. Just because you can conceptualize time extending infinitely in both directions does not make it so. And incidentally, Craig didn't invent the idea of potential infinity. Aristotle dealt with it. Finally, it’s not pointless at all – it’s at the heart of the very real arrow of time .

Do you even know what a model is? It's a description of the real world. Spacetime is a model, does that mean spacetime isn't real? No. You're basically rewording the complaint "such-and-such is only a theory!" Of course it is, but theories/models explain what we find. Your objection to this is pointless.

It depends on which model you’re talking about. I wasn’t actually referring to a theoretical model of spacetime, but let’s go ahead and get into that. If you’re referring to a cosmological model of the big bang, based on general relativity – then I completely agree with you. However, the standard model, which is based on general relativity, does not point to a in infinite past at all. Speculative models that attempt to describe a broader context, such as oscillating big bang/big crunch, multi-verses, colliding branes, etc cannot be argued as “descriptions of reality� – they aren’t complete (e.g. they rely on incomplete and unsupported quantum gravity models, and have practically no empirical support).

What I was actually referring to in my prior post was a generic mathematical model, formulae that can be computed out to infinity. A number line can conceptually extend from –infinity to +infinity; this is a simple mathematical model. My point was that this is just an abstraction, and that this doesn’t necessarily map into reality.

I was referring to spacetime itself, not the big bang. I'm sure you're aware, the standard model is incomplete, and the people who came up with it have stated it's wrong because it doesn't take into account quantum mechanics. Since the standard model is incomplete, you can't use it (by your own reasoning) to say that time must be finite.

I’m not using it to prove time must be finite. I brought it up after pointing out that models (in general) do not necessarily correspond to reality. You responded that they are “representations of the real world.� Well, some are (like the cosmological model) and some aren’t (like a number line from –infinity to +infinity). Then I pointed out that the standard big bang cosmological model, which is a model of reality, points to a beginning of time. You are now pointing out that this model is incomplete. I agree – and also agree with you that this means it does not prove time is finite. However, it does show that time could BE finite. Do you agree?

Any “when� implies a specific point in past time, and it happened a finite number of days ago. You’re basically trying to give the argument that we can just keep right on counting into the infinite past. Yep, you could certainly do that if the past were infinite, but you must first assume the past is infinite in order to start this endless counting. This doesn't make a case for it actually BEING infinite. You're confusing your ability to conceptualize an infinity with it actually existing in reality. A conceptual observation like this certainly does not in any way refute my statement. How can an infinite past NOT entail an infinite number of past days? Clearly, it does.

Yes, any 'when' is a point in time. So?

Here’s the “so� -- Let’s use a conceptual number line, representing time from –infinity to +infinity, centered at 0 (now). “when� is a specific point on this timeline and is a finite number of days from now.

Yes, if you pick a point on a number line, any point you pick is a finite distance away (as long as you aren't dividing).

What do you mean by “as long as you aren’t dividing?� You can’t arrive at infinity by dividing.

I am assuming that the past is infinite, that's what this whole conversation is about. If the past were infinite, then we could just keep on counting. I'm not using this to prove that time is infinite, I'm using to explain how any objections to infinite time are pointless. (Otherwise, I would be begging the question.)

You ARE begging the question. All you are doing is assuming the past is infinite, and refusing to answer the question I posed, and dancing around it. The question I posed is the first step in the logical argument against an infinite past.

I'm not begging the question at all, contrary to what you insist. I will state again, I'm not using explanations that assume an infinite past to prove an infinite past. That would just be absurd. You asked how could we progress in time if it were infinite, and I described how that is irrelevant if[/it] it were infinite. I'm explaining away your objection, not proving it is the truth. There is a difference.

I never asked “how we could progress in time if it were infinite. “ I am asking how we could have a completed infinity.

But again, you ask 'How can an infinite past NOT entail an infinite number of past days?' This is what I'm talking about, an infinite amount of days since when? Infinity isn't a specific number.

There is no “since when� as I said. Your question is a diversion. You are evading the key question that leads to the logical inconsistency of an infinite past. Let me make it easy, please answer yes or no to these questions:
1. Is the past infinite?
2. (assume the past is infinite):Does the past include an infinite number of days?
3. (assume the past is infinite and the number of past days is infinite): Are each of the past days completed (i.e. are they over and done with)?

Please don’t evade the questions.

I haven't been evading any question at all.
(fredonly: Is the past infinite?)
It is logically possible.

Thanks – this clarifies your position.

2. (assume the past is infinite):Does the past include an infinite number of days?
This question makes no sense because you're using infinity as a number, which it is not. Is there a day before today? Yes. Is there a day before that day? Yes. Continue with this, and you will still not reach infinity (even if you could). Why? Because you haven't been doing this for infinity. The only way this question even makes the slightest amount of sense is if you have always been counting. That means there is no beginning an infinite amount of time ago, you've just always been counting.

I’m simply stating an obvious implication: if the past is infinite, then an infinite number of days have passed. From this, where are you deciding I’m using infinity as a number?

Fredonly: (assume the past is infinite and the number of past days is infinite): Are each of the past days completed (i.e. are they over and done with)?

3. If I were to assume what you propose, then yes. The objection 'we could never reach now' is still irrelevant because you can always add. 1+1=2 2+1=3 3+1=4 etc. etc.

My point is that “completeness� is a property of the past, and that this is different from the future. Your comment about successive addition is irrelevant. All this does is demonstrate a mathematical infinity. We agree that “infinity� is a valid mathematical concept. My arguments pertain to the REAL WORLD, and specifically- whether or not if can make sense for past time to be infinite.

Your statement assumes an infinite past, it doesn’t prove there can be one and doesn’t refute my statement that there would have to be an infinite number of past days.

Again, I'm explaining it, not proving it.

Explaining what? You are doing nothing but making an assertion that the past is infinite. You seem vaguely unhappy with the notion that an infinite past implies an infinite number of past days, but you haven’t countered it.

I'm not making an assertion at all, I'm explaining how an infinite past is logically possible. The only thing I'm unhappy with is that you continuously accuse me of committing a logical fallacy, which I have not.

Your arguments are not fallacies within the domain of mathematics, but you are failing to deal with the real-world aspects of time. I believe this is called the fallacy of exclusion. You exclude the key properties of time from your consideration, demonstrate the mathematical consistency of “infinity,� then declare your argument valid.

And how can you have an infinite future without an infinite past? The ability to change it is irrelevant.

Here’s how: big bang happens, time begins. Going forward, we see the days proceeding one after another and no reason for this to stop; ie the future is potentially infinite.

Time doesn't necessarily begin at the big bang, first of all. We use it as time=0 because that's what we know for certain.

I was answering your question, explaining how there can be an infinite future without an infinite past. I assume you accept my answer. To be clear, I’m not insisting that time began at the big bang, that’s simply what the standard model predicts. You were the one who said this about models: “Do you even know what a model is? It's a description of the real world.� I’ll point out that to assume time did NOT begin at the big bang is getting beyond the accepted model and into the realm of speculation. However, this is a tangent - not directly related to the impossibility of an infinite past. It doesn't matter if time started at the big bang, or goes further back. There's still a logical problem.

If you say that there can be an infinite future, then you are left with the same 'problem' that you propose with an infinite past. Why? Because if you were to proceed an infinite number of days in the future (whatever that means), then the past would be an infinite number of days in the past, thus 'you couldn't have traveled in time.'

You keep ignoring the properties of time, and the distinction between actual and potential infinite. The future is potentially infinite: there is a well defined process for counting future days (e.g., beginning today, we’ll place a notch on the wall as each day passes); the process potentially proceeds for an infinitely long time. This is successive addition that never stops – this is what infinity IS, in the real world: it’s a process not a destination: there’s always one more; you can’t reach infinity. Infinity is just the concept of continuing without end. But at any point in time, the past has no capacity to be extended. It has no potential; it is completed. It is this ‘completeness’ property of past-time that is incompatible with infinity.

Again, you are presupposing an infinite past when you say, “if a person has always been walking…� How can that be?

Same as before, I'm not using this to prove an infinite past, I'm using it as an explanation of it. I'm sure this was just a miscommunication between us.

Maybe so. I thought you were insisting the past is infinite. Maybe you simply saying that you don’t know, and that you reject my argument; is that it? I’m OK with that position, but you should give a reason why you reject it. As I said earlier, it’s just seems to be a vague unease.

That's exactly it. We can't measure back to a point called 'infinity,' we can only measure back finite times ago. But, since we know that you can always subtract a number on a time line, I see no logical objection as to why it couldn't be applied to time.

The logical objection, as I stated above, is that it ignores the property of “completeness� (which is inherent in the past), and it ignores the distinction between actual and potential infinity.

How about supporting this assertion. Here’s my support for it being asymmetric:
The past is completed, the future is not completed
The past is immutable, the future is not
Time proceeds in one direction only; there is an arrow of time

Certainly.
First, you are misunderstanding what I mean when I say time is symmetric. I'm not saying that we can travel back in time or that there is no arrow of time, I'm saying that the laws of physics work the same no matter what 'direction' of time you're moving in.
Here's a quote from the particle physicist Victor Stenger about it (not to be used as proof, but an explanation):

A slight time asymmetry in reaction rates on the order of 0.1 percent is observed in the weak interactions of elementary particles. This does not account for the macroscopic arrow of time. Time asymmetry does not forbid reverse processes from occurring; the reaction rate in one direction is simply different than in the other. Even this slight asymmetry goes away if... you change all the particles to antiparticles and take the mirror-image event: that is, you perform the combined operation CPT [charge, parity, time]. Quantum time reversibility does not mean that humans can travel back in time or that time-travel paradoxes do not exist for macroscopic systems. But what it does mean is that one should not assume a direction of time when one is talking about the fundamental processes of nature. The common notion that cause always precedes effect must be modified, so that cause and effect are interchangeable. What we call the effect can just as well be the cause, and the beginning can just as well be the end.

Time symmetry and CPT symmetry. "Space-time symmetry is put to the test" from the CERN Courier. No violations of the combined operation CPT have ever been observed. I can give you a much more detailed explanation if you like, given by Prof. Stenger. I recommend two of his books, "Timeless Reality" and "Comprehensible Cosmos," and the book by Prof. Sean Carroll called "From Eternity to Here." All deal with symmetries used in physics (some books more than others).

That’s certainly interesting, but the points I made still hold. The past and future are different. The past is completed, and the future is not realized, is not complete, but it has potential. It is the notion of ‘completeness’ that presents the problem of an infinite past. An infinite past implies an actual infinite number of days have been completed. You previously expressed displeasure at my suggestion that there’s a difference between actual infinity and potential infinity. These are most certainly very real distinctions, and are at the heart of the matter. You can’t make the distinction go away. An infinite past implies an actual, completed infinity; an infinite future does not – it only implies a potential infinity. This difference is part of the asymmetry of time, and it is the reason it is logically impossible for the past to be infinite. It is logically impossible to have a completed infinity. It seems possible, on the surface, if you consider the symmetric nature of a number line you might draw to represent time. This is the mistake most people make. You have to think deeper than this representation. Time proceeds one day at a time (which is not apparent on a number line). The only way to reach today, from an infinite past, is for an infinite number of days to be completed. But this is impossible, because infinity entails incompleteness. The future is always incomplete; you can always go out one more day, and then another, and so on. If time were symmetric, going both forward and backward, then one could say the same thing about the past. But it's not symmetric. Time moves in one direction. The past has no potential. What's done is done. We can't add one more day to the past (like we can the future) because the past is already completed.

So you hold to a point that is rejected by almost every working physicist, and certainly every working quantum physicist? When anyone says that time is symmetric, again, we aren't saying you can travel back in time or that something hasn't happened. We're saying that the laws of physics work whether you are at point t=2011->infinity or t=-2011-> -infinity. Not to mention that, in quantum mechanics, we see things happen that violate the normal notions of causality.

You’re overstating what physicists say. So what if there are exceptions at the quantum level? The universe appears (as Quentin Smith has said) to be probabilistically causative. I’m just arguing that there is an arrow of time and that time is asymmetric at the macro level. Stenger points to some exceptions on the micro level, and that this implies there’s more to time – an interesting observation, but we still don’t know very much about the nature of time. There is no overall theory of time that explains why we experience an arrow of time on the macro level while we can also observe violations on the micro level. What are the implications? If you see something in Stenger that disproves my argument, pull them out and make the case, because I don’t see it. Our discussion pertains to the passage of time at the macro level, “time� as we know it. If you’d like to outline a model for time that differs from that of our natural, intuitive observations – do so, and we’ll see where it takes us. But it’s invalid to suggest that Stenger’s observations suggest that time is symmetric in a sense relevant to our discussion, that there is no “arrow of time,� or that the past has potential or that the future is actual.

Here’s a quote from another physicist who confronts the question more directly:

The future is unlike the past. This is an absolutely basic observation, as basic as the
observation that “things fall�. We expect that a real understanding of the Arrow of Time — the temporal “direction� defined by the physical differences between the future and the past — will arise only in the context of some deep theory, such as string theory. Conversely, we argue here that such an understanding is urgently required if recent stringtheoretic ideas about cosmology are to be made to function.

In this work, we explain in detail why it is so difficult to find a satisfactory theory of the Arrow of Time. There are several difficulties, but the key problems arise from Roger Penrose’s observation that the Arrow is ultimately connected with the extremely “non-generic� character of the spatial geometry of the earliest Universe. We argue that the explanations of the Arrow proposed hitherto are unsatisfactory, because they do not address this basic point. -- Brett McInnes, from The Arrow Of Time In The Landscape

The key points are in bold. We don’t understand the nature of time, but it is fundamental that the future is unlike the past. Physicists don’t deny that.

You’re being fooled by the math. He defined x(t) to be a function that computes the spatial position at time t. He then integrates this position function over an infinite time span, and calculates a finite number. This implies that over an infinite period of time (that is what he is integrating over), it is possible to traverse a finite distance. That certainly doesn’t demonstrate anything relevant. Integration is a mathematical technique for simultaneously adding together infinitesmals. In this case, it’s infinitesimal distances that are being added together, and they are added together simultaneously. Math is great for being able to do this. However, it’s not a real world transversal of time because in the real world, time intervals (no matter how small) occur one after the other, not simultaneously.

I'm not being fooled by the math at all, actually. He clearly stated that "all that was asked is 'is it logically possible?' and the answer is yes." ("It" being an infinite past.) Did he say that this proves there is an infinite past? No, he said it proves that it is logically possible; you can have infinities and get a finite number. You're still arguing about models, which is pointless.

The assertion he would need to disprove was: “it is impossible to traverse an infinite amount of time by successive addition.� He didn’t do this. What he did was to show that an infinite amount of time could be traversed by addition. But it was through the simultaneous addition of integral calculus, not successive addition. This is what makes traversal of an infinite past impossible; you have to traverse it one day at a time; you can’t traverse it all at once.

Why, if you have been counting for an infinite amount of time, could you not reach a time infinitely far away? You've always been counting, you'll always been counting, and ta da! You've reached 'now.'

You’re reverting to your standard invalid argument. How about acknowledging that I have successfully shown the flaw in that so-called proof that it is possible to tranverse an infinity by successive addition.

Returning to your invalid argument, all you are doing is mapping the set of negative integers into a presumed infinite past. I guess you are saying that you can “traverse� an infinite past by mapping it to an equivalent infinite set (another instantaneous process, as in integral calculus). But the only thing this does is to show that – assuming the past is infinite, the ’number of past days’ has cardinality aleph-null.

Counting forward in time is easy to picture. Start today, and add one each day. The counting process goes in the direction of the arrow of time and is synchronized with time, and matching it exactly 1:1. The act of counting is a process that moves forward with time, always matching it. There is no such matching process with the past, so you can’t actually count the days as you can with the future– you can only count numbers. This is a fundamental difference between the past and the future.

Try defining a counting process for the past, which has always been taking place. Here's the only thing I can come up with:Let’s say an immortal man has always existed and has always been counting the days. What number is he on, today?
Either answer that question, give me an alternative counting process - one that counts days, not merely numbers and merely assumes there is a corresponding day, --or admit defeat.

"Time, Successive Addition, and Kalam Cosmological Arguments" by Graham Oppy

In hindsight, I shouldn’t have responded to your link to that silly calculus argument –because this encouraged you to do more of the same, searching the internet for counters to my argument and then sending me the link and demanding a response. In fairness, you should do what I’ve done – make the case yourself. You are free to educate yourself with any article you find, and adapt their arguments (small quotes are fine, but make the argument your own). But don’t expect me to respond to every random argument you find.

[charris]

I was referring to spacetime itself, not the big bang. I'm sure you're aware, the standard model is incomplete, and the people who came up with it have stated it's wrong because it doesn't take into account quantum mechanics. Since the standard model is incomplete, you can't use it (by your own reasoning) to say that time must be finite.

I’m not using it to prove time must be finite. I brought it up after pointing out that models (in general) do not necessarily correspond to reality. You responded that they are “representations of the real world.� Well, some are (like the cosmological model) and some aren’t (like a number line from –infinity to +infinity). Then I pointed out that the standard big bang cosmological model, which is a model of reality, points to a beginning of time. You are now pointing out that this model is incomplete. I agree – and also agree with you that this means it does not prove time is finite. However, it does show that time could BE finite. Do you agree?

They correspond to reality from what we know. What is to keep the 'number line' model from being one of the models that actually does represent reality? The reason the standard BB model isn't a model of reality is because there is a fraction that we know to be false. So unless you're saying that something we know isn't true is true, then you're using a bad example. I agree that time could be finite. I don't think it is, but that doesn't mean it isn't. (The phrase I saw was, "Reality doesn't give a d--n about your beliefs." ) We pick the model which is accurate to observation. Does that mean it is 'reality?' No, but it is an accurate description of it.

Here’s the “so� -- Let’s use a conceptual number line, representing time from –infinity to +infinity, centered at 0 (now). “when� is a specific point on this timeline and is a finite number of days from now.

Yes, if you pick a point on a number line, any point you pick is a finite distance away (as long as you aren't dividing).

What do you mean by “as long as you aren’t dividing?� You can’t arrive at infinity by dividing.

First, you can't ever 'arrive' at infinity, unless you've already been doing it for 'infinity.' Like I said, infinity isn't a number.
As far as division goes, you can 'reach' infinity by dividing. That's the basis of Zeno's paradoxes. While we know that the paradoxes don't hold up, you can still mathematically divide a section up an 'infinite' number of times.

I'm not begging the question at all, contrary to what you insist. I will state again, I'm not using explanations that assume an infinite past to prove an infinite past. That would just be absurd. You asked how could we progress in time if it were infinite, and I described how that is irrelevant if[/it] it were infinite. I'm explaining away your objection, not proving it is the truth. There is a difference.

I never asked “how we could progress in time if it were infinite. “ I am asking how we could have a completed infinity.

Who said we completed infinity? That doesn't even make sense. This is for two reasons: first, because time is still progressing (like you've said), meaning that we haven't reached any endpoint called 'infinity.' Second, this is avoided because time would have been progressing for infinity. If you've been counting for infinity, why wouldn't you 'reach infinity?'

I haven't been evading any question at all.
(fredonly: Is the past infinite?)
It is logically possible.

Thanks – this clarifies your position.

I can't tell if that is sarcasm, so I'll assume it isn't :p

2. (assume the past is infinite):Does the past include an infinite number of days?
This question makes no sense because you're using infinity as a number, which it is not. Is there a day before today? Yes. Is there a day before that day? Yes. Continue with this, and you will still not reach infinity (even if you could). Why? Because you haven't been doing this for infinity. The only way this question even makes the slightest amount of sense is if you have always been counting. That means there is no beginning an infinite amount of time ago, you've just always been counting.

I’m simply stating an obvious implication: if the past is infinite, then an infinite number of days have passed. From this, where are you deciding I’m using infinity as a number?

"...then an infinite number of days have passed."
Call me crazy, but you just gave infinity a number :p
When I say time is infinite, I'm not saying it as a number, I'm saying it to mean that time never began, it just always was progressing. It never started, it was just always there.

Fredonly: (assume the past is infinite and the number of past days is infinite): Are each of the past days completed (i.e. are they over and done with)?

3. If I were to assume what you propose, then yes. The objection 'we could never reach now' is still irrelevant because you can always add. 1+1=2 2+1=3 3+1=4 etc. etc.

My point is that “completeness� is a property of the past, and that this is different from the future. Your comment about successive addition is irrelevant. All this does is demonstrate a mathematical infinity. We agree that “infinity� is a valid mathematical concept. My arguments pertain to the REAL WORLD, and specifically- whether or not if can make sense for past time to be infinite.

You asked a bit later how you could traverse through infinity by successive addition. When I do this, you say it is irrelevant. Did I miss something?
No one is arguing that the past wouldn't be complete. I'm arguing that these 'infinite number of days' would be complete by having traversed them for an infinite time. If you have an infinite amount of time, what is stopping you from progressing 'to' infinity?

I'm not making an assertion at all, I'm explaining how an infinite past is logically possible. The only thing I'm unhappy with is that you continuously accuse me of committing a logical fallacy, which I have not.

Your arguments are not fallacies within the domain of mathematics, but you are failing to deal with the real-world aspects of time. I believe this is called the fallacy of exclusion. You exclude the key properties of time from your consideration, demonstrate the mathematical consistency of “infinity,� then declare your argument valid.

I'm not excluding the 'real-world aspects of time' at all. You would be committing a straw-man fallacy if you really think this.

If you say that there can be an infinite future, then you are left with the same 'problem' that you propose with an infinite past. Why? Because if you were to proceed an infinite number of days in the future (whatever that means), then the past would be an infinite number of days in the past, thus 'you couldn't have traveled in time.'

You keep ignoring the properties of time, and the distinction between actual and potential infinite. The future is potentially infinite: there is a well defined process for counting future days (e.g., beginning today, we’ll place a notch on the wall as each day passes); the process potentially proceeds for an infinitely long time. This is successive addition that never stops – this is what infinity IS, in the real world: it’s a process not a destination: there’s always one more; you can’t reach infinity. Infinity is just the concept of continuing without end. But at any point in time, the past has no capacity to be extended. It has no potential; it is completed. It is this ‘completeness’ property of past-time that is incompatible with infinity.

I'm not ignoring the properties of time at all, actually.
We pick a t=0 and work from there. That doesn't mean there isn't a t=-1 or t=-n. Time would still work the exact same if it were infinite or finite. We pick an arbitrary point (currently the big bang), and we count how long since then. Time 'flows' because of entropy the same in both models.

That's exactly it. We can't measure back to a point called 'infinity,' we can only measure back finite times ago. But, since we know that you can always subtract a number on a time line, I see no logical objection as to why it couldn't be applied to time.

The logical objection, as I stated above, is that it ignores the property of “completeness� (which is inherent in the past), and it ignores the distinction between actual and potential infinity.

And the property of 'completeness' (which isn't inherent in the past in quantum mechanics, by the way), is dealt with by having been counting for infinity. You count for an 'infinite amount' time and you get 'infinity'.

So you hold to a point that is rejected by almost every working physicist, and certainly every working quantum physicist? When anyone says that time is symmetric, again, we aren't saying you can travel back in time or that something hasn't happened. We're saying that the laws of physics work whether you are at point t=2011->infinity or t=-2011-> -infinity. Not to mention that, in quantum mechanics, we see things happen that violate the normal notions of causality.

You’re overstating what physicists say. So what if there are exceptions at the quantum level? The universe appears (as Quentin Smith has said) to be probabilistically causative. I’m just arguing that there is an arrow of time and that time is asymmetric at the macro level. Stenger points to some exceptions on the micro level, and that this implies there’s more to time – an interesting observation, but we still don’t know very much about the nature of time. There is no overall theory of time that explains why we experience an arrow of time on the macro level while we can also observe violations on the micro level. What are the implications? If you see something in Stenger that disproves my argument, pull them out and make the case, because I don’t see it. Our discussion pertains to the passage of time at the macro level, “time� as we know it. If you’d like to outline a model for time that differs from that of our natural, intuitive observations – do so, and we’ll see where it takes us. But it’s invalid to suggest that Stenger’s observations suggest that time is symmetric in a sense relevant to our discussion, that there is no “arrow of time,� or that the past has potential or that the future is actual.

I'm not overstating what physicists say at all. I'm telling you the working method for quantum physicists that works and is observed. There has never been an observed violation of CPT symmetry, and this is not likely to happen due to the fact that it would also break Lorentz symmetry.
What does the universe being probabilistic have to do with anything? Quantum mechanics is a probabilistic science, as denoted by the wave function. There is an arrow of time, absolutely. No one is arguing against that. (In fact, entropy is the only thing that breaks T-symmetry (which doesn't happen in CPT symmetry).)
Well, if you're like me and a few other inflation-accepting scientists, then a quantum field would have been around before the big bang. Since, at the quantum level, we see violations of normal causality, a quantum field wouldn't have the same 'problem' of 'completing infinity.'

And I think I see where our main disagreement comes in, and it is entirely my fault. I'm not arguing for something like our universe to be infinite (like Sir Roger Penrose does). I'm arguing for something like quantum fields being infinite. I should have clarified, so I apologize.

Here’s a quote from another physicist who confronts the question more directly:

The future is unlike the past. This is an absolutely basic observation, as basic as the observation that “things fall�. We expect that a real understanding of the Arrow of Time — the temporal “direction� defined by the physical differences between the future and the past — will arise only in the context of some deep theory, such as string theory. Conversely, we argue here that such an understanding is urgently required if recent stringtheoretic ideas about cosmology are to be made to function.

In this work, we explain in detail why it is so difficult to find a satisfactory theory of the Arrow of Time. There are several difficulties, but the key problems arise from Roger Penrose’s observation that the Arrow is ultimately connected with the extremely “non-generic� character of the spatial geometry of the earliest Universe. We argue that the explanations of the Arrow proposed hitherto are unsatisfactory, because they do not address this basic point. -- Brett McInnes, from The Arrow Of Time In The Landscape

The key points are in bold. We don’t understand the nature of time, but it is fundamental that the future is unlike the past. Physicists don’t deny that.

Meh, let's not talk about string theory :p

Assuming the validity of the Schrodinger equation has a deep, if somewhat obvious, consequence: time stretches for all of eternity. In classical mechanics, singularities in phase space can disrupt the evolution, causing time to grind to a halt. But in quantum mechanics, unitary evolution ensures that there there is no boundary to time; the variable 't' runs from -∞ to ∞. The modern idea that time does have a beginning arises from the existence of a Big Bang singularity in cosmological models based on general relativity. But from our current perspective, that is an outmoded relic of our stubborn insistence to think in terms of spacetime, rather than directly in terms of the quantum state. Classical general relativity, after all, is not correct; at some point it must be subsumed into a quantum description of gravity. We therefore imagine that the classical Big Bang corresponds to some particular kind of quantum state, which may be obscure from the perspective of our current knowledge, but will ultimately be resolved. It follows, under our assumptions, that there was something before the Big Bang, and time stretches back into the infinite past.

But this raises a problem, well known to anyone who has thought about the mysteries of time: within our observable universe, time has an arrow. Entropy was small near the Big Bang, is somewhat larger today, and will be even larger in the future. On macroscopic scales where the concept of entropy makes sense, the world around us is characterized by irreversible processes, from the mixing of milk into coffee to the collapse of a star to form a black hole. But the Schrodinger equation, on which this is all purportedly based, is perfectly reversible. The Hamiltonian operator may not respect time-reversal invariance (as in the weak interactions of the Standard Model), but that is beside the point. As long as the the Schrodinger equation holds, quantum time evolution is perfectly unitary (information-preserving) - given the current quantum state, we can reliably reconstruct the past just as well as the future. How can we reconcile this with macroscopic irreversibility?

"What If Time Really Exists?" by Sean Carroll
He then attempts to answer the question with a bit of math, and thermodynamics and cosmology.

I think that physicists understand time a little better than you're letting on. It isn't like they have no idea what they're talking about...

Why, if you have been counting for an infinite amount of time, could you not reach a time infinitely far away? You've always been counting, you'll always been counting, and ta da! You've reached 'now.'

You’re reverting to your standard invalid argument. How about acknowledging that I have successfully shown the flaw in that so-called proof that it is possible to tranverse an infinity by successive addition.

Will I use the math from that post? No. But you haven't shown how you can't get a number from simple addition.

Returning to your invalid argument, all you are doing is mapping the set of negative integers into a presumed infinite past. I guess you are saying that you can “traverse� an infinite past by mapping it to an equivalent infinite set (another instantaneous process, as in integral calculus). But the only thing this does is to show that – assuming the past is infinite, the ’number of past days’ has cardinality aleph-null.

What did you think I was talking about? Each day would be given a value, n. Today is n, yesterday was n-1, the day before that was n-2, the day before that was n-3... the day before that was n-∞. And it's the same in the future direction. Tomorrow is n+1, the day after that is n+2, the day after that is n+3... the day after that is n+∞. What else would it be? (Note that I'm not trying to say that infinity is a number, only that days would be continuous in either direction.)

Counting forward in time is easy to picture. Start today, and add one each day. The counting process goes in the direction of the arrow of time and is synchronized with time, and matching it exactly 1:1. The act of counting is a process that moves forward with time, always matching it. There is no such matching process with the past, so you can’t actually count the days as you can with the future– you can only count numbers. This is a fundamental difference between the past and the future.

If we're going by days, then we could only count the past. How do we know the future doesn't end? And I can count past days by seeing what effects it has made on the present. (E.g. I won't have 'x' in front of me if I didn't buy 'x' at some point in the past.) Of course, this isn't the case for quantum mechanics, being that time is symmetric in CPT symmetry.

Try defining a counting process for the past, which has always been taking place. Here's the only thing I can come up with:Let’s say an immortal man has always existed and has always been counting the days. What number is he on, today?

Again, you're trying to give infinity a number. I guess you could say he would be on infinity if that makes sense.

Either answer that question, give me an alternative counting process - one that counts days, not merely numbers and merely assumes there is a corresponding day, --or admit defeat.

Why can't we assign days to numbers, exactly? I could just turn around and say, "Give me an alternative counting process - one that counts minutes, not merely numbers and merely assumes there is a corresponding mark on a clock." See? That doesn't make sense. Time is a product of entropy, and used as a measurement. Asking there to not be a number for the measurement means you couldn't count time at all, in either direction, finite or infinite.

"Time, Successive Addition, and Kalam Cosmological Arguments" by Graham Oppy

In hindsight, I shouldn’t have responded to your link to that silly calculus argument –because this encouraged you to do more of the same, searching the internet for counters to my argument and then sending me the link and demanding a response. In fairness, you should do what I’ve done – make the case yourself. You are free to educate yourself with any article you find, and adapt their arguments (small quotes are fine, but make the argument your own). But don’t expect me to respond to every random argument you find.

Well, it wasn't just some random article that I found. I do think it explains the situation better. But, if you don't want to read it that's perfectly fine.

[fredonly]

Here’s the “so� -- Let’s use a conceptual number line, representing time from –infinity to +infinity, centered at 0 (now). “when� is a specific point on this timeline and is a finite number of days from now.

Yes, if you pick a point on a number line, any point you pick is a finite distance away (as long as you aren't dividing).

What do you mean by “as long as you aren’t dividing?� You can’t arrive at infinity by dividing.

First, you can't ever 'arrive' at infinity, unless you've already been doing it for 'infinity.' Like I said, infinity isn't a number.

It’s not true that you can arrive at infinity if you’re doing it for infinity. Consider the Tristram Shandy Pardox:

Tristram Shandy, who is immortal, is writing his auto-biography. Unfortunately, he writes very slowly; each day of his life takes him a year to write about. Will he ever finish his book? If he starts today, one year from now he will be behind by one year minus one day. In two years he will be behind by two years, minus 2 days… How can you say that his infinite writing will someday catch up to his infinite lifetime, when he keeps getting further and further behind?

As far as division goes, you can 'reach' infinity by dividing. That's the basis of Zeno's paradoxes. While we know that the paradoxes don't hold up, you can still mathematically divide a section up an 'infinite' number of times.

You’ve made 3 errors here: 1) Zeno’s paradox is not a dividing of infinity; it is a division of a finite length an infinite number of times. 2) This repeated division results in smaller and smaller lengths, approaching, but never reaching, a point. Mathematically this is called a limit. The limit, as #divisions approaches infinity, is a length of 0 (i.e. a point). 3) this is mathematics; not real world. I challenge you to personally divide something repeatedly and arrive at a point. You will never get there. You see, a limit is a potential, - it means: this is where we’re headed; but you cannot ever reach there. In the real world, “dividing� is a countable, temporal event. In the real world, you can’t really do it an “infinite number� of times, as you corrected me (thank you, because it’s an important point) – you can only keep doing it and never stop.

Again, you were correct in saying that infinity is not a number. Keep in mind that although a ‘limit’ can often be calculated to be a number, this does not imply the actual limit can be reached in the real world through temporal processes. A limit is approached, never reached.

I'm not begging the question at all, contrary to what you insist. I will state again, I'm not using explanations that assume an infinite past to prove an infinite past. That would just be absurd. You asked how could we progress in time if it were infinite, and I described how that is irrelevant if[/it] it were infinite. I'm explaining away your objection, not proving it is the truth. There is a difference.

I never asked “how we could progress in time if it were infinite. “ I am asking how we could have a completed infinity.

Who said we completed infinity? That doesn't even make sense.

I pointed out that the past is complete, and you agreed in your prior post. Here’s the quote:

How about supporting this assertion. Here’s my support for it being asymmetric:
The past is completed, the future is not completed
The past is immutable, the future is not
Time proceeds in one direction only; there is an arrow of time

Certainly.

But your comment, “Who said we completed infinity? That doesn't even make sense.� Contains a good observation: a completed infinity doesn’t make sense. And that is one of the key points. Let me place it in context:

At point in time “T�:
1. PD is the set of all days prior to T
2. If the past is infinite, then PD is an infinite set.
3. An infinite set cannot be complete
4. At time T, the set PD is completed – no additional days can be added (because of the arrow of time)
5. Therefore PD cannot be an infinite set; i.e. the past is not infinite

This is for two reasons: first, because time is still progressing (like you've said), meaning that we haven't reached any endpoint called 'infinity.'

Yes, time is progressing and more days become past, but to analyze the situation you have to consider “what is past� at a specific point of time. At any specific point in time (T), the past is complete.

Second, this is avoided because time would have been progressing for infinity. If you've been counting for infinity, why wouldn't you 'reach infinity?'

See the Tristram Shandy paradox, above.

I haven't been evading any question at all.
(fredonly: Is the past infinite?)
It is logically possible.

Thanks – this clarifies your position.

I can't tell if that is sarcasm, so I'll assume it isn't :p

Honestly, I wasn’t sure if you were insisting the past is infinite, or were simply saying that it could be infinite. Now I know.

2. (assume the past is infinite):Does the past include an infinite number of days?
This question makes no sense because you're using infinity as a number, which it is not. Is there a day before today? Yes. Is there a day before that day? Yes. Continue with this, and you will still not reach infinity (even if you could). Why? Because you haven't been doing this for infinity. The only way this question even makes the slightest amount of sense is if you have always been counting. That means there is no beginning an infinite amount of time ago, you've just always been counting.

I’m simply stating an obvious implication: if the past is infinite, then an infinite number of days have passed. From this, where are you deciding I’m using infinity as a number?

"...then an infinite number of days have passed."
Call me crazy, but you just gave infinity a number :p

OK – I understand your comment. I’ll rephrase: the set of past days is an infinite set. (I will use this corrected terminology throughout this current post).

When I say time is infinite, I'm not saying it as a number, I'm saying it to mean that time never began, it just always was progressing. It never started, it was just always there.

I get it, but this doesn’t preclude consideration of the set of “past days.� It is the properties of this set that creates the logical problems.

Fredonly: (assume the past is infinite and the number of past days is infinite): Are each of the past days completed (i.e. are they over and done with)?

3. If I were to assume what you propose, then yes. The objection 'we could never reach now' is still irrelevant because you can always add. 1+1=2 2+1=3 3+1=4 etc. etc.

My point is that “completeness� is a property of the past, and that this is different from the future. Your comment about successive addition is irrelevant. All this does is demonstrate a mathematical infinity. We agree that “infinity� is a valid mathematical concept. My arguments pertain to the REAL WORLD, where each addition operation is a temporal event, and occur sequentially. This is different from writing down a conceptual series as you have done (1+1=2 2+1=3, 3+1=4 etc. etc.). In the real world, you have to actually add 1+1. After completing this, you add 2+1, and so on – these take time.

You asked a bit later how you could traverse through infinity by successive addition. When I do this, you say it is irrelevant. Did I miss something? No one is arguing that the past wouldn't be complete. I'm arguing that these 'infinite number of days' would be complete by having traversed them for an infinite time. If you have an infinite amount of time, what is stopping you from progressing 'to' infinity?

Here’s what’s stopping you: Paradoxes. Tristram Shandy is one. Hilbert’s hotel is another:

A hotel has countably infinitely many rooms. All rooms are occupied. Analogous to your view of “reaching infinity in infinite time� – this would imply that it would be impossible for the hotel to accommodate any additional guests. However, when a new customer shows up – the problem is easily solved: move all the current guests to the next highest room number (from room n into room n+1). This frees up room #1 for the new guest, and all the prior guests are also accommodated. Next, what happens if a countably infinite group ofcustomers appear, all demanding rooms? Still not a problem. Move the current guests from room N into room N*2, freeing up all the rooms with odd numbers – this infinity or rooms should have no problem accommodating the infinity of new guests.

The moral of the story is that a “completed infinity� is paradoxical and therefore illogical. This arises because of the nature of cardinality of infinite sets. Any two sets with the same cardinality can be mapped from one to the other. You can map the set of positive integers to the set of even-numbered integers. You can map the set of integers divisible by 1 billion to the set of positive integers. Mapping is not the same as counting.

I'm not making an assertion at all, I'm explaining how an infinite past is logically possible. The only thing I'm unhappy with is that you continuously accuse me of committing a logical fallacy, which I have not.

Your arguments are not fallacies within the domain of mathematics, but you are failing to deal with the real-world aspects of time. I believe this is called the fallacy of exclusion. You exclude the key properties of time from your consideration, demonstrate the mathematical consistency of “infinity,� then declare your argument valid.

I'm not excluding the 'real-world aspects of time' at all. You would be committing a straw-man fallacy if you really think this.

You certainly did exclude real world aspects when you asserted that computation of an integral across a range to (or from) infinity implies an infinite amount of time can be traversed. Same thing when you suggest you can “reach infinity� if you have infinite time. We don’t have to call it a fallacy, but at least it’s a math error.

If you say that there can be an infinite future, then you are left with the same 'problem' that you propose with an infinite past. Why? Because if you were to proceed an infinite number of days in the future (whatever that means), then the past would be an infinite number of days in the past, thus 'you couldn't have traveled in time.'

You keep ignoring these properties of time: the arrow of time; the fact that real-world processes are temporal; and that there’s a distinction between actual and potential infinite. The future is potentially infinite: there is a well defined temporal process for counting future days (e.g., beginning today, we’ll place a notch on the wall as each day passes); the process potentially proceeds without end. In the real world, infinity is such a process and is not a destination: there’s always one more; you can’t reach infinity. Infinity is just the concept of continuing the temporal process without end. Mathematical functions, like integral calculus or mapping members of sets, are atemporal.

We pick a t=0 and work from there. That doesn't mean there isn't a t=-1 or t=-n. Time would still work the exact same if it were infinite or finite.

This is true, but ignores the fact that the past is complete. Consideration of future time (t+1, t+2…) is irrespective of whether or not any future period will actually be reached: the POTENTIAL is still there. The past is different because it lacks potential.

We pick an arbitrary point (currently the big bang), and we count how long since then. Time 'flows' because of entropy the same in both models.

“because of entropy?!� Upon what complete theory of time is THIS based? Or do you take this as an article of faith?

That's exactly it. We can't measure back to a point called 'infinity,' we can only measure back finite times ago. But, since we know that you can always subtract a number on a time line, I see no logical objection as to why it couldn't be applied to time.

The logical objection is that you cannot define a temporal process for exactly counting the past days. The mathematical method you have used is just a mapping, which creates paradoxes.

And the property of 'completeness' (which isn't inherent in the past in quantum mechanics, by the way), is dealt with by having been counting for infinity. You count for an 'infinite amount' time and you get 'infinity'.

Again I refer you to the paradoxes. BTW, the property of “completeness� pertains to set theory.

So you hold to a point that is rejected by almost every working physicist, and certainly every working quantum physicist? When anyone says that time is symmetric, again, we aren't saying you can travel back in time or that something hasn't happened. We're saying that the laws of physics work whether you are at point t=2011->infinity or t=-2011-> -infinity. Not to mention that, in quantum mechanics, we see things happen that violate the normal notions of causality.

You’re overstating what physicists say. So what if there are exceptions at the quantum level? The universe appears (as Quentin Smith has said) to be probabilistically causative. I’m just arguing that there is an arrow of time and that time is asymmetric at the macro level. Stenger points to some exceptions on the micro level, and that this implies there’s more to time – an interesting observation, but we still don’t know very much about the nature of time. There is no overall theory of time that explains why we experience an arrow of time on the macro level while we can also observe violations on the micro level. What are the implications? If you see something in Stenger that disproves my argument, pull them out and make the case, because I don’t see it. Our discussion pertains to the passage of time at the macro level, “time� as we know it. If you’d like to outline a model for time that differs from that of our natural, intuitive observations – do so, and we’ll see where it takes us. But it’s invalid to suggest that Stenger’s observations suggest that time is symmetric in a sense relevant to our discussion, that there is no “arrow of time,� or that the past has potential or that the future is actual.

I'm not overstating what physicists say at all. I'm telling you the working method for quantum physicists that works and is observed. There has never been an observed violation of CPT symmetry, and this is not likely to happen due to the fact that it would also break Lorentz symmetry.

What does the universe being probabilistic have to do with anything? Quantum mechanics is a probabilistic science, as denoted by the wave function. There is an arrow of time, absolutely. No one is arguing against that. (In fact, entropy is the only thing that breaks T-symmetry (which doesn't happen in CPT symmetry).)
Well, if you're like me and a few other inflation-accepting scientists, then a quantum field would have been around before the big bang. Since, at the quantum level, we see violations of normal causality, a quantum field wouldn't have the same 'problem' of 'completing infinity.'

And I think I see where our main disagreement comes in, and it is entirely my fault. I'm not arguing for something like our universe to be infinite (like Sir Roger Penrose does). I'm arguing for something like quantum fields being infinite. I should have clarified, so I apologize.

I don’t think this makes a difference, but correct me if I’m wrong. I’m not insisting that the big bang is necessarily the beginning of time (although it COULD be). I’m just asserting (and supporting) the idea that past time is not infinite. If there is a predecessor to the big bang, the predecessor was either “timeless� (to use William Craig’s terminology) or it existed for a finite amount of time (because the same logical inconsistency applies to this epoch).

“timeless� is a difficult concept, but it implies unchanging and without duration. It’s something like a frozen point in time, except that points in time are preceded by durations of time. Timeless is not an infinite duration of time; it is 0 duration. If the immediate predecessor (or cause) of the big bang was a “quantum field,� it could be considered the timeless entity (only if it had no predecessors). William Craig wouldn’t like it, but I don’t see anything wrong with it.

Assuming the validity of the Schrodinger equation has a deep, if somewhat obvious, consequence: time stretches for all of eternity. In classical mechanics, singularities in phase space can disrupt the evolution, causing time to grind to a halt. But in quantum mechanics, unitary evolution ensures that there there is no boundary to time; the variable 't' runs from -∞ to ∞. The modern idea that time does have a beginning arises from the existence of a Big Bang singularity in cosmological models based on general relativity. But from our current perspective, that is an outmoded relic of our stubborn insistence to think in terms of spacetime, rather than directly in terms of the quantum state. Classical general relativity, after all, is not correct; at some point it must be subsumed into a quantum description of gravity. We therefore imagine that the classical Big Bang corresponds to some particular kind of quantum state, which may be obscure from the perspective of our current knowledge, but will ultimately be resolved. It follows, under our assumptions, that there was something before the Big Bang, and time stretches back into the infinite past.

But this raises a problem, well known to anyone who has thought about the mysteries of time: within our observable universe, time has an arrow. Entropy was small near the Big Bang, is somewhat larger today, and will be even larger in the future. On macroscopic scales where the concept of entropy makes sense, the world around us is characterized by irreversible processes, from the mixing of milk into coffee to the collapse of a star to form a black hole. But the Schrodinger equation, on which this is all purportedly based, is perfectly reversible. The Hamiltonian operator may not respect time-reversal invariance (as in the weak interactions of the Standard Model), but that is beside the point. As long as the the Schrodinger equation holds, quantum time evolution is perfectly unitary (information-preserving) - given the current quantum state, we can reliably reconstruct the past just as well as the future. How can we reconcile this with macroscopic irreversibility?

"What If Time Really Exists?" by Sean Carroll
He then attempts to answer the question with a bit of math, and thermodynamics and cosmology.

I think that physicists understand time a little better than you're letting on. It isn't like they have no idea what they're talking about...

Physicists certainly have some solid observations about time, and some interesting hypotheses. But consider the implications of this statement from the above: “Classical general relativity, after all, is not correct; at some point it must be subsumed into a quantum description of gravity.�--
1) We currently have no no fully developed quantum description of gravity
2) The fact that “general relativity� is wrong demonstrates the problem of making metaphysical assumptions based on theories even when they ARE fully developed.
3) There is no fully developed theory of time. To draw conclusions about time based either on Shrodinger’s equation, or from a partially developed theory of quantum gravity is analogous to drawing conclusions about quantum gravity using General Relativity.
4) Just because some equations can be calculated with infinities, and the equations compute with time going in either direction does not necessitate such infinities as actually existing, or of time truly going in both directions (e.g. no one suggests time travel to the past is possible despite the tidbits of information about some micro exceptions to the arrow of time).

Why, if you have been counting for an infinite amount of time, could you not reach a time infinitely far away? You've always beencounting, you'll always been counting, and ta da! You've reached 'now.'

You’re reverting to your standard invalid argument. How about acknowledging that I have successfully shown the flaw in that so-called proof that it is possible to tranverse an infinity by successive addition.

Will I use the math from that post? No. But you haven't shown how you can't get a number from simple addition.

Integral calculus is not a simple addition, and that is exactly my point.

Returning to your invalid argument, all you are doing is mapping the set of negative integers into a presumed infinite past. I guess you are saying that you can “traverse� an infinite past by mapping it to an equivalent infinite set (another instantaneous process, as in integral calculus). But the only thing this does is to show that – assuming the past is infinite, the ’number of past days’ has cardinality aleph-null.

What did you think I was talking about? Each day would be given a value, n. Today is n, yesterday was n-1, the day before that was n-2, the day before that was n-3... the day before that was n-∞. And it's the same in the future direction. Tomorrow is n+1, the day after that is n+2, the day after that is n+3... the day after that is n+∞. What else would it be? (Note that I'm not trying to say that infinity is a number, only that days would be continuous in either direction.)

Counting forward in time is easy to picture. Start today, and add one each day. The counting process goes in the direction of the arrow of time and is synchronized with time, and matching it exactly 1:1. The act of counting is a process that moves forward with time, always matching it. There is no such matching process with the past, so you can’t actually count the days as you can with the future– you can only count numbers. This is a fundamental difference between the past and the future.

If we're going by days, then we could only count the past. How do we know the future doesn't end?

We don’t! That’s why we say that the counting of future days is only a “potential infinite.�

And I can count past days by seeing what effects it has made on the present. (E.g. I won't have 'x' in front of me if I didn't buy 'x' at some point in the past.)

Nice try, but it doesn’t work. This is essentially what physicists have done by estimating the age of the universe. If time is infinite, this only scratches the surface. How are you going to count the durations of time (the “days�) that preceded this? Even if prior states of the universe could somehow be detected, clearly the only thing we could ever do is to detect a FINITE NUMBER of such states.

Of course, this isn't the case for quantum mechanics, being that time is symmetric in CPT symmetry

Interesting, but still – without a complete theory of time, it’s not valid to pull out some possible implications based on specific interpretations of other theories that have some relationship to time. Otherwise this opens the door to ad hoc interpretations.

Try defining a counting process for the past, which has always been taking place. Here's the only thing I can come up with: Let’s say an immortal man has always existed and has always been counting the days. What number is he on, today?

Again, you're trying to give infinity a number. I guess you could say he would be on infinity if that makes sense.

I’m demonstrating the impossibility of a completed, infinite set. No, it doesn’t make sense to say he’s on “infinity� – that’s not a number. Temporal counting can always be interrupted, and the count queried. It will always be a number, and not infinite. This is true with counting of the future days; the count is always finite - it’s the process that doesn’t end. But hypothetical temporal counting I’ve described of the past HAS ended, at “now.� This is just another way to look at the “completeness� problem.

Either answer that question, give me an alternative counting process - one that counts days, not merely numbers and merely assumes there is a corresponding day, --or admit defeat.

Why can't we assign days to numbers, exactly? I could just turn around and say, "Give me an alternative counting process - one that counts minutes, not merely numbers and merely assumes there is a corresponding mark on a clock." See? That doesn't make sense.

I’m using “day� to represent a fixed finite interval of time. It’s irrelevant how long the interval is, but I’m insisting that there be some sort of sequential counting as we can do with future time. For the future, we enumerate at the start of each interval. If the future comes to an abrupt halt because the god Chronos wills it, then the counting stops. There is no chance that the counting will exceed the days and no chance that the days will exceed the counting. They stay matched and avoid paradoxes.

Time is a product of entropy, and used as a measurement. Asking there to not be a number for the measurement means you couldn't count time at all, in either direction, finite or infinite.

Time is a product of entropy? This is a rather speculative hypothesis, so it’s to draw inferences. Again, there is no well-defined theory of time

"Time, Successive Addition, and Kalam Cosmological Arguments" by Graham Oppy

In hindsight, I shouldn’t have responded to your link to that silly calculus argument –because this encouraged you to do more of the same, searching the internet for counters to my argument and then sending me the link and demanding a response. In fairness, you should do what I’ve done – make the case yourself. You are free to educate yourself with any article you find, and adapt their arguments (small quotes are fine, but make the argument your own). But don’t expect me to respond to every random argument you find.

Well, it wasn't just some random article that I found. I do think it explains the situation better. But, if you don't want to read it that's perfectly fine.

I did read it, and it’s flawed; some of it is completely irrelevant to our discussion. But I’m not going to give you a rebuttal of someone else’s argument. I’m challenging you to read the article and decide which of the arguments seem sound, and present those to me in your own words. Perhaps you’ll actually find some his flaws yourself.

Here’s one of my pet peeves about some non-theists (I myself am agnostic): a tendency to find an argument whose conclusion they agree with, and then use it like scripture. The attitude is: this conclusion matches my thinking, so it must be a good argument. This argument is then posted as a link, or quoted like a verse from scripture. This is nonsense. There is good reasoning, and there is bad reasoning. In theory, we’re supposed to be the rational ones (vs. theists). Pointing to a document or webpage is about the same as pointing to a verse from scripture. If it’s a good argument, learn it and use it, but do not simply assume the argument is good.

[charris]

What do you mean by “as long as you aren’t dividing?� You can’t arrive at infinity by dividing.

First, you can't ever 'arrive' at infinity, unless you've already been doing it for 'infinity.' Like I said, infinity isn't a number.

It’s not true that you can arrive at infinity if you’re doing it for infinity. Consider the Tristram Shandy Pardox:

Tristram Shandy, who is immortal, is writing his auto-biography. Unfortunately, he writes very slowly; each day of his life takes him a year to write about. Will he ever finish his book? If he starts today, one year from now he will be behind by one year minus one day. In two years he will be behind by two years, minus 2 days… How can you say that his infinite writing will someday catch up to his infinite lifetime, when he keeps getting further and further behind?

If I'm not mistaken, Russell, who came up with the paradox, answered it. Know what his answer was? Infinite time.

As far as division goes, you can 'reach' infinity by dividing. That's the basis of Zeno's paradoxes. While we know that the paradoxes don't hold up, you can still mathematically divide a section up an 'infinite' number of times.

You’ve made 3 errors here: 1) Zeno’s paradox is not a dividing of infinity; it is a division of a finite length an infinite number of times. 2) This repeated division results in smaller and smaller lengths, approaching, but never reaching, a point. Mathematically this is called a limit. The limit, as #divisions approaches infinity, is a length of 0 (i.e. a point). 3) this is mathematics; not real world. I challenge you to personally divide something repeatedly and arrive at a point. You will never get there. You see, a limit is a potential, - it means: this is where we’re headed; but you cannot ever reach there. In the real world, “dividing� is a countable, temporal event. In the real world, you can’t really do it an “infinite number� of times, as you corrected me (thank you, because it’s an important point) – you can only keep doing it and never stop.

1) Miscommunication. I thought I had said that 'you' were dividing up a space into infinity.
2) Something similar to 'the limit of 100/2n as n approaches ∞,' which results in 0. So if the tortoise is 100 meters away, and you run half of that, then you take that distance and run half of that... you would eventually not be moving because you would be approaching an infinite division.
3) I don't need to be able to do it in practice, I can do it in principle. Do numbers not exist or something?

Again, you were correct in saying that infinity is not a number. Keep in mind that although a ‘limit’ can often be calculated to be a number, this does not imply the actual limit can be reached in the real world through temporal processes. A limit is approached, never reached.

I wasn't trying to imply that a limit can be reached, even mathematically. You're the one saying that you can reach a limit, not me.

Who said we completed infinity? That doesn't even make sense.

I pointed out that the past is complete, and you agreed in your prior post. Here’s the quote:

How about supporting this assertion. Here’s my support for it being asymmetric:
The past is completed, the future is not completed
The past is immutable, the future is not
Time proceeds in one direction only; there is an arrow of time

Certainly.

That wasn't me agreeing, that was me complying to support the assertion.

But your comment, “Who said we completed infinity? That doesn't even make sense.� Contains a good observation: a completed infinity doesn’t make sense. And that is one of the key points. Let me place it in context:

At point in time “T�:
1. PD is the set of all days prior to T
2. If the past is infinite, then PD is an infinite set.
3. An infinite set cannot be complete
4. At time T, the set PD is completed – no additional days can be added (because of the arrow of time)
5. Therefore PD cannot be an infinite set; i.e. the past is not infinite

I don't agree with premise 4, because as I've said, having a complete infinity doesn't make sense. Or, if you want to stick with the Tristram Shandy paradox, you have an infinite amount of time.

This is for two reasons: first, because time is still progressing (like you've said), meaning that we haven't reached any endpoint called 'infinity.'

Yes, time is progressing and more days become past, but to analyze the situation you have to consider “what is past� at a specific point of time. At any specific point in time (T), the past is complete.

And there could be an infinite number of days into the future. Problem solved.

I can't tell if that is sarcasm, so I'll assume it isn't :p

Honestly, I wasn’t sure if you were insisting the past is infinite, or were simply saying that it could be infinite. Now I know.

Then I'm glad I could clear that up.

"...then an infinite number of days have passed." Call me crazy, but you just gave infinity a number :p

OK – I understand your comment. I’ll rephrase: the set of past days is an infinite set. (I will use this corrected terminology throughout this current post).

Much better Aleph can be worked with. As I'm sure you're aware, aleph-0 is the infinite, countable set of all natural numbers. If you add any natural number to this, then guess what you get? Aleph-0. You are adding to an infinite set and you are still left with the same cardinality of the infinite set. But I'm sure you already know this.

When I say time is infinite, I'm not saying it as a number, I'm saying it to mean that time never began, it just always was progressing. It never started, it was just always there.

I get it, but this doesn’t preclude consideration of the set of “past days.� It is the properties of this set that creates the logical problems.

The set of past days would be included in the set, yes. Contrary to what you keep saying, infinite sets don't just end. You would have to say that the infinite set of past days is finite, which is a contradiction.

Fredonly: (assume the past is infinite and the number of past days is infinite): Are each of the past days completed (i.e. are they over and done with)?

3. If I were to assume what you propose, then yes. The objection 'we could never reach now' is still irrelevant because you can always add. 1+1=2 2+1=3 3+1=4 etc. etc.

My point is that “completeness� is a property of the past, and that this is different from the future. Your comment about successive addition is irrelevant. All this does is demonstrate a mathematical infinity. We agree that “infinity� is a valid mathematical concept. My arguments pertain to the REAL WORLD, where each addition operation is a temporal event, and occur sequentially. This is different from writing down a conceptual series as you have done (1+1=2 2+1=3, 3+1=4 etc. etc.). In the real world, you have to actually add 1+1. After completing this, you add 2+1, and so on – these take time.

So basically your objection to an infinite set is that it is not finite? You said, "In the real world, you have to actually add 1+1. After completing this, you can add 2+1, and so on - these take time." Yes, and I'm arguing that time can be infinite. (1)sec+(1)sec=(2)sec, (2)sec+(1)sec=(3)sec, (3)sec+(1)sec=(4)sec, (N)sec+(1)sec=(N+1)sec...
You basically said that time can't be infinite because it takes time for time to be infinite. Either explain that, or it makes no sense.

You asked a bit later how you could traverse through infinity by successive addition. When I do this, you say it is irrelevant. Did I miss something? No one is arguing that the past wouldn't be complete. I'm arguing that these 'infinite number of days' would be complete by having traversed them for an infinite time. If you have an infinite amount of time, what is stopping you from progressing 'to' infinity?

Here’s what’s stopping you: Paradoxes. Tristram Shandy is one. Hilbert’s hotel is another:

A hotel has countably infinitely many rooms. All rooms are occupied. Analogous to your view of “reaching infinity in infinite time� – this would imply that it would be impossible for the hotel to accommodate any additional guests. However, when a new customer shows up – the problem is easily solved: move all the current guests to the next highest room number (from room n into room n+1). This frees up room #1 for the new guest, and all the prior guests are also accommodated. Next, what happens if a countably infinite group of customers appear, all demanding rooms? Still not a problem. Move the current guests from room N into room N*2, freeing up all the rooms with odd numbers – this infinity or rooms should have no problem accommodating the infinity of new guests.

I'm familiar with Hilbert's Hotel. So thank you for proving to yourself why it makes no sense to say that you can reach infinity, which is what I have continuously stated. Indeed, the only person who is saying you have reached infinity is you. Stick with Tristram Shandy.

The moral of the story is that a “completed infinity� is paradoxical and therefore illogical.

Which is why I don't understand why you keep saying that this would be the case, when you are the only one making this argument. You're attacking a straw-man.

This arises because of the nature of cardinality of infinite sets. Any two sets with the same cardinality can be mapped from one to the other. You can map the set of positive integers to the set of even-numbered integers. You can map the set of integers divisible by 1 billion to the set of positive integers. Mapping is not the same as counting.

This is true. Take the set aleph-0. Map every second to a number so it is a one-to-one correspondence. Done.
But, like you said, mapping isn't the same as counting. But can you not count the numbers in an infinite set? {...1, 2, 3, 4... n-1, n, n+1...} Sure you can. All of those numbers make sense, regardless of there being an infinite number on either side of them.

I'm not excluding the 'real-world aspects of time' at all. You would be committing a straw-man fallacy if you really think this.

You certainly did exclude real world aspects when you asserted that computation of an integral across a range to (or from) infinity implies an infinite amount of time can be traversed. Same thing when you suggest you can “reach infinity� if you have infinite time. We don’t have to call it a fallacy, but at least it’s a math error.

Are you even being serious? You made your objection to the integration, so I quit using it. You then continuously attack a position that I explicitly stated makes no sense.

If you say that there can be an infinite future, then you are left with the same 'problem' that you propose with an infinite past. Why? Because if you were to proceed an infinite number of days in the future (whatever that means), then the past would be an infinite number of days in the past, thus 'you couldn't have traveled in time.'

You keep ignoring these properties of time: the arrow of time; the fact that real-world processes are temporal; and that there’s a distinction between actual and potential infinite. The future is potentially infinite: there is a well defined temporal process for counting future days (e.g., beginning today, we’ll place a notch on the wall as each day passes); the process potentially proceeds without end. In the real world, infinity is such a process and is not a destination: there’s always one more; you can’t reach infinity. Infinity is just the concept of continuing the temporal process without end. Mathematical functions, like integral calculus or mapping members of sets, are atemporal.

I have not ignored any properties, despite your continuous assertion. I've dealt with the arrow of time, and how the laws of physics which contain the arrow of time are not limited by it. The laws of physics work at any point in time, in any direction.
I'm not even sure where you get your second objection unless you're talking about the use of math, in which case I say that if you exclude math from the discussion then it will be rendered completely meaningless.
Potentially infinite from when, exactly? From now? What if I started yesterday? What if I started three years ago? What if it started with the big bang? What if it started before the big bang? All your objection about potential and actual infinities does is move t=0 around to some arbitrary point. The objection I made still stands, even with this. If there was ever a point where we would say is infinite (which wouldn't actually be infinite, just something agreed upon) then the past would be infinitely far away, and this would be an 'actual infinity.' But again, you're the only one arguing that infinity would be reached (which is why I'm glad you started using sets).

We pick a t=0 and work from there. That doesn't mean there isn't a t=-1 or t=-n. Time would still work the exact same if it were infinite or finite.

This is true, but ignores the fact that the past is complete. Consideration of future time (t+1, t+2…) is irrespective of whether or not any future period will actually be reached: the POTENTIAL is still there. The past is different because it lacks potential.

Here you go again, arguing that the past would be some complete thing.
Here's an argument (that you shouldn't take seriously): you have just passed a point of time. This is not possible because it is infinitely small in length. (This is one of the other Zeno's Paradoxes: the arrow.)

Here's a thought experiment:
I'm on a number line, at point n=2. I'm blindfolded, so there is only a potential for me to reach a higher number. It is only possible for me to reach higher numbers. I take a step, and BAM! I reached my potential! :p
The argument of potential/actual infinities is nothing more than an argument from ignorance.

We pick an arbitrary point (currently the big bang), and we count how long since then. Time 'flows' because of entropy the same in both models.

“because of entropy?!� Upon what complete theory of time is THIS based? Or do you take this as an article of faith?

Is that a joke?

That's exactly it. We can't measure back to a point called 'infinity,' we can only measure back finite times ago. But, since we know that you can always subtract a number on a time line, I see no logical objection as to why it couldn't be applied to time.

The logical objection is that you cannot define a temporal process for exactly counting the past days. The mathematical method you have used is just a mapping, which creates paradoxes.

Yes I can. Watch: we have the present day. We have the present day minus a day, which is yesterday. We have the present day minus two days which is the day before yesterday. Continue.

And the property of 'completeness' (which isn't inherent in the past in quantum mechanics, by the way), is dealt with by having been counting for infinity. You count for an 'infinite amount' time and you get 'infinity'.

Again I refer you to the paradoxes. BTW, the property of “completeness� pertains to set theory.

*sigh* I don't think this conversation is getting anywhere...

I'm not overstating what physicists say at all. I'm telling you the working method for quantum physicists that works and is observed. There has never been an observed violation of CPT symmetry, and this is not likely to happen due to the fact that it would also break Lorentz symmetry.

What does the universe being probabilistic have to do with anything? Quantum mechanics is a probabilistic science, as denoted by the wave function. There is an arrow of time, absolutely. No one is arguing against that. (In fact, entropy is the only thing that breaks T-symmetry (which doesn't happen in CPT symmetry).)
Well, if you're like me and a few other inflation-accepting scientists, then a quantum field would have been around before the big bang. Since, at the quantum level, we see violations of normal causality, a quantum field wouldn't have the same 'problem' of 'completing infinity.'

And I think I see where our main disagreement comes in, and it is entirely my fault. I'm not arguing for something like our universe to be infinite (like Sir Roger Penrose does). I'm arguing for something like quantum fields being infinite. I should have clarified, so I apologize.

I don’t think this makes a difference, but correct me if I’m wrong. I’m not insisting that the big bang is necessarily the beginning of time (although it COULD be). I’m just asserting (and supporting) the idea that past time is not infinite. If there is a predecessor to the big bang, the predecessor was either “timeless� (to use William Craig’s terminology) or it existed for a finite amount of time (because the same logical inconsistency applies to this epoch).

I think it would be smarter to leave the concept of time to people who study time, not people who want it to be something...

“timeless� is a difficult concept, but it implies unchanging and without duration. It’s something like a frozen point in time, except that points in time are preceded by durations of time. Timeless is not an infinite duration of time; it is 0 duration. If the immediate predecessor (or cause) of the big bang was a “quantum field,� it could be considered the timeless entity (only if it had no predecessors). William Craig wouldn’t like it, but I don’t see anything wrong with it.

If something is timeless, and would be 'like a frozen point in time,' then there is no way it could do anything. Time is a measurement between to events. No time, no events. No events, no... 'thing' (for a lack of a better word). Timelessness screws both of us over.

Assuming the validity of the Schrodinger equation has a deep, if somewhat obvious, consequence: time stretches for all of eternity. In classical mechanics, singularities in phase space can disrupt the evolution, causing time to grind to a halt. But in quantum mechanics, unitary evolution ensures that there there is no boundary to time; the variable 't' runs from -∞ to ∞. The modern idea that time does have a beginning arises from the existence of a Big Bang singularity in cosmological models based on general relativity. But from our current perspective, that is an outmoded relic of our stubborn insistence to think in terms of spacetime, rather than directly in terms of the quantum state. Classical general relativity, after all, is not correct; at some point it must be subsumed into a quantum description of gravity. We therefore imagine that the classical Big Bang corresponds to some particular kind of quantum state, which may be obscure from the perspective of our current knowledge, but will ultimately be resolved. It follows, under our assumptions, that there was something before the Big Bang, and time stretches back into the infinite past.

But this raises a problem, well known to anyone who has thought about the mysteries of time: within our observable universe, time has an arrow. Entropy was small near the Big Bang, is somewhat larger today, and will be even larger in the future. On macroscopic scales where the concept of entropy makes sense, the world around us is characterized by irreversible processes, from the mixing of milk into coffee to the collapse of a star to form a black hole. But the Schrodinger equation, on which this is all purportedly based, is perfectly reversible. The Hamiltonian operator may not respect time-reversal invariance (as in the weak interactions of the Standard Model), but that is beside the point. As long as the the Schrodinger equation holds, quantum time evolution is perfectly unitary (information-preserving) - given the current quantum state, we can reliably reconstruct the past just as well as the future. How can we reconcile this with macroscopic irreversibility?

"What If Time Really Exists?" by Sean Carroll
He then attempts to answer the question with a bit of math, and thermodynamics and cosmology.

I think that physicists understand time a little better than you're letting on. It isn't like they have no idea what they're talking about...

Physicists certainly have some solid observations about time, and some interesting hypotheses. But consider the implications of this statement from the above: “Classical general relativity, after all, is not correct; at some point it must be subsumed into a quantum description of gravity.�--
1) We currently have no no fully developed quantum description of gravity

Correct. They're still working on it.

2) The fact that “general relativity� is wrong demonstrates the problem of making metaphysical assumptions based on theories even when they ARE fully developed.

I see no objection to making metaphysical assumptions based on complete theories(?) Maybe I just misunderstood...
Even then, there is nothing wrong with speculation. (Isn't this what we are doing?) The difference is that we aren't claiming something is absolute, we are just speculating.

3) There is no fully developed theory of time. To draw conclusions about time based either on Shrodinger’s equation, or from a partially developed theory of quantum gravity is analogous to drawing conclusions about quantum gravity using General Relativity.

Well, I would have given you the entire article which would clear up this objection, but you said that I shouldn't link to articles, so...

4) Just because some equations can be calculated with infinities, and the equations compute with time going in either direction does not necessitate such infinities as actually existing, or of time truly going in both directions (e.g. no one suggests time travel to the past is possible despite the tidbits of information about some micro exceptions to the arrow of time).

So in other words, just because you don't like a necessary conclusion of well-tested equations and ideas we should doubt it? Sorry, that isn't how science works. Your use of time-travel is irrelevant because it is theoretically possible, first of all; second of all, no one is suggesting that the Schrodinger equation or CPT symmetry means you can travel in time. You're using a false analogy.

Will I use the math from that post? No. But you haven't shown how you can't get a number from simple addition.

Integral calculus is not a simple addition, and that is exactly my point.

Which is why I said I wouldn't use it anymore. Or did you just decide to skip over that part (even when you quoted it).

If we're going by days, then we could only count the past. How do we know the future doesn't end?

We don’t! That’s why we say that the counting of future days is only a “potential infinite.�

You can't count the future at all. There is nothing to count. The past, however...

And I can count past days by seeing what effects it has made on the present. (E.g. I won't have 'x' in front of me if I didn't buy 'x' at some point in the past.)

Nice try, but it doesn’t work. This is essentially what physicists have done by estimating the age of the universe. If time is infinite, this only scratches the surface. How are you going to count the durations of time (the “days�) that preceded this? Even if prior states of the universe could somehow be detected, clearly the only thing we could ever do is to detect a FINITE NUMBER of such states.

How are we going to count time if it were to precede the big bang? Simple: pick a point in time. You're doing nothing but making an argument from ignorance. "We can't know if the universe is infinite, therefore it isn't."

Of course, this isn't the case for quantum mechanics, being that time is symmetric in CPT symmetry

Interesting, but still – without a complete theory of time, it’s not valid to pull out some possible implications based on specific interpretations of other theories that have some relationship to time. Otherwise this opens the door to ad hoc interpretations.

CPT symmetry is extremely well tested and is based on observations. There's nothing 'ad hoc' about it, nor is it required to have a complete theory of time. (Even though physicists explain time extremely well and accurately.)

Again, you're trying to give infinity a number. I guess you could say he would be on infinity if that makes sense.

I’m demonstrating the impossibility of a completed, infinite set. No, it doesn’t make sense to say he’s on “infinity� – that’s not a number. Temporal counting can always be interrupted, and the count queried. It will always be a number, and not infinite. This is true with counting of the future days; the count is always finite - it’s the process that doesn’t end. But hypothetical temporal counting I’ve described of the past HAS ended, at “now.� This is just another way to look at the “completeness� problem.

Except that he would have been counting for infinity which means he can reach any number he wants to.

Why can't we assign days to numbers, exactly? I could just turn around and say, "Give me an alternative counting process - one that counts minutes, not merely numbers and merely assumes there is a corresponding mark on a clock." See? That doesn't make sense.

I’m using “day� to represent a fixed finite interval of time. It’s irrelevant how long the interval is, but I’m insisting that there be some sort of sequential counting as we can do with future time. For the future, we enumerate at the start of each interval. If the future comes to an abrupt halt because the god Chronos wills it, then the counting stops. There is no chance that the counting will exceed the days and no chance that the days will exceed the counting. They stay matched and avoid paradoxes.

So minutes aren't fixed finite time intervals? And why can't we divide up a day into infinitely small points of time?

Time is a product of entropy, and used as a measurement. Asking there to not be a number for the measurement means you couldn't count time at all, in either direction, finite or infinite.

Time is a product of entropy? This is a rather speculative hypothesis, so it’s to draw inferences. Again, there is no well-defined theory of time.

Do you even know what the arrow of time is? Or do you think that there is some abstract thing called 'time' which can exist independent of tings? Entropy is the arrow of time.
For someone who makes so many objections, you should know this. There is nothing speculative about it.

Well, it wasn't just some random article that I found. I do think it explains the situation better. But, if you don't want to read it that's perfectly fine.

I did read it, and it’s flawed; some of it is completely irrelevant to our discussion. But I’m not going to give you a rebuttal of someone else’s argument. I’m challenging you to read the article and decide which of the arguments seem sound, and present those to me in your own words. Perhaps you’ll actually find some his flaws yourself.

Of course some of it is irrelevant. He didn't write that paper for us.

Here’s one of my pet peeves about some non-theists (I myself am agnostic): a tendency to find an argument whose conclusion they agree with, and then use it like scripture. The attitude is: this conclusion matches my thinking, so it must be a good argument. This argument is then posted as a link, or quoted like a verse from scripture. This is nonsense. There is good reasoning, and there is bad reasoning. In theory, we’re supposed to be the rational ones (vs. theists). Pointing to a document or webpage is about the same as pointing to a verse from scripture. If it’s a good argument, learn it and use it, but do not simply assume the argument is good.

Then I don't think you understood what I meant when I said, "It wasn't just some random article that I found. I do think it explains the situation better." And then you turn around and say that I don't understand it?

[fredonly]

It is getting unwieldly to keep responding to every remark in one lengthy post. For now, I'm going to respond one specific key point:

At point in time “T�:
1. PD is the set of all days prior to T
2. If the past is infinite, then PD is an infinite set.
3. An infinite set cannot be complete
4. At time T, the set PD is completed – no additional days can be added (because of the arrow of time)
5. Therefore PD cannot be an infinite set; i.e. the past is not infinite

I don't agree with premise 4, because as I've said, having a complete infinity doesn't make sense. Or, if you want to stick with the Tristram Shandy paradox, you have an infinite amount of time.

I am stunned. Let’s get specific. At precisely midnight of the new year, on Jan 1, 2011 – the past consists of all days prior to that point in time. Please explain how another day can be added to the past of Jan 1, 2011, midnight. How exactly does another past day pop into existence, that did not previously exist?

[charris]

It is getting unwieldly to keep responding to every remark in one lengthy post. For now, I'm going to respond one specific key point:

At point in time “T�:
1. PD is the set of all days prior to T
2. If the past is infinite, then PD is an infinite set.
3. An infinite set cannot be complete
4. At time T, the set PD is completed – no additional days can be added (because of the arrow of time)
5. Therefore PD cannot be an infinite set; i.e. the past is not infinite

I don't agree with premise 4, because as I've said, having a complete infinity doesn't make sense. Or, if you want to stick with the Tristram Shandy paradox, you have an infinite amount of time.

I am stunned. Let’s get specific. At precisely midnight of the new year, on Jan 1, 2011 – the past consists of all days prior to that point in time. Please explain how another day can be added to the past of Jan 1, 2011, midnight. How exactly does another past day pop into existence, that did not previously exist?

I know you're going to accuse me of ignoring how time works or something like that, but let's think of the number line. Let's say that Jan 1, 2011 is some point, n. N has infinity surrounding it on both sides, but the one we are concerned with is the one approaching from the negative side. So how do we get more numbers? We move from n to n+1. Or you could say that all the numbers already exist and you aren't even adding anything to it, which is the route I would probably take.

So, to be direct, how can we add a day to the past? Either every point in time already exists or you simply move forward in time. I vote for the former.

[fredonly]

It is getting unwieldly to keep responding to every remark in one lengthy post. For now, I'm going to respond one specific key point:

At point in time “T�:
1. PD is the set of all days prior to T
2. If the past is infinite, then PD is an infinite set.
3. An infinite set cannot be complete
4. At time T, the set PD is completed – no additional days can be added (because of the arrow of time)
5. Therefore PD cannot be an infinite set; i.e. the past is not infinite

I don't agree with premise 4, because as I've said, having a complete infinity doesn't make sense. Or, if you want to stick with the Tristram Shandy paradox, you have an infinite amount of time.

I am stunned. Let’s get specific. At precisely midnight of the new year, on Jan 1, 2011 – the past consists of all days prior to that point in time. Please explain how another day can be added to the past of Jan 1, 2011, midnight. How exactly does another past day pop into existence, that did not previously exist?

I know you're going to accuse me of ignoring how time works or something like that, but let's think of the number line. Let's say that Jan 1, 2011 is some point, n. N has infinity surrounding it on both sides, but the one we are concerned with is the one approaching from the negative side.

Yes, you are ignoring how time works, simply drawing a mental number line, and then using it incorrectly. The real-world activity of time progression proceeds from day T-3 to day T-2, then T-1, then to T (the date in question). We're talking about the progression of time from one day to the next.

So how do we get more numbers? We move from n to n+1.

But you only do this until you reach T. We're talking about the past from date T, not the future.

Or you could say that all the numbers already exist and you aren't even adding anything to it, which is the route I would probably take.

If you aren't "adding anything to it" then you aren't adding another past day and you are agreeing with me that the past (of time T) is complete.

So, to be direct, how can we add a day to the past? Either every point in time already exists or you simply move forward in time. I vote for the former.

You can't create another past day by moving forward in time. We're talking about the past, from time T. Time progresses after T, but that is the FUTURE of T.

"Every point in time already exists" is a false statement. Only today exists. You continue to be confused by thinking in terms of a number line, where all points "exist" simultaneously. Time doesn't work that way. But I'll give you the benefit of the doubt on your terminology. The problem is that you haven't done what you set out to do: show how an ADDITIONAL past day can come into existence that wasn't previously there. Here was my challenge:

At precisely midnight of the new year, on Jan 1, 2011 – the past consists of all days prior to that point in time. Please explain how another day can be added to the past of Jan 1, 2011, midnight. How exactly does another past day pop into existence, that did not previously exist?

To say that "every past day already exist[ed]" is an admission that another past day cannot, somehow, pop into existence. This confirms the past is complete and that my proof is correct.