Does an actual infinte exist?

[lynx]

I used to say that too, but it’s technically incorrect. Indeed, there are infinite numbers, e.g. infinite cardinals and ordinals, and the endpoints of the extended reals. However, you can still say things like this: “Infinity isn’t a number in the traditional sense.” Usually that is a suitable substitute.

I’ll give that sets can be infinite, but I don’t think infinity is a proper symbol in any set representing a number. Also, it doesn’t seem to follow the properties of numbers, e.g. addition and subtraction.

mathpath.org/concepts/number.htm
en.wikipedia.org/wiki/Cardinal_number

 

[hatsoff]

I’ll give that sets can be infinite, but I don’t think infinity is a proper symbol in any set representing a number.

Positive and negative points at infinity are both members of the extended reals. Are they numbers? Well, they’re classified as points in a number system. They behave much as numbers do, with addition and multiplication properties. I’m not sure I’d feel comfortable calling them numbers, though, so perhaps I should not have used them as examples in my previous post. But neither would I feel comfortable denying that they’re numbers.

Also, it doesn’t seem to follow the properties of numbers, e.g. addition and subtraction.

Addition and subtraction are often defined for infinite cardinals and ordinals. However, they do not inherit all the properties of real number subtraction and addition. We definitely classify cardinals and ordinals as numbers, however, without the ambiguity of the afore-mentioned “points at infinity.”

 

[lemondiesel]

if entropy in the universe exists, then once started, infinity exists.

 

[ManOnFire]

I don’t see why you’re ruling out the possibility that the universe exists as a brute fact (without explanation), or that the larger context is simply unknown (as opposed to unknowable). Perhaps that’s what your intuition tells you to do, but I don’t think we should trust our intuitions outside of our usual experience, if then.

“Without explanation, or unknown” - now you have equalled the thoughts of a religious person, except you have chosen to believe that science will eventually know all, but it CAN’T.

Are you honestly claiming that the entire universe simply appearred one day, equalled the speed of light (where time theroetically stands still) to mark the very beginning of time, then, in a godless, spontaneous sort of way, most of the universe spontaneously slowed down, slower than the speed of light, to allow the BEGINNING of time to occur? It’s not logical to claim that “nothing” caused time to begin or change (entropy couldn’t exist before “everything” was created, otherwise it wouldn’t be “everything”). “Something” had to start it. That “something” that started time to begin must have acted upon it. This “something” would then have existed before and apart from time, producing the case for “actual” infinity, where science is no longer an ideology because it can never catch up to actual infinity to solve this mystery.

The way I see it, everyone must choose from one of 2 choices: 1. a godless “Actual” infinity, whose mystery science can never solve because it’s limitless time and space is unsolvable and unknowable, (so why believe in a false ideology?). Remember, it’s impossible to know a godless “actual” infinity, so any claims or beliefs similar to “We just haven’t learned it yet, the instruments needed to detect it haven’t been invented yet, without explanantion, simply unknown” are null and void because any attempt to approach the limits of time and space are equalled by the nature of time and space travel in a godless existence. Science will always be inherently flawed and imperfect with this choice.

1. God created space and time, and it’s limits are on His terms.

So, I like your “without explanation, simply unknown” statements because you have chosen to equal the beliefs of the religious person when you say these things. Well, maybe I should correct my statement. God is perfect, but science will always have at least one mystery that it will never solve, so maybe God is one up on science.

This is why college students should be very weary. They are essentially learning propaganda instead of the Truth. Any admirable professor would place his/her own agenda/beliefs/emotions aside to argue this point to at least a stalemate. But people, including professors and students, have been desensitized and conditioned by pop culture media into choosing to take the feelgood, less sacrificial road of life without realizing that they have become such sheep. People have come to worship pop culture media’s beliefs without realizing it. When are people going to stop becoming such automatons and minions of the unelected media???

 

[itinerant1]

if entropy in the universe exists, then once started, infinity exists.

The laws of entropy say the universe will eventually run down.

 

[hatsoff]

“Without explanation, or unknown” - now you have equalled the thoughts of a religious person, except you have chosen to believe that science will eventually know all, but it CAN’T.

I do not believe that scientists will eventually learn everything about the universe or reality. In fact, I’m all but certain that such a goal will never be realized, since we are fallible human beings with limited intelligence.

However, that’s all beside the point. This conversation is not about the direction of science, but rather the epistemic question of whether or not there must be, in principle, an explanation for every fact. I see no reason to believe this is true, and plenty of reason to suspect it isn’t (cf. my discussion with J. D. Sinclair on W. L. Craig’s forum). In the case of the universe’s existence, we have a prime candidate.

Are you honestly claiming that the entire universe simply appearred one day,

No! By saying that the universe “appeared one day,” you’re implicitly referencing some larger context which is entirely unknown to us, and using it to provide an explanation (albeit a strange one) for the existence of the universe. But if the universe’s existence is a brute fact, then it has no explanation at all: there is no larger context in which it can be said to have “appeared.”

With brute facts, we stop cold. We can’t explain them at all, by definition.

So, in light of this, there is no reason to accept your dichotomy of a godless “actual infinity” versus God. I have other objections to such dichotomies, as well, but the brute fact objection will suffice for now.

 

[stenlis]

Coolduude,

There has been some interesting points made in this forums but here’s two other ones that I haven’t seen spelled out clearly here (I might have overlooked something though):

1. Craig does not really present a proof for impossibility of an actual infinite. Rather, he presents an appeal to common sense. In essence he’s saying ‘you cannot create an infinite amount of things by stacking them’. Which is apparently true but I don’t see how you could conclude from that that an actual infinite cannot exist. It does not follow. Craig did not demonstrate that there are no other ways of creating something infinite.
2. The article from the atheist side largely discusses one point - how can Craig reconcile his belief that no actual infinite exists with the infinite-like properties of god he believes actually exists? From what I saw in Craig’s writings and responses, he cannot really reconcile that contradiction. At most he’s been able to tone it down somewhat.

 

[MindOverMatter2]

Your assumption is that time is already predefined. Again, not being able to observe the past and the future I find this a difficult claim to support.

We observe the present, and we know that we are the product of the past, and that in order to proceed from the past, we need to be able proceed into a “potential future”. There has to be the potentiality of change. This to me is a self evident fact. Once you accept that fact, then you can accept that the future is quantifiable in so far as it adds to present; and given that the past is a procession of events, then we can know that the past is also quantifiable. Thus we can know that ideas concerning “infinities”, such as those which claim that the past has an actual infinite number of additions, is metaphysically/logically impossible when applied to actual events; since there is no such thing as an actual infinite “number” of objective events.

If you don’t agree that events are quantifiable (It is evident to me that events are quantifiable) then you obviously think that scientists are making a subjective claim when they give a probable age to the universe. Perhaps then i should ignore them since they are not speaking about objective truth; since according to you change is not definable.:ehh:

 

[MindOverMatter2]

I do not believe that scientists will eventually learn everything about the universe or reality. In fact, I’m all but certain that such a goal will never be realized, since we are fallible human beings with limited intelligence.

However, that’s all beside the point. This conversation is not about the direction of science, but rather the epistemic question of whether or not there must be, in principle, an explanation for every fact. I see no reason to believe this is true, and plenty of reason to suspect it isn’t (cf. my discussion with J. D. Sinclair on W. L. Craig’s forum). In the case of the universe’s existence, we have a prime candidate.

No! By saying that the universe “appeared one day,” you’re implicitly referencing some larger context which is entirely unknown to us, and using it to provide an explanation (albeit a strange one) for the existence of the universe. But if the universe’s existence is a brute fact, then it has no explanation at all: there is no larger context in which it can be said to have “appeared.”

With brute facts, we stop cold. .

A brute fact means that a thing is just there for no reason; and this necessarily implies that things can exist arbitrarily. For example, a cat just exists, or a dog just exists. But what you fail to understand is that first, unless you have a justification for claiming that such and such is brute fact then your claim is completely unintelligible in respect of are experience of the fact that things tend to have intelligible explanations. You are just claiming that the universe can be a brute fact without giving any intelligible reason why one should think that such an event is even possible. Its an unjustified assumption, born out of an attempt to avoid the necessary existence of a timeless creator. The idea of a brute fact is completely unintelligible and is just as intelligible as saying that a big blue elephant just appeared without explanation.

Secondly, if a thing exists, without a cause, than the explanation is necessarily found in its nature; it exists because of its self; and the explanation has to be in itself, or otherwise there is no reason why it should exist as opposed to anything else. For example, why a sock rather than a shoe? Why a bird rather than the moon? Why a universe rather than God. If there is no intelligible logical reason for why it exists as opposed to some other nature, then its non-existence is equally possible since its existence as a particular thing or nature is not based upon logical necessity, and thus we are left to ask the existential question of why something rather than nothing. This is a completely justifiable question, and if we intend to build up a rational intelligible explanation on that qeustion, we have to do more then say it is just there. In fact the qeustion forces us to find a logical answer, since out of nothing comes nothing. Thus the only justifiable reason somebody can give for there being something rather than nothing is to explain that a truly metaphysical logic entails that a thing must exists because of its “particular nature” and that its nature entails its necessity.

Given that the universe is fundamentally a collection of potential and thus contingent events, and given that it is only intelligible in regards to its dynamism, what reason then do we have to think it exists because of its particular nature? None.

The difference between me you is that i think that our experiences support the idea that reality is fundamentally intelligible and in order to explain why there is something rather than nothing we have to begin with something that intelligibly explains why there is not nothing. The universe does not give an inteligible explanation for why there is such a thing as existence. That’s where the evidence is pointing. We don’t see things just happening or just being there.

You support an extreme skepticism that is not justifiable and thus there is no need for anybody to take your claims seriously. As soon as we accept causality and intelligibility, a perfect timeless being that exists because of its fundamental nature is the only explanation.

 

[MindOverMatter2]

Coolduude,

There has been some interesting points made in this forums but here’s two other ones that I haven’t seen spelled out clearly here (I might have overlooked something though):

1. Craig does not really present a proof for impossibility of an actual infinite. Rather, he presents an appeal to common sense. In essence he’s saying ‘you cannot create an infinite amount of things by stacking them’. Which is apparently true but I don’t see how you could conclude from that that an actual infinite cannot exist. It does not follow. Craig did not demonstrate that there are no other ways of creating something infinite.

Its not an appeal to common sense. Its an appeal logic. If the past is quantifiable, which it obviously is, then to say that there is an infinite past is to say that events have been actualized an infinite “number” of times. But if you agree that you cannot cannot possibly achieve an infinite by adding one thing to another, then you are admitting that an infinite cannot be achieved by the addition of numbers. There is no amount of logically possible additions that can add up to an infinite; it will always be a finite number. An infinite is not quantity. The person who intends to imply that there is an actual infinite in the past, is saying that the past is infinite because an actually infinite “number” of events has been achieved in the past. But if you cannot possibly make up an actually infinite number, you cannot possibly say in same breath that there is an actually infinite past.

1. The article from the atheist side largely discusses one point - how can Craig reconcile his belief that no actual infinite exists with the infinite-like properties of god he believes actually exists?

There is a difference between applying an infinite to numbers and applying an infinite to God. They don’t mean the same thing. God is necessarily infinite because God is timeless and “immaterial”. God is not an actually infinite “quantity”. Thus infinity is being used in a different context when applied to God. Secondly, what ever problems that might arise for the question of God is besides the necessary fact that one cannot have an actually infinite number.

Craig’s inability to answer the contradiction is probably due to a having a process understanding of God, rather than a Thomistic understanding of the divine nature.

From what I saw in Craig’s writings and responses, he cannot really reconcile that contradiction. At most he’s been able to tone it down somewhat.

 

[ManOnFire]

I do not believe that scientists will eventually learn everything about the universe or reality. In fact, I’m all but certain that such a goal will never be realized, since we are fallible human beings with limited intelligence.

However, that’s all beside the point. This conversation is not about the direction of science, but rather the epistemic question of whether or not there must be, in principle, an explanation for every fact. I see no reason to believe this is true, and plenty of reason to suspect it isn’t (cf. my discussion with J. D. Sinclair on W. L. Craig’s forum). In the case of the universe’s existence, we have a prime candidate.

No! By saying that the universe “appeared one day,” you’re implicitly referencing some larger context which is entirely unknown to us, and using it to provide an explanation (albeit a strange one) for the existence of the universe. But if the universe’s existence is a brute fact, then it has no explanation at all: there is no larger context in which it can be said to have “appeared.” (if we exist, there MUST have been a beginning. you simply choose to be ignorant of that which you can’t explain).

With brute facts, we stop cold. We can’t explain them at all, by definition.

So, in light of this, there is no reason to accept your dichotomy of a godless “actual infinity” versus God. What other explanation would you render for the existence of the universe? You’re “humans are too dumb” doesn’t count. What other organism’s brain would you like to borrow? How about an alien? Nah, you’d have to filter the info through your own human brain to understand it. What if the alien said to you “You humans are just not intelligent enough to understand actual infinity, but there is an answer. Just trust me.” Would you believe the alien on blind faith??? Now who is religious? Don’t feel bad. Aliens might be smarter than us, but they wouldn’t know either. Actual infinity is unknowable by definition. I have other objections to such dichotomies, as well, but the brute fact objection will suffice for now.

It’s certainly easier to claim ignorance, but then you are falling back to “We just haven’t learned it yet, without explanantion, simply unknown” with the hope that someday we will. No, we will never know actual infinity. It’s unknowable by definition. Only a God-like power could make something appear from nothing. If you believe there’s not necessarily an explanation for every fact, then fine, but you are CHOOSING to believe this. A “real,” more purely ideological scientist than yourself would disagree with your position. Only a true scientist, not blinded by ego, can admit that actual infinity is unknowable and that science is flawed.

I’m tired of the propaganda that profs are teaching to students. Why must they continue their silly beliefs?

 

[hatsoff]

But what you fail to understand is that first, unless you have a justification for claiming that such and such is brute fact then your claim is completely unintelligible in respect of are experience of the fact that things tend to have intelligible explanations.

If I asserted that the existence of the universe is a brute fact, then I would have to justify my claim, just as you need to justify your claim that it is not. However, I do not suppose it is or is not a brute fact, but only that for all we know it could be. In other words, I am dutifully agnostic as to whether or not we can ever find an explanation for the existence of the universe.

Secondly, if a thing exists, without a cause, than the explanation is necessarily found in its nature; it exists because of its self; and the explanation has to be in itself, or otherwise there is no reason why it should exist as opposed to anything else.

Why is it unacceptable to say that an object exists without reason? Isn’t that the question at stake, here? You seem to be assuming in advance that all facts require explanations, but I see no reason to suppose that must be the case.

You support an extreme skepticism that is not justifiable and thus there is no need for anybody to take your claims seriously.

I do not see anything particularly “extreme” or otherwise outrageous about my skepticism. Is it really so radical to speculate that we may never have an explanation for the existence of the universe?

 

[MindOverMatter2]

Why is it unacceptable to say that an object exists without reason? Isn’t that the question at stake, here? You seem to be assuming in advance that all facts require explanations, but I see no reason to suppose that must be the case.

I do not see anything particularly “extreme” or otherwise outrageous about my skepticism. Is it really so radical to speculate that we may never have an explanation for the existence of the universe?

Everything you conveniently left out of your quote refutes your position of Agnosticism and shows why you must come up with a logical explanation for why there is something instead of nothing. The suggestion that physical reality might just be there for no reason is unintelligible and useless in so far as explaining why there is such a thing as existence. What I will add is that our experience suggests that all things have intelligible explanations, and this provides us with a good reason to seek intelligible explanations for things since the world appears to be intelligible. That you have chosen to stop looking for explanations when it comes to the existence of all physical reality, is telling only of your prejudice toward the idea of there being something other than physical reality. There is no good reason for your agnosticism other than the fact that you are dedicated to a completely naturalist view of reality. Similarly, there is no good reason to doubt the object of our senses, although we can certainly be agnostic about the objective existence of the universe. A good reason for agnosticism would be to come a cross something which cannot be explained any further due to a limitation in your reasoning; and thus you have to be agnostic out of necessity. But you haven’t provided any good reason for us to think that we cannot come up with an intelligible explanation of physical reality.

 

[hatsoff]

You haven’t provided any reason why cannot come up with an intelligible explanation of physical reality.

I’m sorry if I haven’t been clear, but allow me to repeat once more that I am not insisting that the existence of the universe is a brute fact. I am only pointing out that we have no reason at all to suppose that there must be some explanation for it.

 

[MindOverMatter2]

I’m sorry if I haven’t been clear, but allow me to repeat once more that I am not insisting that the existence of the universe is a brute fact. I am only pointing out that we have no reason at all to suppose that there must be some explanation for it.

We have good reason to think that there must be.

 

[coolduude]

Since this is a thread on infinity I have an infinity question:

I’ve read that it’s impossible to transverse an infinite series and the examples seem to demonstrate this as correct (eg counting to infinity, walking to an infinite point, etc). The arguments go on to say that it’s impossible for the past to be infinite because an infinite past would have to count down to ‘time zero’, or the present.

This will explain it better than me:
The idea that the universe has an infinite past is just as problematic as the idea that I have just counted down from infinity. If the universe had an infinite past, then time would have had to count down from infinity to reach time zero, the present, and so would not have reached it. The fact that we have reached the present therefore shows that the past is not infinite but finite. The universe has a beginning. This claim, of course, has been confirmed by modern science, who trace the universe back to a point of origin in the ‘big bang’.

But my question is:
Couldn’t we be working through the infinite past right now, since time is always moving? Couldn’t we be moving through the infinite past to some point in the future when time will hold still? (end of the world maybe?)

This question is probably very dumb sounding so I apologize but this argument (see above quote) always confused me.

Thanks for any help!

Coolduude

 

[lynx]

We observe the present, and we know that we are the product of the past, and that in order to proceed from the past, we need to be able proceed into a “potential future”. There has to be the potentiality of change. This to me is a self evident fact.

Then I guess this is where we part ways because I don’t see anything that validates your claim.

If you don’t agree that events are quantifiable

I didn’t say that, you’re assuming. Events that are observable are quantifiable in relation to time and space, and probably other metrics you would like to use.

then you obviously think that scientists are making a subjective claim when they give a probable age to the universe.

I think you misunderstand the question then. The claim is that using mathematics, one can place an accurate estimate as to how long ago the big bang was. Where the “stuff” in our universe comes from is a mystery.

 

[ManOnFire]

I’m sorry if I haven’t been clear, but allow me to repeat once more that I am not insisting that the existence of the universe is a brute fact. I am only pointing out that we have no reason at all to suppose that there must be some explanation for it.

It’s mighty convenient of you to selectively determine that which has answers based on your “desired” beliefs if the prospect of actual infinity makes you uncomfortable.

 

[ManOnFire]

Since this is a thread on infinity I have an infinity question:

I’ve read that it’s impossible to transverse an infinite series and the examples seem to demonstrate this as correct (eg counting to infinity, walking to an infinite point, etc). The arguments go on to say that it’s impossible for the past to be infinite because an infinite past would have to count down to ‘time zero’, or the present.

This will explain it better than me:
The idea that the universe has an infinite past is just as problematic as the idea that I have just counted down from infinity. If the universe had an infinite past, then time would have had to count down from infinity to reach time zero, the present, and so would not have reached it. The fact that we have reached the present therefore shows that the past is not infinite but finite. The universe has a beginning. This claim, of course, has been confirmed by modern science, who trace the universe back to a point of origin in the ‘big bang’.

But my question is:
Couldn’t we be working through the infinite past right now, since time is always moving? Couldn’t we be moving through the infinite past to some point in the future when time will hold still? (end of the world maybe?)

This question is probably very dumb sounding so I apologize but this argument (see above quote) always confused me.

Thanks for any help!

Coolduude

Einstein’s Theory of Relativity postulates that time stands still when an object, or “everything in the entire universe” (when arguing the beginning of time), is moving EQUAL to the speed of light, which is 186,000 miles per second. Time theoretically is REVERSED and moves backwards when an object or “everything in the entire universe” travels FASTER than the speed of light. If the object or “everything in the entire universe” can travel faster than the speed of light and therefore time is reversed, then, if we wait long enough, we can reach the theoretical “beginning of time” according to godless theory. What happens if we reach it? There’s no reason to believe we can’t continue right on past “the beginning of time” since we traveled there. There can’t be a wall or some other existence to stop us from reaching it unless that entity exists infinitesimally, which necessitates a choice between God and actual infinity. But, reaching the beginning ot time would negate the very definition of it, and make it a falsehood.

Any travel faster than the speed of light that takes us right past “the beginning of time” would negate it’s definition. This also negates a definition of a godless “end of time” since we are simply bouncing around along a linear continuum of forward or reverse according to our speed relative to the speed of light.

Of course, one could argue that Einstein is wrong. Otherwise, the only 2 choices are God created the universe, or an actual infinity exists where it’s mystery is permanently unknowable by definition, and science is inherently flawed. Why do people have such passionate beliefs in something that is so unknowable??? Hmmm. Sounds familiar and equal.

The university profs are threatening students with low grades. They have been quite effective at recruiting minions. We need education, not propaganda.

 

[MindOverMatter2]

Then I guess this is where we part ways because I don’t see anything that validates your claim.

You don’t see the evidence of quantifiable change?