Question on actual infinity

[ddarko]

Actual infinite is needs something that can actually be infinite. You can’t have negative something because then it is not actual. Potential infinite is actual infinite but it contains the infinite number of possibilities. Negative and positive infinite exist here. There is a difference between the two, and no its not logically contradictory.

I am taking it you do not believe in an infinite universe? If its infinite, we can realize it. Stars explode and created new ones, maybe new life, continuously forever. Time is actual and potential. The past is the way we got here, an actual infinite following potential. Potential is the present and the future, because like you said, it hasn’t happened yet. Infinite number of things that could happen.

First, the universe has not existed eternally in the past. The main reason why it couldn’t exist eternally in the past is because an actual infinite cannot exist. Are you claiming that the universe is eternal in the past?

Second, the universe is not necessarily infinite in size. No cosmologist would state that the universe MUST be infinite. Or are you referring to some other attribute of the universe as being infinite?

Picture this. When you are about to speak, you think and there is potential infinite for what you could say. When you say it, you have created the actual infinite because you could continue speaking forever (hypothetically).

Actually the speaker does not consider infinite thoughts before he speaks. That doesn’t make sense. If he was considering infinite things to say, then he would never utter anything since he can’t go through the whole list in finite time. While for the observer, there are infinite possibilities of what a speaker might say, the same does not apply for the speaker. So from the observer point of view, there is a potential infinite. But from the speaker point of view, there is only a finite space of possibilities.

God Bless

 

[uscav_21]

That’s not how infinities work.

No matter how many times a number is added, multiplied, divided etc. it will never reach infinity. Even if your 2,4,6… etc. was continued eternally it would never reach an infinite number.

We call this a potential infinite; because it is not boundaried by a finite sum. However, this will never be an actual infinite; because despite it’s growth it will always be a finite number.

That’s exactly how infinity works. Take both groups of numbers, do they ever have an end point. The answer is no. Infinity is not a place; you cannot reach it because it would not be infinite if you did. Infinity-greater than assignable quantity of countable number; Boundless endless. Just a few of the definitions from the Oxford American Dictionary. So I would recommend that you do not reassign values to what infinity is. Look at group A. 1,2,3,4,5,etc… That line can go forever throughout eternity. It is what we call infinite. It even fits the definition, it is boundless. If you like I can recommend some great resources that cover the topic. Potential infinity, makes no sense. If there is no such thing as infinity, as you describe, and potential infinity is all there is, then I have a question. If something cannot be, then how could anything potentially be something, or that something? You see the problem here, your calming that something can potentially be infinite, but infinity its self can never be, so how can something potentially be something that does not exist, and we might also say we have an infinite amount of potentially? I would say so, but that would mean we have infinity. Hum

 

[lemondiesel]

First, the universe has not existed eternally in the past. The main reason why it couldn’t exist eternally in the past is because an actual infinite cannot exist. Are you claiming that the universe is eternal in the past?

Second, the universe is not necessarily infinite in size. No cosmologist would state that the universe MUST be infinite. Or are you referring to some other attribute of the universe as being infinite?

First, how do you know we have not always just been banging? How do YOU know it has or hasn’t? It’s all speculation mainly, but I do not think the universe has an eternal past but i believe it has an eternal future. This universe could come to an end, compress, and just explode into existence again, we will never know.

Our universe is infinity expanding. There is infinite amount of space for something to exist, because there is not an “outside” to the universe. Time, once started is infinite. Actual time is 1,2,3…etc all the way up to this point. It does not follow days and nights it just continues going up gradually. Time started at 1 and is now at whatever 1+how many secs it took to get to right now, the present time. If that makes any sense.

Actually the speaker does not consider infinite thoughts before he speaks. That doesn’t make sense. If he was considering infinite things to say, then he would never utter anything since he can’t go through the whole list in finite time. While for the observer, there are infinite possibilities of what a speaker might say, the same does not apply for the speaker. So from the observer point of view, there is a potential infinite. But from the speaker point of view, there is only a finite space of possibilities.

God Bless

Obviously you missed my point, so I will just end that debate lol

 

[Just_Lurking]

Well I was talking about succesive addition to form an actual infinite, but this is cool
too. Infinity is an interesting topic isn’t it?

What’s infinity x 2?

In mathematics, there are many different number systems with infinite quantities.

In the hyperreal numbers and in the surreal numbers, 2 x infinity = infinity x 2 > infinity.

In the cardinal numbers, 2 x infinity = infinity x 2 = infinity.

In the ordinal numbers, multiplication is not commutative, and 2 x infinity = infinity, but infinity x 2 > infinity.

Note that each number system above has many different infinite quantities, not just a single “infinity”, but the above applies for any infinite quantity of the respective system, except for the ordinals, where the value of 2 x infinity depends on the particular infinite quantity.

 

[JohnDamian]

That’s exactly how infinity works. Take both groups of numbers, do they ever have an end point. The answer is no. Infinity is not a place; you cannot reach it because it would not be infinite if you did. Infinity-greater than assignable quantity of countable number; Boundless endless. Just a few of the definitions from the Oxford American Dictionary. So I would recommend that you do not reassign values to what infinity is. Look at group A. 1,2,3,4,5,etc… That line can go forever throughout eternity. It is what we call infinite. It even fits the definition, it is boundless. If you like I can recommend some great resources that cover the topic. Potential infinity, makes no sense. If there is no such thing as infinity, as you describe, and potential infinity is all there is, then I have a question. If something cannot be, then how could anything potentially be something, or that something? You see the problem here, your calming that something can potentially be infinite, but infinity its self can never be, so how can something potentially be something that does not exist, and we might also say we have an infinite amount of potentially? I would say so, but that would mean we have infinity. Hum

I will assume you are a beginner at philosophy.

An actual infinite can never be composed by successive addition.

Whilst a line may continue infinitely (emphasis on …ly); the body of that line will never be infinite in length.

The words potential infinite equate to an unboundaried and increasing numerical order; wheras an actual infinite is the composite of a fully progressed order - since no singular progression of finite parts can ever create a sum total accuratly defined as infinite it is impossible to have an actual infinite in reality; wheras; in conception one can produce a potentially infinite chain by determining that X can be divided by Y eternally, or a sum may have X added to it eternally; thus producing a conceptual chain that is not boundaried by finite constraints. However, the progression along this line of finite parts will never reach an infinite number.

If you “think” you know some philosophy books that disproves this; I shall be happy to oblige; but pre-emptivelly I shall provide a good resource on the Topic; and that is the Scholastic debate on the natures of infinites between Richard FitzRalph and Richard Kilvington in the 14th centuary. I shall cite here from Kretzmann’s book (on Kilvington) of 1982; I have emboldened the key point.

The first eleven sophisms use the process of whitening to consider the motion of alteration as a successive entity extrinsically limited at its beginning and end. There is no first instant of alteration, claims Kilvington, only a last instant before the alteration begins; likewise, there is no last instant of alteration, only a first instant marking the introduction of the final degree of the quality in question. Thus, motion yields no minimum degree of whiteness or speed, but rather smaller and smaller degrees ad infinitum down to zero, since the qualities change continuously. The set of integers is* potentially infinite because one can always find a higher integer, but not actually infinite since there is no infinitely great number.** Since, in Kilvington’s opinion, any continuum of time, space, motion, heat, whiteness, etc., is infinitely divisible, it can be understood quantitatively and measured using infinite sets of integers. Sophisms 29-44 reveal Kilvington’s special interest in the causes of local motion, i.e., active and passive potencies, and in effects such as time, distance traversed, and speed. He considers both uniform and difform motion caused by voluntary agents, and calls attention to the dubious measure of instantaneous speed through the comparison of speed in uniform and accelerated motion *

 

[lemondiesel]

In mathematics, there are many different number systems with infinite quantities.

In the hyperreal numbers and in the surreal numbers, 2 x infinity = infinity x 2 > infinity.

In the cardinal numbers, 2 x infinity = infinity x 2 = infinity.

In the ordinal numbers, multiplication is not commutative, and 2 x infinity = infinity, but infinity x 2 > infinity.

Note that each number system above has many different infinite quantities, not just a single “infinity”, but the above applies for any infinite quantity of the respective system, except for the ordinals, where the value of 2 x infinity depends on the particular infinite quantity.

how can infinity x 2 by greater than infinity? how can you take infinity times itself? I think you are assigning a set value for infinity.

infinity x 2 = infinity
infinity x 12220210357259017 = infinity

 

[Just_Lurking]

infinity x 2 = infinity
infinity x 12220210357259017 = infinity

This is the case for cardinal numbers, which represent the sizes of sets.

In the hyperreals (see here) and the surreals (see here), the system forms a mathematical field, so the only solution to N x 2 = N is N = 0, because otherwise you could divide by N to conclude that 2 = 1, which is false.

Arithmetic in the ordinal numbers (see here and here) is harder, but infinity + 1 is always strictly larger than infinity, because the “+ 1” represents a number that is larger than an infinite number of numbers, unlike the positive integer, where each integer is only larger than a finite number of other positive integers.

From everything I can tell, mathematical infinity is completely different than philosophical infinity.

 

[JohnDamian]

From everything I can tell, mathematical infinity is completely different than philosophical infinity.

I don’t claim to know what it is mathematically;

But philosophically there is no number infinity. Infinity is regarded as an unatainable concept, that cannot exist in reality.

 

[lemondiesel]

So infinity - 1 = infinity - 1?

Math is so interesting to think about ha. Okay but ya i am so confused becaused if infinity - 1 = infinity - 1, then infinity is no longer infinity?

could infinity plus/multiply something = infinity?
where as subtract or divide = (infinity minus/divide whatever number)? because we are taking away from the infinitness so it is no longer infinite?

 

[reggieM]

Exactly- a logical contradiction. How can you double something but have the same amount? I think this goes to show that an actual infinite can’t exist

True. In nature or in the universe of material things, an actual infinite cannot exist.

We say, on the other hand, that God is an actual infinite (“the” actual infinite?).

That is how it is possible for God to give to His creation and never be diminished. That is how it is possible for God to recieve from His creatures and never add anything to Him.

That’s why we say God is immutable – not possible to change. Because that’s what happens in an actual infinite also. No change in an actual infinite is possible.

 

[ddarko]

First, how do you know we have not always just been banging? How do YOU know it has or hasn’t? It’s all speculation mainly

Because its not logically possible. The current knowledge we have suggests that we couldn’t have existed eternally. Even the 2nd law of thermo dynamics will be violated if the past was eternal. Now if you want to call these speculations be my guest. But what you are claiming is similar to saying science is speculation.

, but I do not think the universe has an eternal past but i believe it has an eternal future. This universe could come to an end, compress, and just explode into existence again, we will never know.

Your model of the universe has number of problems and has been rejected by prominent cosmologist. For one, the universe would have to slow down in its expansion for it to compress again. But all the scientific evidence show that the expansion is in fact speeding up.

Our universe is infinity expanding. There is infinite amount of space for something to exist, because there is not an “outside” to the universe. Time, once started is infinite. Actual time is 1,2,3…etc all the way up to this point. It does not follow days and nights it just continues going up gradually. Time started at 1 and is now at whatever 1+how many secs it took to get to right now, the present time. If that makes any sense.

Time once started is not an actual infinite. Its a potential infinite. It will just accumulate but never reach infinity.

Secondly, how do you know there is no outside to the universe? Are you a materialist? There has to be an outside of the universe. Otherwise, where did the singularity exist? If you are saying there is no matter outside of the universe I perfectly agree but I do not see how you conclude that the universe is infinite.

I think I can make the same argument I made against time existing eternally in the past to disprove your notion that the universe is infinite.

1. If the universe began at a singularity, at that moment the universe was obviously not infinite.
2. The universe will then have to expand to the size of infinity after the big bang, bit by bit just like time
3. So the universe can potentially be infinite but cannot at any moment be infinite because that is logically contradictory

Now if you want to call the size of the universe now as infinite… we are not talking about the same concept of infinity anymore. Your concept of infinity is that its just a HUGE value which is not the same context as what this discussion is about.

Obviously you missed my point, so I will just end that debate lol

No offense but ending the debate because the other person didn’t get your point is not exactly a valid reason. You could have at least pointed out what I misunderstood. Because from what you wrote, I think what I inferred is correct.

God Bless

 

[Just_Lurking]

So infinity - 1 = infinity - 1?

Math is so interesting to think about ha. Okay but ya i am so confused becaused if infinity - 1 = infinity - 1, then infinity is no longer infinity?

could infinity plus/multiply something = infinity?
where as subtract or divide = (infinity minus/divide whatever number)? because we are taking away from the infinitness so it is no longer infinite?

Cardinals and ordinals don’t have subtraction, so the following only applies to hyperreals and surreals: “Infinity minus 1” is a number, and if you add 1 to it, you get infinity.

A number is defined to be infinite if it is larger than 1, 2, 3, …, that is, if it is larger than all the finite integers. By this definition, “infinity minus 1” is also an infinite quantity. To really get crazy, so is the “square root of infinity”!

 

[reggieM]

It’s interesting also that since an actual infinite cannot be bounded, it’s impossible to fully compare anything with an actual infinity.

Or you could say, it’s not possible to add or subtract a number from an actual infinity.

Because, let’s say – you have to add a number “to the end” of an actual infinite string.

Obviously, you can never get to the end of an actual infinite string so you can never add a number to it. You can’t add to the beginning either because it doesn’t have a beginning (whereas a potential infinite does have a beginning).

 

[uscav_21]

I will assume you are a beginner at philosophy.

An actual infinite can never be composed by successive addition.

Whilst a line may continue infinitely (emphasis on …ly); the body of that line will never be infinite in length.

The words potential infinite equate to an unboundaried and increasing numerical order; wheras an actual infinite is the composite of a fully progressed order - since no singular progression of finite parts can ever create a sum total accuratly defined as infinite it is impossible to have an actual infinite in reality; wheras; in conception one can produce a potentially infinite chain by determining that X can be divided by Y eternally, or a sum may have X added to it eternally; thus producing a conceptual chain that is not boundaried by finite constraints. However, the progression along this line of finite parts will never reach an infinite number.

If you “think” you know some philosophy books that disproves this; I shall be happy to oblige; but pre-emptivelly I shall provide a good resource on the Topic; and that is the Scholastic debate on the natures of infinites between Richard FitzRalph and Richard Kilvington in the 14th centuary. I shall cite here from Kretzmann’s book (on Kilvington) of 1982; I have emboldened the key point.

The first eleven sophisms use the process of whitening to consider the motion of alteration as a successive entity extrinsically limited at its beginning and end. There is no first instant of alteration, claims Kilvington, only a last instant before the alteration begins; likewise, there is no last instant of alteration, only a first instant marking the introduction of the final degree of the quality in question. Thus, motion yields no minimum degree of whiteness or speed, but rather smaller and smaller degrees ad infinitum down to zero, since the qualities change continuously. The set of integers is* potentially infinite because one can always find a higher integer, but not actually infinite since there is no infinitely great number.*** Since, in Kilvington’s opinion, any continuum of time, space, motion, heat, whiteness, etc., is infinitely divisible, it can be understood quantitatively and measured using infinite sets of integers. Sophisms 29-44 reveal Kilvington’s special interest in the causes of local motion, i.e., active and passive potencies, and in effects such as time, distance traversed, and speed. He considers both uniform and difform motion caused by voluntary agents, and calls attention to the dubious measure of instantaneous speed through the comparison of speed in uniform and accelerated motion

Well your first assumption is wrong. I have a degree in Philosophy. Do you? So I believe I have a fairly decent pedigree to discuss some Philosophy.
First I want to ask you a question, do you believe in God? If you do, do you believe God is infinite? Then I want to ask you, does god exist in reality? If so, it would hold that one being exist in reality with the property of being infinite.
For starters I see you are making a common mistake, you are confusing a part with the whole. By stating that successive addition could never equate to infinity is where your confusion takes place.
You state “where as an actual infinite is the composite of a fully progressed order”. This means you are saying that infinite is a set rate something complete, but you must know that infinity is not complete. You have stated the opposite of the meaning of infinity. Another statement you made, “thus producing a conceptual chain that is not boundaried by finite constraints. However, the progression along this line of finite parts will never reach an infinite number”. Okay, now do you see where the action can continuously be done? By having the ability to push the finite numbers into a boundless entity we have infinity. Look I see what you are trying to say, you can take 10 billion and raise it to the 29th billion, and you will receive a finite number. But a person could do this process over and over and never hit an end. Thus the progression is infinite.
Now back one more time to this idea of potential infinity, but no infinity. Something can only potentially be something, if can actually be something. Meaning a tomato seed is a potential tomato plant, and etc…
But the thought I am having in my mind about the planet Mars, does not have the potential to be a tomato plant. Therefore things that can actually become this something can only logically be called potentially. Now, do you see how you are misusing the term potentially? Peace be with you.

 

[JohnDamian]

uscav_21, you raise some intriguing questions!

Firstly, I do not have a scrip in Philosophy.

For starters I see you are making a common mistake, you are confusing a part with the whole. By stating that successive addition could never equate to infinity is where your confusion takes place.
You state “where as an actual infinite is the composite of a fully progressed order”. This means you are saying that infinite is a set rate something complete

I used the term “actual infinite” to refer to an infinite that is the product of a fully progressed order. This distinction has been used for at least hundreds of years; I cited for example - the classic debate between Richard FitzRalph and Richard Kilvington in the 14th centuary - this is common knowlege to anyone with an interest in philosophy. It is made demonstrably clear the difference and distinction between a potential and actual infinite.

To make this easier for you to understand, ( I presume you did not Major in Scholastic Philosophy ) The potential and actual infinites are distinct distinctio intentionalis and distinctio formalis a parte rei, in that the quiddical principal of a genus (infinity) is essentially predicated upon a numerically unitiative part; which essentially indicates that in reality the infinite cannot exist as a genus of finite parts cannot extend to an infinite number by successive addition (in any instant); yet - as the future is presumed to continue ad infinitum it can be said that such a thing is potentially infinite. The actualisation of such a conception however cannot happen.

By having the ability to push the finite numbers into a boundless entity we have infinity.

Your conception of time is absurd. No matter how long the progression on a linear time is that progression will never reach an infinity even if that progression is unbounded. That is to say; at any point in the future the sum multiplication of any number will never reach an infinite number. You seem to misunderstand how time works; if you could elaborate on your conception of time that would be helpful.

But a person could do this process over and over and never hit an end. Thus the progression is infinite.

No. A person could repeat a process ad infinitum and never reach a numerical end, for such would entail the contradiction that the genus of infinity cannot be composed of finite species. The word you are looking for is not infinite; but unbounded, it is sloppy and imprecise language like this that gives philosophy a bad name.

To say the future is “infinite” is absurd.

The future is not infinite; for at any given moment in the future, a finite amount of time will have elapsed; and thus no infinite exists. The unbounded nature of time is irrelevant to this key point.

First I want to ask you a question, do you believe in God? If you do, do you believe God is infinite? Then I want to ask you, does god exist in reality? If so, it would hold that one being exist in reality with the property of being infinite.

I do believe in God, but in accordance with acceptable positions within the church, I hold my view on the “infinity” of God’s attributes as not within the genus of numerical univocity; such a view is espoused in the Ordinatio of Bl Duns Scotus. And by consequence your point is irrelevant.

Now back one more time to this idea of potential infinity, but no infinity. Something can only potentially be something, if can actually be something. Meaning a tomato seed is a potential tomato plant, and etc…

Something can potentially be something if that something is a species or predicate of the thing itself; such a potentiality with regards to the numerical univocity is held back by the logical priority of the quiddiative essence of an infinity’s lack of composition by finite species. I concur that this term is a sloppy term, but again I refer you to the standard Philosophy on infinities (above), which utilises these terms - I did not choose them.

I am afraid if you think I am misusing the terminology you should really lodge that complaint against philosophers long dead, not myself. I am only using philosophy terminology in the philosophy section.

In my opinion, better terms would be the existent infinite and the unbounded finitude. But if everyone just invented their own terms then that would be very difficult, especially if terms already exist for the ideas we use.

Peace

 

[reggieM]

God cannot be *in *reality, but rather “is” reality. God is the source of all being and existence. God is an actual infinite, true – but we’re usually talking about an actual infinite in the universe. That is not possible.

An actual infinite would be complete since there would be nothing that could be left incomplete over an infinite amount of time. That’s a basis of the argument for God’s omniscience, perfection, immutability, omnipotence and goodness.

A potential inifinity is always a finite quantity because it has a fixed beginning point from which to measure. No matter how long it is (for the measure of length), it can never be an infinite measure long. It never reaches an infinite length. It also never arrives at a time where it has gone on for an infinite amount of time. It is always just potentially infinite.

(I’m sorry for interjecting on this … I haven’t read the previous parts and I don’t even know why the issue is being debated. Thanks for your patience. )

 

[uscav_21]

Since I am just about through debating this topic and will agree to disagree on this topic, I will offer a reading for you to understand a better position to think of infinity. This does take a little time to review but given the subject being discussed it is very accessible. This comes from the Stanford Encyclopedia of Philosophy, and it is regarding set theory. plato.stanford.edu/entries/set-theory/

 

[Just_Lurking]

Since I am just about through debating this topic and will agree to disagree on this topic, I will offer a reading for you to understand a better position to think of infinity. This does take a little time to review but given the subject being discussed it is very accessible. This comes from the Stanford Encyclopedia of Philosophy, and it is regarding set theory. plato.stanford.edu/entries/set-theory/

Note that set theory is the mathematical study of infinity. There is no “potential infinity” vs. “actual infinity” distinction here.

 

[uscav_21]

Note: We are trying to determine if infinity is present in reality. Given I believe mathematics is present, than a form of infinity does exist, but I believe I see the issue of our communication. Maybe we should try and distinguish what is reality and what substances exist, before we could settle the question of infinity, but that task would take for infinity. (Joking) So I will consider the manner closed on my end. But I do have a question, does anyone know if Dr. William Lane Craig has an official website? So far I have only been able to locate a few that has very little information on them.

 

[coolduude]

Yep he does. Google ‘Reasonable Faith’.