Metaphysics questions about infinity

[Egervari 0]

I recently came across a person I was debating with, and I think a pretty good job explaining the points, but I wanted to be sure if my responses were truthful and accurate.

This person claimed that it's "statistically impossible" for life, matter, etc. be created. He's one of those fine-tuned universe guys, and because of that theory lends itself to a creator, be believes in god. I am not a physics guy, so I simply asked him, "what evidence do you have to support that it is statistically impossible?"

He goes on to talk about how all these constants, like the cosmological constant, needed to be exactly as they are in order for the universe to exist as it is today. He concluded that since it's a "statistical impossibility", it would take an infinite number of chances to reach it, and thus is not possible.

I stopped him right there, because even assuming that his premise is correct, 1 out of a "very large number" is still not infinitely small, it's just " a very small chance".

Now I don't know much about this, but if there's multiple chances for this to happen, and nobody's around to observe it... eventually it would happen right?

But it doesn't stop there. He showed no evidence that these constants could be anything other than what they are in the first place. He's assuming that by chance they could be anything at all. Again, he showed no proof of this.

I asked him, what are you axioms? He said the same as mine (existence and consciousness). But he says it's not enough for philosophy to simply take for granted that things exists, it needs to explain "why". I stopped him there and said, "No, that's the job of science, not philosophy." I proceeded to give him many examples and proofs that just because we don't know why doesn't mean the axioms and the proofs built on the axioms are in any invalidated. In fact, if we should learn the "why", all of the philosophical knowledge would still be correct.

Of course, he doesn't accept this. He goes into multiverse theory, and says it's logically necessary. I ask him, is multiverse theory proven? He says it is, but we looked on wikipedia and it only acknowledges that it's "hypothetical" at best. I guess that's one more point for me. He was basing all kinds of proofs on top of multiverse theory, which fall apart because multiverse theory isn't proven.

Then he goes on to say, "Evolution is hypothetical too, so they are both proven". Except I reminded him that evolution has perception going for it, not to mention that we can analyze really old fossils and know that certain life forms did not exist like they do today. Oh, we also this thing called "dna" and "the study of genetics" which overwhelmingly points the validation of evolution. So I told him, "No, they aren't even the same league".

I mean, let's consider the fact that our consciousness, according to him, cannot perceive these other existences in the multiverse. So even though we can't even perceive them, let alone rationally prove it... he wants to take it as fact. Yeah right.

And then began to blast me that "my philosophy assumes god does not exist and works from there". And I had to explain to him, from the ground up, that it makes no such assumption. In fact, there is no proof per say because 'god' would be an anti-concept - nothing in reality even suggests that such a being exists in the first place.

I guess the conversation was running in circles, but I was wondering if you have some points that are so clear to shut this down much more easily than I could. Thanks!

[Betsy Speicher 0]

It sounds like he's engaging in a lot of intellectual nonsense in order to rationalize his belief in God. As long as you don't address his need to do so directly, you're not going to get anywhere.

I'd confront that issue directly and ask, "Why is believing in God important to you? What difference would it make in your life if there wasn't a God?" Depending on what he says, you'll have an indication of how to proceed in the discussion or whether you even want to.

[ewv 0]

I recently came across a person I was debating with, and I think a pretty good job explaining the points, but I wanted to be sure if my responses were truthful and accurate.

This person claimed that it's "statistically impossible" for life, matter, etc. be created. He's one of those fine-tuned universe guys, and because of that theory lends itself to a creator, be believes in god. I am not a physics guy, so I simply asked him, "what evidence do you have to support that it is statistically impossible?"

He goes on to talk about how all these constants, like the cosmological constant, needed to be exactly as they are in order for the universe to exist as it is today. He concluded that since it's a "statistical impossibility", it would take an infinite number of chances to reach it, and thus is not possible.

This is all rationalism cut off from reality. He is misusing the concepts of statistics, chance and and probability as metaphysical. They are means of estimating what something may be, based on limited evidence, and have nothing to do with explaining why things are as they are. Things are exactly what they are because they are what they are. There is a 100% "chance" that he is what he is, or he wouldn't be here talking about it. As usual, the attempt to replace causality with supernatural intervention does not solve his original problem and makes his "solution" even more hopelessly complex and fantastically hopeless, which tells you something about his motives that you mistook for rational understanding. He prefers deep mystery.

I stopped him right there, because even assuming that his premise is correct, 1 out of a "very large number" is still not infinitely small, it's just " a very small chance".

Never grant "assuming his premise" to a rationalist, it only keeps his game going for no good purpose.

Now I don't know much about this, but if there's multiple chances for this to happen, and nobody's around to observe it... eventually it would happen right?

But it doesn't stop there. He showed no evidence that these constants could be anything other than what they are in the first place. He's assuming that by chance they could be anything at all. Again, he showed no proof of this.

Multiple chances for anything to happen doesn't mean it will no matter how long you wait. Rolling dice eventually gives all the combinations because all of them are possible because of what they are; there is no chance that one of them will turn into a toad and commune with the tooth fairy no matter how long you wait and whether or not anyone is watching. There is no "all possible worlds", only this one.

I asked him, what are you axioms? He said the same as mine (existence and consciousness). But he says it's not enough for philosophy to simply take for granted that things exists, it needs to explain "why". I stopped him there and said, "No, that's the job of science, not philosophy." I proceeded to give him many examples and proofs that just because we don't know why doesn't mean the axioms and the proofs built on the axioms are in any invalidated. In fact, if we should learn the "why", all of the philosophical knowledge would still be correct.

And if you never know why, they are still correct. But he is not asking "why", he asking "who", assuming primacy of consciousness. He does not accept your axioms of existence and consciousness. He thinks consciousness must create existence rather than being aware of it.

Of course, he doesn't accept this. He goes into multiverse theory, and says it's logically necessary. I ask him, is multiverse theory proven? He says it is, but we looked on wikipedia and it only acknowledges that it's "hypothetical" at best. I guess that's one more point for me. He was basing all kinds of proofs on top of multiverse theory, which fall apart because multiverse theory isn't proven.

You don't need that "point". Existence is everything there is. There is nothing left over for another one. There are no facts outside of existence -- this one -- on which to base a proof of a parallel, independent existence.

Then he goes on to say, "Evolution is hypothetical too, so they are both proven". Except I reminded him that evolution has perception going for it, not to mention that we can analyze really old fossils and know that certain life forms did not exist like they do today. Oh, we also this thing called "dna" and "the study of genetics" which overwhelmingly points the validation of evolution. So I told him, "No, they aren't even the same league".

What if evolution had not been proven -- how does an unproven hypothesis by virtue of its lack of proof make another one proven? His arguments are nonsensical. Arguing over whether or not evolution is proven science does not address that.

I mean, let's consider the fact that our consciousness, according to him, cannot perceive these other existences in the multiverse. So even though we can't even perceive them, let alone rationally prove it... he wants to take it as fact. Yeah right.

And then began to blast me that "my philosophy assumes god does not exist and works from there". And I had to explain to him, from the ground up, that it makes no such assumption. In fact, there is no proof per say because 'god' would be an anti-concept - nothing in reality even suggests that such a being exists in the first place.

He starts with P of C and is unwilling to consider anything else that rejects his belief in the supernatural.

I guess the conversation was running in circles, but I was wondering if you have some points that are so clear to shut this down much more easily than I could. Thanks!

Yes there is an easy way to shut it down. Stop talking to him. The conversation wasn't running in circles, you were, in trying to contend with the impossible because you mistook his rationalism for taking ideas seriously. They weren't the kind of ideas (about reality) you had in mind. You can only spend so much time talking to someone by providing rational explanations before deciding if he is playing a rationalist game not worth your time. Anything else only sanctions and encourages him. You have no obligation to engage anyone who wants to talk to you or to try to convince him. Learn from the experience. You only have so much time on earth to pursue and achieve your values. Use it wisely.

[Egervari 0]

This is all rationalism cut off from reality. He is misusing the concepts of statistics, chance and and probability as metaphysical. They are means of estimating what something may be, based on limited evidence, and have nothing to do with explaining why things are as they are. Things are exactly what they are because they are what they are. There is a 100% "chance" that he is what he is, or he wouldn't be here talking about it. As usual, the attempt to replace causality with supernatural intervention does not solve his original problem and makes his "solution" even more hopelessly complex and fantastically hopeless, which tells you something about his motives that you mistook for rational understanding. He prefers deep mystery.

You put this very nicely. Thanks! I actually tried to tell him that entities are what they are as well, and just because we may not know why they are the way they are, it still doesn't take away the fact that they do exist and have the nature they have.

I also pointed out to him that perhaps the constants that he is referring to also had to be that way, as he didn't present ANY proof at all that they could have been variable. He just assumed that the constants were mere variables before they became constants (kind of funny when one actually types this. lol).

One point I forgot to mention was that he said "your philosophy assumes that existence is infinite, and because it's infinite and nothing infinite can exist in reality, that proves that it must have a starting point." In other words, his starting point is god.

But I went on to tell him, "Well, clearly existence exists... we know this... so it must be finite because it IS something."

Then he went on to say, "But if it's eternal, it you don't have starting point and an ending point. It stretches forwards and backwards infinitely long."

I was reminded that the potentiality is infinite, but in this moment in time, it is clearly finite. But then I got to thinking on it more and realized that there is only 1 existence, and this whole thing about time was just a way to obfuscate the fact that there's only one of them. Like, if I had to model existence in a computer program, I would include time as one of its attributes, but I would only have 1 class and 1 instantiated object of this class in the entire program (we call that a singleton in software design).

I don't know if my explanation is right, but it makes a lot more sense to me than what he's saying.

Never grant "assuming his premise" to a rationalist, it only keeps his game going for no good purpose.

Noted

Multiple chances for anything to happen doesn't mean it will no matter how long you wait. Rolling dice eventually gives all the combinations because all of them are possible because of what they are; there is no chance that one of them will turn into a toad and commune with the tooth fairy no matter how long you wait and whether or not anyone is watching. There is no "all possible worlds", only this one.

Agreed. I was merely going along with his random constant premise and following that out, the very thing you said not to do. LOL.

And if you never know why, they are still correct. But he is not asking "why", he asking "who", assuming primacy of consciousness. He does not accept your axioms of existence and consciousness. He thinks consciousness must create existence rather than being aware of it.

Exactly. I tried so hard to get this point through, but he kept saying, "How convenient for you to ignore this and say it's not an aspect of philosophy so that you can use it as an excuse to not answer my questions."

I asked him several times, "What are your premises?" and "Show me, from the ground up, how you arrive at these conclusions." Of course, he never did. He just kept saying, "I have you the evidence! Why don't you believe it! Argh!" Very frustrating

What if evolution had not been proven -- how does an unproven hypothesis by virtue of its lack of proof make another one proven? His arguments are nonsensical. Arguing over whether or not evolution is proven science does not address that.

Totally agree. I brought this to his attention as well (I didn't type it). He just changed the topic and started attacking me

Yes there is an easy way to shut it down. Stop talking to him. The conversation wasn't running in circles, you were, in trying to contend with the impossible because you mistook his rationalism for taking ideas seriously. They weren't the kind of ideas (about reality) you had in mind. You can only spend so much time talking to someone by providing rational explanations before deciding if he is playing a rationalist game not worth your time. Anything else only sanctions and encourages him. You have no obligation to engage anyone who wants to talk to you or to try to convince him. Learn from the experience. You only have so much time on earth to pursue and achieve your values. Use it wisely.

I have a hard time with this, because I think my world would be much better if the people around me were more rational. I will have to learn when it's time to jump ship next time rather than invest so much, because no good comes out of it other than frustration and wasted time, which you are totally correct.

Thanks for the insights and tips!

[ewv 0]

One point I forgot to mention was that he said "your philosophy assumes that existence is infinite, and because it's infinite and nothing infinite can exist in reality, that proves that it must have a starting point." In other words, his starting point is god.

But I went on to tell him, "Well, clearly existence exists... we know this... so it must be finite because it IS something."

Then he went on to say, "But if it's eternal, it you don't have starting point and an ending point. It stretches forwards and backwards infinitely long."

I was reminded that the potentiality is infinite, but in this moment in time, it is clearly finite. But then I got to thinking on it more and realized that there is only 1 existence, and this whole thing about time was just a way to obfuscate the fact that there's only one of them. Like, if I had to model existence in a computer program, I would include time as one of its attributes, but I would only have 1 class and 1 instantiated object of this class in the entire program (we call that a singleton in software design).

I don't know if my explanation is right, but it makes a lot more sense to me than what he's saying.

Software engineering is method and procedure, not metaphysics. Time is a measure of change. Time is in the universe; the universe is not in time. The universe is eternal means it is outside of time, not that there is an actual infinity. There is a potential infinite in measuring time backwards or forward insofar as change exists. That is an open-ended process of measurement within the universe. It does not mean existence is infinite or a thing called 'time' is infinite. Neither does existence have a beginning in time, it simply is. It changes, and that is how you experience time. The totality of existence does not have a "cause" outside of existence; there is nothing outside of existence to be a cause. Existence is what it is, always, at each point in time. There is no sequence of existences existing in time, only change of the only existence that is.

Yes there is an easy way to shut it down. Stop talking to him. The conversation wasn't running in circles, you were, in trying to contend with the impossible because you mistook his rationalism for taking ideas seriously. They weren't the kind of ideas (about reality) you had in mind. You can only spend so much time talking to someone by providing rational explanations before deciding if he is playing a rationalist game not worth your time. Anything else only sanctions and encourages him. You have no obligation to engage anyone who wants to talk to you or to try to convince him. Learn from the experience. You only have so much time on earth to pursue and achieve your values. Use it wisely.

I have a hard time with this, because I think my world would be much better if the people around me were more rational. I will have to learn when it's time to jump ship next time rather than invest so much, because no good comes out of it other than frustration and wasted time, which you are totally correct.

The world would be much better if people around you were more rational -- in particular better for you. But you can't accomplish that by squandering your life trying to reform people who aren't and don't want to be more rational. If someone wants to believe in a supernatural that is his choice and there isn't anything you can do about it if he is not open to rational persuasion. Choose your battles and don't sacrifice your own values to 'saving the world'. You aren't jumping ship by abandoning a hopeless rationalist; you jump your own ship when you waste time on him.

[Egervari 0]

Software engineering is method and procedure, not metaphysics. Time is a measure of change. Time is in the universe; the universe is not in time. The universe is eternal means it is outside of time, not that there is an actual infinity. There is a potential infinite in measuring time backwards or forward insofar as change exists. That is an open-ended process of measurement within the universe. It does not mean existence is infinite or a thing called 'time' is infinite. Neither does existence have a beginning in time, it simply is. It changes, and that is how you experience time. The totality of existence does not have a "cause" outside of existence; there is nothing outside of existence to be a cause. Existence is what it is, always, at each point in time. There is no sequence of existences existing in time, only change of the only existence that is.

Actually, that is exactly what I meant. In software, we don't just model method and procedures. Maybe they did 30+ years ago, but we actual model entities/concepts first, as well as hierarchies and all kinds of things that are extremely similar to the way Ayn Rand describes entities in metaphysics and concepts in epistemology. Entities in software (called classes) have attributes and behaviour. Good software design mirrors what happens in reality the best it can, although we usually take a snapshot of the things that are of interest to the program and not everything. So, in such a computer program, time would in fact be in the entity 'Existence'

[Paul's Here 0]

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Now I don't know much about this, but if there's multiple chances for this to happen, and nobody's around to observe it... eventually it would happen right?

--------------------

Considering that the universe it eternal, a 1 in infinity chance is pretty good odds.

[Betsy Speicher 0]

Yes there is an easy way to shut it down. Stop talking to him. The conversation wasn't running in circles, you were, in trying to contend with the impossible because you mistook his rationalism for taking ideas seriously. They weren't the kind of ideas (about reality) you had in mind. You can only spend so much time talking to someone by providing rational explanations before deciding if he is playing a rationalist game not worth your time. Anything else only sanctions and encourages him. You have no obligation to engage anyone who wants to talk to you or to try to convince him. Learn from the experience. You only have so much time on earth to pursue and achieve your values. Use it wisely.

I have a hard time with this, because I think my world would be much better if the people around me were more rational.

That's true, but another way of making your world better is to spend more time with people who are basically rational rather than with those who aren't and don't want to be.

If you enjoy persuading people, you will also have more success with essentially rational people. Francisco set his sights on winning over Rearden, not James Taggart.

[ewv 0]

Like, if I had to model existence in a computer program, I would include time as one of its attributes, but I would only have 1 class and 1 instantiated object of this class in the entire program (we call that a singleton in software design).

Software engineering is method and procedure, not metaphysics. Time is a measure of change. Time is in the universe; the universe is not in time. The universe is eternal means it is outside of time, not that there is an actual infinity. There is a potential infinite in measuring time backwards or forward insofar as change exists. That is an open-ended process of measurement within the universe. It does not mean existence is infinite or a thing called 'time' is infinite. Neither does existence have a beginning in time, it simply is. It changes, and that is how you experience time. The totality of existence does not have a "cause" outside of existence; there is nothing outside of existence to be a cause. Existence is what it is, always, at each point in time. There is no sequence of existences existing in time, only change of the only existence that is.

Actually, that is exactly what I meant. In software, we don't just model method and procedures. Maybe they did 30+ years ago, but we actual model entities/concepts first, as well as hierarchies and all kinds of things that are extremely similar to the way Ayn Rand describes entities in metaphysics and concepts in epistemology. Entities in software (called classes) have attributes and behaviour. Good software design mirrors what happens in reality the best it can, although we usually take a snapshot of the things that are of interest to the program and not everything. So, in such a computer program, time would in fact be in the entity 'Existence'

This is not a matter of what kinds of encapsulated objects versus pure procedural code you want to use to "model" things in software. Software is a science of method and procedure. It is not metaphysics or epistemology. Whatever computer language or methods of encapsulation you use, no software is a source of concepts for metaphysics and epistemology. Object oriented software is not "extremely similar" to Ayn Rand's philosophy. Encapsulating data and methods in software objects is not philosophy and has no such meaning. Software analogies are not a substitute for the actual concepts of metaphysics and epistemology. Use of such analogies only causes dangerously rationalistic misrepresentations.

Objectivism does not "model" or "mirror" reality or concepts, and software does not "model" or "mirror" Objectivism. Concepts are not "sets". The Objectivist hierarchy of abstract concepts is not set inclusion or membership.

No software can "model" existence, which is everything that is. Existence as everything is not an entity at all. Time can only be understood as a measure of change, not a free-floating, undefined "attribute" of existence "included" in an entity. Speaking of software "modeling" existence and "including" time as an "attribute" of existence as a "singleton" is cut off from reality even in terms of what you can do in software, let alone its meaning in Objectivism, and is itself an example of rationalism disconnected from meaning in reality.

You should learn and use the actual concepts and principles of Objectivism for thinking and talking about philosophical subjects and drop the idea of using software metaphors as a substitute.

[ewv 0]

Considering that the universe it eternal, a 1 in infinity chance is pretty good odds.

Speaking of rationalism, what does that even mean? What "odds" for what? What is a "1 in infinity chance"? Infinity is not a number and 1/infinity is not a fraction.

[Paul's Here 0]

Considering that the universe it eternal, a 1 in infinity chance is pretty good odds.

Speaking of rationalism, what does that even mean? What "odds" for what? What is a "1 in infinity chance"? Infinity is not a number and 1/infinity is not a fraction.

Just being sarcastic. If the universe is eternal and the odds of some event happening were once in every 10 trillion years, then that event has had many chances of occurring.

[ewv 0]

Considering that the universe it eternal, a 1 in infinity chance is pretty good odds.

Speaking of rationalism, what does that even mean? What "odds" for what? What is a "1 in infinity chance"? Infinity is not a number and 1/infinity is not a fraction.

Just being sarcastic. If the universe is eternal and the odds of some event happening were once in every 10 trillion years, then that event has had many chances of occurring.

What does that mean in reality? What odds, under what conditions, for what event, under what possible causal conditions, determined how, for what time period? Earth is about 4 1/2 billion years old. The physical astronomical universe as we know it -- the galaxies -- is estimated to be about 13 3/4 billion years old, less than .14% of 10 trillion years. How can one know what the "odds" are for "some event" recurring through "eternity" and what that means?

[inventor 0]

[...]

I regret not having the time to write more extensively on the topic of infinity, and that is one of my favorite polemical scientific topics.

Infinity is a false concept. It is an anti-concept, that is, it is a destructive concept that functions like an intellectual land-mine that stops further thought. Infinity was a notion that was labelled as an ideal by Plato, for lack of a better, more factual, definition. Aristotle, on the other hand, called infinity a religious concept in that it had no finite or verifiable identity.

The proper concept that should stand in its place is the concept of continuity, and specifically, the continuous functioning, or existence of the universe.

The universe is a continuing plurality of existents that have properties, the potentials of the existents becoming what they will become according to their natures and their relationships with other existents.

Non-existence is not the cause of the universe. There is no such thing as non-existence. Existence only, is the cause of the changing continuous universe; that is, existents, and their functioning properties, are the cause of what will be, or of what is. The actualized functioning of existents to current completed states of being is the final cause of the universe. Of its being.

There is no goal to which the universe and all of its existents extends. There is no spatial or temporal boundary or limit to the universe; there is only what is and the functioning and actualized properties of what is in the here and now.

For more written bits and pieces on the subject of the universe, and the topic of infinity, see what I have written. Search the Internet on Google with the search term, "ralph hertle, infinity", to find a limited miscellany of notes, posts and replies on several Usenet newsgroups. Scroll to the items signed by me, and ignore the other items for reasons of consistent viewpoint and idea. Also, search for, "ralph hertle, universe", or "ralph hertle, big bang".

The answer to all infinity arguments, which are not so coincidently false, are these remarks.

"Existence is existing", said Ayn Rand, and Aristotle also remarked, and I paraphrase, that, "everything functions continuously".

Stay with the finite.

Inventor

[Betsy Speicher 0]

[...]

Infinity is a false concept. It is an anti-concept, that is, it is a destructive concept that functions like an intellectual land-mine that stops further thought.

That was not Ayn Rand's view. She considered it a useful concept of method.

A concept is like an arithmetical sequence of specifically defined units, going off in both directions, open at both ends and including all units of that particular kind. For instance, the concept "man" includes all men who live at present, who have ever lived or will ever live. An arithmetical sequence extends into infinity, without implying that infinity actually exists; such extension means only that whatever number of units does exist, it is to be included in the same sequence.

The concept of "infinity" has a very definite purpose in mathematical calculation, and there it is a concept of method. But that isn't what is meant by the term "infinity" as such. "Infinity" in the metaphysical sense, as something existing in reality, is another invalid concept. The concept "infinity," in that sense, means something without identity, something not limited by anything, not definable. <ioe2_149> Therefore, the measurements omitted here are all measurements and all reality.

[inventor 0]

[...]

Infinity is a false concept. It is an anti-concept, that is, it is a destructive concept that functions like an intellectual land-mine that stops further thought.

That was not Ayn Rand's view. She considered it a useful concept of method.

A concept is like an arithmetical sequence of specifically defined units, going off in both directions, open at both ends and including all units of that particular kind. For instance, the concept "man" includes all men who live at present, who have ever lived or will ever live. An arithmetical sequence extends into infinity, without implying that infinity actually exists; such extension means only that whatever number of units does exist, it is to be included in the same sequence.

The concept of "infinity" has a very definite purpose in mathematical calculation, and there it is a concept of method. But that isn't what is meant by the term "infinity" as such. "Infinity" in the metaphysical sense, as something existing in reality, is another invalid concept. The concept "infinity," in that sense, means something without identity, something not limited by anything, not definable. <ioe2_149> Therefore, the measurements omitted here are all measurements and all reality.

I didn't mean to say that what I said as quoted above was what Ayn Rand intended or meant. Actually, I completely agree with Rand on the points made in the quotations from ITOE that you posted. I don't disagree with that in any way.

Regarding what I said, that, "Infinity is a false concept . . . . that stops further thought," I meant that it is fine to imagine infinity as a concept that is continually extended, and where the principle being discussed is the process of continuation. However, when the process must be stopped, and the concept being extended must be given a measurement or particular number, the end result must be finite. At that time or place, the end result must be both infinite and finite at the same time and place, which is impossible [Aris., Law of Non-contradiction]. That's why when you end up with God out there at the end of the line, or hugeness, you find no physical entity or finite number. That's why I said that further thought stops.

Note that the advocates of infinity as a metaphysical or even epistemological non-finite existent will repair to the concept of continuation of the process being extended as their justification. That's a stolen concept, for the concept of the continuation of a concept is a valid meatphysical or epistemological method in its own right. As a method or process that acts upon particular existents the concept of continuity is a universal, and the end result is necessarily particular or finite. A line may be extended a finite amount, says Euclid. And the result is finite. If one accepts continuity as a process or method insofar as metaphysical or epistemological exstents are concerned the result cannot be infinite.

The other argument for infinity is the concept of mere large or small size. Gigantic explosions, or limitless love, or huge numbers, etc., are posited. All of which, in order to be realized must be finite. I say that there is no universal that is particular, and nothing infinite that is finite. I'll add to that the notion that one cannot conceive of any type of existent that has been continued a great amount and that is also infinite. Only the finite results of an extension, method, process, or continuation may be actualized or realized. Any discovery or demonstration of any universal must be finite, and hence the proposed concept of infinity is impossible in reality or as a knowable idea.

Nor is smallness an example of an infinite metaphysical existent, for the itty bitty witty gritty is finite. And, in the sense of an epistemological existent, for example, a point is a location only, which is finite.

Inventor

[ewv 0]

[...]

Infinity is a false concept. It is an anti-concept, that is, it is a destructive concept that functions like an intellectual land-mine that stops further thought.

That was not Ayn Rand's view. She considered it a useful concept of method.

As the quotes Betsy provided show, it is not just "useful", but a valid concept of method, contradicting the unqualified claim that it is a "false concept", and "anti-concept", and "destructive", "stop[ping] further thought". One cannot agree with both positions. This is also discussed in Leonard Peikoff's OPAR.

The obscure ruminations about an undefined concept of "continuity" are also incorrect. The continuous is not a valid concept of metaphysics "standing in the place" of the invalid metaphysical infinite, and is not used by Ayn Rand that way either. To the extent that continuous as 'unbroken', etc. is used in a valid way, it has no connection with the role of the metaphysical infinite. The fallacies of the metaphysically infinite are not corrected or explained by using an undefined "continuity" in its place. As a concept of mathematical method, continuity, like the mathematical infinite, is valid and important, but that is not the way it has been used here.

The ruminations in the above few posts are unrelated to the questions in the original post and the subsequent discussion addressing them. The proper and improper uses of 'infinity' in different contexts have been far more cogently discussed many times in detail by some of us here on the Forum, but that wasn't necessary for Egervari's level of understanding and the kinds of questions he raised here, regardless of anyone's claimed interest in a diversion into obscurely formulated "favorite polemics" on alleged "scientific topics".

[inventor 0]

[...]That was not Ayn Rand's view. She considered it a useful concept of method.

My understanding of the concept of infinity is based mostly upon the work of the Ancient Greek philosphers and geometers. I also concur with Ayn Rand regarding the meaning that she offered.

My use of the term, 'continuity', is based on Aristotle's use of the term to mean the universal concept of the functioning of a principle that yields a particular result, for example, that the line of a circle is generated evenly at every point on the circle based upon the principle of the constant distance of every point on the circle from the center. The finite result is the complete circle. Continuity, demonstrated, yields finite results.

The principle of the generation of infinity, that is claimed by the advocates of infinity, is that which is continuously extended to a claimed infinite result. They claim that the end of the continuous process is an infinite existent.

That disagrees with the other sciences, e.g., mathematics, that says, for example, that the extension of a concept of number, say by adding one to the previous number, will result in a finite number.

There it is. Is the infinite result infinite? Or does the continuous process of addition yield a finite number? It can't be both at the same time and respect. Which is infinity? An infinite result of a claim? Or is it the finite result of the continuous application of a principle, in which case infinity is not proved?

Do you have a different concept of 'infinity'?

Or a more modern, or more modern, mathematical concept of infinity?

If so what is your definition?

Inventor

[ewv 0]

[...]That was not Ayn Rand's view. She considered it a useful concept of method.

I did not write what he quoted. He did not acknowledge or address what i wrote.

My understanding of the concept of infinity is based mostly upon the work of the Ancient Greek philosphers and geometers. I also concur with Ayn Rand regarding the meaning that she offered.

...

There it is. Is the infinite result infinite? Or does the continuous process of addition yield a finite number? It can't be both at the same time and respect. Which is infinity? An infinite result of a claim? Or is it the finite result of the continuous application of a principle, in which case infinity is not proved?

Do you have a different concept of 'infinity'?

Or a more modern, or more modern, mathematical concept of infinity?

If so what is your definition?

This is all incomprehensible. Betsy already quoted Ayn Rand's views on the distinction between the actual infinite, which is invalid, and the mathematical infinite as a concept of method. This distinction and the meaning of the valid concept of method is well known and discussed and used with great clarity in several places in IOE and OPAR.

[inventor 0]

[...] That was not Ayn Rand's view. She considered it a useful concept of method. [...]

What is the method that Ayn Rand was referring to?

I don't speak high-level mathematics, and I would probably find the answer comprehensible if it were stated in philosophical conceptual terms.

I understand that mathematics uses the concept of infinity in some limited uses, and I have heard it explained that the concept of infinity does not identify anything in physical reality, or, for that matter, in epistemology that cannot be explained by the use of the concepts, continuity, continuous application of a universal concept, extension, endless, or non-finite, for example.

What is the method of infinity used in mathematics?

What is the method of infinity used in physics?

Inventor

[Betsy Speicher 0]

[...] That was not Ayn Rand's view. She considered it a useful concept of method. [...]

What is the method that Ayn Rand was referring to?

The method is the process of continually adding more.

[ewv 0]

I don't speak high-level mathematics, and I would probably find the answer comprehensible if it were stated in philosophical conceptual terms.

You don't need high level mathematics or philosophy.

In arithmetic there is a sequence of integers that is open-ended. It does not exist as an entirety -- an infinity of numbers that exist, but there is always the potential to add more numbers as the need arises.

In geometry a straight line does not exist as an infinite entirety, but as the need arises there is always the potential to consider a segment as long as you need.

What is the method of infinity used in mathematics?

What is the method of infinity used in physics?

Physics is mathematical and uses the same concepts.

[inventor 0]

[...] That was not Ayn Rand's view. She considered it a useful concept of method. [...]

What is the method that Ayn Rand was referring to?

The method is the process of continually adding more.

Then why not simply use the concept of 'continuation' and ignore, or not use, the concept of infinity which identifies nothing factual in the realms of physical existence or ideas?

Continuation in the metaphysical sense is a corllary to the concept of existence. Neither existence nor continuity can exist without the other. Existince is the continued being of everything.

Continuation in the epistemological sense is a corollary to the concept of the universality of concepts. Neither the functioning (and potential application) of a concept nor the continuation of identification of an existent may exist without the other.

Infinity is a claimed substitution for the concept of existence in some uses in language and religion, however, the concepts of existence, continuity, size, universal concept, or extended functioning are the claimed synonyms for infinity. The so-called concept of infinity, however, has no actual or finite referent in the realms of physics and ideas. Infinity identifies nothing.

I suspect that Ayn Rand may have accepted the concept of method as valid on the say so of mathematicians who have promoted the concept of infinity based upon the meanings of the above mentioned synonyms. To a limited extent the synonyms function, however, when the concept being extended must be actualized or given number no finite existent is to be found. The metaphysical idea of infinity has been rejected by her in that there is nothing in the universe except that which exists, and only existents exist. There is no more in the universe than that which exists, and entensions of being have no physical referents. All instances of epistemology identify all instances of metaphysics. I suspect that if Ayn Rand had taken the concept of infinity in the sense of epistemology to identify the so-called huge or small extents of the pro-infinitist's claims, that there would have been found nothing.

It would have been fun to discuss the concept of infinity with Ayn Rand. That idea may have been one of the problem or unfinished ideas that she left here and there in her writings. It isn't a big issue; the idewa of infinity simply is relatively useless in the sense of method.

The method implied by the concept of continuity functions for all epistemological concepts, and insofar as concepts identify the facts of existents in the universe, so does the concept of continuity function with finite results.

Inventor

[Betsy Speicher 0]

I suspect that Ayn Rand may have accepted the concept of method as valid on the say so of mathematicians who have promoted the concept of infinity based upon the meanings of the above mentioned synonyms.

Speculating on people motives -- especially Ayn Rand's -- is an attempt at mind-reading which is explicitly forbidden by THE FORUM's Rules and Guidelines. Please don't do it again.

[ewv 0]

[...] That was not Ayn Rand's view. She considered it a useful concept of method. [...]

What is the method that Ayn Rand was referring to?

The method is the process of continually adding more.

Then why not simply use the concept of 'continuation' and ignore, or not use, the concept of infinity which identifies nothing factual in the realms of physical existence or ideas?

The mathematically infinite is a concept of method that does identify facts. All valid concepts, including concepts of consciousness that include concepts of method, identify facts, and are ultimately based on sense perception of reality.

Continuation in the metaphysical sense is a corllary to the concept of existence. Neither existence nor continuity can exist without the other. Existince is the continued being of everything.

Continuation in the epistemological sense is a corollary to the concept of the universality of concepts. Neither the functioning (and potential application) of a concept nor the continuation of identification of an existent may exist without the other.

Infinity is a claimed substitution for the concept of existence in some uses in language and religion, however, the concepts of existence, continuity, size, universal concept, or extended functioning are the claimed synonyms for infinity. The so-called concept of infinity, however, has no actual or finite referent in the realms of physics and ideas. Infinity identifies nothing.

This makes no sense and has nothing to do with Objectivism.

I suspect that Ayn Rand may have accepted the concept of method as valid on the say so of mathematicians who have promoted the concept of infinity based upon the meanings of the above mentioned synonyms. To a limited extent the synonyms function, however, when the concept being extended must be actualized or given number no finite existent is to be found. The metaphysical idea of infinity has been rejected by her in that there is nothing in the universe except that which exists, and only existents exist. There is no more in the universe than that which exists, and entensions of being have no physical referents. All instances of epistemology identify all instances of metaphysics. I suspect that if Ayn Rand had taken the concept of infinity in the sense of epistemology to identify the so-called huge or small extents of the pro-infinitist's claims, that there would have been found nothing.

It would have been fun to discuss the concept of infinity with Ayn Rand. That idea may have been one of the problem or unfinished ideas that she left here and there in her writings. It isn't a big issue; the idewa of infinity simply is relatively useless in the sense of method.

The method implied by the concept of continuity functions for all epistemological concepts, and insofar as concepts identify the facts of existents in the universe, so does the concept of continuity function with finite results.

Understanding the valid concept of infinity and the invalid metaphysical infinity were not "unfinished ideas" that Ayn Rand "left here and there". They are not "synonyms" and she was not duped by "mathematicians" leading to your "suspicions" held without evidence. Her views were very clear and complete. One can read them in IOE. There is nothing else to say about it at that level. She was not discussing technical aspects of the science of mathematics and had no need to. She did not have much education in mathematics, but did study basic algebra in college and had a very clear and correct understanding of what it meant, which she used to great effect in explaining similarities with her epistemology.

[inventor 0]

[...]

The method implied by the concept of continuity functions for all epistemological concepts, and insofar as concepts identify the facts of existents in the universe, so does the concept of continuity function with finite results. [...]

The concept of the continuity of functioning of concepts is a corollary to the concept of the universal identity of concepts.

All concepts identify only finite metaphysical and epistemological existents, and all functionings, proofs, and demonstrations of concepts have finite results.

Everything in the universe is finite, that is, all things are exist only as finite existents. The is nothing else except the continuum of all finite things which exist. All concepts identify finite existents or are completed only in finite results. No concepts identify nothing or result in nothing.

Inventor