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Post 60

Wednesday, March 7, 2007 - 12:05pmSanction this postReply
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I wrote, “the main point being that existence in some form always was and always will be.” Jon replied,
According to arguments you made in our infinity discussions, the above is a nonsensical assertion. “Always” contains that “all” word, which you insisted means ‘none left out.’ You said one may not assert an infinitude of future events—but rather that one must specify a period in order to have any meaning (otherwise, some would be “left out”.)

So, when you say that existence always will be, what duration do you mean to specify?
First of all, one must be careful to distinguish between actual infinity and potential infinity. There is no actual infinity, but there is potential infinity. By "potential infinity" I mean the idea that one can continue to extend a particular quantity without limit -- that there is no theoretical limit beyond which one cannot extend it. By "actual infinity" I mean the idea that however far one actually extends it, one will always be at an actual, finite quantity.

In the statement you quoted, I was referring to any and all durations that one chooses to specify (e.g., one year, a thousand years, a million years, etc.), for one must specify a particular duration or a particular number of durations in order for the concept of time to make sense. In order for time to exist, it must be some particular period(s) of time. The concept of an actual infinity makes no sense, because you are saying that certain things actually exist (using "thing" in the broadest possible sense) but that there is no particular number of them.

In saying that the universe always existed, I was saying that for any and all period(s) of time that you choose to specify, the universe has existed and will exist -- that there was never a period of time when the universe didn't exist, nor will there ever be a period of time when it doesn't.

Does that mean that the universe has existed and will exist for an infinite period of time? No, because there is no infinite period of time. Whatever period of time you choose to specify, it must be specific and therefore finite.

- Bill

Post 61

Wednesday, March 7, 2007 - 7:57pmSanction this postReply
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I wrote, “But the universe does not inhere in space-time; space-time inheres in the universe. Space and time refer to relationships among entities within the universe, not to the universe as a whole.” GWL replied,
But this is just false. I don't want to go into the physics of it, but contemporary cosmology has shown that space-time actually is something. It's a 3+1dimensional substratum of sorts, and string theorists conjecture that it may be broken down into calabi-yao manifolds-- little bundles of 6 dimensional space-time.
Define your terms. What is time? It is a measurement of motion. Motion presupposes bodies that move. If nothing existed, there would be no time. Since time depends on things that already exist, time is a property of the universe, and exists within the universe. The universe does not exist within time. What is space? It is a relationship between bodies. If nothing existed, there would be no space. Since space depends on things that already exist, space is a property of the universe, and exists within the universe. The universe does not exist within space.

I wrote, “What is expanding are things in the universe, not the universe itself, since there is nothing in relation to which the universe itself could be seen as getting larger. What a person sees through the Hubble telescope, he sees in relation to himself, as a relatively stationary observer.”
People often act as though the redshift perceived by the Hubble only shows a relative expansion. This is a common misconception. I don't have the time to explain it, but I'm sure there are ample resources available on the Internet which can clear the matter up for you.
Is it your view that the idea of relative motion is a common misconception? Unless it is, I don't see how you can say that the entire universe is expanding. For the question then arises: what is it expanding in relation to?

I wrote, “The universe as a whole is neither changing nor static, since both these concepts presuppose a relationship between entities, and there is nothing outside the universe to which it could bear any such relationship.”
I just don't see how this can be. If the 'universe', for example, began as just one uninflated balloon, and then began to expand (as if it were being blown up) an observer on the surface would notice a steadily decreasing curvature contiguous with the expansion, and therefrom would be able to deduce the expansion of his 'universe' itself.
But in that case, the balloon on which you are situated would be expanding relative to you, the observer. For suppose that you were expanding at the same rate as the balloon. In that case, you would notice no difference in the balloon’s curvature. Remember, the universe is the totality of existence, not just part of it, in which case, you as an observer must be included.

I wrote, “I am using the term ‘universe’ to refer to the totality of existence. If God exists, then he is part of the universe; if he is not part of the universe, then he does not exist."
By all means, use the nomenclature you see fit. I would just point out that theists make a distinction between the universe and God in order to highlight what they believe to be the ontological dissimilarity of the two: God is uncreated, the universe is created.
But it’s an arbitrary distinction. Why include within the universe everything in existence except for one other thing, especially when the term “universe” refers to what is universal, i.e., to everything?

Furthermore, if God can be uncreated, why can’t the universe be uncreated? If God can be considered a “necessary” being, then why can’t the universe be considered a necessary being? On the other hand, if the universe requires a creator, why doesn’t God require one? The ontological distinction that you make between God and the universe is arbitrary. Besides, as I stated earlier, even if it did make sense to talk of the entire universe as being created, the creator could not possibly have been a pure spirit or a pure consciousness, since a pure consciousness would have no means of awareness, no form of awareness and nothing to be aware of prior to its supposed act of creation.

In fact, the science of biology indicates that rather than existing at the so-called beginning of the universe, consciousness could only have arisen at the end of a long chain of evolutionary development.

I wrote, “the fundamental constituents of the natural world are ‘necessary beings.’” GLW replied,
This doesn't make sense to me, since it would impute necessity to all events.

Consider the factual historical proposition: Leibniz was given a tour of the Roman crypt by the secretary to the Pope.

Would you call an historical event of this sort necessary?
By “necessary beings” in this context, I was referring not to the evolutionary forms that these fundamental constituents take, but to the fact that there was no alternative to the existence of the constituents themselves. They were necessary beings in that sense of the term – i.e., in the same sense that you consider God a necessary being. I do believe, however, that the evolutionary forms are themselves a necessary consequence of the antecedent conditions that gave rise to them.

I wrote, “If I understand him correctly, Aristotle is saying that being is more universal than motion, because there are things that move and things that don’t. So being – i.e., existence – is, in Aristotle’s terminology, a higher 'cause' than motion, because it is more universal than motion. Not everything can be said to move, but everything can be said to exist.“ GWL replied,
I think you interpret him correctly.
I continued, “Now, Aristotle can call this higher cause ‘God’ if he wishes, but, in that case, wouldn’t ‘God’ simply be another name for being or existence? And if not, then what does Aristotle mean by ‘God’? GWL replied,
Yes, for Aristotle, God would be a kind of Supreme Being, the highest form of Life, and the Unmoved Mover of the universe. This is similar to the Christian God, but certainly not the same.
But, you see, I don’t agree with this interpretation. My understanding of Aristotle’s God is simply existence, whatever its form. I don’t see him as implying that it must be a life form or a living entity.

Aquinas wrote: "Succession is proper to movement. But creation is not movement. Therefore there is in it no succession." I responded: “Not true. Creation involves change, and change is a kind of movement.”
St. Thomas is referring to creatio ex nihilo, i.e. the creation of being from non-being. He rightly says that there can be no intermediate productive stage between non-being and being.
Okay, but I don’t see that kind of creation – creatio ex nihilo – as being a possibility. Nihilo ex nihilo --- from nothing comes nothing. To create something, you need the material out of which to make it. You can’t make something out of nothing.

Aquinas wrote: "In every making, in which there is succession, the process of being made is before the state of achieved completion. But this cannot happen in creation, because, for the process of being made to precede the achieved completion of the creature, there would be required some subject in which the process might take place. Such a subject cannot be the creature itself, of whose creation we are speaking, because that creature is not till the state of its achieved completion is realised. Nor can it be the Maker, because to be in movement is an actuality, not of mover, but of moved. And as for the process of being made having for its subject any pre-existing material, that is against the very idea of creation. Thus succession is impossible in the act of creation."

GWL commented,
All Aquinas is doing is tracing out the implications of creatio ex nihilo.
In any case, I responded, "This entire argument ignores the fact that creation presupposes existence; existence does not presuppose creation. What we have here is another exercise in floating abstractions -- abstractions removed from their base in concrete reality."
Aquinas isn't writing this "ex nihilo", as it were. ;) In his mind, he's already proved that God exists in the opening chapters of the Summa. And, for Aquinas, it is not existence itself that presupposes a creator, but rather the nature of existence that our universe embodies. (Aquinas obviously thinks God exists, and that He doesn't need a creator.)
Fair enough, but the nature of existence that our universe embodies is sufficiently explained by the existential conditions that preceded it. No God is required.

I wrote, “The concept of ‘creation’ is grasped from observing its occurrence in reality. Creation occurs within a context of things that already exist.”
Aquinas would agree.
I continued, “There is no such thing as creation out of nothing, nor could there be. The concept makes no sense, because creation of any kind requires pre-existing material out of which the creation is made.”
Aquinas agrees that there can be no creatio ex nihilo within the created order, under that created order's "own steam", as it were. But his contention is that God, who is Perfect Being, possesses the power to impute being "from the ground up".
But his contention is inconsistent with our understanding of the nature of the creative process. What it means for something to be created is for it to be created out of something. It doesn’t make any sense to say that something can be created out of nothing.

I wrote, “Yes, there has to be something there to start with – something that was not itself created - but it doesn’t have to be a Christian God.”
True. The Christian God can only be known through revelation. Philosophers just hold that we can arrive at the conclusion of a 'natural' or 'philosophical' God through reason and experience.
But I wouldn’t call the prime material “God.” The prime material is the fundamental constituents out of which everything else is composed.

I wrote, “The principle of parsimony? But the fact that a single ummoved mover is more parsimonious than multiple unmoved movers does not imply that there must therefore BE a single unmoved mover.”
Right, but it is more in conformity with right reason to assume that there is only one.
Why? It seems to me entirely arbitrary to assume that there is only one.
I reproduced a section of Aristotle's Metaphysics, and Bill replied:
Interesting. Aristotle’s rationalism was never more apparent than in this passage. I won’t repeat my arguments against a pure consciousness, but they are certainly relevant here.
?
(See below.) ... what I am arguing is that they [i.e. creation from nothing and annihilation] are logically impossible, because the acts of creation and destruction presuppose a cause, which precedes the creation and succeeds the destruction.
Right, and this cause is God.
I was referring to a material cause, whereas you are evidently referring to an efficient cause. What I am saying is that you can’t have creation without a material cause; an efficient cause is not enough, because the creator must rearrange matter to effect the creation.

I wrote, “My objection is twofold: First, a consciousness conscious of nothing but itself is a contradiction in terms; before it could identify itself as consciousness, it would have to be conscious of something other than itself; otherwise, it wouldn’t be conscious to begin with, and therefore couldn’t identify itself as a consciousness.”

GWL replied,
OK, this is getting tiresome. In any event, though I believe I can defend the notion of God's consciousness from your criticism, I also believe I can circumvent your objection by invoking the Christian God, which is Triune: three Persons in one Divine Substance, and they are mutually aware of one another. This interrelationship of consciousness and mutual exchange of love between the Persons accounts for the consciousness of the Godhead.
Nice try, but I don’t think that will work. To simplify matters, let’s assume that there are only two consciousnesses, A and B. Before A could exist (as a consciousness), it would have to be conscious of something. You say it could be conscious of B. But, by the same token, before B could exist to be conscious of, it would have to be conscious of A. Thus, A could exist only if B already existed, and B could exist only if A already existed, which means that neither could exist. In the absence of an external world – without an object of awareness - no consciousness is possible.

Besides, no mind can be aware of another mind, except inferentially via its physical manifestations. The only consciousness it can be aware of directly is its own through a process of introspection. So, since there is no physical form by which these three "divine persons" could be aware of each other inferentially, they could only be conscious if they were aware of an external world, which means that in the absence of such a world, they could not exist to create it.

Furthermore, what does it mean to say that there are “Three Persons in one Divine Substance?” The Catholic Encyclopedia says that “these Three Persons are truly distinct from one another.” If so, then there are three gods instead of one, which makes Catholicism a polytheistic religion. Besides, to say that there are three distinct persons in one substance doesn’t make sense. If they are three separate and distinct persons, then how could they be one substance?

I continued, “Second, a consciousness has to have a means of awareness and a form of awareness.”
More anthopomorphism.
As I already explained in an earlier reply, this is not anthropomorphism. Once again, I am not saying that in order for an entity to be conscious, it has to be human. Obviously, there are non-human forms of consciousness. I am saying that in order for an entity to be conscious, it has to be conscious in a particular way and by a particular means, because such is the nature of consciousness. A formless consciousness is a contradiction in terms. Perhaps an analogy will help. Communication doesn’t have to be in one particular language, like English, but it does have to be in some particular language. Communication is impossible without a method of communication. Similarly, a plain figure can be any shape, but it must be some shape. You cannot have a shapeless plain figure. In the same way, perception is impossible without a means and a form of perception. An entity perceives reality in a particular form by means of its sensory receptor(s), which is true of any consciousness, human or non-human.

I wrote, “The point I was making is that possibility depends on existence (not the other way around) in the sense that what is possible to an entity depends on its nature or identity.”
Right, it depends upon the kind of existence: possible or necessary.
No, you're missing the point. It depends on the kind of entity it is: what is possible to a man is not possible to a bird; what is possible to a bird is not possible to a cat, etc.

I wrote, “It's determined by the character of the things that already exist.”
Only if you assume the necessity of the universe. (An assumption which you nowhere support.)
I thought I did support it in a previous reply. At any rate, let me make the argument here. There is a sense in which it is possible for me not to have existed – e.g., if my parents choose not to conceive a child. But what would it mean to say that it’s possible for the universe not to have existed? I can only say that it’s possible for the universe not to have existed, if a certain condition had not been fulfilled. But what condition could that possibly be? There is nothing on which the non-existence of the universe could depend, since the universe is all there is.

I wrote, “By ‘contingent,’ I assume that you mean dependent on something else. However, the fundamental constituents of existence, out of which everything else is composed, are not dependent on anything else, in which case, they are not contingent, but necessary."
Let me use the reductio ad adsurdum. If this is the case (that everything is necessary), all events are necessary. And I'm not sure you're prepared to accept this (since it's absurd).
With respect, I think you’re missing the point. To say that the fundamental constituents of existence out of which everything else is composed are not dependent on anything else is not to say that all events are necessary; it’s only to say that the fundamental constituents themselves could not have been otherwise.

However, you say it is absurd that all events should be necessary. Why? Because it denies free will? It denies libertarian free will, to be sure, but it does not deny compatibilist free will. A person’s choices can still be necessitated by his value judgments, which in turn can depend on his heredity and environment. Does that mean that he cannot be held responsible for his actions? No. To hold someone responsible for his actions is simply to recognize that they are based on his conscious choices.

For example, we can properly imprison someone for stealing a car, even if he didn’t think it was morally wrong and saw no reason to avoid doing it. All that needs to be established is that he knew what he was doing and deliberately chose the action. Putting him in prison is a way of protecting others and of sending a message to him and to others like him that if they commit such an act, they will suffer the consequences. Punishment is thus a form of deterrence; it does not require libertarian free will.

Just as there is no absurdity in the idea that the fundamental constituents of the universe exist necessarily, so there is no absurdity in the idea that all events occur necessarily.

- Bill

(Edited by William Dwyer
on 3/08, 10:05am)


Post 62

Sunday, March 11, 2007 - 10:29pmSanction this postReply
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Bill,

Thanks for continuing to engage me on this topic. I hope you don’t feel as though I am haranguing you about it.

We agree that existence always was and always will be. There may or may not be scientific reasons to believe this, but I certainly think it is a most reasonable working assumption.

We disagree about the finitude of existence—with you arguing that finitude is philosophically assured and I arguing that it is not, that it is a scientific, empirical question and that a universe of infinite extensiveness is logically possible.

For the sake of conversation, let us assume a finite universe. Even assuming this, I have a nagging belief that one aspect of your position contradicts itself. Namely, your resistance to the notion of an infinite quantity of events having already occurred.

The question on the table is: How many events have occurred?

You have answered this by saying that a period must be attached. So we get: How many events have occurred in the last million years? Answer: Some large but finite quantity. Obviously this answer is correct, given a finite universe and a discrete period of past. Same for a billion years, a trillion, etc.

This amounts to gaming the question. Of course we get a finite answer if we insist on answering only for discrete periods. But the question is not, ‘How many events have occurred in past period X,’ rather the question is: How many events have occurred—period.’

THIS question can have only one of two answers: Either a limited quantity or a quantity not limited. If you choose to answer with a limited quantity then you imply that something limits the past—you imply a start to existence, a point in the past prior to which there was nothing happening, i.e., there was nothing. But you don’t want to do that, as you also hold that existence always was.

I suspect that at this point you are thinking: “No, there is no theoretical limit to the past. There is always the potential to consider a period beginning even earlier, and earlier than that, etc. But no matter how far back we consider, we have gone back a finite period—and the answer that follows is: Some large but finite quantity of events.”

The problem with that is that the past doesn’t care how much of it we consider, because ALL of it happened whether we are able cognitively to gather it all up and consider it, or not. In other words, you are imposing the epistemological need to deal with discrete portions of reality at a time onto reality itself, as though reality (or in this case, the past) is also delimited by like discreteness.

If you believe that there is no limit to how far back a period can be named, then it follows that there is no limit to how large an answer may be given to the question: “How many events have occurred?” And having no limit is all that “infinite” means. Again, it’s either—or. Either there is a limit to the quantity of the answer, or there isn’t. If there is a limit, then existence began at some point in the past. It won’t do to say, “There is no theoretical limit, but yes, there is an operative limit because I can only deal with discrete chunks at a time.”


Post 63

Monday, March 12, 2007 - 5:57pmSanction this postReply
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Regarding “actual vs. potential,” it may make some sense applied to the future since the future hasn’t happened yet. It makes no sense applied to the past, however, since there is nothing potential about the past—all of it actually happened already.

Speaking of actual vs. potential for the past implies that the past stands back there as mere potential…waiting for someone to mentally lasso it, whereupon it becomes “actual.”


Post 64

Monday, March 12, 2007 - 6:32pmSanction this postReply
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Jon,

Good post. You've done an excellent job of clarifying the issue. I do see where you're coming from, and it's an argument that I would have made a couple of years ago (if I were as careful a thinker as you).
The question on the table is: How many events have occurred?

You have answered this by saying that a period must be attached. So we get: How many events have occurred in the last million years? Answer: Some large but finite quantity. Obviously this answer is correct, given a finite universe and a discrete period of past. Same for a billion years, a trillion, etc.

This amounts to gaming the question. Of course we get a finite answer if we insist on answering only for discrete periods. But the question is not, ‘How many events have occurred in past period X,’ rather the question is: How many events have occurred—period.’

THIS question can have only one of two answers: Either a limited quantity or a quantity not limited.
"A quantity not limited" is not an answer, because the question, "How many events occurred?" presupposes that there is a specific number. If there is no specific number, then the question is meaningless.
If you choose to answer with a limited quantity then you imply that something limits the past—you imply a start to existence, a point in the past prior to which there was nothing happening, i.e., there was nothing. But you don’t want to do that, as you also hold that existence always was.

I suspect that at this point you are thinking: “No, there is no theoretical limit to the past. There is always the potential to consider a period beginning even earlier, and earlier than that, etc. But no matter how far back we consider, we have gone back a finite period—and the answer that follows is: Some large but finite quantity of events.”

The problem with that is that the past doesn’t care how much of it we consider, because ALL of it happened whether we are able cognitively to gather it all up and consider it, or not.
Again, if the quantity is infinite, as you say, then there is no "ALL of it," because "ALL" implies that there isn't any more, and for an infinite quantity, there is always more -- as the quantity is never exhausted. When you talk of "all" events that happened, or of the "entire" past, you imply a finite quantity, however large.

Suppose I ask, "How many events will happen in the future?" How would you answer that question? Wouldn't you regard it as nonsensical? Since the future is indefinite, the question has no an answer. In order to justify an answer, I would need to specify a time period. Similarly, since the past is indefinite, the question of how many events happened in the past also has no answer. Here as well, you would need to specify the time period if you want an answer.
In other words, you are imposing the epistemological need to deal with discrete portions of reality at a time onto reality itself, as though reality (or in this case, the past) is also delimited by like discreteness.

If you believe that there is no limit to how far back a period can be named, then it follows that there is no limit to how large an answer may be given to the question: “How many events have occurred?” And having no limit is all that “infinite” means.
In other words, what you are saying is that there is no answer to the question, "How many events occurred in the past?" -- not that the answer is "An unlimited number" -- because there is no such thing as an unlimited number. Every number, no matter how large, is finite.

I'm pretty sure that my reply won't satisfy you, but it's the best I can do for now. Perhaps God, in his infinite wisdom, can provide an answer that will satisfy both of us. I'll ask our resident theist, Gottfried W. Leibniz for divine inspiration.

- Bill ;-)

Post 65

Monday, March 12, 2007 - 8:10pmSanction this postReply
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Bill,

You are correct that I am not satisfied with your response—but I am quite satisfied in the confidence that there IS no good response, save total concession, ;-).

Thanks again. The conversation (and we both know that it’s extension is indefinite (see you next time!)) has been very beneficial to me.

Jon


Post 66

Tuesday, March 13, 2007 - 8:16pmSanction this postReply
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"Again, if the quantity is infinite, as you say, then there is no "ALL of it," because "ALL" implies that there isn't any more, and for an infinite quantity, there is always more -- as the quantity is never exhausted. When you talk of "all" events that happened, or of the "entire" past, you imply a finite quantity, however large.

Suppose I ask, "How many events will happen in the future?" How would you answer that question? Wouldn't you regard it as nonsensical? Since the future is indefinite, the question has no an answer. In order to justify an answer, I would need to specify a time period. Similarly, since the past is indefinite, the question of how many events happened in the past also has no answer. Here as well, you would need to specify the time period if you want an answer. "

****************************************************************

ALL the real numbers between "1" and "0" are less than "1" and greater than "0."  I can make an infinite number of additional provably true claims about "ALL" of these numbers, as in, every number in the set so defined is less than "3."  Every number in the set so defined is less than "4."  ....  Every number in the set so defined is less than any number "N" ; "N" > "1." 


Post 67

Tuesday, March 13, 2007 - 9:52pmSanction this postReply
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ALL the real numbers between "1" and "0" are less than "1" and greater than "0." I can make an infinite number of additional provably true claims about "ALL" of these numbers, as in, every number in the set so defined is less than "3." Every number in the set so defined is less than "4." .... Every number in the set so defined is less than any number "N" ; "N" > "1."
No, you can't make an infinite number of provably true claims about "ALL" of these numbers.

First, there is no such thing as "ALL" of the numbers in an infinite series, since again, "ALL" implies that there is no more, and for an infinite series, there is always more; the series is never exhausted.

Secondly, you cannot make an infinite number of provably true claims about anything. However many claims you make, the number will be finite. To be sure, there is no theoretical limit on extending the number. So, in that sense, the number is potentially infinite -- meaning that there is no theoretical limit beyond which the number of claims cannot be extended. The point I am making is that the number cannot be actually infinite.

According to Aristotle, "nothing can be both actual and indefinite. Therefore, there cannot be an actual infinity of any sort -- an actually infinite number of coexisting atoms, an actually infinite world, an actually infinite space that is filled with actually existing units of matter.

"The only infinities that there can be, according to Aristotle, are the potential infinities that are involved in the endless processes of addition or division." (Mortimer J. Adler, Aristotle for Everybody, p. 174)

- Bill

(Edited by William Dwyer
on 3/13, 9:54pm)


Post 68

Tuesday, March 13, 2007 - 11:41pmSanction this postReply
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Phil,

Were you thinking of, say, 0.5? Well then think of it. OK, now it is actual. There is the potential to think up more, are you up to it? Good. 0.55 is out there waiting for you, languishing in potential status. Have you thought of 0.55 yet? Excellent! Now it is actual. 0.555 anyone? It’s waiting…

Seriously, Bill, I am dumbfounded that you don’t see the fallacy in your argument, especially when talking about the past.

Past events have ALREADY actually occurred. They’re not potentialities waiting to become actual when someone names the period in which they occurred.

As I wrote earlier, you are attempting to impose the cognitive need to cut reality into digestible chunks onto reality itself, as though it (or, the past) becomes actual only in chunks and only once the chunks are mentally demarcated.


Post 69

Wednesday, March 14, 2007 - 5:34pmSanction this postReply
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Jon,

This is tricky. The past has already occurred, granted. Does that mean that discrete events have already occurred? Yes. How many? You can't say, "an infinite number," because there is no infinite number. Every number is specific and therefore finite. Moreover, if you are referring to the entire past and not just to a part of it, then you are covering all of the events that have occurred. But if the number of events is infinite, then you can't cover all of them, because the total can never be exhausted.

On the other hand, if the number is finite, then the universe had to begin at some point in time, which is also not true. So the number of events is neither finite nor infinite, in which case, there is no total number of past events.

Of course, if by "infinite number," you simply mean that there is no total number of past events, fine. But that's not how I understand the term "infinite number." An infinite number means a number that is not any specific number, and there is no such thing.

- Bill

Post 70

Wednesday, March 14, 2007 - 7:41pmSanction this postReply
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It is my understanding that most concepts - proper nouns and similar instances excepted - stand for a potentially infinite number of possible discrete instances.  "All" is simply the concept that refers to each and every member of a set, finite or infinite.  "All men are mortal" refers to each and every man who lives, has lived, will live, or might potentially live or have lived.


Post 71

Wednesday, March 14, 2007 - 10:59pmSanction this postReply
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It is my understanding that most concepts - proper nouns and similar instances excepted - stand for a potentially infinite number of possible discrete instances. "All" is simply the concept that refers to each and every member of a set, finite or infinite. "All men are mortal" refers to each and every man who lives, has lived, will live, or might potentially live or have lived.
Well, "every" member of a set exhausts the set, but an infinite series is, by definition, inexhaustible. Consequently, there is no such thing as "every" member of an infinite series. Yes, "'All men are mortal' refers to each and every man who lives, has lived, will live, or might potentially live or have lived," as you so carefully put it. But however many of these men have been, are or will be, the number is finite.

When Rand talks about a concept as referring to a "potentially infinite" number of units, she simply means that a concept refers to all of the units subsumed by the concept, whatever their number. But their actual number can never be infinite.

- Bill
(Edited by William Dwyer
on 3/14, 11:04pm)


Post 72

Thursday, March 15, 2007 - 1:05pmSanction this postReply
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Bill,

If we presume no extinction anywhere in the future for the human race then doesn't the number of men become infinite? 

(I understand your statement in post #69 which, technically, makes it a contradiction to say "infinite number" but it is akward to say "the instances of individuals of this class continue to appear indefinitely into the future and therefore, leaving us no stopping point to take a total, can not be totaled, and are for that reason  are a class whose members are beyond any finite number.")

If the concept subsumes all units, including those in the future, then the actual number is not be known in the present.  And it could turn out to be finite or infinite - true?  Wouldn't that be the meaning of "potentially infinite"? 

"The only infinities that there can be, according to Aristotle, are the potential infinities that are involved in the endless processes of addition or division." (Mortimer J. Adler, Aristotle for Everybody, p. 174)
       Procreating is a process of addition and barring extinction it will be endless ;-)

Say we are talking about some species of bird.  Then I might say it subsumes an 'infinite number' of units unless it goes extinct. Then should it's extinction become predictable I could then say it subsumes a finite number of units.

(I recognize I am jumping into the middle of a fairly long, on-going discussion - let me know if my post just reveals a  need to go back and read from the beginning.)


Post 73

Thursday, March 15, 2007 - 5:05pmSanction this postReply
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Hi Steve,

I am glad you spoke up. Please do read back and comment. The current discussion begins (on this thread anyway) at my Post 58. (You can skip the posts where Bill and Leibniz are discussing just about everything.)

Please do join in!


Post 74

Thursday, March 15, 2007 - 11:56pmSanction this postReply
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(You can skip the posts where Bill and Leibniz are discussing just about everything.)
Jon, that's funny! That's really funny!

- Bill :-)))


Post 75

Friday, March 16, 2007 - 12:15amSanction this postReply
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Steve, yes I second Jon's encouragement. Please feel free to "jump in the middle"; no need to go back and read everything.

You wrote,
If we presume no extinction anywhere in the future for the human race then doesn't the number of men become infinite?
It doesn't become infinite. No matter how far you extend it, the number of men will always be finite. Suppose I were immortal and could count continuously without dying. No matter how far I counted, the number I counted to would always be finite. It would always be a specific number, no matter how large.
(I understand your statement in post #69 which, technically, makes it a contradiction to say "infinite number" but it is akward to say "the instances of individuals of this class continue to appear indefinitely into the future and therefore, leaving us no stopping point to take a total, can not be totaled, and are for that reason are a class whose members are beyond any finite number.")
If that's all you mean by "infinite," fine. But what you're really referring to here is the concept of "potential infinity."
If the concept subsumes all units, including those in the future, then the actual number is not be known in the present. And it could turn out to be finite or infinite - true? Wouldn't that be the meaning of "potentially infinite"?
No, I don't think so, because there is no way that the number could turn out to be (actually) infinite.

- Bill

Post 76

Sunday, March 18, 2007 - 6:51pmSanction this postReply
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Bill Wrote:


On the other hand, if the number is finite, then the universe had to begin at some point in time, which is also not true.
Why is it not true?

Regards,

G. Brady Lenardos


Post 77

Sunday, March 18, 2007 - 9:14pmSanction this postReply
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Aristotle’s Prime Mover got him out of the same bind Bill is in. The idea that existence always was conflicts with the refusal to accept actual infinitude—namely, the infinitude of events of the past. The Prime Mover solves this by positing a start, not of existence itself, but of motion (and thereby, events.)

I doubt Bill accepts any prime mover, however, sensing that an existence doing nothing would mean there was really nothing, which amounts to positing a start to existence.

Without a prime mover, Bill is left with existence that always was, and not an infinitude of past events. A real bind. I wish I could help.


Post 78

Sunday, March 18, 2007 - 10:18pmSanction this postReply
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I wrote, "On the other hand, if the number is finite, then the universe had to begin at some point in time, which is also not true."
Why is it not true?
Because nihilo ex nihilo -- from nothing comes nothing. If nothing exists, then there can be no creator to bring it into existence.

Nor does the fact that universe didn't begin at some point in time mean that it has existed for an infinite period of time. In fact, the universe hasn't existed for any period of time, because in order for something to exist "for a period of time," its duration must be measured by a standard of motion outside itself, and since the universe is all that exists, there is nothing outside the universe against which the duration of its existence can be measured. In that respect, the universe is "eternal" in the original sense of that term, meaning non-temporal. Things within the universe can have a duration vis-a-vis other things, but the universe itself cannot. It is literally outside of time.

For that reason, it was perhaps misleading for me to say that the universe "always" existed. By saying that it always existed, I simply meant that there is no period of time one can identify in which the universe did not exist. But strictly speaking, since the universe does not exist "in" time, it cannot have existed for any period of time.

- Bill

Post 79

Sunday, March 18, 2007 - 11:27pmSanction this postReply
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“In fact, the universe hasn't existed for any period of time…”

“…it cannot have existed for any period of time.”

Bullshit. You wrote that at 10:18 PM and now it is 11:27 PM. (Anyway, you’ve reverted to “time.” I was discussing quantity of events.)

Your last paragraph could be interpreted to mean that you believe existence DID have a start, with time starting alongside it. This would be consistent with “there is no period of time one can identify in which the universe did not exist.”

Is this your position?


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