Sunday, September 7, 2014

Theistic Arguments Series: On the Impossibility of an Actual Infinite


One of the key concepts found in some theological arguments such as the Kalam Cosmological Argument is the assertion that the universe must have had a beginning, which is based on the notion that it is logically impossible for an "actual infinite" to exist.  Theists have made numerous defenses of this assertion.  It appeared in my previous post, where my interlocutor said:

This is a metaphysically untenable position. Why can't there be an eternal succession of people? Well, person one (p1) is going to have to give birth to them-self before they can give birth to p2. How can p1 give birth to them-self if they don't exist. Since contingent p1 can't be accounted for contingent p2...pn are not accounted for, and so the whole chain fails to exist.
He seems to follow the logic of William Lane Craig, who has been one of the most prominent defenders of this position, as seen here.  In this paper, Craig argues in support of the Kalam argument on two main fronts:  that the existence of an actual infinite (whether it be a series of events, objects, or instances of time) is logically absurd, and also that physics does not allow for any kind of infinite succession of cosmological beginnings.  It is my intention here to address only the first of these.  Craig gives two main arguments against the existence of an actual infinite.  One is that it is impossible for an actual infinite (and specifically, an infinite temporal regress) to exist, and the other is that an actual infinite cannot be formed by successively adding elements to a set.

Let me clarify a few term before I go on. 

First, when speaking of a beginning of the universe, it is my contention that our known universe had a beginning (of sorts), with the big bang.  But that doesn't mean that there could not be something (other than God) that preceded or caused it - some larger natural reality from which the known universe arises.  Examples of this might be a multiverse, or it might be an infinite succession of cosmological epochs in which a universe is spawned, lives for some finite time, and then collapses, only to be spawned again.  So when I postulate that there might be no beginning, I mean that there might be no beginning to this larger natural reality, not to our specific known instance of a universe.  This is an idea that Craig specifically rejects.  In his view the universe that we know is all there is in the natural world.

Second, the term "actual infinite" refers to a set or series of things that are instantiated, or that have actual physical existence.  So while it may be acceptable to Craig to speak of an infinite set as a purely theoretical thing, there can be no real infinite set of existing things, including moments of time.

Craig's first argument against an infinite regress is based on the apparent absurdities that arise in the hypothetical Hilbert's Hotel.

What exactly is meant by "infinite"?  In mathematics, there are different kinds or orders of infinity, and they are not the same size.  But with respect to arguments such as Craig's, we are talking about something called "countably infinite".  This does not imply that it is possible for people to actually count all the elements of a countably infinite set.  It does imply that there is a method of pairing all the elements of a countably infinite set in one-to-one correspondence with the set of counting numbers: [ 1, 2, 3, ... ].  Any such set is said to be the same size as any other countably infinite set.  Even if you add or subtract elements from it, it is still possible to pair a set like this with the set of counting numbers in perfect one-to-one correspondence, as we see in this example where the first ten elements have been removed.
             [11, 12, 13, ... ]
              /   /   /
            [1,  2,  3,  ... ]
           
This is a concept that Craig can't seem to grasp, as is evident in his discussion of Hilbert's Hotel.  What is intuitively logical for finite numbers is not logical for infinite numbers.  When working with infinite numbers, our intuition fails us.  Infinity is not a definite quantity like the number 57, for example.  It can't be treated as if it were a definite quantity.  As mathematicians will attest, it is not logically valid to attempt to subtract some number of elements from an infinite set and obtain a definite difference.  Attempting to do so will inevitably result in absurdities, as Craig notes:
But suppose instead the persons in room number 4, 5, 6, . . . checked out. At a single stroke the hotel would be virtually emptied, the guest register reduced to three names, and the infinite converted to finitude. And yet it would remain true that the same number of guests checked out this time as when the guests in room numbers 1, 3, 5, . . . checked out. Can anyone sincerely believe that such a hotel could exist in reality? These sorts of absurdities illustrate the impossibility of the existence of an actually infinite number of things.
The absurdity is not due to the impossibility of the existence of infinite sets, it is due to Craig's faulty application of arithmetic logic.

Craig's second argument states that an actual infinity cannot be formed, because one cannot "reach actual infinity" by "successively adding one member after another."  He further argues that this isn't dependent on the amount of time available.  Craig refers to this as the impossibility of "traversing an infinite set".

At its heart, this boils down to Craig's self-contradictory use of the term 'infinite'.  On the one hand, he acknowledges that an infinite series is an open-ended set - it lacks a bound, at least on one side.  On the other hand, he speaks of "reaching" infinity, as if it were a definite value that corresponds to a bound at the far end of the set.  The very term to 'traverse' a set implies that it is a closed set, bounded on both ends.  Craig speaks about "counting down" moments of time from negative infinity to the present. 
suppose we meet a man who claims to have been counting from eternity and is now finishing: . . ., -3, -2, -1, 0. We could ask, why did he not finish counting yesterday or the day before or the year before? By then an infinite time had already elapsed, so that he should already have finished by then.
Notice that this implies both a starting and an ending point (even if Craig doesn't admit it) - a set of moments that is bounded on both ends.  To see this more clearly, recall the definition of "infinite".  Consider that in order to follow the correspondence of moments to the set of natural numbers, there is only one 'end' of the set at which you could begin enumerating this correspondence.  Craig wants to start at the far 'end', even while acknowledging that there is no far end.  But this violates the definition of infinity.  It isn't good enough for him to simply say that the set contains an infinite number of elements.  When he speaks of traversing the set from one end to the other, he is using contradictory terms.  Again, he is treating infinity as if it were a definite quantity.  Notice also that my interlocutor's argument, cited at the beginning of this post, follows this same pattern - speaking about an infinite series that begins at the far 'end'.

As an aside, one thing Craig never explains is why it must be necessary for an infinite set to be "traversed" at all.  Or why it must be "formed" by successive additions.  Why couldn't it simply exist?

So Craig concludes that something cannot exist for an eternity.  It is metaphysically impossible for the universe to exist without a beginning, since that would imply the existence of an actual infinite - an infinite set of moments in time.  But if that were true, wouldn't the same logic apply to God?  Why should it be the case that an actual infinite is impossible it it refers to the existence of the universe, but not impossible if it refers to the existence of God?  Most theists agree that God can't do what is logically impossible.  So if it is logically impossible for something to exist without beginning, that must apply to God as well.

107 comments:

  1. im-skeptical wrote: "Second, the term "actual infinite" refers to a set or series of things that are instantiated, or that have actual physical existence."

    No, you've missed the meaning of this term. An actual infinite is unbounded on both sides while a possible infinite is unbounded on one side. Craig is arguing that an actual infinite can't be instantiated while a possible infinite can be. An example of an actual infinite is a being who has been counting forever, while an example of a potential infinite is a being who starts counting at zero and continues counting forever. Notice that the person counting from zero will never count an infinite amount of numbers because there are always more numbers to count.

    im-skeptical wrote: "This is a concept that Craig can't seem to grasp, as is evident in his discussion of Hilbert's Hotel. What is intuitively logical for finite numbers is not logical for infinite numbers. When working with infinite numbers, our intuition fails us."

    You're missing Craigs' point here. The point is that the absurdities show that an actual infinite can't be instantiated. If an actual infinite exists then there are not more things in a multitude M than there are in a multitude M' if there is a one-to-one correspondence of their members. It is also true that if an actual infinite exists then there are more things in M than there are in M' if M' is a proper sub-multitude of M. However, the Law of None Contradiction states that a state of affairs can't be simultaneously true and not true. Given an actual infinity, both states of affairs are true. Since both states of affairs are simultaneously true and not true an actual infinite doesn't exist.

    im-skeptical wrote: "As an aside, one thing Craig never explains is why it must be necessary for an infinite set to be "traversed" at all. Or why it must be "formed" by successive additions."

    Well, if we're talking about a series of contingent states of affair that cause other states of affairs then the problem is that if the tail end of infinity can't be reached, because there is no end, then contingent state of affairs number negative infinity's cause hasn't been actualized. If contingent state of affairs number negative infinity's cause has not been actualized then the successive contingent state of affairs that depend on the initial state have no actualization and so the whole chain fails to exist.

    im-skeptical wrote: "It is metaphysically impossible for the universe to exist without a beginning, since that would imply the existence of an actual infinite - an infinite set of moments in time. But if that were true, wouldn't the same logic apply to God? Why should it be the case that an actual infinite is impossible it it refers to the existence of the universe, but not impossible if it refers to the existence of God?"

    There are two huge differences between God and the universe. The first difference is that God is an eternal, un-caused being while the universe is not. God is not dependent on a series of an actual infinite number of causes in order to exist. If all that exists are contingent entities then the universe would be dependent on the actual infinite chain of causes.

    Another major difference is that God is immaterial while the universe is not. Immaterial objects have no changes of state while material objects do. Changes in state are actualized by previous changes of state. This would have to go on for an actual infinity of changes in state, but an actual infinity can't be formed this way because it is never reached in this manner.

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    1. Keith: "No, you've missed the meaning of this term. An actual infinite is unbounded on both sides while a possible infinite is unbounded on one side."

      I don't think that what Aristotle had in mind, and I don't think it's what Craig had in mind. In fact, there's no difference between a set that is unbounded on one side, and one that is unbounded on both sides. Both are still countably infinite. Consider the series [0, 1, -1, 2, -2, 3 ... ]. This is clearly bounded on one side, yet it corresponds one-to-one with the set of integers, from negative infinity to positive infinity, which is unbounded on both sides. To Aristotle, an actual infinity is a complete set, while a potential infinity is a set that can never be achieved, because it must be formed by some process of traversal. This is consistent with what Craig said.

      Keith: "You're missing Craigs' point here. The point is that the absurdities show that an actual infinite can't be instantiated."

      No, you missed my point, perhaps because I don't explain things very well. I said that the absurdities are due to Craig's misapplication of logic. Craig doesn't understand the relevant mathematics. He disagrees with the mathematicians. He is so impressed with his own logical skills that he thinks he understands the math better than mathematicians do. This sounds very much like the conversation earlier today between Ilion and grodrigues (who has a PhD in mathematics). Craig has been called out on this point over and over again (including some that he mentions), but he thinks he knows better than everyone. He doesn't.
      http://spot.colorado.edu/~morristo/infpast.html
      http://infidels.org/library/modern/arnold_guminski/kalam.html
      http://www.skepticink.com/reasonablyfaithless/2013/03/25/infinity-minus-infinity/

      Keith: "If contingent state of affairs number negative infinity's cause has not been actualized then the successive contingent state of affairs that depend on the initial state have no actualization and so the whole chain fails to exist."

      Here, you are making an argument that even Craig doesn't. You make the assumption a priori that any chain of contingent things must be finite and must begin with a non-contingent thing. At least Craig was trying to show through logic that this is true. You dispense with the logical argument and just make the (very circular) case that there can't be an actual infinite because there are no actual infinites.

      Keith: "There are two huge differences between God and the universe."

      So you contend that logic is different for God than for us? I doubt it. I think what you are really saying is that God can traverse an infinite set, but we can't, due to our physical limitations. But Craig said it doesn't matter how much time is involved. If we were eternal in the same manner as God, we could traverse an infinite too. But Craig says that it is logically impossible to traverse an infinite set, even if we have all eternity to do it. Of course, if we limit our thinking to what can be accomplished in the physical world, it may well be impossible to traverse an infinite set, but the whole point of this argument is to show that there can be nothing beyond our physical universe because it is logically impossible. In other words, you must consider what might be logically possible without any limitations imposed by being confined to our physical universe. That would include the ability to do what God could logically do. Otherwise, you are only making the point that there can be no actual infinite within the confines of our physical universe. But that says nothing about what is possible outside our universe, and in particular, it says nothing about whether there must be a beginning.

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    2. im-skeptical wrote: "To Aristotle, an actual infinity is a complete set, while a potential infinity is a set that can never be achieved, because it must be formed by some process of traversal. This is consistent with what Craig said."

      I'm inclined to agree that an actual infinite is a complete set, as this seems to agree with Craig's definition taken from his Q & A which says, "An actual infinite is a collection which includes an infinite number of members, that is, the numbers of members in the collection exceeds any natural number."

      im-skeptical wrote: "No, you missed my point, perhaps because I don't explain things very well. I said that the absurdities are due to Craig's misapplication of logic."

      Perhaps it would help if we dealt with concrete examples such as those of Hilbert's Hotel. Do you disagree that if an actual infinite exists then there are not more things in a multitude M than there are in a multitude M' if there is a one-to-one correspondence of their members. And that if an actual infinite exists then there are more things in M than there are in M' if M' is a proper sub-multitude of M?

      im-skeptical wrote: "You make the assumption a priori that any chain of contingent things must be finite and must begin with a non-contingent thing...You dispense with the logical argument and just make the (very circular) case that there can't be an actual infinite because there are no actual infinites."

      You're so busy psychoanalyzing my motivations that you're incapable of actually taking in what I'm saying, and so you turn what I say into a straw man. If you keep on engaging in this behavior I'm going to be forced to conclude that you are incapable of rational dialogue, and I don't waste my time trying to reason with irrational people. Please pay attention to what I'm saying.

      What I'm saying is a chain of contingent states or beings consist of a series of finite states or beings that need to be actualized by prior states or beings. Morriston tries to get around the problem of traversing an actual infinite by saying that one can skip around in counting or even make huge leaps like 1, 100, 200, 1000, but this doesn't work when we're talking about one contingent state needing to cause another. Contingent -10 can't be caused by -3 because c-10 was caused by c-9 which in turn was caused by c-8 and so on. It also doesn't help to arbitrarily start with c-400, since there is no real beginning in an actual infinite, because it's still the case the c-400 was caused by c-399. The set of contingents can never be completed by adding on contingent after contingent because there's always one more to add. The problem with the chain of contingents is that with no beginning cause there are no future causes. Think of an infinite number of people borrowing a book from each other, if no one actually has the book then how can the book be given up the chain?

      im-skeptical wrote: "So you contend that logic is different for God than for us? I doubt it. I think what you are really saying is that God can traverse an infinite set, but we can't, due to our physical limitations."

      No, that's not what I'm saying at all. If you're asking can God count to an actual infinity then my answer is no because not even God is capable of doing the impossible. However, in regards to God's existence, traversing an actual infinity is irrelevant because God has no beginning, cause or changes of state. He just eternally existing changelessly (at least prior to the creation of the universe).

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    3. Keith: "Do you disagree that if an actual infinite exists then there are not more things in a multitude M than there are in a multitude M' if there is a one-to-one correspondence of their members. And that if an actual infinite exists then there are more things in M than there are in M' if M' is a proper sub-multitude of M?"

      Yes, I disagree with that. First, I assume that when you say 'multitude', you are referring to an infinite set. Second, I think that the rules of logic apply whether or not there is an 'actual infinite'. Mathematics makes no distinction between actual and potential infinities. With regard to the proper subset, they are demonstrably the same size. Consider the set M of counting numbers [1, 2, 3, ...], and the set M' of squares [1^2, 2^2, 3^2, ...]. M' is a proper subset of M, and yet there is a one-to-one correspondence between the elements.

      This gets back to the problem: If you think of infinite sets in the same way as finite sets, as Craig does, you are bound to encounter absurdities. It's not valid logic. Listen to someone who understands the math, instead of Craig.

      Keith: "You're so busy psychoanalyzing my motivations that you're incapable of actually taking in what I'm saying. ... The problem with the chain of contingents is that with no beginning cause there are no future causes."

      No psychoanalysis going on - I was only discussing the argument you made. And do I think I understand the point (as you first stated it), that since you can't ever traverse an infinite causal chain, there would be no first cause to actualize everything that comes after it. It is perfectly clear from what you said that you assume a priori that there must be a first cause. Unlike Craig, you simply dismiss the possibility of any infinite (causal) chain because it can have no first element, and thus it can have no first cause. Therefore, any series must have a starting point. If you didn't make this a priori first cause assumption, the whole line of reasoning would vanish. This is not about your motivations.

      Keith: "in regards to God's existence, traversing an actual infinity is irrelevant because God has no beginning, cause or changes of state. He just eternally existing changelessly (at least prior to the creation of the universe)."

      So if I understand this, the changeless aspect of God is essential because it eliminates the need for any first cause. So an infinite succession of worlds, because it is not changeless, is a succession of contingent things, which must still have a first cause (by your logic). As I pointed out already, though, if you don't make the assumption that a first cause is needed (if you simply assume instead that every element has a prior cause), then there is no logical reason to deny the possibility an infinite series could exist.

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    4. im-skeptical wrote: "Yes, I disagree with that. First, I assume that when you say 'multitude', you are referring to an infinite set. Second, I think that the rules of logic apply whether or not there is an 'actual infinite'. Mathematics makes no distinction between actual and potential infinities. With regard to the proper subset, they are demonstrably the same size."

      If I'm understanding you correctly, you're agreeing with principle one, that an infinite multitude M,which is all cardinal numbers, is equal to M', which is a sub-multitude in one-to-one correspondence (i.e. all of the odd numbers from infinite M). However, you seem to disagree with principle two which says that there are more things in infinite M than M' if M' is a proper sub-multitude of M (i.e. 1, 2 & 3). M' is equal to M and less than M. This seems to be a contradiction.

      im-skeptical wrote: "This gets back to the problem: If you think of infinite sets in the same way as finite sets, as Craig does, you are bound to encounter absurdities."

      In the abstract world of mathematics there are axioms that protect from the absurdities that you talk about, but in the real world of what exits these protections don't exist. If we try to place the concept of an actual infinity in the real world we can see that is full of contradictions, such as an infinitely full hotel accommodating an infinite number of people, which show that it is nothing more than a useful fiction that allows us to do transfinite math.

      im-skeptical wrote: "It is perfectly clear from what you said that you assume a priori that there must be a first cause. Unlike Craig, you simply dismiss the possibility of any infinite (causal) chain because it can have no first element, and thus it can have no first cause."

      I think it is uncontroversial to say that contingent states need to be actualized by some other actual state or thing; that if a contingent state is not actualized by something then the contingent state will not exist. I think it is also uncontroversial to say that the series of contingent causes and effects can't be an actual infinite because there can always be one more cause and effect and so the set is never complete.

      In the actually infinite chain of contingent beings there is no beginning, and since there is no beginning cause there is no cause for whatever contingent state or object that you pick in the chain. Since there is no cause for whatever contingent state you pick then there is no cause for following states. How is what I'm saying unreasonable? Is it reasonable to expect an infinite chain of boxcars, which are at rest, to start moving without a source of movement such as an engine? Adding more boxcars to the scenario won't cause movement.

      im-skeptical wrote: "As I pointed out already, though, if you don't make the assumption that a first cause is needed (if you simply assume instead that every element has a prior cause), then there is no logical reason to deny the possibility an infinite series could exist."

      Why assume that every contingent has a prior cause? How can there even be a prior cause without a beginning? The only way to get out of this problem is to say that some contingent in the chain is not contingent, but that, of course, is a contradiction.

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  2. Another problem with the concept of an actual infinity is your anti-Platonic view of numbers and sets. If sets only exist in minds, as we both say, then why should we say that an actual infinity, which is the set of all cardinal numbers, exists? As the concept of an instantiated actual infinity entails absurdities, and as we have no evidence that an actual infinity exists as a thing it makes sense to think of it as a useful fiction that allows us to do transfinite math.

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    1. Keith: "This seems to be a contradiction. "

      Yes, it seems to be a contradiction if you think in terms of finite sets. That's what Craig does, and that's why he's wrong. It may be helpful to read the material I supplied.

      Keith: " If we try to place the concept of an actual infinity in the real world we can see that is full of contradictions, such as an infinitely full hotel accommodating an infinite number of people, which show that it is nothing more than a useful fiction that allows us to do transfinite math."

      That's the crux of the biscuit (so to speak). We are talking about what might exist outside the confines of our known physical universe. We need not (and indeed we should not) confine our thinking to what can exist in our limited physical world.

      Keith: "and since there is no beginning cause there is no cause for whatever contingent state or object that you pick in the chain ..."

      Unless, of course, you allow that the cause for any given element can be just the prior element in an infinite chain. This is still perfectly logical if you don't presume first that there must be a first cause in the chain.

      Keith: "How can there even be a prior cause without a beginning? The only way to get out of this problem is to say that some contingent in the chain is not contingent, but that, of course, is a contradiction."

      No, there's no contradiction. The prior cause is the preceding element, and the chain is infinitely long. If you don't think in terms of our limited physical world, then there's no problem with it. This is what I have been trying to get across.

      Keith: "Another problem with the concept of an actual infinity is your anti-Platonic view of numbers and sets. If sets only exist in minds, as we both say, then why should we say that an actual infinity, which is the set of all cardinal numbers, exists?"

      I would say that the set of counting numbers is an abstract thing. I said before that mathematics makes no distinction between 'actual' and 'potential' infinite sets. Those are terms used (typically by theists) to describe Aristotelian metaphysical concepts that have little or no bearing on reality. You generally don't hear mathematicians or scientists speaking in those terms.

      Keith: "... and as we have no evidence that an actual infinity exists as a thing it makes sense to think of it as a useful fiction that allows us to do transfinite math."

      There is no more evidence for God than there is for the existence if infinite sets. Useful fiction, indeed.

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    2. im-skeptical wrote: "Yes, it seems to be a contradiction if you think in terms of finite sets. That's what Craig does, and that's why he's wrong. It may be helpful to read the material I supplied."

      You never said which principle you're rejecting and why. Are you accepting both?

      I have read the Morriston paper and the post from James at Reasonably Faithless prior to my last response, in fact I've read some sections multiple times. Thanks for the links, by the way. They make some interesting points and miss the mark at times. Morriston charitably tries to argue that an actual infinite can be traversed by skipping around and making huge leaps in counting, but this is not applicable to an instantiated series of contingent events where each contingent is caused by the previous contingent. James does a pretty good job of down playing the absurdities that would result from an instantiated actual infinite, but never-the-less an infinitely full hotel accommodating an infinite number of people is absurd.

      After reading several pieces for and against an instantiated actual infinite I agree with mathematician James Lindsay who wrote, "[I]nfinity is an abstract concept. Indeed, this is the mainstream interpretation of infinity among mathematicians: it's an abstraction--a useful one--that represents the idea embodied by the Peano Axioms of "can't say only finitely many" and it "exists" only as such--as an axiomatically defined abstraction. This is the camp I find myself in, intrigued by the fringe groups that explore infinity and that reject it but not swayed to any of their causes."

      im-skeptical wrote: "We are talking about what might exist outside the confines of our known physical universe. We need not (and indeed we should not) confine our thinking to what can exist in our limited physical world."

      So, you say that it's inconceivable that a being can exist without a physical brain and yet you're willing to accept that there MIGHT be some mysterious object X outside our universe that is not subject to the universal laws of logic or the physical constraints of the observable universe. How is this consistent?

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    3. im-skeptical wrote: "Unless, of course, you allow that the cause for any given element can be just the prior element in an infinite chain. This is still perfectly logical if you don't presume first that there must be a first cause in the chain."

      And what is the prior contingent's cause? We could play this game for all of eternity, if it wasn't for the whole business of death, of course, because the set will never be completed this way and your chain will never get the cause it needs. You failed to answer my non-rhetorical question about the infinite box cars last time, so I'll ask it again. Is it reasonable to expect an infinite chain of boxcars, which are at rest, to start moving without a source of movement such as an engine? Please explain to me how an infinite number of box cars, which are rest, can start moving without a source of movement as from an engine because I don't see how adding on more still boxcars can generate the movement needed to get the chain going.

      im-skeptical wrote: "If you don't think in terms of our limited physical world, then there's no problem with it. This is what I have been trying to get across."

      The problem is that contingents need causes no matter what possible world we're talking about. If something does not need a cause then that thing is not a contingent.

      im-skeptical wrote: "I would say that the set of counting numbers is an abstract thing. I said before that mathematics makes no distinction between 'actual' and 'potential' infinite sets."

      OK, so how do we get from sets are abstract to there exists an actually infinite set?

      You second sentence is completely irrelevant, as we're talking about what actually exists and not abstract mathematical concepts.

      im-skeptical wrote: "There is no more evidence for God than there is for the existence if infinite sets. Useful fiction, indeed."

      So, in our dialogues we've concluded that there is no direct evidence for God, infinite sets, eternal brute facts, and mulitverses. Hmm, perhaps the existence of the universe shows that there's indirect evidence for one of these entities, however I won't name names (*cough God cough it's God) :-)

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    4. Keith: "You never said which principle you're rejecting and why. Are you accepting both?"

      You use imprecise terminology, which leads to confusion. I don't say "multitude" - I say 'infinite set'. I don't say it consists of "all cardinal numbers" - I say it consists of all 'counting numbers'. I don't say it is "equal to" another infinite set - I prefer to say it has the same 'cardinality' as another set. So to repeat, I claimed that one set is a proper subset of the other, and that they both have the same size (or cardinality). This is true, and it is not an absurdity or contradiction. It only seems to be a contradiction to people who don't understand it.

      Keith: "Morriston tries to get around the problem of traversing an actual infinite by saying that one can skip around in counting or even make huge leaps like 1, 100, 200, 1000, but this doesn't work when we're talking about one contingent state needing to cause another"

      I didn't see where Morriston said that. If he did, he would be incorrect, because no matter how big the steps are, it wouldn't help you traverse the infinite set. But he does point out some of the same problems in Craig's argument that I do.

      Keith: "James does a pretty good job of down playing the absurdities ..."

      Dr. McGrath is a mathematician. He understands what Craig doesn't.

      Keith: "I agree with mathematician James Lindsay who wrote ... "This is the camp I find myself in, intrigued by the fringe groups that explore infinity and that reject it but not swayed to any of their causes.""

      I don't think you understand Lindsay, either. He is the author of Dot, Dot, Dot: Infinity Plus God Equals Folly. See his blog.

      Keith: So, you say that it's inconceivable that a being can exist without a physical brain and yet you're willing to accept that there MIGHT be some mysterious object X outside our universe that is not subject to the universal laws of logic or the physical constraints of the observable universe. How is this consistent?"

      I don't think I said any of that, except that something that exists outside the physical universe would not be bound by the physical limitations of things within the universe. Perhaps you misunderstood what I did say.

      Keith: "And what is the prior contingent's cause? We could play this game for all of eternity ..."

      Thats true. Eternity doesn't have a beginning. There is no logical reason for you to assume that it must.

      Keith: "OK, so how do we get from sets are abstract to there exists an actually infinite set?"

      If there is no God, but there is some other reality from which our universe arises, then there would be some kind of 'actual' infinity. We both agree on this, but you insist that it must be God, and I don't.

      Keith: "You second sentence is completely irrelevant, as we're talking about what actually exists and not abstract mathematical concepts."

      Who says there is no actual infinite? I think there is. And it is not inconsistent with mathematics.

      "Hmm, perhaps the existence of the universe shows that there's indirect evidence for one of these entities, however I won't name names"

      Exactly. But it ain't God.

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    5. You have now evaded my question about how motion could result from an infinite number of still box cars. Your silence is very telling, as you obviously don't have a good answer.

      im-skeptical wrote: "You use imprecise terminology, which leads to confusion."

      I use terminology that is merely different. I think that all these complaints about terminology are a red herring that you hope will distract me from noticing that you're evading my questions.

      im-skeptical wrote: "I didn't see where Morriston said that. If he did, he would be incorrect, because no matter how big the steps are, it wouldn't help you traverse the infinite set."

      The skipping argument occurs in section one where he writes, "This is not a good argument. For one thing, (2) does not follow from (1). If one were foolish enough to begin counting all the members of this series, one would have to start somewhere, but one need not start with zero. One could, for example, count them in the following order: <–1, 0, –3, –2, –5, –4 ...>."

      The argument about making leaps is in section three where he talks about Tristram Shandy. He writes, "What, exactly, is Craig’s argument at this point? I believe it must go something like this.

      1. If the past is possibly infinite, then it is possible that Tristram Shandy has always been writing his autobiography at the rate of one year to a day.
      2. If Tristram Shandy had been doing that, then he would always have been infinitely behind.
      3. But this is impossible.
      4. Therefore it is impossible that the past is infinite.

      If we can assume that (1) and (2) are necessary truths, then the argument is valid. But I don’t see how they can be. To begin with, it looks as if there is a way for (1) to be true that makes (2) false. All we have to do is to relax the restriction that says Tristram Shandy must always be writing about a day that has already gone by. If we allow him to write about future days as well as past ones, then the years can in principle be mapped onto the days in such a way that Tristram Shandy is now fini shing writing about every day of his life. Here is one possible mapping.

      This year, he writes about the last day of this year. Last year, he wrote about the next to the last day of this year, and so on..."

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    6. im-skeptical wrote: "Dr. McGrath is a mathematician. He understands what Craig doesn't."

      Having a strong understanding of abstract mathematical axioms is all well-and-good, but the point of this discussion is whether or not these axioms are instantiated in reality. Craig and I don't dispute that the concept of an actually infinite set is a useful fiction that allows us to do transfinite math.

      im-skeptical wrote: "I don't think you understand Lindsay, either. He is the author of Dot, Dot, Dot: Infinity Plus God Equals Folly. See his blog."

      I have no need for your link as I have followed Lindsay's blog for some time, and have even participated in discussions there. Also, I took the quote directly from one of his blog posts. No, I think I do have a good understanding of what Lindsay is saying. He bites the bullet by concurring with most mathematicians that infinite sets are only useful fictions. Where he and I disagree is in that he mistakenly thinks that the lack of an instantiated infinity shows that God can't have the attributes he is said to have. What is not clear is if he understands that biting the bullet in this way has serious, perhaps fatal, consequences for naturalistic explanations of the universe.

      im-skeptical wrote: "I said any of that, except that something that exists outside the physical universe would not be bound by the physical limitations of things within the universe."

      You're making the assumption that physical properties are different outside of the observable universe.

      im-skeptical wrote: "If there is no God, but there is some other reality from which our universe arises, then there would be some kind of 'actual' infinity."

      No, there's a more plausible option that you've excluded: that there exists a physical Eternal Brute Fact (EBF) that inexplicably exists without a cause. The problem is that physical objects have changes of state which implies a series of changes of state. There also is the problem of what initiates these changes of state.

      im-skeptical wrote: "Exactly. But it ain't God."

      Well, I guess our biases have been laid out on the table.

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    7. Keith: "You have now evaded my question about how motion could result from an infinite number of still box cars. Your silence is very telling, as you obviously don't have a good answer. "

      But I answered it as clearly as I know how. Each box car is moved by the car before it. What you can't fathom is the idea that this chain of contingency need not have a beginning.

      Keith: "I think that all these complaints about terminology are a red herring that you hope will distract me from noticing that you're evading my questions."

      I answer. You don't hear. But my complaints about precise language stem in part from my own professional experience as an engineer. Vague or imprecise project specifications lead to indeterminate time and cost, as well as unsatisfactory results. Legal documents go to extreme lengths to nail down exact definitions of the terms, because so much may be riding on it. In philosophy, too, precision is important. If two people don't agree on the meaning of a particular statement used in an argument, they may have completely different views about the truth of that statement. See here.

      Keith: "The argument about making leaps is in section three ..."

      OK, now I see where your confusion comes from. He's not talking about skipping or making leaps at all. He gave a simple example (<–1, 0, –3, –2, –5, –4 ...>) to show that zero need not be the terminus of an infinite sequence. Notice here that he has merely reversed the order of each even/odd pair. He then went on to propose a scenario in which a future time (say day 365) in the terminus, and it counts down in sequence from there - no skipping or leaping involved.

      Keith: "Craig and I don't dispute that the concept of an actually infinite set is a useful fiction that allows us to do transfinite math."

      And I don't dispute that the concept of God is a useful fiction for theists.

      Keith: "What is not clear is if he understands that biting the bullet in this way has serious, perhaps fatal, consequences for naturalistic explanations of the universe."

      What you don't understand is that the lack of an instantiated infinite is only a consequence of the finiteness of our known universe. It wasn't until recent times that we had scientific reason to believe that the universe is bounded. If not for that, then there would in fact be actual infinites. And as I said, if the universe is one of many (which might very well be the case), then there are actual infinites. We just can't see them.

      "You're making the assumption that physical properties are different outside of the observable universe."

      It's not an assumption. It's a fact. Physics describes the laws that govern space, time, and matter. Those are the physical things that exist within our universe. I'm not saying that there are no laws that would apply outside the universe, but they would necessarily be different, or at least broader in scope, since they would apply to things that are outside the scope of our physical realm.

      Keith: "No, there's a more plausible option that you've excluded: that there exists a physical Eternal Brute Fact (EBF) that inexplicably exists without a cause."

      I'm not sure that the "larger natural reality" I speak of is anything different from your EBF.

      Keith: "The problem is that physical objects have changes of state which implies a series of changes of state."

      This is not a problem unless you assume there must be a beginning. I don't.

      Keith: "Well, I guess our biases have been laid out on the table."

      Yes. You assume a beginning. You assume a God. I don't.

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    8. im-skeptical wrote: "But I answered it as clearly as I know how. Each box car is moved by the car before it.'

      No, you have not answered the question because, remember, box cars have no source of movement--each box car is motionless. How can you cause the chain of infinite box cars start to move just by adding more motionless box cars?

      im-skeptical wrote: "I answer. You don't hear."

      You have not answered the question about whether or not you endorse principle two--you have just evasively danced around it.

      im-skeptical wrote: "It's not an assumption. It's a fact."

      What actual evidence do you have to back up your fact? We don't have the faintest clue what's beyond the observable universe or even how to observe it. So, to say that it's a "fact" that "[the laws] would necessarily be different" is not really true. It may be true, but, at least at this point, we have no idea whether or not it is.

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    9. Keith:
      "No, you have not answered the question because, remember, box cars have no source of movement--each box car is motionless. How can you cause the chain of infinite box cars start to move just by adding more motionless box cars?"

      I answered the question. You just don't like the answer. What makes a boxcar move in a train? The car before it. As long as there's another car ahead, that's what makes the cars behind move. Now, I know, you think in terms of the finite, as does Craig. I'm asking you to think about what might be possible in a broader transfinite or transcendent world.

      Keith: "What actual evidence do you have to back up your fact? "

      The same evidence that you have that leads you to conclude that the universe must have been caused by God. Do you believe God is bound by physical laws that govern our material universe? Not a chance. You don't even believe that Jesus, a man who lived in our material world, was bound by physical law, right? So this is a little disingenuous of you. I'm only saying that something that might exist outside our universe need not be bound by all the same laws that govern things within our universe. It's logically necessary, and your own logic agrees with that, unless you think God is bound by physical law, which I seriously doubt..

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    10. I noticed that you're still avoiding answering my question about whether or not you endorse principle two and why or why not.

      im-skeptical wrote: "I answered the question. You just don't like the answer."

      I don't like the answer because it's preposterous. Your answer is ridiculous because box cars have no independent source of movement. Where is this movement coming from? It's certainly not the box cars. Do you seriously believe that if you form a long enough chain of box cars that they'll magically start moving on their own?

      im-skeptical wrote: "Do you believe God is bound by physical laws that govern our material universe? Not a chance. You don't even believe that Jesus, a man who lived in our material world, was bound by physical law, right? So this is a little disingenuous of you. I'm only saying that something that might exist outside our universe need not be bound by all the same laws that govern things within our universe. It's logically necessary, and your own logic agrees with that, unless you think God is bound by physical law, which I seriously doubt."

      I don't believe that God is bound by physical laws because God is not physical. Physical laws only apply to physical things. Since Jesus took on a body he was, for the most part, subject to physical laws, as he ate, slept and fell, while carrying the cross.

      Due to your own anti-Platonic stance on laws, I think that we'd have to say that whatever physical object might exist beyond the universe is made up of some sort of quasi matter that is different then what we observe here because the only recourse you have is to say that the laws are merely a description of how matter behaves. If the material object was identical to what is seen here then, according to your view, the laws would be identical as well. Is it conceivable that there's some sort of quasi material object beyond the universe? Yeah. But what good reason do I have to believe that this thing is out there? Why is the matter here different than there?

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    11. Keith: "I don't like the answer because it's preposterous. Your answer is ridiculous because box cars have no independent source of movement."

      My answer is preposterous only to someone who presupposes that there can be no infinite regression. Each box car is moved by the car before it. Your insistence that there must be a beginning is a theistic argument that is not supported by valid logic. That's what the mathematicians are trying to tell Craig. That's what prominent philosophers like Graham Oppy say.

      Keith: "I don't believe that God is bound by physical laws because God is not physical. Physical laws only apply to physical things."

      My point exactly. Physical things, by definition, are things within the universe. Something that exists outside the universe (which may be responsible for the existence of the universe) is not what we would call physical, at least in the ordinary sense of the word, and need not be bound by the regularities of behavior (physical law) that apply to the the physical things in our experience. See here.

      Keith: "Is it conceivable that there's some sort of quasi material object beyond the universe? Yeah. But what good reason do I have to believe that this thing is out there? Why is the matter here different than there?"

      I don't know what exists outside our universe any better than you do. I have no reason to suppose it is made of matter, or quasi-matter, any more than you have to suppose it consists of pure being, or whatever you think is the substance of God.

      But let's get back to the point of this post. Craig is making a logical argument in support of his theistic beliefs - an argument that says an infinite regression of causes is logically impossible. His logic is invalid. He doesn't understand the relevant math. If Craig conceded that his logic is invalid, the consequence would be that the Kalam argument, and other related theistic arguments fail. This logical assertion (that there can be no infinite regress) is a key assertion upon which theists depend to justify the existence of God. That's why Craig will never admit his logical fallacy. And I'm afraid the same can be said of all theists who are guided by faith above reason.

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    12. You guys are mixing up to completely different arguments. Craig argues against the possibility of an infinite series, via such arguments as the impossibility of traversing an infinite, or of reach infinity through successive counting. Not only does Thomas Aquinas not use this argument, he specifically refutes it. That's right. He refutes Craig's Kalam argument. Here is the relevant section of Thomas' Contra Gentiles.

      When he argues against an infinite, he is not arguing against an infinite qua infinite. Rather, what he is arguing could be seen as something like this: circular explanations are fallacious. He is arguing that you cannot explain X by appealing to X, since X is the very thing you are trying to explain. To explain X, you must postulate not-X. Your explanation cannot be your explanandum, since that is circular. He allows for an infinite series, unlike Craig.

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    13. Martin,

      "Rather, what he is arguing could be seen as something like this: circular explanations are fallacious. He is arguing that you cannot explain X by appealing to X, since X is the very thing you are trying to explain. To explain X, you must postulate not-X. Your explanation cannot be your explanandum, since that is circular."

      Thank you for pointing this out. I was unfamiliar with this particular line of reasoning by Aquinas. The way I read it, he is saying that the most convincing reason for the world not having eternal existence is the "fact" that it is the manifestation of God's goodness, and therefore must have been created by him.

      "[15] However, a more effective approach toward proving the non-eternity of the world can be made from the point of view of the end of the divine will, as we have previously indicated. For in the production of things the end of God’s will is His own goodness as it is manifested in His effects. Now, His power and goodness are made manifest above all by the fact that things other than Himself were not always in existence. For this fact shows clearly that these things owe their existence to Him, and also is proof that God does not act by a necessity of His nature, and that His power of acting is infinite. Respecting the divine goodness, therefore, it was entirely fitting that God should have given created things a temporal beginning."

      Interesting that you characterize this statement as a refutation of circular arguments, because Aquinas says nothing about that here. On the other hand, his own argument seems to be quite circular, because he uses the impossibility of infinite regression as a premise in his own "proofs" of God's existence, and here he uses God's nature as premise to the argument that there must have been a beginning. What am I missing here?

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    14. >he is saying that the most convincing reason for the world not having eternal existence

      He precisely does not say that the world does not have eternal existence. In fact, he says the opposite:

      "The most efficacious way to prove that God exists is on the supposition that the world is eternal." - SCG I 13

      "By faith alone do we hold, and by no demonstration can it be proven, that the world did not always exist..." - ST I 46

      Consider two different kinds of creators. A carpenter who creates a birdhouse, and a musician who creates music. When the carpenter creates his birdhouse, the birdhouse necessarily has a beginning to its existence at some point in the past. But when the musician creates his music, it is theoretically possible that the musician has always been playing music. No beginning necessary, at least in principle. The unmoved mover is like the musician, not like the carpenter.

      >the "fact" that it is the manifestation of God's goodness, and therefore must have been created by him.

      He never says anything remotely like this. The briefest way of putting it is that motion requires an explanation, and that explanation cannot be in motion since that is circular. Motion is what is being explained, so the explanation for it must be something other than motion. I.e., something not in motion. An unmoved mover.

      That's it. That's what he is arguing. Not that an infinity is impossible, not that the universe must have had a beginning in the past.

      >because he uses the impossibility of infinite regression as a premise in his own "proofs" of God's existence

      He does not explicitly argue against the impossibility of an infinite. He argues that explanations cannot be circular. So that if you need to explain X, you need to explain it with not-X. But if you stretch to infinity in Xs, then you don't have not-X and hence no explanation for X. In principle, he could allow an infinite string of Xs and then just say that there still has to be a not-X to explain them. He certainly never argues from the finitude of the past to the existence of God.

      >here he uses God's nature as premise to the argument that there must have been a beginning.

      In this paragraph, he is arguing from God to the finiteness of the past just for the sake of argument. Like saying, "If you really want to argue to the finiteness of the past, William Lane Craig's arguments are no good. So here is a better way to do it, though I don't make any claims as to how strong or weak this is. I'm just throwing it out there to reflect upon."

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    15. im-skeptical wrote: "My answer is preposterous only to someone who presupposes that there can be no infinite regression. Each box car is moved by the car before it. Your insistence that there must be a beginning is a theistic argument that is not supported by valid logic."

      Your answer is preposterous to anyone who doesn't presuppose that box cars can move themselves. You say, "Each box car is moved by the car before it," but the engine ultimately moves the train because box cars have no independent motion. If you don't believe me, go out and get a level model train track and fill it with box cars, and see if the box cars start moving around the track. Next replace a box car or two with a working engine and see if the box cars start moving around the track.

      im-skeptical wrote: "Physical things, by definition, are things within the universe. Something that exists outside the universe (which may be responsible for the existence of the universe) is not what we would call physical, at least in the ordinary sense of the word, and need not be bound by the regularities of behavior (physical law) that apply to the the physical things in our experience."

      The definition of physical is, "of or pertaining to that which is material (Dictionary.com)." I don't see that physical things must necessarily be in the observable universe. Given your anti-Platonic materialistic view, I think that your only recourse is to say that physical laws are descriptions of how matter behaves, so matter, of a particular sort will behave the same whether it's in the observable or un-observable part of the universe. The whole question then is matter fundamentally different here compared there. That's something we just don't know.

      im-skeptical wrote: "I don't know what exists outside our universe any better than you do."

      And out of this ignorance you confidently assert, "But it ain't God."

      im-skeptical wrote: "Craig is making a logical argument in support of his theistic beliefs - an argument that says an infinite regression of causes is logically impossible. His logic is invalid. He doesn't understand the relevant math. If Craig conceded that his logic is invalid, the consequence would be that the Kalam argument, and other related theistic arguments fail. This logical assertion (that there can be no infinite regress) is a key assertion upon which theists depend to justify the existence of God."

      Who cares if some mathematical axioms say that the concept of infinity is coherent. The whole point of this discussion is if the concept of infinity can be instantiated in the real world. The concept of an instantiated infinity does entail absurdities, so I think we can say that it does not plausibly exist.

      First of all, the papers and posts in defense of an instantiated actual infinity, that you marshaled, don't show that an infinity has or could be real, they possibly show that concept is a mere possibility because Craig hasn't demonstrated with absolute certainty that it can't be instantiated.

      Secondly, only the philosophical defense of the Kalam fails in the sense that it can't be demonstrated with absolute certainty (an unrealistic criterion) that an actual infinity can't be instantiated. Remember there's also the defense that comes from scientific knowledge.

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    16. Martin wrote: "You guys are mixing up to completely different arguments. Craig argues against the possibility of an infinite series, via such arguments as the impossibility of traversing an infinite, or of reach infinity through successive counting. Not only does Thomas Aquinas not use this argument, he specifically refutes it."

      Hi Martin. Yeah, you caught me red handed knowingly smuggling in Aquinas' First Way into this discussion via the box car argument, but I thought it was germane to discussion of an infinite regress of contingents. I straddle the Kalam and the First Way, even though there's some tension between the two, because I don't want to choose one over the other, as I think that each cosmological argument has its strong points.

      However, I guess this conversation does sort of validate Aquinas' dislike of the Kalam in that the skeptic can always cling to the infinitesimally small possibility that an instantiated actual infinity could exist. The fact that the First Way does not need to show that an instantiated infinity is impossible is definitely one of the argument's strong points. I also think that Aquinas' argument about the impossibility of an infinite essentially ordered series is an incredibly powerful one.

      By the way, I've followed your blog for some time now and enjoy it.

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    17. im-skeptical, if you want a good explanation of Aquinas' First Way, which I've alluded to with my box car question, I recommend that you check out our friend Martin's excellent blog post which can be found here: http://rocketphilosophy.blogspot.com/2011/07/aquinas-first-way.html.

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    18. Thanks Keith. Although, my explanation/understanding of the argument continually evolves over time. I no longer like my article on the First Way on that page. It confuses people too much. It allows for too many ways to "escape" the argument illegitimately, like by thinking that it is some kind of primitive mechanics, when the boxcars are simply to illustrate the problem of circular explanations.

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    19. Martin: "He precisely does not say that the world does not have eternal existence. In fact, he says the opposite."

      We've seen three quotes from Aquinas here:
      1. "His power and goodness are made manifest above all by the fact that things other than Himself were not always in existence." which says that the world had a beginning.
      2. "The most efficacious way to prove that God exists is on the supposition that the world is eternal." which says that the world did not have a beginning.
      3. "By faith alone do we hold, and by no demonstration can it be proven, that the world did not always exist" which says that the world had a beginning (we hold this by faith, not by demonstration).

      Is Aquinas contradicting himself? No. Go back to SCG 13 and read what it says immediately before the quote: "The first consideration is that, as arguments, they presuppose the eternity of motion, which Catholics consider to be false." So Aquinas says this is a false supposition. He does not contradict himself. He definitely believes that the world had a beginning, and that it was created by God.

      Martin: "He does not explicitly argue against the impossibility of an infinite."
      I didn't say that. Craig makes that argument. I agree that Aquinas refutes Craig's argument, but he still believes that the world had a beginning. That is absolutely central to Catholic theism.

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    20. Keith: "Your answer is preposterous to anyone who doesn't presuppose that box cars can move themselves."
      I'm in agreement with Aquinas (and many others) on the logical possibility of an infinite regress.

      Keith: "I don't see that physical things must necessarily be in the observable universe."
      But that is the general understanding of what it means to be physical. Matter exists within space, and therefore exists within the universe. Space and time, along with matter, were created in the big bang.

      Keith: "And out of this ignorance you confidently assert, "But it ain't God.""
      Out of this ignorance you confidently assert that it is God. I make no such assertion. I said I don't know what exists outside the universe.

      Keith: "The whole point of this discussion is if the concept of infinity can be instantiated in the real world."
      No, it isn't. The point is that there could be an infinity of causes outside the world we know. And you have absolutely no basis to say it's improbable.

      Keith: " they possibly show that concept is a mere possibility because Craig hasn't demonstrated with absolute certainty that it can't be instantiated."
      Craig has attempted to prove that it is a logical impossibility. And his proof misses the mark.

      Keith: "Remember there's also the defense that comes from scientific knowledge."
      Craig's scientific defense of Kalam ignores the most prevalent theories among cosmologists today. His scientific defense is something that I chose not to address in this post, but it also misses the mark.

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    21. He thinks the universe had a beginning, but does not think this can be (tightly) proven through argument/evidence, and more importantly, does not think this can be used to prove the existence of God.

      More relevant, his argument against an infinity is not an argument against infinity qua infinity. If you take my earlier example of the musician making music, what he is saying is that since music can't play itself, it must be coming from something that can make music. I.e., it boils down to an argument against circular explanations. To explain X, you need something not-X to explain it.

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    22. im-skeptical wrote: "I'm in agreement with Aquinas (and many others) on the logical possibility of an infinite regress."

      Oh, you agree with Aquinas that, "Whatever is in motion is moved by another : and it is clear to the sense that something, the sun for instance, is in motion. Therefore it is set in motion by something else moving it. Now that which moves it is itself either moved or not. If it be not moved, then the point is proved that we must needs postulate an immovable mover : and this we call God. If, however, it be moved, it is moved by another mover. Either, therefore, we must proceed to infinity, or we must come to an immovable mover. But it is not possible to proceed to infinity. There- fore it is necessary to postulate an immovable mover (THE SUMMA CONTRA GENTILES)." I'm so glad that you came to your senses about the impossibility of proceeding to infinity with an essentially ordered series of contingents like the box cars. It took a while for you to see ridiculousness of saying that an infinite chain of motionless box cars were moving themselves, even though box cars have no independent means of motion, but you finally got it.

      By the way, Aquinas didn't believe in the existence of an actual infinity, in fact believed that the universe was created by God, he believed that it is not possible to demonstrate with absolute certainty that an actual infinity can't exist.

      im-skeptical wrote: "Space and time, along with matter, were created in the big bang."

      Are you saying that space, time and matter didn't exist anywhere prior to the big bang? If so, how did the material thing that might exist beyond the observable universe exist?

      im-skeptical wrote: "Out of this ignorance you confidently assert that it is God. I make no such assertion. I said I don't know what exists outside the universe."

      So, now you're claiming that you never said "But it ain't God," even though the words are right before our faces. You clearly claimed that God did not cause the universe to exist.

      im-skeptical wrote: "No, it isn't. The point is that there could be an infinity of causes outside the world we know. And you have absolutely no basis to say it's improbable."

      And you have no basis to say that an actual infinity is probable. Besides, stepping outside the observable universe doesn't solve the problem of the impossibility of an essentially ordered series. An unmoved mover is essential for the existence/state of contingents.

      im-skeptical wrote: "Craig has attempted to prove that it is a logical impossibility. And his proof misses the mark."

      Craig never attempted to prove that an actual infinity is logically impossible, he merely attempted to prove that it is metaphysically impossible, and he succeeded in showing that it likely doesn't exist.

      im-skeptical wrote: "Craig's scientific defense of Kalam ignores the most prevalent theories among cosmologists today."

      First of all, it's only natural that his older literature doesn't deal with theories that hadn't been advanced yet. Secondly, many of the current theories such as Sting Theory aren't even testable, so there're really just interesting ideas.

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    23. Martin: "He thinks the universe had a beginning, but does not think this can be (tightly) proven through argument/evidence, and more importantly, does not think this can be used to prove the existence of God. "

      We agree that Aquinas thinks the universe had a beginning. And he holds this assumption as a matter of faith, yet he very clearly uses this assumption as a premise to his first way argument.

      Martin: "More relevant, his argument against an infinity is not an argument against infinity qua infinity. ... it boils down to an argument against circular explanations."

      We agree that he refutes the logical impossibility of infinity, but he thinks that there must be a first mover, and therefore there can be no actual infinite regress. This agrees with what Keith says. "But this cannot go on to infinity, because then there would be no first mover ..." [from Summa Theologica]. This is what makes his argument circular. The first way says that there can't be an infinite regress of movers, because that would preclude a first mover, and then goes on to conclude that there must be a first mover, which is God. In my book, this is circular reasoning.

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    24. ** I meant to say String Theory, not Sting Theory. **

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    25. Keith: "Oh, you agree with Aquinas that, ... "

      No. I agree with Aquinas that Craig's argument misses the mark. That's all I said.

      Keith: "By the way, Aquinas didn't believe in the existence of an actual infinity, in fact believed that the universe was created by God, he believed that it is not possible to demonstrate with absolute certainty that an actual infinity can't exist."

      We agree. He also thinks that Craig's argument misses the mark.

      Keith: "Are you saying that space, time and matter didn't exist anywhere prior to the big bang? If so, how did the material thing that might exist beyond the observable universe exist?"

      I said that space, time, and matter were created in the big bang. That's physics. I didn't say there were no other instances of these things before. Something gave rise to our universe, and may well have given rise to many others. Whatever that thing is, I don't know. But it must necessarily exist outside our own instance of a universe, and therefore is not bound by the same physical laws that we observe within our universe.

      Keith: "So, now you're claiming that you never said "But it ain't God," even though the words are right before our faces. You clearly claimed that God did not cause the universe to exist."

      What I was saying (as I have already explained) is that you have no basis to assume that this thing is God, other than your religious faith. There is ABSOLUTELY no empirical evidence to support what YOU claim.

      Keith: "And you have no basis to say that an actual infinity is probable. Besides, stepping outside the observable universe doesn't solve the problem of the impossibility of an essentially ordered series. An unmoved mover is essential for the existence/state of contingents."

      I didn't say it was probable. I said that Craig's argument is faulty.

      Keith: "Craig never attempted to prove that an actual infinity is logically impossible"

      Yes, he did. That's what all those "absurdities" are supposed to prove.

      Keith: "First of all, it's only natural that his older literature doesn't deal with theories that hadn't been advanced yet. Secondly, many of the current theories such as Sting Theory aren't even testable, so there're really just interesting ideas."

      First of all, there were plenty of such theories when Craig wrote this. Secondly, what makes you think a theory like string theory isn't testable? It's a mathematical model of how things work, like any theory of physics. All we need to do to falsify the theory is make an observation where things don't behave according to this model.

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    26. >We agree that Aquinas thinks the universe had a beginning. And he holds this assumption as a matter of faith, yet he very clearly uses this assumption as a premise to his first way argument.

      Umm, no. I just got through explaining above that that is not a premise of the first way. That the universe had a beginning.

      >We agree that he refutes the logical impossibility of infinity, but he thinks that there must be a first mover, and therefore there can be no actual infinite regress.

      Two different types of infinities. One vertical, one horizontal. He thinks a horizontal infinite series is acceptable, but that a vertical one is not. Again, he isn't really arguing against an infinite series per se. He is arguing that if X needs an explanation, then there must be not-X which explains it.

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    27. Martin,

      I misspoke in the previous reply.

      "We agree that he refutes the logical impossibility of infinity" should have said "We agree that he refutes Craig's argument against the logical impossibility of infinity"

      What I don't see is where in any of these quotes he says something like "if X needs an explanation, then there must be not-X which explains it" - unless, of course, by X you mean that which is moved and by not-X you mean that which is not moved ?? Perhaps you can clarify this.

      But I quoted directly from Aquinas in Summa Theologica. First he says the infinite regress of movers is impossible because that would mean there is no first mover. Then he goes on to conclude that there must be a first mover. It sure sounds like circular reasoning to me, but you say he's not actually saying what he said. Here it is again: "But this cannot go on to infinity, because then there would be no first mover [premise or assumption] ... Therefore it is necessary to arrive at a first mover, put in motion by no other; and this everyone understands to be God. [conclusion]" These are the words of Aquinas in his first way argument. I'm not making it up or twisting his words. He says what he says. How is this not begging the question?

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    28. It's not circular. It's a simple modus tollens. X cannot account for itself, so there must be something not-X that accounts for it. Hence:

      1. If there is no not-X, then there is no X
      2. There is X
      3. Therefore is not-X

      That's the core. Aquinas simply adds in an extra premise:

      1. If there is no not-X, then there is no X
      2. If everything that exists is X, then there is no not-X (by definition)
      3. There is X
      4. Therefore, not everything is X
      5. Therefore, there is something that is not-X

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    29. Martin,

      I'm trying to make sense of your logic, and I must confess that it eludes me. I asked you to clarify what you said, and you declined to do so, so I am left wondering what you mean. Here's my interpretation of it:

      "There is X" is an existential proposition, and X could represent some type of thing - let's say a bear.
      "not-X" evidently refers to something that is not an X - let's say a unicorn.

      Your syllogism can be restated with substitutions for X and not-X as:
      1. If there is no unicorn [not-X], then there is no bear [X].
      2. There is a bear.
      3. Therefore there is a unicorn.

      This is nonsense. The main problem with it is that the existence of two different kinds of things is generally independent. The existence of bears does not depend on the existence of unicorns, and vice versa. So statement 1 cannot be a generality where X could represent anything. It must refer to something more specific, where there is an existential dependency.

      So let's try again. Say X is an offspring and not-X is a parent. Here, there is an existential relationship.

      Your syllogism can be restated with substitutions for X and not-X as:
      1. If there is no parent [not-X], then there is no offspring [X].
      2. There is an offspring.
      3. Therefore there is a parent.

      That's a little better. Now we come to the second syllogism:
      1. If there is no parent [not-X], then there is no offspring [X].
      2. If everything that exists is an offspring, then there is no parent (by definition).
      3. There is an offspring.
      4. Therefore, not everything is an offspring.
      5. Therefore, there is something that is a parent.

      Now we see another problem. Even with an existential dependency, statement 2 is clearly false, since an offspring can also be a parent. So once again, we have to narrow down the meaning of X and not-X to something very specific if we hope to make any sense of what you are saying.

      The question I have for you is what do you mean by X and not-X? Unless you put these in concrete terms, your syllogisms are demonstrably invalid.

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    30. As I said above: "X cannot account for itself, so there must be something not-X that accounts for it."

      E.g., music cannot play itself, so there must be something (a musician, a record, etc) that is capable of causing music.

      1. If there is no [record, musician, etc; something capable of playing music] then there is no music (because music cannot play itself)
      2. There is music (e.g., we are hearing it right now)
      3. Therefore, there is [a record, musician, etc]

      The difference between my music and your offspring is exactly what I said earlier: the difference between a horizontal series, and a vertical series. You are expressing a horizontal series, whereas me and Aquinas are expressing vertical series.

      In a horizontal series, each member of the series is an original cause of an effect, and that effect can then go on to be an original cause of a new effect:

      (X --> Y) --> (X --> Y) --> (X --> Y)

      Example is your offspring. Each parent generates an offspring, which can then generate its own offspring, etc. Each member of the series is a source of the next effect.

      In a vertical series, most members of the series can only pass along the effect but cannot generate it:

      (A --> (B --> (C --> (D --> (E)))))

      Example is the music coming out of your radio. Your radio can only pass along the effect (music). It cannot generate it originally. It's coming from the radio tower. But the radio tower cannot generate the effect any more than your radio can. It too is just passing the effect along. Passing it along from...the DJ's booth. Or whatever. You get the point.

      Most of the members of a vertical series cannot generate the effect originally, and so there must be at least one member of the series that can generate the effect originally, otherwise there would be no effect to be passed along in the first place. If there is no record, or singer in the radio studio, etc, then there is no music for the radio tower to pass along to your radio.

      You understand now, I hope?

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    31. Martin: "You understand now, I hope?"

      Yes. Thank you for explaining. Unfortunately, this does not address the issue of the infinite regression of movers or causes. And I think this is still a problem regardless of whether the series is horizontal or vertical. Theists take it on faith that there must be a first cause or first mover, and therefore there can't be an infinite regression. Aquinas openly admits this. But if you allow that there can be an infinite series without a first cause, then each element of the series can still have a cause, which is the element that comes before it. This is a logical possibility, and it is certainly no more outlandish than claiming that an uncaused God must be the first cause.

      Furthermore, we still have the problem of the circularity of Aquinas' argument. I stated this problem explicitly, and I have yet to hear any cogent response.

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    32. >this does not address the issue of the infinite regression of movers or causes

      But it does. If all you have are, say, radio towers, that is, things capable of passing along the effect, then you have no source of the effect, like the record or the singer. Thus, the argument is that if you have endless string of "passers", you have no source of the effect and hence no effect. The argument is not against an infinity qua infinity, as I've said above.

      >Theists take it on faith that there must be a first cause or first mover, and therefore there can't be an infinite regression.

      Well, no, that's precisely not what the argument is arguing. It is not arguing that, by faith, we know there is a prime mover and that therefore the regress can't be infinite. Rather, it is that the regress can't be infinite and that therefore we know there must be a prime mover. We hear music, we know that radio towers can't produce music, and so we know there must be a source of that music like a record or a singer, which would be the "prime mover" in this sense. "Prime mover" means the primary cause, as opposed to the secondary causes of the radio towers which can only pass along the effect but cannot generate it.

      >But if you allow that there can be an infinite series without a first cause, then each element of the series can still have a cause, which is the element that comes before it.

      A horizontal series can go to infinity. As Aquinas himself says: "..it is not impossible to proceed to infinity 'accidentally' as regards efficient causes; for instance, if all the causes thus infinitely multiplied should have the order of only one cause, their multiplication being accidental, as an artificer acts by means of many hammers accidentally, because one after the other may be broken."

      (I'm calling "horizontal" what he is calling "accidental.")

      The artificer may have been breaking hammers for infinity, for all we know. There is nothing about this horizontal/accidental series that logically demands a first member.

      However, in a vertical series, "...it is impossible to proceed to infinity...thus, there cannot be an infinite number of causes that are...required for a certain effect; for instance, that a stone be moved by a stick, the stick by the hand, and so on..."

      The motion of the rock in the example he gives is entirely derived from the stick, but the motion of the stick drives its motion from the hand. No hand, no motion of stick or rock. Like my music example: just radio towers, no music. The hand/record is the cause of the effect, and the stick/towers can only pass the effect along. If you stretch to infinity in passers-alongers, then there is no source of the effect, by definition. And no source of the effect = no effect. No record, no music. No hand, no rock moving. The argument allows in principle there to be an infinity. Perhaps there is an finity of radio towers. Perhaps there is an infinity of sticks. But then there still has to be a record somewhere, otherwise you would have no music. An infinite chain of sticks would still need a hand grabbing it somewhere along the chain to move it, otherwise it won't move.

      This is why it really just boils down to explanations not being circular. Since radio towers can't play music, then it is no good explaining where the music is coming from by postulating another radio tower. Similarly, since motion can't move itself, it is no good explaining motion with something in motion, since motion is the very thing we are explaining.

      >we still have the problem of the circularity of Aquinas' argument.

      I don't know what you mean. I explicitly responded to this. Twice. Above.

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    33. "The motion of the rock in the example he gives is entirely derived from the stick, but the motion of the stick drives its motion from the hand."

      So what? What difference does it make what the cause is? The point is that there is something that causes motion. And in a chain of causation, there is something that causes each item in the chain to move: namely, the item that comes before it. If the chain continues forever, the causation continues forever. You haven't given any cogent reason for assuming that the chain must have a beginning. You simply take it on faith.

      Now, there's no need to keep repeating the same non-reason you have already stated. I heard it. What I didn't hear is why there has to be a first mover instead of a continuing chain of movers. You say that something has to originate the movement, and I say there is no origination. It's an infinite series. It has always been causing movement. Prove me wrong.

      As Aquinas said, "But this cannot go on to infinity, because then there would be no first mover". In other words, we simply assume the necessity of a first mover, and reject the possibility of an infinite regression, because it is a key step in the logic that leads us to conclude that God exists. If we don't feel the need to prove that God exists, then there is no logical reason to assume there must be a first mover.

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    34. im-skeptical wrote: "And I think this is still a problem regardless of whether the series is horizontal or vertical. Theists take it on faith that there must be a first cause or first mover, and therefore there can't be an infinite regression. Aquinas openly admits this. But if you allow that there can be an infinite series without a first cause, then each element of the series can still have a cause, which is the element that comes before it. This is a logical possibility, and it is certainly no more outlandish than claiming that an uncaused God must be the first cause."

      Theists do not take the unmoved mover on faith, the unmoved mover is demonstrated to exist from deducing that there is motion in the world and from the impossibility of an infinite essentially ordered contingents. Your solution to the problem of the infinite essentially ordered contingents violates the Law of Non-contradiction, and is therefore logically untenable, as you're saying there are contingents that are simultaneously not contingent. Contingents depend on something else to actualize their motion/existence, and this is true in all possible worlds. Even an infinite number of contingents, such as an infinite number of music, remains contingent, so when you say that music plays itself or box cars move themselves you're saying there is some X that is -X which is a logical contradiction. Either the music is contingent or it's not, you can't have it both ways. If the music is contingent then even an infinite amount of it is incapable of motion/existence.

      im-skeptical wrote: "Furthermore, we still have the problem of the circularity of Aquinas' argument. I stated this problem explicitly, and I have yet to hear any cogent response."

      Earlier you wrote, "On the other hand, his own argument seems to be quite circular, because he uses the impossibility of infinite regression as a premise in his own "proofs" of God's existence, and here he uses God's nature as premise to the argument that there must have been a beginning. "

      There is absolutely no circularity in Aquinas' argument. He is moving from noticing that there is movement in the world to the metaphysical truth that things that are being moved are being moved by something else. In premise three he eliminates the possibility of an infinite essentially ordered series of contingents, as they would absurdly have to actualize their own motion even though they have no independent source of motion, which leaves an unmoved mover as the only source of ultimate movement. From the existence of motion to the truth that moving things needing to be moved by something else to the impossibility of an essentially ordered series of contingents it logically follows that there is an unmoved mover which actualizes the motion we observe.

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    35. To emphasize the point, I've used the following example. Consider a flower pot suspended in mid-air. Flower pots qua flower pots are not able to suspend themselves in mid-air. So something other than the flower pot must be causing this effect. The flower pot is attached to an infinite chain of links going up into the sky. To infinity. It won't fall, because the Earth's gravity can't pull it down.

      So now we have here the same kind of reasoning: an effect (suspension), an object incapable of causing the effect (flower pot), and something that is capable of causing the effect (infinite chain of links).

      This example works perfectly well to get at the core of the reasoning, and show that it is NOT an infinity qua infinity that Aquinas is arguing against.

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    36. Keith: "Theists do not take the unmoved mover on faith"

      I quoted Aquinas saying that they take the existence of a first mover (the creation of the universe) on faith, not by proof or demonstration. This is true. You can say "something has to set it in motion" all you like, but that's not proof.

      Keith: "Your solution to the problem of the infinite essentially ordered contingents violates the Law of Non-contradiction, and is therefore logically untenable, as you're saying there are contingents that are simultaneously not contingent."

      Show me where I said that.

      Keith: "so when you say that music plays itself or box cars move themselves you're saying there is some X that is -X which is a logical contradiction."

      I didn't say that. I said everything has a cause, which is the element that comes before it. Nothing is causing itself. Nothing is both contingent and non-contingent. No contradiction.

      Keith: "In premise three he eliminates the possibility of an infinite essentially ordered series of contingents, as they would absurdly have to actualize their own motion even though they have no independent source of motion, which leaves an unmoved mover as the only source of ultimate movement."

      This is false logic. As I said, nothing has to move itself. Everything is moved by something else in an infinite chain of causation. Aquinas assumes there must be a first mover, and he admits that he takes this on faith, not by any kind of proof.

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    37. Martin: "This example works perfectly well to get at the core of the reasoning, and show that it is NOT an infinity qua infinity that Aquinas is arguing against."

      You are arguing against a strawman. I didn't say Aquinas argues against "infinity qua infinity". I thought we already agreed on this earlier.

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    38. Oh, OK. Not sure what your disagreement is, then...?

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    39. Martin,

      I disagree with the idea that there must be a first mover. There is no logical difficulty if we abandon the idea that there must be a beginning to the chain of movement.

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    40. There is logical difficult if we have, for example, a flower pot suspended in mid-air when flower pots are not capable of suspending themselves in mid-air. We need a second thing that IS capable of holding up flower pots.

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    41. Martin,

      We are talking about a chain of causation, not about individual things that actualize themselves.

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    42. I never said anything about something actualizing itself, which would be impossible.

      Do you agree with this basic principle, that if there is some effect (suspension) that can't be accounted for by the thing itself (flower pot), that there must be something else responsible for the effect?

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    43. I never said anything about a "beginning." Aquinas specifically argues against a beginning.

      The point is that if X cannot explain itself, then there must be something not-X that explains it. Do you agree with this?

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    44. Martin,

      "Do you agree with this basic principle, that if there is some effect (suspension) that can't be accounted for by the thing itself (flower pot), that there must be something else responsible for the effect?"

      Yes. That's what I've been saying. Actualization, causation, whatever you like to call it. In a chain of causation, it would be the previous thing in the chain. From the perspective of physics, a "chain" of causation is a dubious concept. Objects are acted upon by the cumulative effects of everything around them (as well as things that may not be on the immediate vicinity). But the point remains - there is no logical necessity for this causation to have a beginning point, and scant evidence supports the idea that causation does have a beginning point. This is nothing more than theistic rationalization.

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    45. "Aquinas specifically argues against a beginning."

      That's not true. Aquinas argues for a first cause. He believes that all movement is ultimately caused by a first mover. He believes that the universe had a beginning and that God caused it to exist.

      "The point is that if X cannot explain itself, then there must be something not-X that explains it. Do you agree with this?"

      Not really. I had this discussion in a previous post. The word 'explain' is not being used properly here. I can explain my own existence. I can't cause my own existence.

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    46. Not in the first way, though, which is what we are talking about.

      OK, explanation. You can't cause your own existence, so your existence must be caused by something other than you. That is what is happening in the first way. Motion cannot cause itself, so there must be something other than motion that causes motion.

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    47. The first way argument says:
      Whatever is in motion must be put in motion by another.
      That which puts something in motion must itself be put in motion by yet another.
      This can't continue to infinity because there must be a first mover.
      So, it is necessary to arrive at a first mover, which is God.

      Aquinas' assumption that there must be a first mover simply begs the question. If the chain did continue to infinity, then there would always be a mover for everything that is moved.

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    48. The argument I just gave above is the essence of the first way, worded a bit different but getting at the same reasoning:

      1. Motion cannot explain itself
      2. Therefore, there must be an explanation for motion
      3. Explanations cannot be circular
      4. Therefore, not-motion must be the explanation for motion

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    49. im-skeptical wrote: "I didn't say that. I said everything has a cause, which is the element that comes before it. Nothing is causing itself. Nothing is both contingent and non-contingent. No contradiction."

      You didn't say that, but you're unwittingly implying it when you say that each box car can move the one before it because you're smuggling in motion that doesn't exist. An infinite number of box cars will remain at rest for all of eternity unless some external things initiates motion because box cars have no independent means of moving themselves. So, if you're trying to say that the infinite chain of box cars are moving themselves there has to be some box car in the chain that is capable of causing motion even though it's incapable of causing motion--which of course is logical contradiction.

      im-skeptical wrote: "Aquinas' assumption that there must be a first mover simply begs the question. If the chain did continue to infinity, then there would always be a mover for everything that is moved."

      I think that you begging the question by assuming that some mysterious motion has been inexplicably inserted in the chain of contingents. Where is this motion coming from that you keep alluding to?

      If the chain continues to infinity then you have an infinitely long chain of motionless things because nothing in the chain is capable of causing motion.

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    50. Keith,

      I'm no philosopher, but I believe that in order to beg the question, you have to be making an argument that includes an assumption or premise that is the same as the conclusion. Like what Aquinas does in the first way. I'm not making the argument, I'm critiquing it.

      "If the chain continues to infinity then you have an infinitely long chain of motionless things because nothing in the chain is capable of causing motion. "

      I'm postulating a chain of things moving things, not a chain of motionless things. And yes, the things in the chain do cause motion. And everything in the chain that moves something is also moved by something else. Where does the motion come from? Further up the chain. If you insist that "some mysterious motion has been inexplicably inserted in the chain", you have God for that.

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    51. Martin,

      You say that a 'horizontal' (sequential) series can be infinite, but a 'vertical' (simultaneous) series can't be infinite. Why not? The same logic applies. Aquinas is still begging the question.

      By the way, chains of things moving things are sequential, and I challenge you to show me an example that isn't. Even Aquinas agrees with this: "For succession characterizes motion." [SCG 2 19]

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    52. > Why not?

      http://www.academia.edu/4415427/There_Must_Be_A_First_Why_Thomas_Aquinas_Rejects_Infinite_Essentially_Ordered_Causal_Series

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    53. Martin,

      I read the paper. This is rationalization for those who already believe. There is nothing here to convince someone who is not already a believer. You can declare that a causal series is "wholly derivative", and thus claim that the series must have a beginning by definition, but that is absolutely meaningless to those of us who see causation as a matter of physics.

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    54. I don't understand what you mean. I have to be a "believer" to believe that if a toy car is missing its batteries, and begins to move that something else (gravity, the wind, a string) must be moving it? A believer in what?

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    55. "I have to be a "believer" to believe that if a toy car is missing its batteries, and begins to move that something else (gravity, the wind, a string) must be moving it?"

      Nothing controversial about that. But you also believe that whatever is moving the car is "ontologically dependent" on God as the first mover. If you buy that, you may be willing to buy what this paper says. Otherwise, you would have no reason to believe it.

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    56. The premise has nothing to do with God. The premise says that if an effect is not produced by an object, then it must be coming from something outside that object. The premise says nothing about God.

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    57. "The premise has nothing to do with God. The premise says that if an effect is not produced by an object, then it must be coming from something outside that object. The premise says nothing about God."

      Like I said, the part about about cause coming from "something outside" is not controversial. Nobody is arguing about that. I don't understand why you keep repeating it. The issue at hand is whether there can be an infinite chain of causation. If you believe in God, you must believe there must be this unmoved mover at the start of the chain. If you don't believe in God, you have no reason to believe that.

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    58. That's the conclusion of two premises. In fact, not even that. Just that there is something not in motion. That comes from the very premise you just called uncontroversial.

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    59. This is going nowhere. If something is moved, it requires a mover. We both agree on that. You say that ultimately, there must be an unmoved mover (and I see nothing in the argument that implies this), and I say that there must be a mover of some kind (which would be satisfied by an infinite chain).

      Can you explain how you get from "there must be an explanation for motion" to "that explanation must be an unmoved mover" without resorting to your a priori held theistic concepts?

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    60. Yes, I've explained that already. You get to it because explanations cannot be circular. With the battery-powered car, the explanandum (the thing being explained) is: (A) something incapable of self-movement. So the explanation cannot be (A). It must be: (B) something that IS capable of self-movement.

      In the case of motion, the explanandum is: (A) all motion. So the explanation cannot be (A), since that would be circular. So the explanation must be: (B) something other than motion.

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    61. Forgive me for saying, but that's sheer nonsense. Something can be moved by something that moves. And if you don't like circularity, try linearity.

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    62. It's sheer nonsense that explanations cannot be circular? That the homunculus fallacy is a fallacy?

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    63. "It's sheer nonsense that explanations cannot be circular? That the homunculus fallacy is a fallacy?"

      No, it's sheer nonsense that "X is explained by not-X". And an infinite succession of causes is not circular.

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    64. So, you are saying that non-circular explanations are not "sheer nonsense," but that "X is explained by not-X", which is a description of non-circular explanations, is "sheer nonsense." So you are saying that non-circular explanations both (a) are, and (b) are not "sheer nonsense."

      ???

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    65. An infinite succession is not circular.

      In Aristotelian parlance, movement is explained by things that move, not by things that don't move. We NEVER observe that an inert, unmoving object imparts energy or causes change to some other object. And we NEVER observe something imparting energy or causing change to something else without itself being changed.

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    66. im-skeptical wrote: "Like I said, the part about about cause coming from "something outside" is not controversial. Nobody is arguing about that. I don't understand why you keep repeating it. The issue at hand is whether there can be an infinite chain of causation. If you believe in God, you must believe there must be this unmoved mover at the start of the chain. If you don't believe in God, you have no reason to believe that."

      It befuddles me that you can say, "If something is moved, it requires a mover. We both agree on that," and then go on to say that an infinite chain of box cars, which can only move when moved by an outside force like an engine, are moving because each successive box car is moving the one behind it. The two statements are completely incompatible because according to the first premise the box cars will be eternally at rest until an outside force causes them to move. If what you're saying is true then train companies would not need to spend money on engines and engineers because the box cars would just magically be moving on their own around the track, but unfortunately for the train companies this is not how things work.

      How is believing the obvious fact that contingent things, like box cars, need to be moved by an outside force is an article of faith? This is not faith, this is something any sensible person would believe regardless of their beliefs about God. Quite frankly, I think that your distaste for the conclusion of Aquinas' argument is blinding you from thinking rationally about the premises of the argument. That's the only way I can explain how you can think that contingent objects require an outside source of movement in order to move and yet think that an infinite chain of essentially ordered contingent are moving themselves sans an outside force.

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    67. im-skeptical wrote: I'm no philosopher, but I believe that in order to beg the question, you have to be making an argument that includes an assumption or premise that is the same as the conclusion. Like what Aquinas does in the first way. I'm not making the argument, I'm critiquing it."

      First, of all, whether you realize it or not, you're making a counterargument when you're critiquing Aquinas' argument. Your counterargument looks like:

      1. If an essentially ordered chain of contingents is moving eternally without an outside source of movement then it doesn't require an outside source of movement in order to move.
      2. An essentially ordered chain of contingents is moving eternally without an outside source of movement.
      3. Therefore an essentially ordered chain of contingents is moving eternally without an outside source of movement.

      According to to Fallacy Files, "[A]n argument begs the question when it assumes any controversial point not conceded by the other side," and premise two is indeed controversial as no sensible person thinks that an essentially ordered chain of contingents could move at all without an outside source of movement. What's even worse, is that you're assuming what you're trying to prove, that contingents can move without an outside source of movement--you're just assuming that they're somehow moving.

      Secondly, Aquinas' argument is not circular because the un-moved mover is not assumed to exist--the existence of the un-moved mover is deduced by eliminating all other possible sources of movement. Since there is movement; and all moving things are moved by something else; and an essentially ordered chain of contingents can't move itself there has to be an un-moved mover. By a process of elimination we determine that there must be an un-moved mover that accounts for the movement we see.

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    68. Keith,

      Using boxcars as an example was your idea, not mine. I don't think it's the best analogy, because all trains in our experience are finite and contingent. I'm trying to stay with your analogy, but think of boxcars as a series of universes, spawned by some infinite series of cosmic creation events.

      You are using the term 'outside force' in an equivocal manner. When I say the boxcar requires an outside force to move it, I mean a force from outside the boxcar. That can very well be another boxcar pulling on it. If the chain is FINITE, there is obviously a first car in the chain, and so there must be an engine pulling it to move the first boxcar. After that, all the rest of the boxcars are pulled by other boxcars in the chain. If the chain is infinite, there is no first car in the chain, and each car is pulling the one after it. Now you say there must be an 'outside force', meaning a force that originates outside the chain, not just a force external to the individual boxcar. But there's no requirement for that. As long as there is a previous boxcar pulling, then all boxcars in the chain are moved by an outside force (external to the individual boxcar).

      If by "first premise" you mean the first way as I formulated it above, there's no inconsistency or incompatibility. You are simply reading your own assumptions into the argument. In particular (following Scotus, I presume), the "essential ordering" of the sequence presumes a cascading causal dependency, which is purely a (medieval) metaphysical concept that has no meaning in a modern understanding of physical reality. And in so-doing, you insert the requirement for a first cause on the sly. I won't buy it. And you shouldn't either. This is a simple argument, until theists, feeling the need for rational justification of their beliefs, insert their hidden assumptions and preconceptions.

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    69. I already said above that we can accept your "infinite box cars" for the sake of argument, although I used the flower pot example. Same principle. A flowerpot, or boxcar, are incapable of suspending or moving themselves. So there must be something else (an infinite chain, an infinite train of boxcars) that is the source of the effect.

      This is the principle at work, and is perfectly acceptable for the sake of argument. It still answers the core of what Aquinas is saying with his regress argument, which is this: for any given effect, insofar as it is an effect, there must be a cause capable of producing it.

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    70. Martin,

      It sounds like you are saying exactly what I have been saying. We just disagree about the nature of the causation.

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    71. That's what I've been trying to explain to you this whole time. The principle that Aquinas is appealing to is exactly what I just said above. Aquinas is the anti-fundie. Skeptics really ought to like him. He doesn't just accept anything just because it supports theism. He explicitly rejects both the ontological and kalam arguments, because he thinks they are no good. Modern day apologetics is like a used car salesman. Whatever gets you to buy. Aquinas ain't like that.

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    72. Martin,

      "He doesn't just accept anything just because it supports theism."

      Aquinas buys into a whole philosophical culture that supports his theism. I don't blame him for that, because here was little else at the time that would refute that system of beliefs. But today we know much more about how things work, about the physical realities that govern things like causation. I can only wonder how different Aquinas' beliefs would have been if he had access to the knowledge available to us now. In this scientific age, if you deny modern scientific knowledge in favor of medieval metaphysical concepts, you are a "fundie".

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    73. We are talking about his "regress." The principle that is doing the work in his anti-regress argument is what I just said: for any given effect, insofar as it is an effect, there must be a cause capable of producing it.Flower pot can't suspend itself, so there must be some source of that effect to found outside the flower pot, such as an infinite chain of links. So you can see now, hopefully, that this is not an argument against an infinite series qua infinite series.

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    74. I'm talking about his regress, too. Aquinas says right in the first way argument "But this cannot go on to infinity, because then there would be no first mover ...". He is relying on a metaphysical concept known as the "essentially ordered series" that entails a first cause or mover. There is no reason in modern physics that we should assume any such thing. In fact, it violates our understanding of causation. But Aquinas assumes it. And in so doing, he presupposes his God.

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    75. We are going around in circles. I just showed how the principle doing the work in his argument is that for any given effect, insofar as it is an effect, there must be a cause capable of producing it. That is the principle that is doing the work in his anti-regress argument. The point has nothing to do with "modern physics," whatever that means, nor does it "violate our understanding of causation," whatever that means. It means that if, for example, a flower pot is incapable of suspending itself, there must be something else in addition to the flower pot that is causing that effect, since flower pots are incapable of suspending themselves. That's what he is saying in his anti-regress argument.

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    76. "It means that if, for example, a flower pot is incapable of suspending itself, there must be something else in addition to the flower pot that is causing that effect"

      You keep saying that, but you deny that an infinite regress of causes could suspend the pot. As long as the link above it holds up the pot, what difference does it make how many links there are?

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    77. im-skeptical wrote: "As long as the link above it holds up the pot, what difference does it make how many links there are?"

      Because if nothing is actually holding up the links and the pot then the whole chain will never get off the ground. The only way to make sense of what you're saying about the links holding up the pot is to assume that the links are somehow floating in the air. The only way to make sense of what you're saying about the infinite chain of box cars is to assume that the box cars have always somehow been moving, even though there is no way to account for their movement as box cars will remain motionless unless some force is exerted on them. These assumptions are unreasonable and question begging.

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    78. "These assumptions are unreasonable and question begging. "

      That is precisely what you are doing. I said, "As long as the link above it holds up the pot ..." That means there IS something holding the pot up - namely the link that it is attached to. And what holds that up? the next link. Now here's where your hidden assumption comes in: there has to be an end to the chain (this is your essentially ordered series). Why? Because your belief demands it. Why can't it just be a series of links that goes on forever, with each link being supported by the one above it? Because you say nothing would be supporting the chain. If we were talking about an actual finite chain, I would agree, but that's not what we're talking about. Any given link of the chain is supported by the link above it. And that's what holds up the pot. This goes right back to the early discussion. You think in terms of the finite things you know, but you can't apply the same logic to the infinite.

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    79. >you deny that an infinite regress of causes could suspend the pot.

      Not only did I not deny this, I explicitly allowed it, at least for the sake of argument. A flower pot is incapable of suspending itself, so there must be something capable of suspending it, such as an infinite chain of links. I said this three times, above.

      We really are just spinning around endlessly in a circle.

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    80. Martin,

      I reviewed the conversation, and I agree that we are going in circles. For my part, I am confused by what you are saying. To some degree, I see that you make remarks that seem cryptic to me, and lacking further explanation, I don't know what you are trying to tell me.

      Example: (speaking of Aquinas' first way) "circular explanations are fallacious. He is arguing that you cannot explain X by appealing to X, since X is the very thing you are trying to explain. To explain X, you must postulate not-X." Really? I read what Aquinas said, and it didn't sound anything like that. (But it does sound a lot like Scotus' causal argument.) So I try to get some further explanation, and you don't seem to be willing to give an explanation that relates the two things in a way that makes sense to me.

      So your point, I guess is that a chain of motion must start with something that is not in motion. Then, I object that this doesn't seem to be true - motion is caused by motion, not by non-motion. Furthermore, why can't this chain go on forever? That's when you bring up the flower pot. Now I am confused, because we were talking about a chain, and I assume you are using this as an example of an essentially ordered series, which supposedly can't continue to infinity, but it turns out that you are really saying that the chain holding up the flower pot can be infinite after all. So we agree. Well, what was the disagreement about? Oh right - it was about how X must be caused by not-X. So what does this flower pot have to do with the discussion of infinite causal series? And at this point, we are back where we started.

      It would be most helpful if you were a bit more forthcoming with explanations. I'm not stupid, just a little slow. It is not obvious to me how some of the things you say relate to the discussion.

      Bottom line: You appear to be following the causal argument of Scotus, including his explanation of essentially ordered series, which he asserts cannot be infinite (by definition). Aquinas seems to make the same assumption in the first way. I still think this is nothing more than an assumption, lacking any kind of proof. It also happens to be essential if you want to conclude there is a first mover. I contend that by assuming an essentially ordered series, you are automatically assuming God, because God is seen as the first mover. You can argue that the first mover is a conclusion rather than an assumption, but this is disingenuous, because it was not necessary to assume an essentially ordered series.

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    81. >So what does this flower pot have to do with the discussion of infinite causal series?

      I don't know what else to do. I've explained it as clearly as I know how. The flower pot is incapable of suspending itself. So there must be something in addition to the flower pot that IS capable of suspending flower pots, such as a ceiling, or an infinite chain stretching up into the sky. That is what an essentially ordered series is. It doesn't necessarily have a single terminus at the head of it, or even a terminus at all. Rather, it has something capable of producing an effect in something that doesn't have that capability.

      Please tell me you understand now. I don't know how much longer I can keep this up.

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    82. "That is what an essentially ordered series is. It doesn't necessarily have a single terminus at the head of it, or even a terminus at all."

      The paper you pointed to: There_Must_Be_A_First_Why_Thomas_Aquinas_Rejects_Infinite_Essentially_Ordered_Causal_Series purports to explain that this type of series MUST NOT continue to infinity.

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    83. And the last fifty comments of mine have been trying to explain to you, to no avail, that it is not an argument against infinity per se. That an infinite series is technically acceptable. That what is at the heart of it is that if an effect cannot be accounted for by an object, that there must be some other factor (including, in principle, an infinite chain of links) that does account for it.

      The paper you supposedly read even says exactly that! To quote from page 4:

      "It also does not rely on the claim that infinite series are impossible...Aquinas merely claims that an effect, insofar as it is an effect, must have a cause capable of producing it."

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    84. We both agreed long ago that infinite series are not logically impossible. I don't understand why we keep coming back to this. I'm not trying to rehash things that were already agreed between us. The paper argues that an essentially ordered causal series cannot continue to infinity. This is the principle that both Scotus and Aquinas rely on in their proof of God. And now you're claiming that it can. "That is what an essentially ordered series is. It doesn't necessarily have a single terminus at the head of it, or even a terminus at all." A series without a terminus is an infinite series. You seem to be contradicting yourself, and when I ask for further clarification, you act exasperated. "And the last fifty comments of mine have been trying to explain to you, to no avail ..."

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    85. So it appears that Martin has departed in frustration due to my inability to understand his contradiction.

      If anyone can help explain this to me, I would be most appreciative. Martin makes the case that an essentially ordered causal series (which he calls a vertical series) must be finite - ie. begins with a first mover, at September 22, 2014 at 12:37 PM. Then he insists that such a series can be infinite at September 24, 2014 at 9:39 PM.

      I'm sorry - I'm trying to understand what he says, but it doesn't make sense.

      For the record, I did read the paper he referred to, and I get what it says, but I don't buy it. The difference between 'essentially ordered' or 'vertical' and 'accidental' or 'horizontal' series seems rather arbitrary and contrived. The only reason to make such a distinction appears to be as justification for assuming a first mover. That's why I say that Aquinas begs the question in his first way argument.

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    86. Quite frankly, I had given up hope of ever reasoning with you, and had resolved to never participate in another futile discussion with you, but you seem to genuinely want to understand Aquinas' argument, so I'm going to take one more stab at trying to explain it to you. I really hope that I'm not wasting more of time by doing this.

      First, let's take on the distinction between essentially and accidentally ordered series which, by the way, has absolutely nothing to do with assuming a first mover. The Stanford Encyclopedia of Philosophy has a good explanation of each. It says, " In an accidentally ordered series, the fact that a given member of that series is itself caused is accidental to that member's own causal activity. For example, Grandpa A generates a son, Dad B, who in turn generates a son of his own, Grandson C. B's generating C in no way depends on A—A could be long dead by the time B starts having children. The fact that B was caused by A is irrelevant to B's own causal activity. That's how an accidentally ordered series of causes works.

      In an essentially ordered series, by contrast, the causal activity of later members of the series depends essentially on the causal activity of earlier members. For example, my shoulders move my arms, which in turn move my golf club. My arms are capable of moving the golf club only because they are being moved by my shoulders." So, oscillating theories where a big crunch causes a big bang is an example of an essentially ordered series. Another example of an essentially ordered series is the bubble universe model of the multiverse where quantum fluctuation waves stack up and create intense disruptions in scalar fields which lead to new bubble universes which lead to more waves stacking up.

      Now, on to how an essentially ordered series of contingents can be moving eternally as long as there's some non-contingent which causes motion. Picture an engine, which has been moving eternally, which is attached to an infinitely long series of box cars on an infinitely long track. Since the engine has been moving eternally the contingent box cars have been moving eternally as well. Why can't the infinitely long chain of box cars be moving eternally on their own? Because each box car's movement depends on the movement of something else, so without the engine the box cars would just be motionless.

      Now the conflict in this discussion lies in your assumption that some contingents have inexplicably been in motion forever. What I don't understand is how there can be motion in the chain of contingents if nothing in the chain is capable of producing motion. It seems like you're trying to say that if an infinite number of people put $0 in a pot you'll end up with an infinite amount of money in the pot. The only way to get an infinite amount of money is if people are putting actual money in the pot.

      In a similar way, each contingent in a essentially infinite series only has potential motion--no contingent actually has motion. If there's only potential motion in the chain then there's not actual motion in the chain and it remains eternally at rest.

      You may want us to just grant that it's just a brute fact that there's a series of contingents that have been inexplicably moving forever, but I see no reason to grant this assumption because you trying to turn an infinite collection of contingents into a collection of non-contingents.

      Also, there is no evidence that there are contingents which have existed in motion forever. All evidence shows that contingents are finite and are dependent on other things for their existence/motion.

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    87. Keith,

      Thank you for replying. Let me first say that I value these discussions and I learn from them. You may never get me to agree with certain theistic concepts, but you just might help me to understand them. So your efforts are not entirely fruitless. By the same token, I don't expect you, or any other theist to abandon your belief, but I hope that you can at least see these things from a different perspective. This can be frustrating for me, too.

      Now, you say "Why can't the infinitely long chain of box cars be moving eternally on their own? Because each box car's movement depends on the movement of something else, so without the engine the box cars would just be motionless."

      I have been desperately trying to get you and Martin to see the problem from another perspective: if each boxcar needs something else to move it, that problem is completely solved. The preceding boxcar does that. I know you object that there is no first mover in this scenario. But that is looking at it from a finite perspective, which doesn't work when we are dealing with transfinite values. This is Craig's problem in trying to show the absurdity of infinite values. And it is my contention that Aquinas also suffers from this fallacious view of the infinite.

      Another issue with essentially ordered series is that they are nebulous things, in my mind. Exactly how do you define this causal dependency? If I postulate a causal series of some kind, will you be able to tell me whether it is either accidental or not? I have my doubts. As I mentioned before, causality in the real world is much more complex than simple chains of events.

      "I see no reason to grant this assumption because you trying to turn an infinite collection of contingents into a collection of non-contingents. "

      That is explicitly wrong. The view I postulate is an infinite collection of contingents (if you insist on calling them that) and nothing more. The collection itself (as a whole) might be seen as non-contingent, but not the items in it.

      "Also, there is no evidence that there are contingents which have existed in motion forever. All evidence shows that contingents are finite and are dependent on other things for their existence/motion. "

      Again, I don't say that any contingent thing has been in motion forever. But given a series of bang-crunch events, or some other mechanism for spawning universes that are individually finite, it is to be expected that our experience is limited to the finite. Still, you believe there is something that brought about our little world, and so do I. So I don't see why you should complain about my lack of evidence. You don't have any, either. It boils down to a question of what might best explain what we see.

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    88. Ugh.

      Here is the way to think about it. Is the cause of an effect the source of that effect, or is it just passing the effect along?

      In an essentially ordered series, there is some cause of an effect (yes, it could be multiple things together causing an effect), the effect is passed through "secondary causes" which cannot generate the effect themselves but can only pass it along The concept illustrated.

      In an accidentally ordered series, by contrast, each member is the originating cause of the next effect. Although they may have a cause for their own existence, they are the originating cause of the next effect. The concept illustrated.

      Dear God, Please let im-skeptical get it now, so I don't have to type anything more. I have a lot of patience, Lord, but this test you are throwing at me is very trying. I'm not sure how much longer I can hold out. PLEASE, Lord, I beg you!

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    89. This comment has been removed by the author.

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    90. Thanks for the opening paragraph, im-skeptical. I do feel a little bit better about the time I've spent on these discussions.

      I understand that you're trying to get us to see things from your perspective, but when it comes to motion you're trying to get us to assume that there's something there which can't possibly be there--namely motion. Your solution to the problem of motion is intensely circular, as you're trying to explain the existence of motion by saying that there is inexplicable motion despite there being no actual source of motion.

      All along you've assumed that Martin and I are making a leap of faith with premise three of Aquinas' argument, but I don't think I am. I honestly can't see how things, which are incapable of self-locomotion, are moving around without any source of motion. To me, saying that the contingents are inexplicably moving without any source of motion is making a leap of faith.

      im-skeptical wrote: "Another issue with essentially ordered series is that they are nebulous things, in my mind. Exactly how do you define this causal dependency?

      I'll grant that it's not the easiest concept to understand in the world, but it's hardly impossible. The distinction between accidental and essential ordered causal series is whether or not the causation is simultaneous. In the case of myself both types are going on. The causal relationship with my family is accidental because my father doesn't need to currently actually exist in order for myself to exist and cause my own children to exist. However, the causal relationship between me and the atoms that compose my body is essential because if my atoms didn't actually exist right now then I could not actually exist and cause these words I'm typing to exist.

      im-skeptical wrote: "The view I postulate is an infinite collection of contingents (if you insist on calling them that) and nothing more. The collection itself (as a whole) might be seen as non-contingent, but not the items in it."

      This is like saying if I take an infinite number of mortals then I'll end up with an infinite collection immortals. How does taking an infinite number of X's create an infinite collection of Y's?

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    91. "Dear God, Please let im-skeptical get it now, so I don't have to type anything more."

      Martin,

      I appreciate your patience with me, honestly. You need to understand that the problem here is not my inability to understand concepts. I'm really not that stupid. There are things I haven't been exposed to before, and there are things that I simply don't agree with. It's true that I had never heard of essentially ordered causal series before this discussion. Having heard some explanation of this concept (from medieval philosophy), I get the basic picture. Believe me, there's noting about this that requires the intellect of Einstein. But then there are more problems I see.

      First, if the concept doesn't agree with my existing understanding of how things work (based on modern a modern scientific education), I am faced with a choice: I can try to reconcile the differences, I can deny the medieval philosophy, or I can deny the modern science.

      Second, there is the question of whether I should accept the consequences that are claimed to be entailed by this concept.

      To address the first issue, in a modern understanding of causation, there is no one thing that causes some effect. Rather, the total state of a closed dynamic system at one moment leads to the total state of the system at the next moment, with each element of the system exerting some influence on all other elements. The notion of a causal chain is really a fiction.

      I think your graph on the accidentally ordered series is a tacit admission of this. You show originating causes, but you don't show where they come from, and I'm certain you don't think they happen spontaneously. The truth is, they are consequences of the total system. And as such, they are no different from the causes in an essentially ordered chain. To make a long story short, in a modern understanding of dynamic systems, "causes" are intermediate, and "effects" are intermediate. It is impossible to distinguish between "accidental" and "essentially ordered", except perhaps that some causes are more immediate and direct than others. But it would be impossible to draw a clear line that separates them.

      On the second question, does any of this really imply that causation can't continue to infinity? In my view, whether it is essentially ordered or accidental is irrelevant. You may be able to wind the system back to some initial state. If so, something caused the system to have some initial state. For our finite universe, we might see the singularity that led to the big bang as an initial state. And from that, everything unfolded. So everything going back to the singularity is finite (you might say there is a finite succession of causality). The real question is whether there is some greater system of which our finite universe is an element. Is there something that comes before our designated initial state? And if there is, can that be extended back in an infinite succession?

      We have already discussed the logical possibility of this. I have tried to explain to you that if we go outside our finite universe, we are no longer limited to finite actuals. There could be many universes, either sequentially, or simultaneously, or both. Or it could be that something just caused our universe to pop into existence as a unique event. Something that happens uniquely in nature is what I would call a miracle.

      Anyway, I think I do understand the concept of an essentially ordered series. And I still don't buy it. If that makes me stupid, so be it. My question to you is, do you understand what I have been trying to get across?

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    92. >in a modern understanding of causation, there is no one thing that causes some effect

      You see, this is why it's so frustrating talking to you. I specifically said above, and I quote: "yes, it could be multiple things together causing an effect"

      Why bother continuing if I know that whatever I say will stop somewhere outside your skull and not actually enter? Are you just thinking about what you want to say next, rather than paying attention to what I'm saying? Why do you do this?

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    93. "Why bother continuing if I know that whatever I say will stop somewhere outside your skull and not actually enter? Are you just thinking about what you want to say next, rather than paying attention to what I'm saying? Why do you do this?"

      Oh, brother. So now you're upset that I said something that partially agreed with something you said? I was giving you my concept of causality, and making a case for the inter-dependency of all things in the system. The point is not that there "could be multiple things together causing an effect", but there certainly are multiple things that contribute to an effect. In fact, everything influences everything else to some degree. This concept refutes the notion of a causal series. Well, at least you answered my question.

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    94. This needs to be hashed out in real time. You available for chat? Here is a private room. I'll just sit there till you show up:

      http://us21.chatzy.com/54968600317020

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    95. Keith: "Your solution to the problem of motion is intensely circular, as you're trying to explain the existence of motion by saying that there is inexplicable motion despite there being no actual source of motion."

      It's not circular to say that motion causes motion. It would be circular If I said object A moves object B, which moves ... which moves object A. But that's not what I say. Yes something moves object A, and it isn't anything that comes after A. It's whatever comes before object A *which is in motion*. Is this inexplicable? Maybe so. Maybe there simply has always been some natural thing there, and it's simply a brute fact. How is this any different from saying God exists without explanation?

      Keith: "I honestly can't see how things, which are incapable of self-locomotion, are moving around without any source of motion."

      For the thousandth time, they DO have a source of motion. It is whatever came before them. What is missing in this equation is a FIRST source of motion. Your assumption that there must be a first mover is the leap of faith you make.

      Keith: "However, the causal relationship between me and the atoms that compose my body is essential because if my atoms didn't actually exist right now then I could not actually exist"

      The atoms that make you up all came together as a result of countless interactions between things in the history of the universe. If you only look at a very limited subset of interactions, you might think that this is simultaneous causation of the kind that you would call "essentially ordered". But this limited view of causation never goes beyond a single object or a small set of objects. The big picture of what causes something to happen would have to include everything that led up to the current state of affairs, and this would include all the causes that you call accidental. If you want to talk about a first mover, I don't see how you can leave those things out. So, in a very real sense, they are all essential.

      Keith: "How does taking an infinite number of X's create an infinite collection of Y's?"

      I didn't say that. What I said is more like Y is an infinite collection of X's.

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    96. Martin,

      I make these comments in between other activities and commitments. I don't want to get into a chat session.

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    97. Fine. Then go here to this editable document and see if the statements I extracted from your comment are correct. Then watch for comments from me:

      https://docs.google.com/document/d/1kJl7CACGmcj4KR1qh75qTp9biKcHu_9F-u2rtXMC180/edit?usp=sharing

      Delete
    98. OK. I've made some changes. Also, do you have an email address or something...?

      Delete
  3. "Those are terms used (typically by theists) to describe Aristotelian metaphysical concepts that have little or no bearing on reality."

    Of course they have bearing on reality. It's just that the issue was essentially settled 2500 years ago and you don't consciously think about it anymore. Just like evolution was settled a long time ago and you don't see every biology paper starting with the basic concept of evolution, because it is now accepted.

    You will have dinner later today, and may already be planning it. But, right now, you are not having dinner. Those are the concepts of potentiality and actuality.

    "Those are terms used (typically by theists) "

    And no, they are not typically used by theists. In fact, I rarely see theists EVER use them. Theists use fine tuning, objective morality, and the impossibilty of actual infinites, etc. But rarely actuality and potentiality. These terms are typically used every day by every one, just not consciously. Right now you are thinking about what to write in response but have not actually written it yet. Then, you will write a response.

    The technical terms are typically used, again not by theists, but by people studying and discussing classical philosophy like Plato and Parmenides.

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  4. Hello, Martin.

    In modern everyday language, I never see the terms 'actuality' and 'potentiality'. I do see related words in common usage. We say 'potentially' as an adverb, meaning possibly. We say 'potential' as a noun, meaning possibility. We say 'actual' as an adjective, meaning real. We never speak of 'potentiality' becoming 'actualized'. Where might we encounter language like that? Perhaps in the Summa Theologica, or Aristotle's Physics. To Aristotle, potential was the material cause of something that is actualized. In modern physics, there remnants of the terminology, but they are used in a technical sense that is very different from Aristotle's usage. The Aristotelian/Thomistic concepts of potentiality and actuality are never to be found outside theistic circles.

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  5. Yes, you are correct. The terminology is not often used the same way. But the concepts remain.

    And when the terms are used, they are not used primarily in theistic circles but in classical philosophical contexts.

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