Free Will Thought Experiment 1

I came across an interesting article with a thought experiment I wish to explore[1].

Often, free will is defined as:

(1) An action is free, in the sense of moral responsibility, only if the person could have done otherwise than she actually did.

A corollary is:

(2) An action is free, in the sense of moral responsibility, only if the person could have chosen otherwise than she actually did.

Let us conduct the following thought experiment[2]:

Suppose the subject of the thought experiment is named Sally. She underwent brain surgery by the surgeon Randolf. Randolf is an unethical surgeon who, unknown to Sally, implanted a tiny computer with sensors and electrodes in Sally's brain so that Randolf can control Sally's behavior. One of the things that Randolf monitors is Sally's voting behavior. Randolf has programmed the computer in such a way so that if Sally's brain shows any inclination to vote for John McCain, the computer intervenes so that Sally will vote for Barack Obama. If Sally decides on her own to vote for Barack Obama, the computer will do nothing, not effecting anything inside Sally's brain.

Now, suppose that Sally votes for Barack Obama on her own, just as she would have if Randolf had not inserted the computer in her brain.

Question: Was Sally responsible for her vote for Barack Obama?

The answer is yes, Sally was responsible for her vote for Barack Obama, even though she could not have done otherwise. In this analysis, we see that the two conditions, (1) and (2), listed above are irrelevant in strictly determining if someone acted freely and is responsible for their actions.

This analysis was done by John Fischer, currently a professor of philosophy at the University of California, Riverside[3]. It is one of those thought experiments that eliminates some of the chaff of what people think freedom and responsibility are.

I am going to stop the article here. Feel free to explore the links I have listed below to further explore the topic. All of the people I mention are people I just discovered within the past hour as I write this (August 27, I have scheduled this article for later posting). I don't know where these people take the concepts. It is fascinating and should provide some thought provoking and interesting reading. I love these kind of adventures!

Notes/Sources:

[1] Living Without Free Will, Derk Pereboom, University of Vermont (2001, Cambridge University Press).

[2] ibid, p. 2. This example is derived from Dr. Pereboom's use of John Martin Fischer, "Responsibility and Control," in Moral Responsibility, Fischer, ed. (1986, Cornell University Press), p. 176.

[3] See John M. Fischer webpage at U.C. Riverside, and background information at The Information Philosopher website. Dr. Fischer is a founder and general adviser to the The Garden of Forking Paths group blog on free will and moral responsibility.

...finally, a note to me for a further article to explore.

God Foreseeing

Question: Is there a difference between the idea of God predetermining everything versus God predetermining based on what God foresaw what someone would do? Would that difference allow for free will to exist in the latter case?

The English language can be very imprecise. Sometimes logic can help. There is a notion in logic known as the general condition and the more specific condition.

Consider the statements:

(1) God determined to permit them to act as He knew beforehand

(2) God determined.

Statement (2) is the more general condition, statement (1) is the more specific condition. This is because statement (1) is a more detailed specification of statement (2). Statement (1) has God's determination which is contained in statement (2), along with the more specific to permit them to act as He knew beforehand.

The word determine means: "to fix conclusively or authoritatively" (see determine in www.m-w.com), the words "to permit them to act as He knew beforehand" is an addition to determine, but the word still implies "to fix conclusively or authoritatively". You'll notice there are other possible definitions of determine, such as "to find out or come to a decision about by investigation, reasoning" -- but the problem with that sense of the definition is that God needed no finding out, he knew from all eternity. Thus the statement God determined to permit them to act as He knew beforehand implies the simple statement that God predetermined.

We can reason further another way. Because (1) happened before the foundation of the world, it means by the definition of predetermined, that God predetermined their actions before they existed. There is no temporal sequence in God's foreknowledge, or in his foreordaining -- because God's foreknowledge and purposes are unchanging (otherwise at one point in time there was knowledge about the future that God did not possess -- which would make him not omniscient at that point, which contradicts God's character and being).

It is possible to logically order God's predeterminations because that is not temporally ordered; logical ordering is true for all eternity. We can say that someone's future activity will imply God's foreknowledge of it and thus imply God's permissive foreordaining. But logical orderings need not be unique, and in most cases they are not unique. Another equally valid logical ordering is that is God's foreordaining necessitates the actions of people in the future.

So, consider the case: God determined beforehand to permit someone to act as He knew beforehand. This implies the action of someone in the future necessitates God's knowledge of the person's action in the future. But the reverse ordering is also true: God's predetermined knowledge necessitates someone to act in a particular way. When it deals with someone's ultimate destination, then that is predestination.

In other words, in all cases, God predetermining and God's predetermining to permit all result in predestining.

Free Will Perspectives

I have written a number of blog entries on free will before. What I am curious about is what are the differing views on free will. Not only are there the various Christian views on free will, but there are various views on free will in other disciplines. This is an attempt to put together a partial list of different approaches. It is done without deep consideration. I'll gladly take the comments of others. Note: I am biased. You will probably see it show up in the descriptions.

Christian Views:
(1) Augustinian -- God sovereignly ordains all that will be. Human freedom is subordinate to God's sovereignty.
(2) Molinism -- Middle knowledge gives freedom to humans.
(3) Arminian(?) -- This is probably not the best name. God does not ordain human action, but merely foresees all their actions.
(4) Open Theism -- God does not know all the future and so the human will is not constrained by God's foreknowledge.

Evolutionary Biology -- Human free will fits within brain stimuli and neural activity that supports survival of the genome.

Physics -- Human free will is ultimately determined by the physical processes surrounding the human organism, including the random activity at the quantum physical level.

Any other views?

Earl's Conjecture

I have encountered various people on the Internet who advocate Molinism. My first encounter was back in the mid 1990s with a pastor who had a PhD in philosophy from Notre Dame. We debated Calvinism versus Molinism and that is where I first discovered Molinism.

Molinism is an attempt to reconcile God's omniscience with human free will. It was named after the 16th century Jesuit theologian Luis de Molina[1]. The basic thought is that God knew all the possibilities where he is not the active agent in those activities involving the human will. While God knew what would happen in his creation, he also knew what could have happened in all the various contingencies. It is in this what could have happened that separates God's human freedom from the tyranny of God's foreknowledge. William Lane Craig is probably the most visible modern advocate of Molinism[2][3].

I am going to make a conjecture than can be proved to be true or false with a little bit of work (to see the answer to the conjecture, click here). My conjecture, which I will not-so-humbly call Earl's Conjecture is:

Calvinism is a subset of Molinism.

Diagrammatically, it is illustrated as follows:



In other words, the logical propositions of Calvinism is a subset of the logical propositions of Molinism. This means if you assume Molinism, Calvinism is logical consequence. But it should be noted that the reverse does not follow in my conjecture, that is, if you merely assume Calvinism, you cannot have Molinism as a logical consequence.

Now, let me sharpen this a bit. I will define Calvinism as the set of beliefs that are common to the Westminster Confession of Faith[4] and the London Baptist Confession[5]. This is an arbitrary definition, but it is a concrete definition. For Molinism, I refer you to William Lane Craig's website[3].

Admittedly, the definition of Molinism is not as sharp as Calvinism. There is some gray area in the Molinism definition. If anyone has a set of "confessional" documents for Molinism, let me know.

Please contribute with your thoughts. I will post some of my thoughts in time.

Sources/Notes

1. For a very brief description of Molinism, see Wikipedia's article on Molinism.

2. William Lane Craig, "No Other Name": A Middle Knowledge Perspective on the Exclusivity of SalvationThrough Christ.

3. See William Lane Craig's scholarly section of his website for more papers on Molinism. You will need to register, but it is free.

4. See the Westminster Confession of Faith for the content of the confession.

5. See the London Baptist Confession of 1689 for the content of that confession. This particular one had some minor modifications by Spurgeon.

What Would Pilate Do?

Rose and John Cole are gracious, hospitable, internet hosts. Rose just recently posed a question asked by a frequent contributer, Colin Maxwell, aka "goodnightsafehome", from a previous discussion,

Yes or No – Answer first and then qualify afterwards, Could Pilate have said “No” to the Jews’ demand to have Christ crucified and let Him go?

Here is how I answer the question.

At one point, only God existed in eternity. God, in all eternity, knew what, how, and why he was going to create the universe along with all the ramifications of it. God's knowledge was complete, perfect, and good -- because God is complete, perfect, and good. Because God's knowledge was complete and perfect, he did not at any point say, I wonder what will happen if..., then muse and ruminate over it, then think, hmmm, how about if I do this..., then ruminate over that, and then pick what the universe would be like and how he would act in its creation and his providential care of it. Because if he did, his knowledge before that point would not be complete. God would not have been omniscient. God's being and character are unchangeable -- thus God was/is/will be always omniscient.

God, being perfect and omnipotent, also had perfectly set his thoughts and plans from all eternity. There are many alternative ways in which God could have planned everything -- but God had perfectly arranged in his mind all that will be.

So, before the foundation of the world, God had arranged in his mind -- to use an anthropomorphic analogy (remember, God is eternal and arranging his mind is tenseless, it is always been arranged as he desired) -- that Adam would fall, that sin would enter the world, that Christ would be arrested, that Peter would deny Christ, that the disciples would flee Christ, that Pilate would pronounce the death sentence on Christ and have him crucified.

These are logical necessities of a perfect, omniscient, omnipotent God. No matter how you dice it and slice it, I don't see how you can get around it, unless you deny some basic feature of the classically known attributes of God -- such as done in Open Theism.

In the past, various theologians have tried to get around the problem -- including Molinism and "Middle Knowledge" -- but that is a theory that the Bible is silent about and really ends up with a predetermined universe anyway -- at least how one of the major Protestant proponents of Molinism, William Lane Craig, presents it.

Others have tried to say that God chooses people who will choose God. However, that is a linguistic convenience -- because God from all eternity had arranged his thoughts so that, by logical necessity, determined who will choose him.

A Calvinist at this point will say that we have no theory of why God chooses, other than in one sense it pleased him (using an anthropomorphic analogy) in his perfect and good will to have things happen this way and that God does things for his glory and the good of his people. Does this mean that God takes delight in punishing people? No. Understanding God requires much more subtle and nuanced thinking than trying to force extremes out these logical results in understanding God.

Asking the question, could Pilate have done anything other than what God had planned? The question actually has multiple senses to it, which makes it an ambiguous question. This is part of the problem with arguments in theology -- people are not precise in what they say AND there is a point where our reasoning cannot take us further.

The question, could Pilate have done anything other than what God had planned? has at least these possible meanings:

(1) Logically speaking, could Pilate have done anything else other than what God had in his mind about Pilate from all eternity?

(2) Physically and emotionally, was there anything that was preventing Pilate from acquitting Christ?

(3) In Pilate's spiritual condition, was Pilate able to do the right thing?

The answer to (1) is no. This follows from God's omniscience and omnipotence in arranging all things so that the answer follows just as you prove a theorem in geometry.

The answer to (2) is no. There is nothing in Pilate's physical nature and condition that made him condemn Christ. Pilate was under pressure from the leaders and people around him, but Pilate was not coerced in some ultimate sense. He was free to do as he wished.

The answer to (3) is no. Pilate was in enmity and rebellion against God. As Romans 3 points out, this is the natural condition of all human kind. This, along with the freedom of coercion, makes all of us guilty before God -- and all of us deserve death. God is not required to intervene to save us from our rebellion -- precisely because we deserve it. This part is hard to understand in today's society, because we don't really believe we all deserve death. We think God owes us a chance -- but if we think in any way like this, then we are saying we don't deserve death.

God was not required to step in and apply grace to Pilate -- just as God was not required to apply grace to your life. You deserve death. That means God did not have to send Jesus to die for you whatsoever.

But blessed are you that you do see, that Jesus did die for you. To you has been given the secret of the kingdom of God. Rejoice and marvel at God being for you and rescuing you -- when you did not deserve it at all.

Another Christian History Series

I love studying history -- particularly history of the Christian church. Church history reveals people, groups, tribes, and nations in which Christianity spread. History is not orderly. At times it is very messy, with humans who greatly mess up, and others who display amazing sacrifice. There are councils where the orthodox faith is confirmed -- in spite of politics, bloodshed, rancor, and deception.

I just discovered an interesting history series by Dr. Maxie Burch of North Phoenix Baptist Church. If you go to iTunes, got to Podcasts, Audio Podcasts, Christianity, History of Christianity by Dr. Maxie Burch.

There is much that is helpful in this series. Reading and listening to history from multiple sources gives different perspectives that helps understanding history. One helpful notion is that history does not happen in neat logical compartments, but rather it all happens at once and unplanned by the historical participants.

Also -- I heard the helpful reminder that the classic proofs of the existence of God use the word proof in a different way than I often use the word. I have a mathematics background and proof in my mind is a formal logical argument with axioms and premises that result in a necessary logical conclusion. Proof, in the sense Thomas Aquinas used it, is an observation, a suggestion pointing to the existence of God -- not an airtight case.

This is helpful in seeing how to employ these arguments. These are not to be used as a proof beyond all doubt. Instead these paint a picture that suggests it is reasonable that God exists -- that it is just as reasonable as any alternative.

A suggestion, an observation, rather than an earnest formal proof. In conversations these can be employed as a reason when asked why you believe, why you find faith in God compelling against the alternatives. That is the home where these proofs may be the most effective.

Worship and Music

My church is going through a transition on the worship director. The current worship director is a phenomenal man, gifted in music, not only in leading music, but in composing and arranging. He has written a book on worship that is used in a seminary. Not only is he gifted, but his wife as well. Both contribute substantially to the worship and music of the church. They are leaving soon to go to a church in California.

Our music in the church has been great. The music makes extensive use of electric guitars and drums. My tastes, however, are heavily on the "traditional" side. My heart resonates with hymns. I prefer piano, pipe organ, violin, cello. I like choirs -- if done well, and it is hard for small to medium churches to do it well.

I've always enjoyed classical music since childhood. But I also enjoyed rock to some extent. My musical preferences in worship have changed over the years. Our church has always tended towards contemporary music with a nod in past years to traditional. It was one of the things that drew me to the church -- but my tastes have become much more traditional. However, many in my church prefer contemporary music.

Some people have left our church over the issue of music. These people have preferred traditional music. I have talked with several and encouraged them to stick it out -- to no avail. Why stay if you don't like the style of music? Why do I stay?

First, the gospel of Christ is being proclaimed in the worship service. This is done in the music, the liturgy, the preaching, and in the sacraments. Throughout the service we hear how we fall far short of reaching God's standard of perfection, but we have the sweetness of the gospel of Christ redeeming us.

Secondly, our church is a community of committed believers, working together in Christ. I have submitted myself to this church and am accountable to the body. It is a community that loves and helps my family. I can't tell you how many ways we have been helped, how others have helped in raising our children, how the church has helped me in so many ways.

Thirdly, I am a servant in the community of believers. I am committed to the body. I need to serve the church even more than I am now.

Pulling away from the church means tearing away from a place where the gospel is proclaimed. Sure I can go to another church where the gospel is proclaimed -- but there is a sense where I have been nurtured in a special way at this church with the gospel. In many ways it will not be the same. Also, pulling away tears at the fabric of Christian community, which is a very precious commodity. Finally, I would be shirking my responsibility to the Christian community.

Can I worship God effectively with music I don't like? Absolutely I can. I do struggle with the music, my heart is not fully content. But I realize I need to be more fully engaged in the words in the songs and in worship. While I might not be emotionally carried away as I might be with a pipe organ, I also know that my emotions do not necessarily indicate what is going on in the worship service. God is at work in the congregation. The church service is not about me. It is about God for us, all of us, where God is taking his delight in us, even in our individual struggles, or more pointedly, in spite of my sin.

My struggle with worship is good. I need to go through this to see what is really important. In this, I think I am seeing what worship is more clearly than if I were elevated to the emotional highs of my enjoyment of traditional music

The Utility of Cosmological Arguments

To review the Kalam Cosmological Argument:

1. Whatever begins to exist has a cause for 
   its existence.

2. The universe began to exist.

3. Therefore the universe has a cause for
   existence.

All the versions of the Kalam arguments I have read are not formal proofs. Usually people will accept point 1. Point 2 is the point of dispute. The persuasiveness of the argument depends on whether those who consider the argument perceive whether the problems with infinities means the universe (or meta-universe) cannot be infinite in its duration. If the meta-universe cannot be infinite in its duration, then the universe began to exist and point 3 follows.

I have talked with people with the concepts of the Kalam argument. All where intelligent non-scientists with technical undergraduate degrees (math, computer science, physics, engineering). Infinity is not a problem with almost all people I talk with. Thus the Kalam argument does not carry much weight.

Does this mean the Kalam argument is useless? I don't think so. I think it has use -- but it cannot be relied upon exclusively. It needs to be part of a full spectrum of presenting the case for God. There are other arguments: the moral argument, the cosmological design argument in its more modern version dealing with fine tuning, historical evidence for Jesus' resurrection, and evidence in changing lives.

So by itself, the Kalam can be persuasive, but not necessarily -- not with a segment of people comfortable with the concepts of infinity. Another point to consider is the persuasive power of the Holy Spirit. Ultimately, it is God's grace that opens the eyes to his presence.

Why Consider Old Universe Arguments?

Most theologically conservative Protestant or Evangelical Christians believe that the universe was created in the span of six 24-hour days, 6,000 to 10,000 years ago. The Kalam Cosmological Argument for the existence of God, in its modern forms, such as the version employed by William Lane Craig, are assuming the existence of an old universe, with an age in the billions of years old. Perhaps many young universe creationists would dismiss the Kalam argument out of hand because of its old universe assumptions. However, I would advocate considering using the Kalam argument, even if you are a young universe creationist.

The reasons I advocate employing old universe arguments are as follows:

1. Most of the scientific literate people people assume an old universe. Arguing for a young universe adds to the work of a young universe creationist to provide reasonable evidence for a young universe. Depending on the background of the people you are talking to, providing the evidence can be a lot of work.

2. Providing evidence that the universe began to exist is relatively easy. Simply observing that the universe is expanding implies an upper bound to the age of the universe. This is because if you "run the clock backwards" on the current expansion rate, you will arrive at a time where you cannot run the clock backwards any more. The universe is already at an infinitely small point.

3. Using the assumptions of many scientists and showing an absurdity means that the original assumptions were wrong. This is the point of the Kalam argument.

The last point needs a little more explanation. One way to show that an eternal uncaused agent, namely God, created the universe is to assume the opposite and show there is a contradiction that results from that opposite assumption. So, if we assume that the uncaused eternal God did not create the universe, then there must be some other mechanism that created this universe. The mechanism most often used by scientists speculating on this is an infinite series of universes. When we assume such a thing, there results some serious contradictions and problems, such as what I noted in, Meet Yourself, Infinitely Many Times. Therefore an uncaused eternal agent caused the universe to begin to exist. This removes the obstacles for considering the existence of God sooner than if you construct the case for a young universe. When the possibility for God's existence is on the table, then other evidences can be considered, such as the resurrection of Jesus.

In this argument you do not need to surrender the view of a young universe. You can assume, for advancing the argument, an old universe and then look at the evidence for God's existence even in those conditions. This gives breathing room to consider the case for Christ.

The Kalam Cosomological Argument

The past series of blog entries have loosely presented the Kalam Cosmological Argument for the existence of God. The argument has been popularized by William Lane Craig. Dr. Craig's outline is[1]:

1. Whatever begins to exist has a cause of its
  existence.
2. The universe began to exist.

  2.1 Argument based on the impossibility of an
      actual infinite.

        2.11 An actual infinite cannot exist.
        2.12 An infinite temporal regress of
             events is an actual infinite.
        2.13 Therefore, an infinite temporal
             regress of events cannot exist.

  2.2   Argument based on the impossibility of
        the formation of an actual infinite by
        successive addition.

        2.21 A collection formed by successive
             addition cannot be actually infinite.
        2.22 The temporal series of past events
             is a collection formed by successive
             addition.
        2.23 Therefore, the temporal series of
             past events cannot be actually
             infinite.

3. Therefore, the universe has a cause of its
  existence.

In the approach I am more comfortable with is:

1. Whatever begins to exist has a cause of its
  existence.
2. The universe began to exist.

  2.3 The argument based on the absurdity of an
      infinitely generated series or branching trees
      of universes.

      2.31 All highly improbable non-impossible
           universes will occur infinitely many
           times.
      2.32 The infinite number of improbable universes
           makes scientific understanding of the
           history of any particular universe impossible.
      2.33 Therefore an infinitely generated universes
           is defeats scientific investigation and
           logically impossible.

3. Therefore, the universe has a cause of its
  existence.

The reason I am more comfortable with this approach is because I don't think Dr. Craig's arguments against an actual infinity (argument 2.1) and against the formation of an actual infinity from successive addition (argument 2.2) in his article are strong. Perhaps it is my bias towards my mathematical training going through set theory. In Dr. Craig's argument against an actual infinity, he simply stated the consequences of Hilbert's Hotel are absurd[2].

Simply declaring infinity absurd after discussing the Hilbert Hotel example points out a weakness of argument 2.1. For many people, simply stating the example is grounds enough for rejecting that actual infinity is possible. But there are others, such as astrophysicists at some leading research institutions (such as Caltech and MIT) who do not see it is necessarily impossible. Simply believing something because they are a professor at a prestigious college or university is an unwarranted appeal to authority -- but it does show that infinities are thought possible by intelligent scientists.

Argument 2.2 has some issues too -- which I thought I wrote about in a previous blog, but I don't see it. I will comment on this later[3].

Argument 2.3 is presented in the previous blog, Meet Yourself, Infinitely Many Times.

Notes/Sources:

[1] See William Lane Craig's presentation of the Kalam Cosmological Argument. The outline is copied directly from Dr. Craig's article.

[2] I write about Hilbert's Hotel in Can an Actual Infinity Exist?

[3] Actually I did comment about this in a comment. Alvin Plantigna critiques Immanuel Kant when he makes a similar argument. See p. 25 of Warranted Christian Belief by Alvin Plantinga.

Meet Yourself, Infinitely Many Times

In a previous series of posts I presented a proposal by some astrophysicists for our universe to be one of a series of spontaneously generated universes. In fact, the proposal is that this universe is one of an infinite number of universes that have been generated spontaneously. I've already given two critiques of that view, and I will give another critique.

Infinite number of universes. Why infinite? Because there is a recognition on the part of these astrophysicists, to quote the highly philosophical movie, The Sound of Music, "nothing comes from nothing." Either you have an uncaused agent that started the who process, which sounds awfully like God, our you have an infinite tree of generating universes, branching into other universes, and so on. In the previous critiques I discussed supertasks and the problem of counting down from infinity. Now I will examine another issue.

Infinite number of universes. Imagine the possibilities. Because there are an infinite number of universes, anything that is extremely unlikely to occur, and I mean extremely unlikely but not absolutely impossible, will have occurred infinitely many times. Is evolution unlikely? Is it extremely unlikely? Well, in an infinite number of universes it occurred infinitely many times.

But, think of this. What is the likelihood that our universe just simply spawned into existence just 10 minutes ago? All the galaxies, everything that we see in telescopes, everything, from the Hubble Telescope, to this planet, to the computer that you are looking at this blog entry from, everything, just 10 minutes ago.

Wait a minute. The Hubble Telescope was blasted in to orbit sometime ago, years ago, and we got all those great pictures. The people in the same room I am sitting in can vouch for that. -- But suppose the universe spontaneously generated just 10 minutes and 3 seconds ago (you can read quickly, can't you? -- from the first time I proposed a 10 minute universe). You were generated 10 minutes ago with memories, along with everyone else you run into. They happen to match -- for the most part. Have you ever noticed that you and your spouse's memory don't quite jibe. You talk about past events, and there are things that don't quite match up? Or you and your boss (or school teacher or professor)? That's because in this spontaneous generated universe the memory "generation" was not quite perfect.

A 10 minute universe? That's impossible -- or is it extremely, extremely unlikely? If it is not absolutely impossible out of the laws of quantum physics, or whatever the physics is at work in the metauniverse we came from (or multiverses), then such a universe, identical to our present universe, did indeed spontaneously generate -- not just once or twice, but infinitely many times.

Infinity is a two edged sword. It allows for fine tuning of the universe and evolution. It also allows for really crazy universes, ones that look identical but are generated differently.

But that isn't all the weirdness with infinitely generating universes.

Okay, you're reading this and you are not buying this blog argument at all. But there are infinitely many universes where you are reading this, and because of some quantum activity in your head, at this point, you're changing your mind and saying this argument is convincing -- an infinite number of you (along with an infinite number that are not changing their minds). This raises the question, how do we know are thinking accurately that reflects the real universe? We are seekers of truth, but how do we know we are grasping the truth? If we are an infinite assemble of universes, with infinite variation that is not ruled out as being absolutely impossible, then there exist an infinite number of us with a staggering number of different views about life, the universe, and everything -- and within each of those infinite numbers for each view, there are an infinite number where each are absolutely sure their view is correct.

Imagine this -- Hillary Clinton leaves Bill and elopes with Rush Limbaugh. Extremely unlikely -- but not theoretically impossible from the physics point of view? Then it happens during August 2008 in an infinite number of other universes. Or try this one, conservative political pundit and adviser Mary Matalin marries arch liberal, rival adviser and pundit James Carville. In infinitely many universes they do not, but in infinitely many universes they do.

David Hume argued that miracles are impossible. But it is recognized today that technically miracles are not absolutely impossible -- just extraordinarily unlikely. Let's say that God doesn't exist, and there are an infinite number of universes that have been spawned. The miracles of Jesus, naturally speaking, are extremely unlikely -- everything from turning water into wine, healing the sick, raising the dead, and his resurrection. Naturally speaking, very, very, very unlikely. But in infinitely generated universes, Jesus lived and did all those things -- in an infinite number of universes.

So, is our universe 12 minutes old, or billions of years old? In infinitely generating universes, there is an infinite set that are 12 minutes old, an infinite set that as 2 hours old, as well as an infinite set that are billions of years old.

Proposing infinitely generating universes saws off the branch we are sitting on, epistemologically. It defeats whether we can know the truth.

There is a simpler, more logically consistent solution. In the beginning, God created the heavens and the earth.

Zeno's Paradox

Zeno of Elea[1] lived from 490 BC – 430 BC, although the times are not certain[2]. Zeno is noted for several famous paradoxes. I will present one of them from the Stanford Encyclopedia of Philosophy:

Suppose a very fast runner — such as mythical Atalanta — needs to run for the bus. Clearly before she reaches the bus stop she must run half-way, as Aristotle says. There's no problem there; supposing a constant motion it will take her 1/2 the time to run half-way there and 1/2 the time to run the rest of the way. Now she must also run half-way to the half-way point — i.e., a 1/4 of the total distance — before she reaches the half-way point, but again she is left with a finite number of finite lengths to run, and plenty of time to do it. And before she reaches 1/4 of the way she must reach 1/2 of 1/4 = 1/8 of the way; and before that a 1/16; and so on. There is no problem at any finite point in this series, but what if the halving is carried out infinitely many times? The resulting series contains no first distance to run, for any possible first distance could be divided in half, and hence would not be first after all. However it does contain a final distance, namely 1/2 of the way; and a penultimate distance, 1/4 of the way; and a third to last distance, 1/8 of the way; and so on. Thus the series of distances that Atalanta is required to run is: …, then 1/16 of the way, then 1/8 of the way, then 1/4 of the way, and finally 1/2 of the way (of course we are not suggesting that she stops at the end of each segment and then starts running at the beginning of the next — we are thinking of her continuous run being composed of such parts). And now there is a problem, for this description of her run has her travelling an infinite number of finite distances, which, Zeno would have us conclude, must take an infinite time, which is to say it is never completed. And since the argument does not depend on the distance or who or what the mover is, it follows that no finite distance can ever be traveled, which is to say that all motion is impossible. (Note that the paradox could easily be generated in the other direction so that Atalanta must first run half way, then half the remaining way, then half of that and so on, so that she must run the following endless sequence of fractions of the total distance: 1/2, 1/4, 1/8 ….)[3]

Zeno's motivation was to prove that there cannot be a plurality of entities. Instead, everything is one. Motion is an illusion. There have been many attempts to answer this paradox.

One solution came with the advent of Calculus, by Sir Isaac Newton and Gottfried Wilhelm Leibniz. A means was developed to sum an infinite series of diminishing intervals, showing that the sum was finite. Other mathematicians, such as Cauchy, further refined Calculus, putting on a firmer rigorous foundation. However, while Calculus and General Relativity view space and time as a continuum of infinite points between any interval, Quantum Physics assumes a discrete, rather than a continuous, nature to space and time. Ultimately, Quantum Physics might prove to be the ultimate answer to this paradox -- because space and time are not infinitely divisible.

However, there is a related concept, called a supertask[4]. A supertask is an action that takes a finite time to complete. If Atalanta's run has infinite steps with an infinite series of supertasks associated with it, the run will never complete. But since space and time appear to be discrete, not continuous, supertasks do not apply to this particular Zeno paradox. But there are other ways in which supertask analysis gives us interesting insights.

For instance, lets assume that humans that with Christ's second coming, humans who belong to Christ are raised and live forever. Let's further assume that resurrected humans start with a finite amount of knowledge, and that they learn new knowledge incrementally in finite amounts throughout the rest of eternity. While people gain infinite knowledge? The answer is no. Supertasks can be applied to show that humans will never achieve infinite knowledge. This is because to acquire infinite knowledge, people will go through the task of gaining knowledge, which takes some amount of finite, non-zero time. This acquisition of knowledge is a supertask. The activity can never be completed and thus infinite knowledge never achieved.

What about God? God has infinite knowledge in that he is aware of infinite things, as shown in the last post. Did God ever not have infinite knowledge? No. This is because the previous analysis of humans, starting with finite knowledge, shows that humans will never gain infinite knowledge. Thus God's knowledge was always infinite, always complete.

This is an important thing to note about God. God, being eternal, having the unchanging properties of infinite knowledge, is a logically consistent being.

What about the universe? Is it possible for our universe to be part of an infinite succession of universes, that ultimately spawned this universe? Supertasks would suggest not. William Lane Craig frames the argument this way:

One cannot form an actually infinite collection of things by successively adding one member after another. Since one can always add one more before arriving at infinity, it is impossible to reach actual infinity. Sometimes this is called the impossibility of "counting to infinity" or "traversing the infinite." It is important to understand that this impossibility has nothing to do with the amount of time available: it belongs to the nature of infinity that it cannot be so formed[5].

In particular, the reason this infinity cannot be formed is because each spawned universe is a supertask that takes a non-zero amount of time. Further, it is postulated in the "spontaneously generating" universes that this universe is the result from an infinite sequence of universes in the past.

Someone might reply to this argument of supertasks to say that there never was a beginning point. An infinite collection of universes could happened, in which case case our universe arose from that collection. But the solution stated is a mirror reflection of the problem of a person counting to infinity, only you start with zero and count backwards[6].

For example, imagine you come across a man who claims to have been counting down from infinity and just reached zero today. The problem is that the man has been counting down from infinity forever, but yesterday was forever also, and so was the day before, and the year before. Why didn't that man reach zero then at those times? He should have already have been finished by any of those times. Thus there is no time when we would find a man finishing counting down to zero from infinity.

This is another critique of the infinitely spontaneously generating universes. A logical, simpler explanation is that an eternal being, God, created the universe.

But wouldn't God be in a temporal infinity, and don't we find a similar paradox for God's first action in creating the universe? Here is where we find God different from the universe. There was no temporal succession "before" the universe came into existence. Time and space came into existence when the universe began, so there is no infinite regress on the part of God to create the universe.

I am very finite, and so I end this finite post for tonight....

Notes/Sources:

[1] Picture of Zeno of Elea is from MacTutor article on Zeno.

[2] Zeno's Paradoxes, Stanford Encyclopedia of Philosophy.

[3] ibid

[4] ibid, Supertasks.

[5] William Lane Craig, The Existence of God and the Beginning of the Universe.

[6] ibid. This point and the following example are taken from Dr. Craig's article.